Keywords:

Waszkowska Karolina | Study and diagnostic of the physicochemical properties of new -conjugated (metallo)supramolecular architectures for nonlinear optics.

1 their versatile applications in various fields, such as electronics, optics, space industry, and aviation [7]. These studies gave rise to numerous inventions, for example, in the form of active and passive elements, piezoelectric devices, power microminiaturization, elements for solar energy processing and storage, magnetic memories, superconductors, reflective and antireflective coatings. Why are thin film structures important? One of the simplest reasons is the desire to produce materials with properties that differ significantly from those of bulk homogeneous materials. It often happens that the properties of bulky materials required for non-engineering applications differ significantly for their corresponding thin films materials and nanomaterials. An example of such unique properties is the relatively easy protection of electrical contacts between semiconductor devices by Chapter 1 Nonlinear Optics ___________________________________________________________________________ Waszkowska Karolina | Study and diagnostic of the physicochemical properties of new -conjugated (metallo)supramolecular architectures for nonlinear optics. 22 is a source of a new wave with frequency 𝜔 4 . Complexed amplitudes of the polarization 𝑃(𝜔 𝑛 )

for positive frequencies can be written as form:

.5.

INTRODUCTION

With the construction of the first laser in 1960, the opportunities to observe new properties in materials appeared. A year later, the generation of the second harmonic was observed, it was the first discovery of nonlinear optics [1]. Nonlinear phenomenon appears in the case when applying high radiation power, the response of the medium, for example electric polarization, is a nonlinear field function. Usually, second and third order nonlinear effects are studied, since radiation sources of sufficient power effectively achieve these responses. Why nonlinear optics is important? As a matter of fact current daily life without nonlinear optics would be more difficult. For instance, without nonlinear optics, telecommunication would be missing of high-quality fibre systems that power the internet. Moreover, current medicine is rich in advanced technology, based on laser analytical tools that are used for medical diagnosis. Furthermore, nonlinear optical effects are used to monitor water and air pollution. Besides, new materials are characterized using nonlinear optical phenomena. In addition to telecommunications, medicine and environmental protection, scientific instruments, new laser colours, advanced spectroscopy, data storage are important. All these applications have a significant impact on everyday life. Materials that have unique nonlinear responses are in the spotlight of scientists research because they are used in fields such as photonics, optoelectronics, optical calculations, optical signal processing and more. The extraordinary nonlinear properties often result from conjugated 𝜋 -electron bonding networks in materials.

The science of supramolecular systems is a relatively new field of knowledge, which includes not only chemistry, but also physics, biochemistry and material engineering. Supramolecular chemistry, which is about 60 years old, is currently a very dynamically developing field of organic chemistry dealing with structures composed of many subunits that arise spontaneously as a result of weak intermolecular interactions [2]. The study of noncovalent interactions is key to understanding

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Waszkowska Karolina | Study and diagnostic of the physicochemical properties of new -conjugated (metallo)supramolecular architectures for nonlinear optics. 2 inherently all processes in living cells. The voluminous macromolecular biological systems have been the inspiration for similar systems created by humans. On the one hand, supramolecular chemistry deals with the study of already existing, natural supramolecular structures, such as ionophore antibiotics, cell membranes or nucleic acids, and on the other, on the design and synthesis of completely new, non-naturally occurring structures such as nanotubes, liquid crystals, dendrimers, macrocyclic compounds and many others. The main objectives of this work lies on the design and elaboration of new multifunctional supramolecular architectures for nonlinear optical applications. In this respect, dynamic metal-ligand (M-L) interaction is continuously emerging as a powerful tool for the design and the development of various types of multiresponsive material properties. Such materials can therefore be classified to the kind of stimuli that they respond to, such as thermo-, photo-, chemo-, electro-, mechano-, and offer applications in diverse fields, including biomedicine, nanoelectronics and catalysis [3][4][5][6]. Recently a huge interest has been devoted to the preparation of different supramolecular assemblies by the use of suitable ligands that leads to the formation through self-assembly processes to self-assembled metal complexes and/or metallo-supramolecular networks.

On the other hand, there is no doubt that the phenomenal increase in thin film research is due to ___________________________________________________________________________ Waszkowska Karolina | Study and diagnostic of the physicochemical properties of new -conjugated (metallo)supramolecular architectures for nonlinear optics. 3

depositing a thin layer on the contact surface. Construction materials intended for high temperatures are often coated with appropriate coatings based on thin film technology, due to which it is possible to reduce wear of the element and extend its life. Thin film deposition technology has an effect on increasing efficiency, reducing costs, and control over various surfaces.

These features allow the development of completely new products, improving the design and production process. This allows achieving better functionality of products, thus saving resources and materials and reducing the amount of waste encountered in traditional production. The electronic, magnetic and optical properties of thin layers are the key to creating communication electronics. It is therefore clear that thin films play an important role in shaping society in the future.

This doctoral thesis consists of 8 chapters divided into subsections. The first chapter discusses mathematically nonlinear optical phenomena using a wave equation. Second-and third-order nonlinear phenomena have been characterized, which include the generation of the second harmonic (SHG) and the generation of the third harmonic (THG). Tensors characterizing nonlinear optical susceptibility for these effects were derived. The other part of this chapter describes other effects that are characterized by complex nonlinear electrical susceptibility.

Imaginary part present phenomena of nonlinear absorption, which is divided into saturable absorption (SA) and reverse saturable absorption (RSA). The real part is described by variations in the refractive index, which were described using forced birefringence, the electro-optical Kerr phenomenon, as well as self-focusing and self-defocusing. nonlinear optics are also described, which is also the main topic of this work. In the following, various types of supramolecules are described, which include helicates, metal organic frameworks (MOF) called also coordinating polymers, and porphyrins, from which supramolecular architectures are very often built. The unique properties of these structures and their applications are represented.

The third chapter is a description of thin films and their properties and manufacturing methods.

The phenomenon of luminescence and what is its lifetime are described, as well as electronic properties of materials. In this thesis, thin films based on a two-dimensional structure model and are described mathematically. The following three most popular methods for producing thin films are presented. The first is the spin coating method. This method is based on the production of layers from a solution. The other two methods allow the production of powder layers in a vacuum, they are physical vapor deposition (PVD) and pulsed laser deposition (PLD) also known as laser ablation.

The next chapter, fourth, consists of descriptions of experimental techniques. First, theoretical models were described, from which it is possible to determine the second and third order nonlinear susceptibility from experimental data depending on the given parameters and the method of measurement. The following are experimental apparatus that were used to study the second and third harmonic generation. The next part describes what the corona poling method is, which allows possibility of SHG measurements. Next, the Z-scan technique is described, which is divided into 3 ways. This method allows the determination of nonlinear absorption and nonlinear refractive index during one measurement. Further in the fourth chapter, spectroscopic devices were described, where the absorption and luminescence spectra of the studied thin films were obtained.

The surfaces of the investigated layers were characterized by means of an atomic force microscope (AFM) and the next section describes its operation. The last experimental technique presented in ___________________________________________________________________________ Waszkowska Karolina | Study and diagnostic of the physicochemical properties of new -conjugated (metallo)supramolecular architectures for nonlinear optics. 5

this work is ellipsometry, which allows to determine constants such as the extinction coefficient or refractive index.

The next three chapters present the experimental results of the studied chemicals, which are triple stranded helicates with different metal cations: Fe 2+ , Co 2+ , Ni 2+ and Zn 2+ [8], and metalloporphyrins with different metals : Fe, Ru, Pd and Pt, as well as modified pyrene-based complexes contacting zinc Zn(II) and cadmium Cd(II) cations. The method of sample preparation was first presented and then samples were characterized by AFM. The following sections present spectroscopic results:

absorption and their luminescence. Then, the nonlinear properties of the supramolecular systems studied, which are the generation of the second and third harmonics, and the effects determined using the Z-scan technique are presented. Each of these chapters ends with a summary of the obtained experimental results.

Chapter 8 presents the nonlinear optical properties research of nanoporous membranes on which second harmonic generation studies were performed for each type of the investigated samples: porphyrin complexes, triple stranded helicates and modified pyrene-based supramolecular complexes. One sample was selected from each type of studied complexes.

The presented doctoral dissertation ends with a conclusion and analysis of the obtained experimental data. The results obtained for each supramolecular system presented in this paper were summarized and their potential applications, usefulness in nonlinear optics and perspectives for further research are presented.

Literature [1] R. W. Boyd, Nonlinear Optics, Academic Press, 2008.

[2] H. Dodziuk, Introduction to Supramolecular Chemistry, Kluwer Academic Publishers,

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CHAPTER 1: NONLINEAR OPTICS

Visible light is a small but very important part of the electromagnetic wave spectrum. Generally, the propagation of the light in the free space can be described by classical physics, nevertheless interactions between matter and light (for instance absorption and emission) can be described only by quantum physics. The classical relevant description is in form of Maxwell's equations, which describe the velocity of propagation the electromagnetic waves in a vacuum. This velocity is in close relation to the measured speed of light. This observation strongly determines the light in the field of electromagnetic waves.

Wave Description

All of electromagnetic phenomena including light propagation can be fully written in relation to

Maxwell's equations (in SI units) [1.1 -1.3]:

∇ • 𝐷 ⃗ ⃗ = 𝜌 (1.1) ∇ • 𝐵 ⃗ = 0 (1.2) ∇ × 𝐸 ⃗ = - 𝜕𝐵 ⃗ 𝜕𝑡 (1.3)
∇ × 𝐻 ⃗ ⃗ = 𝜕𝐷 ⃗ ⃗ 𝜕𝑡 + 𝐽 (1.4) where: 𝐸 ⃗ describes vector of electric field strength, 𝐻 ⃗ ⃗ -vector of magnetic field strength, 𝐷 ⃗ ⃗ is a vector of electric induction, 𝐵 ⃗ describes vector of magnetic induction, 𝜌 is a volumetric density of charge and 𝐽 is a vector of total current density. Material equations allow us to determine vectors 𝐷 ⃗ ⃗ and 𝐻 ⃗ ⃗ by using the vectors 𝐸 ⃗ and 𝐵 ⃗ . They depend on the properties of the material. However, we can write those vectors as follows:

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𝐷 ⃗ ⃗ = 𝜀 0 𝐸 ⃗ + 𝑃 ⃗ (1.5)

𝐵 ⃗ = 𝜇𝐻 ⃗ ⃗ + 𝑀 ⃗⃗ (1.6) Vector 𝑃 ⃗ describes electric polarity and it can be written by:

𝑃 ⃗ = 𝜀 0 𝜒 𝑒 𝐸 ⃗ (1.7)
where 𝜒 𝑒 is known as electrical susceptibility, 𝜀 0 = 8,85 • 10 -12 𝐶 2 /(𝑁 • 𝑚 2 ) and is known as electric permittivity of the vacuum. The magnetic polarization vector 𝑀 ⃗⃗ is expressed by the following relation:

𝑀 ⃗⃗ = 𝜒 𝑚 𝐻 ⃗ ⃗ (1.8)
where 𝜒 𝑚 describes magnetic susceptibility. Specifically interesting are the solutions of Maxwell's equations in areas of free space where there are no free charges and there are no conduction currents, that means: 𝜌 = 0 (1.9)

𝐽 = 0 (1.10)
It is also important that we should have non-magnetic medium, so that means the vector of magnetic polarization 𝑀 ⃗⃗ is equal to zero. In this case, the vector of magnetic induction 𝐵 ⃗ is equal to: 11) where 𝜇 is magnetic permittivity of the medium. Equivalently important is fact, that electrical polarization 𝑃 ⃗ cannot be ignored. In strong electric fields, the response of the material medium to ___________________________________________________________________________ Waszkowska Karolina | Study and diagnostic of the physicochemical properties of new -conjugated (metallo)supramolecular architectures for nonlinear optics. 9

𝐵 ⃗ = 𝜇𝐻 ⃗ ⃗ (1.
the applied field changes its nature, and beside the linear response 𝑃 ⃗ 𝐿 there is also nonlinear response 𝑃 ⃗ 𝑁𝐿 , that means:

𝑃 ⃗ = 𝑃 ⃗ 𝐿 + 𝑃 ⃗ 𝑁𝐿 (1.12) where the linear dependence of the electric field is expressed as follows:

𝑃 ⃗ 𝐿 = 𝜀 0 𝜒 𝑒 (1) 𝐸 ⃗ (1.13) 𝜒 𝑒 (1) describes linear electric susceptibility. In spite of this, nonlinear polarization is a complex function of the electric field 𝐸 ⃗ :

𝑃 ⃗ 𝑁𝐿 = 𝜀 0 [𝜒 𝑒 (2) • 𝐸 ⃗ 2 + 𝜒 𝑒 (3) • 𝐸 ⃗ 3 + ⋯ ] (1.14) where 𝜒 𝑒 (2) and 𝜒 𝑒 (3) are second-and third-order nonlinear electrical susceptibilities, respectively. Now electric polarization can be written as follows:

𝑃 ⃗ = 𝑃 ⃗ (1) + 𝑃 ⃗ (2) + 𝑃 ⃗ (3) + ⋯ (1.15) where 𝑃 ⃗ (𝑛) describes n-order polarization, 𝑛 = 1,2,3, … Currently we can look at the output of the optical wave equation. Let us take the curl of the curl of the electric field 𝐸 ⃗ from the (1.3). As a consequence of the continuity of the function we substitute the order of the derivative after time and space on the right of the resulting equation, and then using equations (1.4), (1.10) and (1.11) to express ∇ × 𝐵 ⃗ with 𝜇 0 (𝜕𝐷 ⃗ ⃗ /𝜕𝑡) we have the following result:

∇ × ∇ × 𝐸 ⃗ + 𝜇 0 𝜕 2 𝜕𝑡 2 𝐷 ⃗ ⃗ = 0 (1.16)
Under certain conditions, equation (1.16) can be simplified. For example, using a vector calculus we can write the first element of the equation as:

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∇ × ∇ × 𝐸 ⃗ = ∇(∇ • E ⃗ ⃗ ) -∇ 2 𝐸 ⃗ (1.17)
In the case of nonlinear optics exist a relation between 𝐷 ⃗ ⃗ and 𝐸 ⃗ , so it cannot be assumed that ∇ • 𝐸 ⃗ = 0 as a resulting from ∇ • 𝐷 ⃗ ⃗ = 0. Nevertheless we can assume that ∇(∇ • E ⃗ ⃗ ) is negligible in (1.17) so that equation (1.16) can be written as follows:

∇ 2 𝐸 ⃗ -𝜇 0 𝜕 2 𝜕𝑡 2 𝐷 ⃗ ⃗ = 0 (1.18)
To eliminate 𝐷 ⃗ ⃗ from the (1.18), we can use equation (1.5) and replace, for convenience 𝜇 0 as 1/𝜀 0 𝑐 2 , where c is the speed of light in vacuum. In this way, the most general wave equation in nonlinear optics takes form:

∇ 2 𝐸 ⃗ - 1 𝑐 2 𝜕 2 𝜕𝑡 2 𝐸 ⃗ = 1 𝜀 0 𝑐 2 𝜕 2 𝜕𝑡 2 𝑃 ⃗ (1.19)
While electromagnetic radiation passes through matter, the electric field of this radiation causes a periodic shift of electric charges with the frequency of the radiation, however, these oscillating displacements in turn generate electromagnetic radiation (Fig. 1.1). When the intensity of the incident light is low, the deviations of the electric charges from the rest position are also smallthey behave like harmonic oscillators driven by a frequency other than resonance: motion contains only the same frequency components as excitation. The potential that drives the dipole back to its original position is approximately parabolic-shaped only for small charge displacements. However, in the case of large displacements, the potential deviates from this parabolic behavior, because the nuclear charge of the neighboring atoms acts. This deviation is called nonlinearity because it denotes a nonlinear relationship between the deflection and the restoring force. The shape and strength of the nonlinearity depends on the structure of the material through which the light passes.

The moving charge is accelerated towards the zero position by the potential, resulting in a sinusoidal velocity waveform only for the square potential. In the event of deviations, the load is ___________________________________________________________________________ Waszkowska Karolina | Study and diagnostic of the physicochemical properties of new -conjugated (metallo)supramolecular architectures for nonlinear optics. 11

in the meantime accelerated too slowly or too quickly, which leads to deviations from the sinusoidal shape in the velocity curve and consequently to deviations in the electric field of the light emitted by the load. In the spectrum of light, this means that not only the incidence frequency, but also its harmonics are contained in different powers. As the conversion efficiency drops sharply with the harmonic degree, only the second (SHG) or third (THG) is mainly of technical importance.

Second Harmonic Generation

Nonlinear second-order processes occur in the case of specific combinations of frequency, intensity and phase in the relation to the electric field and its manifestation in a nonlinear medium.

The laser beam whose electric field, dependent on the time t and coordinates r which propagates towards 𝑘 ⃗ direction, is represented as [1.1 -1.3]:

𝐸 ⃗ (𝑟, 𝑡) = 𝐸 • sin(𝜔𝑡 -𝑘 ⃗ • 𝑟) (1.20) This laser beam appears in the medium for which the electrical second-order susceptibility 𝜒 𝑒 (2) is not equal to zero. The nonlinear polarization that arises in such medium is given by relation:

Chapter 1

Nonlinear Optics ___________________________________________________________________________ Waszkowska Karolina | Study and diagnostic of the physicochemical properties of new -conjugated (metallo)supramolecular architectures for nonlinear optics. 12 𝑃 ⃗ (2) (𝑟, 𝑡) = 𝜀 0 𝜒 𝑒 (2) • 𝐸 ⃗ 2 (1.21) Taking into account the wave equation (1.20) we get following relation:

𝑃 ⃗ (2) (𝑟, 𝑡) = 1 2 𝜀 0 𝜒 𝑒 (2) 𝐸 2 [1 -cos 2(𝜔𝑡 -𝑘 ⃗ • 𝑟)]

(1 .22) We see therefore, that the second order polarity consists of a member independent of the time t in which there is frequency zero and the member changing with the frequency of 2 at time t. It should be also noted that the first component of the equation does not indicate electromagnetic radiation, because the second derivative disappears, however it leads to the formation of a static electric field through a nonlinear medium.

The second harmonic generation effect is illustrated schematically in Fig. 1.2. The nonlinear medium on which an electromagnetic wave propagates in the 𝑘 ⃗ direction with a frequency , the new wave with a doubled frequency is created. Second harmonic generation can be also described by energy diagram level, where two photons of frequency  are destroyed from the virtual state to the frequency 2 in single quantum-mechanics process (Fig. 1.2).

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The intensity of generated second harmonic in a nonlinear medium with a thickness d can be expressed by: 𝐼(2𝜔, 𝑑) ≈ 𝐼 𝜔 2 (𝜒 𝑒 (2) ) 1.23) where I describes the intensity of the incident light, while ∆𝑘 is the phase matching parameter:

2 [ sin ( 1 2 𝑑∆𝑘) 1 2 𝑑∆𝑘 ] 2 (
|∆𝑘| = |𝑘 ⃗ 2 -2𝑘 ⃗ 1 | = ( 2𝜔 𝑐 ) (𝑛 2𝜔 -𝑛 𝜔 ) (1.24)
where 𝑘 ⃗ 1 and 𝑘 ⃗ 2 are vectors of fundamental wavelength and generated second harmonic, respectively. It can be also noted, that the intensity of generated second harmonic increases quadratically with the intensity of incident light I . The influence on increase of the intensity have also the condition which for phase velocities of fundamental and generated harmonic wavelength are equal, which means ∆𝑘 = 0. Besides, for small values of any x, the sinx function in Maclaurin's theorem takes form:

sin 𝑥 = 𝑥 -𝑥 3 3! + 𝑥 5 5! -𝑥 7 7! + ⋯

This means, when the phase matching condition (1.24) is met, it can be expressed by: ∆𝑘 = 0 ⇒ 𝑛 2𝜔 = 𝑛 𝜔 (1.25) Then, along with the square of the thickness d of the medium, the intensity of the generated second harmonic will increase. Otherwise, if this condition is not met, we have to deal with the periodicity of the SHG intensity as a function of the thickness d of the medium. The phase matching condition (1.24) is often difficult to achieve because the refractive index is a function of the frequency, and this is associated with an effect known as dispersion. Generally, phase matching is be divided into two types. Type I occurs in case when two polarizations vector (fundamental and generated ___________________________________________________________________________ Waszkowska Karolina | Study and diagnostic of the physicochemical properties of new -conjugated (metallo)supramolecular architectures for nonlinear optics. 14 harmonic) are in parallel position: 𝑛 𝑧 2𝜔 = 𝑛 𝑥𝑦 𝜔 , while type II appears in case when polarizations vector are in orthogonal position: 𝑛 𝑧 2𝜔 = 1 2 (𝑛 𝑥𝑦 𝜔 + 𝑛 𝑧 𝜔 ).

It should be also noted that for a given value of thickness d, the mismatch parameter ∆𝑘 is not proportional to d. For a mismatch ∆𝑘, a value called the coherence length LC is included, which is a measure of the maximum length within which the parametric cooperation process is effective.

This value is expressed by the formula [1.4]:

𝐿 𝑐 = 𝜋 |∆𝑘| (1.26)
The behavior described by equation (1.23) was firstly experimentally observed in 1962 by P. D.

Maker [1.5]. The experiment consisted in the fact that the ruby laser beam was focused on the surface of the quartz crystal, and then was measured how the intensity of the generated second harmonic signal changes when the crystal is rotating, thus changing the effective length of the optical path through the crystal. The phase mismatch ∆𝑘 was different from zero and more or less the same for all orientations used in the experiment, which is not true for all nonlinear materials.

∆𝑘 in general strongly depends on crystal orientation, as well as with respect to polarization of fundamental and generated harmonic wavelengths.

As it turns out, the process of second harmonic generation strongly depends on the crystal structure of the material. It was noted earlier, that the second order polarization is the square of the electric field (1.21). In centrosymmetric medium must appear an inversion, that is:

-𝑃 ⃗ (2) = 𝜀 0 𝜒 𝑒 (2) • (-𝐸 ⃗ ) 2 -𝑃 ⃗ (2) = 𝜀 0 𝜒 𝑒 (2) • 𝐸 ⃗ 2 It means that 𝑃 ⃗ (2) = -𝑃 ⃗ (2) only if the second-order nonlinear susceptibility is equal to zero 𝜒 𝑒 (2) = 0. As the result, only materials devoid of the symmetry center exhibit nonlinear optical properties.

The second harmonic generation has many applications. One of them is strict diagnostics of surface properties of optical materials. As mentioned above, coherent SHG is impossible to obtain in medium that are centrosymmetrical. The intensity as a function of the incident angle depends to the large extent on the morphology of the surface and the presence of impurities on the surface of the material.

1.3. Second-order nonlinear optical susceptibility tensor  (2) In previous paragraph we already said that second-order polarization is equal to (1.21):

𝑃 ⃗ (𝑁𝐿) = 𝜀 0 𝜒 𝑒 (2) • 𝐸 ⃗ • 𝐸 ⃗

Taking into account electromagnetic plane wave equation:

𝐸(𝑧, 𝑡) = 𝐸(𝑧) exp(-𝑖𝜔𝑡) + 𝑐. 𝑐. (1.28) where c.c. is a complex conjugate, we can also write relation (1.21) as:

𝑃 (𝑁𝐿) (𝑡) = 2𝜀 0 𝜒 𝑒 (2) • 𝐸𝐸 * + 𝜀 0 𝜒 𝑒 (2) [𝐸 2 exp ( -2𝑖𝜔𝑡) + 𝑐. 𝑐. ] (1.29)

An expression with a double frequency of 2 appears, which is responsible for generating the second harmonic. Basically, the second order nonlinear optical susceptibility 𝜒 𝑒 (2) is a three-rank tensor made up of 27 components ijk along the axes (x, y, z) which express three perpendicular directions. The components of the tensor 𝜒 𝑖𝑗𝑘 (2) exhibit an invariance during the permutation of the indices j and k. Indeed, the commutativity of the elements 𝐸 𝑗 (𝜔)𝐸 𝑘 (𝜔) = 𝐸 𝑘 (𝜔)𝐸 𝑗 (𝜔) (which is ___________________________________________________________________________ Waszkowska Karolina | Study and diagnostic of the physicochemical properties of new -conjugated (metallo)supramolecular architectures for nonlinear optics. 16

true for non-resonant materials) makes it possible to reduce the number of independent components to a number equal to 18 and to write the polarization by following expression: (1.30)

[
According to Kleinman symmetry [1.6 -1.7], in the pulsation domain outside of the absorption resonance, tensor 𝜒 𝑒 (2) is symmetrical with respect to the permutations of the three indices ijk.

Taking that claim into account we obtain following relation:

𝜒 𝑖𝑗𝑘 = 𝜒 𝑖𝑘𝑗 = 𝜒 𝑗𝑖𝑘 = 𝜒 𝑗𝑘𝑖 = 𝜒 𝑘𝑖𝑗 = 𝜒 𝑘𝑗𝑖 (1.40) And it leads to fact that only 10 components of the tensor remain independent. The elements of the polarization 𝑃 (𝑁𝐿) By considering a monochromatic plane wave propagating in a linear medium with an index 𝑛 0 and wave vector 𝑘 0 ⃗⃗⃗⃗ (Fig. 1.3) after enter to nonlinear medium with index n, wave vector 𝑘 1 ⃗⃗⃗⃗ locally creates a macroscopic polarization with oscillating component 2. This forced wave is expressed by wave vector 𝑘 𝑝 ⃗⃗⃗⃗ with amplitude [1.9]:

𝑘 𝑝 = 2𝑘 1 = 2𝜔 𝑐 𝑛(𝜔) (1.43)
Chapter 1

Nonlinear Optics

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Therefore, this wave propagates collinearly and at the same speed as the fundamental wave : (2) 𝐸(𝜔)𝐸(𝜔)]𝑒𝑥𝑝(𝑖𝑘 𝑝 𝑧) (1.44) These two waves will therefore interfere throughout their propagation within the material. The energy transfer 𝜔 → 2𝜔 will be maximum when these two waves oscillate in phase, that is to say when 𝑘 2 ⃗⃗⃗⃗ = 𝑘 𝑝 ⃗⃗⃗⃗ or 𝑘 2 ⃗⃗⃗⃗ = 2𝑘 1 ⃗⃗⃗⃗ . That relation describes the condition of phase matching. Third-order nonlinear optical interactions give a rich variety of the phenomena that can provide both basic and useful information about the structure and dynamics of molecules, and can be used to create new devices. There are many third-order processes that can be distinguished based on the frequency of input and output waves as well as on the nature of the resonance material encountered. Third harmonic generation process (THG) is schematically presented in Fig. 1.4.

𝑃 2𝜔 ⃗⃗⃗⃗⃗⃗⃗ = 𝜀 0 [𝜒

Third Harmonic Generation

The nonlinear polarization, which is created as a result of the relationship with the electric field and the function of nonlinear optical susceptibility, can be expressed as follows [1.1 -1.3 𝑃 ⃗ (3) (𝑟, 𝑡) = 𝜀 0 𝜒 𝑒 (3) • 𝐸 ⃗ 3 (1.45) Taking into account the wave equation, we get the following result:

𝑃 ⃗ (3) (𝑟, 𝑡) = 1 4 𝜀 0 𝜒 𝑒 (3) 𝐸 3 cos 3(𝜔𝑡 -𝑘 ⃗ • 𝑟) + 3 4 𝜀 0 𝜒 𝑒 (3) 𝐸 3 cos(𝜔𝑡 -𝑘 ⃗ • 𝑟) (1.46)
The first polarization element describes the response at frequency of 3, which is created by the frequency field  (Fig. 1.4). It provides to the third harmonic generation process, which can be schematically presented by energy diagram. Three photons of frequency  are destroyed from the virtual state and in microscopic nature of this effect one photon of frequency 3 is created.

As it can be observed, third harmonic generation process is similar to the second-order nonlinear optical process. Analogously, the intensity of generated third harmonic in a nonlinear medium with the thickness d is expressed by: 𝐼(3𝜔, 𝑑) ≈ 𝐼 𝜔 3 (𝜒 𝑒 (3) ) 1.47) In this case, the value of mismatch parameter is given by: .48) where 𝑘 ⃗ 1 and 𝑘 ⃗ 2 are vectors of fundamental wavelength and generated third harmonic, 𝑛 3𝜔 and 𝑛 𝜔 are refractive indexes of this vector values. The rules for obtain the maximum intensity in third harmonic generation process are the same as for SHG. The difference is that there is no structural restriction for THG process. Generation of third harmonic is possible in both:

2 [ sin ( 1 2 𝑑∆𝑘) 1 2 𝑑∆𝑘 ] 2 (
|∆𝑘| = |𝑘 ⃗ 3 -3𝑘 ⃗ 1 | = ( 3𝜔 𝑐 ) (𝑛 3𝜔 -𝑛 𝜔 ) (1
noncentrosymmetric and centrosymmetric materials. Considering the situation, where three monochromatic plane waves propagate in medium, their electric field can be described as follows: .49) In this case, third-order nonlinear polarization P:

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𝐸 ⃗ (𝑡) = 𝐸 1 ⃗⃗⃗⃗ 𝑒𝑥𝑝(-𝑖𝜔 1 𝑡) + 𝐸 2 ⃗⃗⃗⃗ 𝑒𝑥𝑝(-𝑖𝜔 2 𝑡) + 𝐸 3 ⃗⃗⃗⃗ 𝑒𝑥𝑝(-𝑖𝜔 3 𝑡) + 𝑐. 𝑐. ( 1
𝑃 (3) = 𝜒 𝑖𝑗𝑘𝑙 (3) 𝐸 𝑗 𝐸 𝑘 𝐸 𝑙 (1.50) is composed of 44 elements including 22 elements whose direction is the same as the direction of propagation of the waves (and 22 elements with opposite direction of propagation as well):

𝜔 1 , 𝜔 2 , 𝜔 3 , 3𝜔 1 , 3𝜔 2 , 3𝜔 3 , (𝜔 1 + 𝜔 2 + 𝜔 3 ), (𝜔 1 + 𝜔 2 -𝜔 3 ), (𝜔 1 + 𝜔 3 -𝜔 2 ), (𝜔 2 + 𝜔 3 -𝜔 1 ), (2𝜔 1 ± 𝜔 2 ), (2𝜔 1 ± 𝜔 3 ),
(2𝜔 2 ± 𝜔 1 ), (2𝜔 2 ± 𝜔 3 ), (2𝜔 3 ± 𝜔 1 ), (2𝜔 3 ± 𝜔 2 )

(1.51)

At this time we can describe nonlinear polarization as a sum of partial polarizations:

𝑃 ⃗ (3) = ∑ 𝑃 ⃗ (𝜔 𝑛 ) 𝑛 𝑒𝑥𝑝(-𝑖𝜔 𝑛 𝑡) (1.52)
However, in isotropic medium, the nonlinear optical response of electromagnetic waves appears only after taking into consideration the third order nonlinear electrical polarization written in the form:

𝑃 𝑖 (3) (𝑟 , 𝑡) = 𝜒 𝑖𝑗𝑘𝑙 (3) 𝐸 𝑗 𝐸 𝑘 𝐸 𝑙 (𝑟 , 𝑡) (1.53)
Moreover, elements of the tensor 𝜒 𝑖𝑗𝑘𝑙 (3) are non-zero even in the case of isotropic medium. Taking that into account isotropic second-order tensor 𝛿 𝑖𝑗 , we obtain following relation:

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𝜒 𝑖𝑗𝑘𝑙 (3) = 𝜒 𝑥𝑥𝑦𝑦 (3) 𝛿 𝑖𝑗 𝛿 𝑘𝑙 + 𝜒 𝑥𝑦𝑥𝑦 (3) 𝛿 𝑖𝑘 𝛿 𝑗𝑙 + 𝜒 𝑥𝑦𝑦𝑥 (3) 𝛿 𝑖𝑙 𝛿 𝑘𝑗 (1.53) 𝜒 𝑖𝑖𝑖𝑖 (3) = 𝜒 𝑗𝑗𝑗𝑗 (3) = 𝜒 𝑘𝑘𝑘𝑘 (3) = 𝜒 𝑥𝑥𝑦𝑦 (3) + 𝜒 𝑥𝑦𝑥𝑦 (3) + 𝜒 𝑥𝑦𝑦𝑥

( 1.54) The interaction between nonlinear medium and with three electromagnetic waves 𝜔 1 , 𝜔 2 , 𝜔 3 associated with the wave vectors 𝑘 1 ⃗⃗⃗⃗ , 𝑘 2 ⃗⃗⃗⃗ , 𝑘 3 ⃗⃗⃗⃗ , respectively, generates third-order polarization, which is described by:

𝑃 𝑖 (3) (𝜔 4 , 𝑘 4 ⃗⃗⃗⃗ ) = 𝜒 𝑖𝑗𝑘𝑙 (3) (-𝜔 4 , 𝜔 1 , 𝜔 2 , 𝜔 3 )𝐸 𝑗 (𝜔 1 , 𝑘 1 ⃗⃗⃗⃗ )𝐸 𝑘 (𝜔 2 , 𝑘 2 ⃗⃗⃗⃗ )𝐸 𝑙 (𝜔 3 , 𝑘 3 ⃗⃗⃗⃗ ) (1.55)
This relation is fulfilled provided that the principle of energy conservation and phase matching are fulfilled, that means:

𝜔 4 = 𝜔 1 + 𝜔 2 + 𝜔 3 (1.56) 𝑘 4 ⃗⃗⃗⃗ = 𝑘 1 ⃗⃗⃗⃗ + 𝑘 2 ⃗⃗⃗⃗ + 𝑘 3 ⃗⃗⃗⃗ (1.57)
Third-order nonlinear optical susceptibility tensor 𝜒 (3) is dependent on interaction between frequencies of the applied electric fields with the medium, and the spatial components of the nonlinear polarization can be written as follows:

𝑃 𝑖 (3) (𝜔 4 ) = 𝐾𝜒 𝑖𝑗𝑘𝑙 (3) (-𝜔 4 , 𝜔 1 , 𝜔 2 , 𝜔 3 )𝐸 𝑗 (𝜔 1 )𝐸 𝑘 (𝜔 2 )𝐸 𝑙 (𝜔 3 ) (1.58)
where the indices j,k,l can take the values from x,y,z and K describes degeneration factor:

𝐾 = { 1 𝑓𝑜𝑟 𝜔 1 = 𝜔 2 = 𝜔 3 3 𝑓𝑜𝑟 𝜔 1 = 𝜔 2 ≠ 𝜔 3 6 𝑓𝑜𝑟 𝜔 1 ≠ 𝜔 2 ≠ 𝜔 3 (1.59)
The coefficients 1,3 and 6 come from number of permutations of the applied fields which introduce a contribution to the component of the electric field at the considered frequency. The third-order nonlinear electrical polarization is, in fact, a sum function of the frequencies (1.56) and

The third-order nonlinear optical susceptibility tensor 𝜒 𝑖𝑗𝑘𝑙 (3) describes the third-order optical effects at the macroscopic and 𝜒 𝑖𝑗𝑘𝑙 (3) is a four-rank tensor with a total 81 components. That means while determining the nonlinear optical susceptibility of a medium, we have to determine all the elements of the tensor. In case of isotropic medium, the tensor 𝜒 𝑖𝑗𝑘𝑙 (3) has following characteristics of symmetry (according to Kleinman symmetry): This properties of symmetry allows to reduce the number of elements of tensor 𝜒 𝑖𝑗𝑘𝑙 (3) .

𝜒 𝑥𝑥𝑥𝑥 =
Consequently, the third-order nonlinear optical susceptibility tensor has only three independent components: 𝜒 𝑥𝑥𝑥𝑥 , 𝜒 𝑥𝑦𝑥𝑦 and 𝜒 𝑥𝑥𝑦𝑦 .

Basically, the elements of third-order nonlinear optical susceptibility tensor are complex of real and imaginary part [1.1]: [START_REF] White | A Rapid and Straightforward Supramolecular Self-Assembly Experiment To Prepare and Characterize a Triple Helicate Complex[END_REF] where: 𝜒 ′(3) is the real part responsible for nonlinear variations in the refractive index and 𝜒 ′′(3) is the imaginary part related to nonlinear absorption of light and stimulated scattering.

𝜒 (3) = 𝜒 ′(3) + 𝑖𝜒 ′′(3) (1.
Moreover, during experiments of nonlinear optical properties of isotropic medium subjected to the action of laser pulses of short duration, we can consider that only two effects contribute to the third-order electrical nonlinear optical susceptibility: deformation of the electronic cloud and movements of the molecule (translations, rotations and vibrations). Furthermore, when we consider Born-Oppenheimer approximation, which means that the frequency of the incident beam is far from the resonant frequencies of the medium, the contributions due to the deformation of the electronic cloud can be separated from the movements of the molecule. Consequently, we can describe third-order nonlinear optical susceptibility as the arithmetic sum of two terms:

𝜒 (3) = 𝜒 𝑒𝑙𝑒𝑐 (3) + 𝜒 𝑚𝑜𝑙 (3)
( 1.63) where: 𝜒 𝑒𝑙𝑒𝑐 (3) and 𝜒 𝑚𝑜𝑙 (3) denote the electronic component linked to the deformation of the electronic cloud and the molecular component linked to the movements of the molecule, respectively. Besides, the components of the tensor for isotropic medium can be written as follows [1.10 -1.11]:

Chapter In the process of photon absorption with energy:

ℎ𝜈 = 𝐸 2 -𝐸 1 (1.66)
where: ℎ is a Planck's constant and 𝜈 is the frequency, the particle is excited to the energy level E2 from level E1. This process is called stimulated absorption (see Fig. molecule. Transitions between energy levels only take place between permitted levels. Absorption occurs only for those quanta, whose energy is strictly determined by the energies of the allowed energy levels [1.13]. Moreover, when a molecule passes from a higher energy level E2 to a lower level E1 under the influence of a radiation field, a photon is emitted with energy ℎ𝜈. This means that the number of photons increases by one -besides to the incident photon, another one with the same frequency is emitted. This process is called stimulated emission. In the case of returning system from a higher E2 energy to a lower level E1 irrespective of the external field, while radiating the appropriate photon, the process called spontaneous emission occurs.

In the spectroscopic experiment, a signal is recorded in the form of bands corresponding to the amount of energy absorbed by the sample from radiation passing through the sample. The absorption spectrum is characterized by three parameters: I -intensity,𝜈 -frequency corresponding to the position of the band and the width at half maximum (FWHM) [1.14]. Absorption intensity is determined by two quantities that are proportional: T -transmittance and A -absorbance, which determine the percentage number of transmission and absorption, respectively. Transmittance is a quantity that determines the ratio of the intensity of radiation passing through sample I to the intensity of radiation falling on sample I0, which can be expressed by:

𝑇 = 𝐼 𝐼 0 (1.67)
At the moment, when the radiation has completely passed through the medium, transmittance is equal to 1, otherwise this value is equal to 0. Absorbance A defines the amount of energy that has been absorbed by the medium. This quantity is recorded as the logarithm of the inverse transmittance: When all the radiation passes through the material, the absorbance value is 0 whereas when the radiation has been absorbed, this value tends to infinity. The values of transmittance and absorbance are usually written as a percentage form, as follows:

𝐴 = log 1 𝑇 = log 𝐼 0 𝐼 (
%𝑇 = 100 𝐼 𝐼 0 , 𝐴 = log 100 %𝑇 (1.69)
The absorption spectrum can also be characterized by two parameters, which are: the wavelength that corresponds to the maximum intensity max and the specific absorption coefficient  at the point max. The relation between the coefficient , and the thickness of the absorbing medium l is described by the Lambert-Beer law. where  = 0.4343 • k is called the correct absorption coefficient and its value is given in [cm -3 ]. This is the characteristic value for a given substance. Generally, the value of the factor  is determined at the wavelength at which the highest absorption occurs, however, it can be calculated for any wavelength of the absorption spectrum. Equation (1.71) is called the Lambert-Beer law. At the moment when the medium is excited by very high laser radiation, it happens that more than one photon is absorbed (see Fig. 1.8). This phenomenon is called multi-photon absorption, but from the perspective of this work, the most important phenomenon is two-photon absorption (TPA), which is a third-order phenomenon, and in this paper we will denote it as nonlinear absorption. In that case the absorption coefficient becomes nonlinear:

𝛼 = 𝛼 0 + 𝛽𝐼 (1.72)
where 𝛼 0 is the linear absorption coefficient and 𝛽 nonlinear absorption coefficient. As we already said in previous paragraph, components of third-order nonlinear optical susceptibility tensor is a complex of real and imaginary part:

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𝜒 (3) = 𝜒 ′(3) + 𝑖𝜒 ′′(3) where 𝜒 ′′(3) is the imaginary part related to nonlinear absorption of light and stimulated scattering and is described as [1.15]: [START_REF] Prakasam | Topological transformation of a trefoil knot into a [2]catenane[END_REF] where: 𝑛 0 is linear refractive index, c -speed of light.

𝜒 ′′(3) = 𝑛 0 2 𝜀 0 𝑐𝜆 3𝜋 𝛽 [𝑚𝑊 -1 ] (1.
Basically, we distinguish two types of nonlinear absorption depending on the change in the amount of radiation passing through the material: saturable absorption (SA) and reverse saturable absorption (RSA).

Saturable absorption (SA) characterizes decreasing of light absorption while light intensity increases. Saturable absorber can be characterized as a two-level electron system in which the electrons are in the ground state. When irradiating electrons with a low intensity source, these electrons are excited to a higher energy level -the light is absorbed. By applying a sufficiently high intensity of the incident light, molecules in the ground state of the saturable material are excited to the energy E1 with high speed that they do not have enough time to return to the ground state E0.

Additionally, in an ion-doping medium, the high intensity applied leads to exhaustion of the ground state of these ions. Another example is the effect found in semiconductors, where the excitation of electrons from the conductivity band causes a reduction in the absorption of photon energy just above the band gap. The SA property is bound to all high-power materials, however the advantage of the saturable absorber is the low-power absorption. The main application of saturable absorbers are Q-switching lasers. Insertion of a saturable absorbent into the laser cavity causes significant losses in the cavity until the absorbent is saturated. When the absorbent is saturated, it practically does not cause major losses, so laser amplification becomes very important.

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The opposite process to SA is Reverse Saturation Absorption (RSA). In this case, the material's transmittance decreases as the incident radiation intensity increases, where strong radiation absorption occurs from higher energy levels. In the matter of RSA, the absorption cross section of the saturated absorber from the excitation level to the higher level must be larger compared with the absorption cross section from the ground state to the excited state. Moreover, the cross section of the ground state absorption must be that large enough so as the first excited level can be completely filled. Subsequently, excitation to a higher energy level should be fast enough for the electrons to be reabsorbed.

Nonlinear Refractive Index

Generally in optics, the refractive index of a medium is a measure of the change in the velocity of propagation of a wave in a given medium in relation to the velocity in another (reference) medium.

A strong electric field of high intensity light can cause changes in the refractive index of the medium as the light passes through the medium. Such phenomena are described by nonlinear optics. If the coefficient changes in proportion to the square of the electric field strength (linearly with the light intensity), such a phenomenon is called the optical Kerr effect and causes further phenomena such as self-focusing and phase self-modulation, and if the coefficient changes linearly with the field strength (this only occurs in crystals without a center of symmetry) is called the Pockels effect.

As we previously said, we can describe third-order nonlinear optical susceptibility as: 3) + 𝑖𝜒 ′′(3) where: 𝜒 ′(3) is the real part responsible for nonlinear variations in the refractive index [1.16]:

𝜒 (3) = 𝜒 ′(
𝜒 ′(3) = 4𝑛 0 2 𝜀 0 𝑐 3 𝑛 2 [𝑚 2 𝑊 -1 ] (1.74) Chapter 1
Nonlinear Optics

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The value of n2 which is nonlinear refractive index is expressed in units [m 2 W -1 ]. Pockels effect is called a linear electro-optical effect -forced birefringence. The phenomenon consists in changing the refractive index in proportion to the external electric field. Occurs only in crystals that do not show inversion symmetry (and therefore exhibit a piezoelectric effect). One of the properties of the linear electro-optical effect is the low inertia, which allows to modulate light in the high frequency range of several dozen gigahertz. This effect is described by a linear relationship between the change of the crystal optical indicator coefficients and the external electric field. The external electric field causes the ellipsoid's refractive indexes to rotate and deform. In general, the main axes of the ellipsoid do not coincide with the primary main axes. Equation describing Pockels effect is given in form of refractive index:

𝑛(𝐸) = 𝑛 0 + 𝑛 1 𝐸 (1.75)
The Kerr electro-optical phenomenon is the appearance of birefringence in an isotropic medium under the influence of an applied electric field. It arises as a result of the arrangement of polar molecules of the medium towards the external electric field, due to which the medium becomes birefringent. After switching off the field, the material loses this property again becoming an optically isotropic medium. The ordering of the particles is counteracted by their thermal movements, which is why the Kerr coefficient decreases as the temperature increases. To observe the Kerr phenomenon, application an electric field is carried out perpendicular to the running beam of linearly polarized light at an angle of 45° to the electric field. At the cell output, the light is polarized elliptically depending on the light path in the medium, the electric field strength and the type of substance. The device built in this way is called a Kerr cell. Therefore, refractive index is given by following equation [1.17]:

𝑛(𝐸) = 𝑛 0 + 𝑛 2 2 𝐸 2 (1.76)

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Self-focusing is a nonlinear optical process induced by changing the refractive index of materials exposed to intense electromagnetic radiation. The medium, whose refractive index increases with the intensity of the electric field, acts as a focusing lens for the electromagnetic wave characterized by the initial transverse intensity gradient, as in a laser beam. The peak intensity of the self-focused region is steadily increasing as the wave passes through the medium until defocusing effects or medium damage interrupt this process. The opposite situation is when the refractive index increases while the intensity of laser beam decreases. This effect is called self-defocusing. Fig. 1.8

presents phenomena of both effects.

Applications

Generally, nonlinear optics has a huge influence on everyday life [1.18]. One of the most distinctive uses of nonlinear optics is frequency doubling and second harmonic generation. An example is the use of Nd: YAG laser light with a wavelength of 1064 nm, which, upon contact with a nonlinear material, is converted into visible light with a wavelength of 532 nm (green color). Although there exist many nonlinear materials and new materials with strong nonlinearity are still being sought,

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the most commonly used in this process are crystals such as BBO (beta-barium borate), KTP (potassium titanyl phosphate), KDP (potassium dihydrogen phosphate), and also LiNbO3 (lithium niobate) [1.19 -1.22]. These crystals are distinguished due to their unique properties, which is strong birefringence, thanks to which the phase matching described in subsection 1.2 is obtained.

Besides, the crystals have a certain symmetry, which is necessary to obtain a nonlinear second-order effect, and are optically transparent to laser light with the incident wavelength and the generated harmonic.

Another application that uses second-order nonlinear optical phenomena is high-resolution microscopic SHG imaging, most often used in biological and medical sciences [1.23]. One of the non-centrosymmetric SHG-emitting structures is collagen, which is found in most tissues. By comparing the images of the generated second harmonic, it is possible to see the microstructure of collagen, identify changes in its structure and recognize tumor characteristics (breast cancer, ovarian cancer, skin cancer, lung cancer, and other neoplasms), as well as its progression. Apart from neoplastic changes detected in collagen tissues, thanks to SHG microscopy, it is possible to diagnose pathologies occurring in tissues, cartilage or skin with separation of SHG polarization [1.24]. Other examples of applications of SHG imaging are the study of the eye structure [1.25], as well as tissue engineering that allows for the design of artificial tissues by imaging the orientation and amount of distribution of materials in the tissue [1.26].

In addition to the aforementioned second order effect applications, SHG is commonly used to characterize both organic and inorganic materials. As mentioned before, this effect is only possible in materials that do not contain a center of symmetry. Therefore, thanks to the SHG technique, it is possible to easily and quickly detect material noncentrosymmetry, both in crystals and in powdered form, using the apparatus constructed by Kurtz and Perry [1.27].

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Additionally to second-order nonlinear phenomena, third-order NLO effects are used in many applications in everyday life. One of them is, among others, phase conjugation, which uses, inter alia, mixing four waves, mixing three waves, and holography. In this process, two incident waves interact simultaneously in a nonlinear optical material, and the third (or fourth) wave at this time deflects in the resulting dynamic hologram and reads the conjugated phase [1.28]. Besides, another example of applications using 𝜒 (3) is mode-locking, consisting in generating pulses of laser light in a very short time, on the order of pico-and femtoseconds [1.29], which are commonly used in medicine and nonlinear optics.

Materials with strong nonlinear absorption are used, among other things, for optical 3D data storage and imaging. Due to the phenomenon of two-photon absorption (TPA) in the depths of the material, it is possible to record and read information not only on its surface [1.30]. Another example is semiconductor imaging, thanks to which we obtain information about the properties of charge transfer in semiconductor devices. Moreover, TPA is widely used in medicine, in imaging with dyes showing a strong absorption nonlinearity [1.31], and in photodynamic therapy, which is a method of cancer treatment, by using materials characterized by a strong NLO absorption in the infrared range [1.32]. Furthermore, materials with strong reverse saturable absorption (RSA) find potential applications as optical limiters, which are widely used as detectors to protect the eyes from strong laser radiation. Optical limiting is based on the phenomena when the intensity of the laser light is increased, the transmittance of such material decreases [1.33]. Moreover, materials

showing nonlinear absorption and/or nonlinearity in refractive index find applications in Qswitching: the optical element of the laser, thanks to which it is possible to create a pulsed beam of high power, much higher than the continuous beam. This method differs from the abovementioned mode locking due to lower frequencies and longer pulse durations (ns). There are two main types of Q-switching: active, which often uses magneto-optic effects and the Pockels effect and the Kerr effect; passive -a saturable absorber is used, i.e. a material whose transmittance increases when the light intensity reaches a certain value. Q-switching lasers are most often used when very high intensity laser beams with short pulses, usually nanoseconds, are required, including in holography or metal cutting, as well as for data storage.

Another effect that is based on NLO is optical bistability, which is used in optical devices such as memory devices, optical transmitters. This effect is obtained in two ways, the first being absorption bistability, in which the absorber blocks the laser light depending on its intensity [1.34]. Then two transmission states occur, in which once the absorber is not used at a given intensity, and in the second case the state occurs when, for a certain intensity, the light crosses the blockage of the absorber. Another way is to use the changes in the refractive index in the same way [1.35].

Other phenomena that exploit the nonlinear refractive index is the photorefractive effect, in which the material (most often a crystal) reacts to light by changing n2, using, for example, the electrooptical effect and the formation of interference gratings. The most common application of photorefractive effect is creating dynamic holography [1.36]. Moreover, another application of the Kerr effect, in which the nonlinear refractive index changes, is self-phase modulation, which is the phase shift of the pulse, causing the pulse frequency spectrum to change with the change of n2.

This effect is commonly used in optical fibers [1.37]. The first occurrence of intermolecular interactions was postulated by J. D. van der Waals in 1873 [2.1] but the first concept consistent with the supramolecular chemistry was the Lock-and-Key mechanism described by E. Fisher in 1894 [2.2]; proposed mechanism explained the recognition of the substrate by the enzyme. Further development of intermolecular interaction research took place at the beginning of the 20th century with the discovery of hydrogen bonds [2.3]. This research enabled a much better way to understand the structure of protein and nucleic acids, culminating in the discovery of DNA in 1953 by J. Watson and F. Crick [2.4]. During this period, research and synthesis of artificial systems based on noncovalent interactions begun as well. However, another breakthrough was the synthesis of crown ethers by C. J. Pedersen in 1960s [2.5]. Based on his studies, successive chemists, such as D.J. Cram, J-M. Lehn, have investigated various kinds of artificial ion receptors and mechanically intertwined systems [2.6]. The importance of supramolecular chemistry had increased significantly while D. J. Cram, J-M. Lehn and C. J.

Literature

Pedersen received the Nobel Prize in chemistry of their studies in 1987 [2.7].

Supramolecular chemistry is the chemistry of 21 st century. It finds application in the areas of science: conversion of light by energy transfer [2.8], conductors of electricity [2.9], optical sensing [2.10], and others. Due to their unique properties, supramolecular complexes are promising in nonlinear optics as well as in nanophotonics.

Main Concepts

Supramolecular chemistry refers to systems composed of more than one molecule -complexes.

In [2.11 -2.12]. These weak interactions play a very important role, inter alia, in polymers, charge transfer complexes, mono-and poly-layers, liquid crystals that fall within the scope of supramolecular chemistry. Each of these interactions has unique advantages. One of the most obvious advantages are their response to external factors including polarity of the medium, concentration and temperature, as well as their inherent nature.

Hydrogen bonds seems to be most interesting according to their long lifetime, dynamic control and directionality [2.13]. Electrostatic ion-ion interactions take place between two differently charged molecules, for example NaCl (Fig. 2.1 a). Contrary to ionic bonds, the charge in the interacting molecules is not concentrated on one atom, but is delocalized (it occurs on several or a dozen atoms). The force of its interaction is proportional to 1 𝑟 2 ⁄ (where 𝑟 is the distance between molecules), in the case of a medium containing other charges (e.g. electrolyte solution), the effect of the interaction is smaller.

The bond energies are placed between 100-350 kJ mol -1 making them the strongest non-covalent ___________________________________________________________________________ Waszkowska Karolina | Study and diagnostic of the physicochemical properties of new -conjugated (metallo)supramolecular architectures for nonlinear optics. 42 interaction, however this energy is comparable in strength to covalent bonding. An example of an ion-ion interaction in supramolecular materials can be the interaction of a tris(diazabicyclooctane) (Fig. 2.1 b), present as a host, with anions such as Fe(CN)6 3-[2.14] Ion-dipole interactions are characterized by the fact that they occur in both the liquid and solid state. Such an interaction occurs during the interaction of an ion (cation) with the free pairs (polar part) of a molecule on oxygen, nitrogen or sulfur atoms. This interaction is characterized by the energy of 50 -200 kJ mol -1 . Examples of supramolecular compounds in which an ion-dipole interaction occurs are, inter alia, metal-crown ether complexes [2.15] as well as [Ru(BPy)3] 2+ [2.16].

Schematic chemical structures with ion-dipole interactions are presented in Fig. 2.2. The dipole-dipole interaction is formed between molecules that have permanent dipole moments.

Such particles have an excess of negative charge in some places, and its deficiency in others, and they also interact with each other like ions, but the interaction is weaker, because partial (not total) electric charges are involved, as well as the attraction of unlike charges. it is always accompanied by the repulsion of the homonymous charges, the interaction energy is between 5 -50 kJ mol -1 .

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There are two types of dipole dipole interaction: the first type occurs in the case of attraction resulting from the pairing of single pairs of poles of adjacent molecules, while the second type is the opposite orientation of one of the dipoles in relation to the other. Such an interaction is typical for organic carbonyl compounds [2.17]. The principle of dipole-dipole interactions is presented in The most important interaction -Hydrogen bonds are a kind of electrostatic interaction between a hydrogen atom and an electronegative atom containing free electron pair, which makes them a special type of dipole-dipole interaction. There are three types of hydrogen bonds [2.18]: a) strong hydrogen bonds -the interaction between two centre bonds are involved with short distance and bond energies higher than 40 kJ mol -1 ; b) medium and weak hydrogen bonds -the directionality is lost in part and the bond energies are placed between 20-40 kJ mol -1 ; c) unconventional hydrogen bonds -where -systems or transitions metals or boron hydrides plays acceptor role. Fig. 2.

4
presents examples of two main types of hydrogen bonds. The bonds discussed are relatively strong interactions directed in a specific direction, so that they enable to obtain well-defined structures whose durability can be regulated based on the conditions in which they are located. The structure of the DNA double helix is based largely on the occurrence of a number of hydrogen bonds [2.19] (Fig. In contrast to hydrogen bond, van der Waals interactions [2.24] are the interactions between persistent and induced dipole. In molecules without a stable dipole moment, it can be excited by molecules with a permanent moment, then such an excited dipole and stable dipole interact as well as two persistent dipoles, with an energy less than 5 kJ mol - example is the interaction between the aromatic ring in nucleophilic nucleobases of a DNA helix [2.26 -2.27]. The most popular - interaction geometries are edge to face (herringbone pattern)

and offset face to face. The energy of such stacking is 0-50 kJ mol -1 . On the other hand, the cationpi interactions may be slightly stronger and have an energy of 5-80 kJ mol -1 , which may even be comparable to the energy of a hydrogen bond. These are non-covalent interactions between the  orbitals of an aromatic ring rich in electrons with the adjacent metallic or organic (for example pyrazolinium) cation [2.28]. The weakest non-covalent effect is the hydrophobic effect (Fig. 2.9). This effect occurs when molecules lacking a dipole moment (nonpolar) repel the solvent, which is water, from each other. One of the main terms in supramolecular chemistry is the concept of a complex-forming ligand, called as molecular "host". Such ligand is made of electron-donning atoms of oxygen, sulphur or nitrogen. These ligands can form complexes with, for example, metal ions, which are "guest" molecules. The resulting "guest-host" complexes are created on the basis of so-called concepts, including molecular recognition. Due to Fig. 2.11, when the "guest" molecule connects to the ligand molecule, the "lock and key" effect is created.

Applications

Modern supramolecular systems are refined and complex, and some of them are molecular machines modelled on such biomolecules as motor proteins or cancer system cells [2.33 -2.34].

Therefore, there are increasingly frequent applications of the achievements of electrochemistry for the design of new supramolecular systems [2.35]. Processes of self-assembly of matter have been successfully used to create new materials. As example may be various supramolecular polymers composed of organic molecules, connected to each other by noncovalent interactions [2.36].

Another example is the design of new porous materials made of small molecules connected by weak noncovalent forces as well [2.37]. Supramolecular materials play a very important role in medicine. Assemblies are used, in example, to study the interactions of ligands with biomolecules, such as proteins or nucleic acids [2.38]. The knowledge about this interactions is currently of great ___________________________________________________________________________ Waszkowska Karolina | Study and diagnostic of the physicochemical properties of new -conjugated (metallo)supramolecular architectures for nonlinear optics. 50

importance in the design of drug delivery [2.39] or in the treatment of cancer [2.40]. One of the statutory tasks of supramolecular chemistry is the use of matter to perform calculations at the atomic scale. The storage of the information in supramolecular systems is usually done through use the molecular switches. Many publications present data storage in supramolecular systems, such as two-photon induced data storage in supramolecular azopolymers [2.41] or in thin films formed by supramolecular assembly [2.42]. Supramolecular systems were studied for nonlinear optics as well.

Studies of the second order nonlinearity in supramolecular polymers were described in [2.43],

however other tests present the third order optical nonlinearity of metallo-supramolecular complexes based on phthalocyanine [2.44], fullerenes connected with rotaxanes [2.45] or of ammonium picrates [2.46]. Most of the experiments investigated nonlinear optical responses were examined by using the Z-scan technique [2.47 -2.48]. Nevertheless, other studies of supramolecular systems were performed for light up-conversion [2.49].

Supramolecular systems

Supramolecular chemistry is characterized by the fact that chemical compounds are rarely made from "zero". For this purpose, the previously obtained systems are used as building blocks for new supramolecular structures. The following subchapters present some specific examples of chemical compounds from macrocyclic groups, compounds of metal complexes, as well as systems of biological origin. As mentioned before, most often these are guest-host systems, where the host is usually an organic macrocyclic compound, and the guest is a much smaller structure, that may be a cation or anion, which is located in a special place of the host, thus creating complex.

Crown Ethers

They belong to the group of macrocyclic organic compounds of synthetic origin.

Rotaxanes

Rotaxane compounds belong to the class of chemical compounds in which the molecules are a system of two chemically unrelated molecules, one of which has a linear structure and the other is a macrocycle. The first linear molecule is the axis and is developed into functional groups at the ends (so-called stoppers) that prevent the macrocyclic structure from escaping the axis, which causes both structures to be mechanically linked, which is schematically shown in Fig. 2.17.

Rotaxane compounds are very often used for the construction and research of molecular switches [2.64 -2.65], but also in nonlinear optics as photonics materials, tested in terms of SHG, THG, nonlinear absorption and nonlinear refractive index described in [2.66 -2.68].

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Peptides, Proteins and Helicates

Peptides belong to the group of organic chemical compounds, so-called amides, formed by bonding two or more amino acid molecules with a peptide bond, i.e. one that connects the α-amino group of one amino acid with the α-carboxyl group of another amino acid. Short peptides are called oligopeptides, longer chains are called polypeptides or proteins, and the boundary between polypeptides and proteins is determined either by molecular weight or by functionality criteria. On the other hand, proteins are macromolecular biopolymers connected by peptide bonds, the composition of which, in addition to carbon, oxygen, hydrogen, nitrogen and sulfur, phosphorus, sometimes also includes metal cations such as zinc Zn double helix is a process that can not be interrupted until the completion of the pairs is fully achieved. Some molecules spontaneously form as a result of complexation with a metal ion, forming a helix. Generally, in recent years there has been a great deal of interest in self-organized helicates and helical fibers. Understanding and using the rules associated with the formation of helicates, described by J-M Lehn's research groups, led to the formation of structures such as double helix, triple helix, as well as quadruple helix [2.86 -2.88]. Fig.

Metal Organic Frameworks

MOFs are microporous materials that consist of inorganic building blocks (SBU -Secondary Building Units) and organic molecules (linker) which connect elements between the inorganic units [2.95]. Metal organic frameworks are also so-called coordination polymers or coordination

networks with an open framework that contains possible pores. Usually they are in form of crystalline and based on Werner complexes. Complex (coordinate) compounds contain at least one central atom that is surrounded by other atoms or groups of atoms (ligands), wherein at least one central atom-ligand bond is a coordinate bond -a covalent bond, the essence of which is the commonality of the electron pair between two atoms, both of which are electrons formally derived from one atom. After synthesis, the pores of the three-dimensional structures are filled with guest molecules (solvents, unreacted linkers). MOF-5 is one of the most studied MOFs, its simplified empirical formula is Zn4O(BDC)3 (Fig. 2.21) [2.96]. MOFs serve as models from which they are built metallo-supramolecular architectures.

The large inner surface is important for possible applications as catalysts. The pore size can be precisely determined via the size of the organic ligands, so that only reactants of a certain size fit into it. A high selectivity can thus be expected. Some MOFs have very good adsorption properties [2.97], which make them interesting for use in adsorption chillers. In an adsorption refrigerator, heat or cold is generated by adsorption or evaporation of a solvent. For this purpose, the system is divided into two subsystems, one containing a solvent and the other the MOF. Both subsystems are connected to the valve by a connecting pipe. If the valve is opened, solvent can evaporate and extract heat from the environment (enthalpy of vaporization), while heat is released when the solvent is adsorbed on the MOF (enthalpy of adsorption). Moreover, MOFs can be used as

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heterogeneous catalysts, due to their large surface area, the adjustable porosity and the diversity of the chemical composition [2.98]. Nevertheless, potential areas of application can be found in biological imaging and sensing, which are based on unique luminescent properties of MOFs [2.99].

Very often MOFs are combined with rare earth ions due to their photoluminescence, that make it ideal for imaging applications, such as the sharp and essentially non-overlapping emission bands

Porphyrins

The most studied and frequently used building blocks in supramolecular chemistry include systems based on the porphyrin backbone and related compounds. These compounds have interesting electrochemical and photochemical properties that can be easily modified, they also have the ability to form very stable transition metal chelate complexes.

Porphyrin is a molecule made up of a characteristic aromatic macrocycle that consists of four pyrrole rings connected by methine bridges = CH -(Fig. 2.22). This combination creates a system of conjugated double bonds that contain 18 delocalized  electrons. In this arrangement, Huckle's aromatic rule is fulfilled (4𝑛 + 2); 𝑛 = 4. Pyrrole rings form a closed aromatic plane that forms the nucleus of the molecule. One of the results of a large conjugate system is that porphyrin molecules usually very intensively absorb electromagnetic radiation in the visible area and can be deeply colored. Porphyrins find application in many fields of science CHAPTER 3: THIN FILMS PHYSICS

Luminescence

The luminescence of a material is the emission of radiation that occurs from a state with energy higher than the basic state. There are many types of luminescence, depending on the caused factor, the phenomenon of light wave emission as a result of chemical reactions, however, electroluminescence is a phenomenon that occurs under the influence of current flow.

Nonetheless, in this work we will focus on photoluminescence -phenomenon in which light acts as an excitatory stimulus. Photoluminescence, due to its duration, is divided into fluorescence and occurs is called the intersystem crossing. However, if from the triplet excited state T1 there is a transition to the ground state S0, in a time not shorter than 10 -8 seconds [3.1], then we deal with phosphorescence. The energy differences between higher excited states of a given S2 and S1

multiplet are usually much smaller than between the lowest singlet S1 or triplet T1 and the ground state S0, which means that the rate of internal conversion significantly exceeds the rate of fluorescence and phosphorescence.

The name fluorescence was first used by G. G. Stokes, who discovered in 1852 that mineral fluorite emits visible light when it is illuminated by UV light [3.2]. It turns out that the maximum emission is mainly shifted towards longer waves in relation to the maximum absorption. This effect is called Stokes shift. In addition, the analysis of the Jabłoński diagram shows that the absorption energy exceeds the emission energy. In fact, the total energy absorbed by the molecule is released in the substrate in various ways, including photon emission, so the energy of the emitted photons is therefore smaller than the energy of the absorbed photons.

Another property is that fluorescence itself is observed regardless of the excitation wavelength.

This principle was described in 1950 by M. Kasha [3.3]. Investigating the emission properties of complex molecules, he discovered that when a photon is absorbed from the S0 base level, it can be excited to any higher SN energy level. However, photon emission occurs only from the lowest excited state S1, therefore it is correct to say that it does not depend on the excitation wavelength (needs a minimum energy of photon). Kasha's rule is important in understanding the emission says that the excitation wave length also does not affect the quantum efficiency of fluorescence [3.4].

An interesting phenomenon is also the Mirror -Image Rule. It occurs when the fluorophore emission spectrum is a mirror reflection of the absorption spectrum [3.5]. This happens when the probability of transition from S1 excited singlet level to S0 base level is identical to S0 to S1 transition.

One of the most important parameters of the fluorophore is the fluorescence lifetime, which characterizes the average time during which the molecule remains in the excited state S1 shortly before returning to the ground state S0 [3.5]. Fluorescence lifetime is best described by the simplified Jabłoński diagram (Fig. 3.2). In the situation presented in Fig. 3.2 the excited fluorophore is characterized by two main parameters: radiation emission rate (Γ) and non-radiative decay to ground state S0 (𝑘 𝑛𝑟 ). The fluorescence lifetime (𝜏 𝐿 ) is therefore described by the equation:

𝜏 𝐿 = 1 Γ + 𝑘 𝑛𝑟 (3.1)

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In general, the values of 𝜏 𝐿 are very small, on the order of 10 ns [3.1]. In many cases, fluorescence lifetimes depend on the fluorophore structure. Lifetime can also be modified by factors affecting one of the speed parameters. For example, the molecule may be non-fluorescent due to high internal conversion rates or slow emissions.

Electronic Properties of Materials

A very important feature of all materials is their ability to conduct electricity or lack thereof. Under the influence of the applied voltage, the phenomenon of electric current through materials occurs.

Conductivity occurs through charge carriers that can be positively charged -then their displacement occurs in the direction of field strength, or negatively charged -they move in the opposite direction.

The basic charge carriers are electrons (negative) and holes (positive), which indicate the absence of an electron in a solid at the binding site. Electron conductivity occurs in materials with a covalent bond, i.e. one in which electron pairs belonging to the two nearest atoms bind together. It is different in the case of ionic bonds, in which conductivity takes place through ions. In such a system, positive carriers are cations, while negative carriers are anions.

It is convenient to discuss the electronic properties of materials using solid state band theory. When the atoms approach each other over very small distances, the discrete energy levels of the electrons change to form a solid. The electrons that surround the atomic nucleus can only fill precisely defined energy states with the lowest possible energy. According to the Pauli principle, two identical fermions cannot be in the same quantum state at the same time, which means that a maximum of two electrons with opposite spins can occupy one energy state [3.6]. Therefore, as the atoms approach each other, the valence electrons interact with each other, which causes the energy level to split. Generally, the differences between energy states are very small, so they are said to form continuous energy bands. The band resulting from the split of the base band is called the valence band, while the band above it is the conductivity band. The energy gap, i.e. the area between these bands, is forbidden for electrons.

It turns out, however, that these bands can be filled completely, partly or not at all. Then the quantity, called Fermi EF energy, is entered, which determines the energy of the highest occupied level in the energy band at 0 K. Fermi energy is from 2 eV to 12 eV [3.7]. This energy distribution of a large number of particles and its changes with temperature T can be calculated by statistical considerations. The kinetic energy of the electron gas is regulated by the Fermi-Dirac distribution, which gives information that the Fermi energy EF is determined by the probability of filling a certain energy level E by electrons 𝑓(𝐸):

𝑓(𝐸) = 1 𝑒𝑥𝑝 ( 𝐸 -𝐸 𝐹 𝑘 𝐵 𝑇 ) + 1 (3.2)
where: 𝑘 𝐵 -Boltzmann constant, T -absolute temperature. If the energy level E is completely occupied by electrons, then the Fermi-Dirac distribution is 1. In turn, for the empty energy level 𝑓(𝐸) = 0. Electricity conduction occurs for electrons with energy similar to Fermi energy.

There are two types of molecular orbitals: HOMO (Highest Occupied Molecular Orbital), which means the highest occupied molecular orbital and LUMO (Lowest Unoccupied Molecular Orbital), which means the lowest unfilled molecular orbital [3.6]. In solid state physics, HOMO means the maximum valence band, LUMO means the minimum conductivity band (Fig.

Thin Film Structures

Over the last few decades, there has been a significant increase in the interesting in thin films. Used in many types of engineering systems, thin films make a important contribution to technological processes, including accelerating the development of highly integrated electronic systems.

In order to understand the definition of the thin film, it is convenient to introduce general classification of structures in terms of their geometrical configuration and character of spatial constraints, as it is shown in Fig. configuration. The degree of limitation is defined as the interaction of the structure with other solid states to which it may be attached or with which it may be in contact. The layer or film is often called a two-dimensional structure, a quantum wire is a one-dimensional structure and a quantum dot a zero-dimensional structure. However, it is not standard terminology [3.8]. The adoption of the classification scheme which is shown on Fig. 3.4. makes it easier to distinguish low-dimensional structures. Generally, a thin film is defined as a low-dimensional material created by applying single atoms, molecules or ions to the substrate. The thin film technology applies to a wide spectrum covering from a few nanometres to several microns. It is believed that thin films act to as a "bridge" between monolayers and volume structures. There are no rigid rules that allow you to classify films as thick or thin. However, the dependence of film properties on the dimension is important.

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Regardless of the thickness boundary, the ideal film can be defined mathematically as a homogenous solid material contained between two parallel planes and stretched infinitely in two directions, for example x and y, but bounded along the third direction z which is perpendicular to the x-y plane. The dimension along the direction z denotes the film thickness d [3.9]. This value can vary from 𝑑 → 0 to any value up to 10 microns or more, but always remains much smaller than those that are along the order two directions x and y. In fact, this deviates significantly from the ideal case, because the two planes are never exactly parallel, even when they were created in the best setting conditions, and the material contained between two planes is rarely homogenous, evenly distributed, or the same species. It is also known that the film may contain many defects, impurities, dislocations, grain boundaries and other defects and discontinuities. The upper surface of the film often exhibits some topographic characteristics which are characteristic of growth conditions, which are often noticeable by the sense of sight. Some of these features can be undoubtedly minimized by adequate control of deposition, but they can not be avoided. The bottom surface of the layer exhibits topographical features of the substrate with which is in contact.

As mentioned before, all films produced in various techniques are invariably associated with some of the defects in layer growth. The surface state of the layer plays a dominant role in modifying, inter alia, electrical properties. In addition, due to the high surface-to-volume ratio of the thin film, the newly formed surface of the layer becomes highly reactive. Due to imbalance of forces close to the surface, such phenomena as thermal emission, gas adsorption, solid state reactions and other surface-related features are often observed. That is why it is extremely important to study thin films not only because of the enormous technological importance, but also because of insufficient knowledge about their interaction with electric, magnetic and electromagnetic fields.

Spin Coating

One of the most important, well-known and cheapest method of thin films deposition is spin coating technique. Deposition is divided into 4 steps (Fig. 3.5): in this method, the layers are applied from a solution, so before applying the layers it is necessary to dissolve the studied compounds in a suitable solvent; (1) in the first step, a specific amount of solution is spread on substrate, which is held by vacuum through a spinning device; (2) when the rotatable stage is accelerating, most of the solution is spun outside the substrate, however part of the solution remains on the ground and covers its entire surface; (3) followed by rotation in constant speed, making the layer thinner and homogenous; (4) after evaporation of the solvent, additional drying is carried out on a special hot plate, at a temperature depending on the material used. tension. However, the final thickness 𝑑 𝑓 of the sample can be estimated from the semi-empirical equation of Meyerhofer [3.10]:

𝑑 𝑓 = ( 3 2 ) 1 3 ⁄ 𝑐 0 (1 -𝑐 0 ) -1 3 ⁄ 𝜔 𝑟 -2 3 ⁄ 𝑣 0 𝑒 1 3 ⁄ (3.3)
where 𝑐 0 describes initial coating concentration, 𝜔 𝑟 is connected to the angular rotation speed (in

𝑠 -1
), 𝑣 0 is the initial kinetic viscosity (in 𝑚 2 𝑠 -1 ), e describes the evaporation rate (in 𝑚 𝑠 -1 ).

Spin coating technique is very popular in the production of photoresistive layers, devices including LEDs, photovoltaic cells, light-sensitive and conjugated polymers, semiconductor wafers, emerging industries of organic electronics. Moreover, is widely used in the preparation of samples for investigations in nonlinear optics [3.11 -3.12]. This method has many advantages: uses lowcost equipment, is very simple and it is possible to use various kinds of substrates. However, also has its drawbacks. One of them is the fact that each sample should be prepared separately, so mass production of samples of the same thickness is almost impossible. Also the fact that the production of thin layers is carried out only for laboratory samples -of small size. For successful coating, the following conditions must be met: first, prepared solvent must wet substrate, otherwise all of the solution will be ejected during acceleration; secondly, the material that we want to apply to the substrate must be soluble; besides, the solvent we use must be volatile. In addition, spin speed versus thickness correlations should be observed, otherwise wrong calculations can lead to structure defects such as pinhole, air bubbles, uneven sample thickness at the center and at the edges.

Physical Vapor Deposition

PVD process generally takes place in three stages. The first is the production of the proper particles: atoms, molecules or ions. In the second stage, the particles are transported to the substrate in the form of vapor by low gas or plasma pressure. In the last stage, condensation occurs on the substrate, the aim of which is to create a stable layer. The final product may be in the form of a single crystal layer as well as a polycrystalline layer, as well as an amorphous layer. Typically, the gas-phase deposition is used to deposit films with thicknesses ranging from a few to thousands of nanometres, but it can also be used to form multilayer coatings and thick layers. Typical deposition rates are 1-10 nm per second [3.13].

Extensive experimental and theoretical studies of the deposition process at different stages of growth allowed to observe that there are three different types of nucleation and layer growth. The three basic types are: the Volmer -Weber model, the Frank -Van der Merwe model and the Stranski -Krastanov model [3.14]. A diagram illustrating each of these three types of thin film growth is presented on Fig. 3.6. n the Volmer -Weber model (Fig. 3.6a), the balance exists between the three-dimensional crystal of the layer in contact with the substrate, while the rest of the substrate is depleted of any condensed phase. The growth process takes place in the form of islands on the surface of the substrate until the atoms do not form a continuous layer. In the Frank -Van der Merwe model (Fig. 3.6b) nucleation takes place in the form of a single-layer island. Finally, monolayers grow together, forming a complex monolayer. This process is repeated in a multilayered manner. In this growth model, the layer after the layer of interaction between the substrate and the atoms of the layer are stronger than between adjacent atoms of the layer. The Stranski -Krastanov model (Fig. 3.6c) combines the features of layered growth and nucleation in three dimensions. In this model, nucleation and growth occur as in the Frank -Van der Merwe model, therefore a finite number of monolayers is created. Subsequent formation of the layer occurs by creating separate nuclei. The mismatch between the substrate and the resulting layer can not be taken into account when the thickness of the layer increases so that the three-dimensional growth promotes the growth of the layer by layer. Alternatively, the symmetry of orientation over the layers relative to the substrate may be responsible for producing growth in this mode.

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reaching the substrate per unit area of the substrate per unit on time. Generally, the substrates are placed at a significant distance from the source of evaporation to reduce their radiation of the substrate heating by the source of evaporation. The PVD method is widely used as a method of sample preparation for testing non-linear optics of both inorganic and organic samples [3.15].

Pulsed Laser Deposition

Pulsed Laser Deposition (PLD), called as well Laser Ablation (Fig. 3.9) is one of the most famous techniques of thin film deposition. In this method deposition takes place from the gas phase in the vacuum system. This is a technique that uses a pulse laser which is focused on the purpose of the deposited material [3.16]. In the next step the surface is heated by the laser's interaction, which initiates the evaporation process. By evaporating a small amount of material with each material impulse, a plasma plume is formed and begins to expand. Plasma is moving towards the substrate, where it condenses. In this way, a thin film is formed. In the case of inorganic materials, the laser desorption conditions are chosen such that the plasma plume is composed of atoms and other lowmass particles. The Lee model is used to determine the second-order nonlinear susceptibility [4.1]. Quartz glass is the most commonly material used as a reference. Second-order nonlinear optical susceptibility 𝜒 (2) of sample with thickness d can be calculated by:

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𝜒 (2) = 𝜒 𝑄𝑢𝑎𝑟𝑡𝑧 (2)
𝐿 𝑄𝑢𝑎𝑟𝑡𝑧 𝑐𝑜ℎ = 𝜆 𝜔 4 • |𝑛 2𝜔 -𝑛 𝜔 | (4.2)
where 𝜆 𝜔 is the wavelength of the fundamental beam, while 𝑛 2𝜔 and 𝑛 𝜔 are refractive indexes of the reference material for the fundamental beam and the generated second harmonic, respectively.

In the case where the optical absorption of the material is not negligible, the formula (4.1) takes form:

𝜒 (2) = 𝜒 𝑄𝑢𝑎𝑟𝑡𝑧 (2) ( 2 𝜋 ) ( 𝐿 𝑄𝑢𝑎𝑟𝑡𝑧 𝑐𝑜ℎ 𝑑 ) √ 𝐼 2𝜔 𝐼 𝑄𝑢𝑎𝑟𝑡𝑧 2𝜔 ( 𝛼𝑑 2 1 -𝑒𝑥𝑝 (- 𝛼𝑑 2
)

) (4.3)
where  is optical absorption coefficient.

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Kurtz -Perry

The streamlined model of Kurtz and Perry was developed for microcrystalline powders [4.3]. This model is based on the comparison of the macroscopic second-order nonlinear optical properties of the samples with reference material -yellow powder 3-methyl-4-nitropyridine-1-oxide, called formally POM:

𝜒 (2) = 𝜒 𝑃𝑂𝑀 (2) √ 𝐼 2𝜔 𝐼 𝑃𝑂𝑀 2𝜔 (4.4) where: 𝜒 (2) and 𝜒 𝑃𝑂𝑀 (2) = (21 ± 3) • 10 -9 𝑒𝑠𝑢 [4.4] are the second-order nonlinear optical susceptibilities of studied material and reference powder, respectively, 𝐼 2𝜔 and 𝐼 𝑃𝑂𝑀 2𝜔 are the maximum amplitudes of SHG of the investigated material and POM, respectively.

The main disadvantage of this simplistic model is the strong influence of the crystallinity of the investigated material on the intensities of the second harmonic signal measurements. Indeed, the size of the crystallites influences the phase agreement and therefore the intensity of the second harmonic signal. In this case, it is consequently essential to know the exact size of the crystallites.

Herman -Hayden

The model of Herman and Hayden is used for characterization of thin films and solid materials and was developed in 1995 [4.5]. This theoretical model has this advantage, unlike the model of This model assumed that the electromagnetic wave with the frequency 𝜔 falls on the studied medium from the bottom under angle 𝜃 and the plane 𝑥 -𝑧 is the plane of incidence. At the frequency 𝑚𝜔, the refractive index of nonlinear medium with thickness 𝑑 is equal to 𝑛 𝑚 and 𝑛 𝑚𝑠 of substrate. When the electromagnetic wave, described by:

𝐸 1𝜐 ⃗⃗⃗⃗⃗⃗ = 𝑒υ𝐸 1 𝑒𝑥𝑝[𝑖(𝑘 ⃗ 1 • 𝑟 -𝜔𝑡)] (4.5)
where: Air:

𝑒υ = (0,
𝐸 ⃗ 2 = 𝑅𝑒̂𝑃 𝑟 𝑒𝑥𝑝 {𝑖𝑘 ⃗ 2 𝑟 [𝑟 + ( 𝑑 2 ) 𝑧]} (4.5) 𝐻 ⃗ ⃗ 2 = -( 𝑖𝑐 2𝜔 ) ∇ × 𝑊 ⃗⃗⃗ = 𝑅𝑒̂𝑆 𝑟 𝑒𝑥𝑝 {𝑖𝑘 ⃗ 2 𝑟 [𝑟 + ( 𝑑 2 ) 𝑧]} (4.6) Medium: 𝐸 ⃗ 2 = 𝑒 𝑏 𝑒𝑥𝑝(𝑖2𝑘 ⃗ 1 • 𝑟 ) + 𝐴𝑒2 𝑃 𝑒𝑥𝑝(𝑖𝑘 ⃗ 2 • 𝑟 ) + 𝐵𝑒̂2 𝑃 𝑟 𝑒𝑥𝑝(𝑖𝑘 ⃗ 2 𝑟 • 𝑟 ) (4.7) 𝐸 ⃗ 𝐻 = ℎ ⃗ 𝑏 𝑒𝑥𝑝(𝑖2𝑘 ⃗ 1 • 𝑟 ) + 𝑛 2 𝐴𝑒2 𝑆 𝑒𝑥𝑝(𝑖𝑘 ⃗ 2 • 𝑟 ) + 𝑛 2 𝐵𝑒̂2 𝑆 𝑟 𝑒𝑥𝑝(𝑖𝑘 ⃗ 2 𝑟 • 𝑟 ) (4.8) Substrate: 𝐸 ⃗ 2 = 𝑇𝑒̂2 𝑃 𝑆𝑈𝐵 𝑒𝑥𝑝 [𝑖𝑘 ⃗ 2 𝑆𝑈𝐵 • (𝑟 -( 𝑑 2 ) 𝑧)] (4.9) 𝐸 ⃗ 2 = 𝑛 2 𝑇𝑒̂2 𝑆 𝑆𝑈𝐵 × 𝑒𝑥𝑝 [𝑖𝑘 ⃗ 2 𝑆𝑈𝐵 • (𝑟 -( 𝑑 2 ) 𝑧)] (4.10)
where 𝑒̂𝑆 𝑟 = (0,1,0) and 𝑒̂𝑃 𝑟 = (cos 𝜃 , 0, -sin 𝜃) and is called by unit polarization vector of the reflected second harmonic field in the air, 𝐴 and 𝐵 are complex amplitudes of the second harmonic generation of free waves in a nonlinear medium, running forward and backward, respectively, 𝑅 and 𝑇 correspond to these amplitudes in substrate and air, respectively. The unit polarization vectors in nonlinear medium are described by: 𝑒̂2 𝑃 𝑆𝑈𝐵 = (0,1,0); and 𝑒̂2 𝑆 𝑆𝑈𝐵 = (𝑐 2𝑆 , 0, 𝑠 2𝑆 ). The vector waves are equal to:

Air: 𝑘 ⃗ 2 𝑟 = ( 2𝜔 𝑐 ) (sin 𝜃 , 0, -cos 𝜃) Medium: 𝑘 ⃗ 𝑚 = ( 𝑚𝜔𝑛 𝑚 𝑐 ) (𝑠 𝑚 , 0, 𝑐 𝑚 ) 𝑘 ⃗ 𝑚 𝑟 = ( 𝑚𝜔𝑛 𝑚 𝑐 ) (𝑠 𝑚 , 0, -𝑐 𝑚 ) Substrate: 𝑘 ⃗ 𝑚 𝑆𝑈𝐵 = ( 2𝜔𝑛 𝑠 𝑐 ) (𝑠 2𝑆 , 0, 𝑐 2𝑆 )
where: 𝑠 𝑚 =

𝑒 𝑏 = 4𝜋 𝑛 1 2 -𝑛 2 2 [𝑃 ⃗ 𝑁𝐿 - 𝑘 ⃗ 𝑏 (𝑘 ⃗ 𝑏 •𝑃 ⃗ 𝑁𝐿 ) |𝑘 ⃗ 2 | 2 ]
where 𝑘 ⃗ 2 = 2𝑘 ⃗ 1 (4.11) ℎ ⃗ 𝑏 = 𝑛 1 𝑘 ⃗ 1 × 𝑒 𝑏 (4.12)

𝑃 ⃗ 𝑁𝐿 = |𝐸 1 | 2 𝑑 : 𝑒1𝑒2 (4.13)
In this case, the power of generated second harmonic passing through the isotropic nonlinear medium (see Fig. 4.1) without dispersion is expressed by: 2𝑃) ] cos 4𝜙 2 (4.14) where 𝑡 and 𝑟 are the standard Fresnel coefficients for transmission and reflection, respectively, the indices 𝑎𝑓 are air-medium (f -film), 𝑓𝑠 are medium-substrate, and 𝑠𝑎 are substrate-air, and:

𝑃 2𝜔 (𝛾→𝑃) = = 128 𝑐𝐴 [𝑡 𝑎𝑓 (1𝛾) ] 4 [𝑡 𝑓𝑠 (2𝑃) ] 2 [𝑡 𝑠𝑎 (2𝑃) ] 2 𝑛 2 2 𝑐 2 2 𝑃 𝜔 2 ( 2𝜋𝑑 𝜆 ) 2 𝑑 𝑒𝑓𝑓 2 sin 2 Φ Φ 2 + [𝑟 𝑎𝑓 (2𝑃) ] 2 𝑅 2 sin 2 Ψ Ψ 2 -2 [𝑟 𝑎𝑓 (2𝑃) ] 𝑅 sin Φ sin 𝜑 Φ𝜑 cos 2𝜙 2 1 + [𝑟 𝑎𝑓 (2𝑃) ] 2 [𝑟 𝑓𝑠 (2𝑃) ] 2 + 2 [𝑟 𝑎𝑓 (2𝑃) ] [𝑟 𝑓𝑠 (
𝑅 = 𝑑 𝑒𝑓𝑓 𝑟 𝑑 𝑒𝑓𝑓
where

𝑑 𝑒𝑓𝑓 = 𝑑 ⃡ : 𝑒1𝑒2 𝜑 = 2𝜋𝑑 𝜆 (𝑛 1 𝑐 1 -𝑛 2 𝑐 2 ) Φ = 2𝜋𝑑 𝜆 (𝑛 1 𝑐 1 + 𝑛 2 𝑐 2 ) 𝜙 2 = 2𝜋𝑑 𝜆 𝑛 2 𝑐 2
In the case of non-zero absorption in the medium, complex equation of refractive index is included in equation (4.14):

𝑛 ̃𝑚 = 𝑛 𝑚 + 𝑖𝜅 𝑚 (4.15)
where 𝜅 𝑚 is extinction coefficient of the nonlinear medium at the frequency of 𝑚𝜔. Therefore, equation (4.14) for the absorbing medium, neglecting reflection from the layer, takes the form: ___________________________________________________________________________ Waszkowska Karolina | Study and diagnostic of the physicochemical properties of new -conjugated (metallo)supramolecular architectures for nonlinear optics. 99 [START_REF] Kleinman | Theory of Second Harmonic Generation of Light[END_REF] where:

𝑃 2𝜔 (𝛾→𝑃) = 128 𝑐𝐴 [𝑡 𝑎𝑓 (1𝛾) ] 4 [𝑡 𝑓𝑠 (2𝑃) ] 2 [𝑡 𝑠𝑎 (2𝑃) ] 2 𝑛 2 2 𝑐 2 2 𝑃 𝜔 2 ( 2𝜋𝑑 𝜆 ) 2 𝑑 𝑒𝑓𝑓 2 × 𝑒𝑥𝑝[-2𝛿 1 + 𝛿 2 ] sin 2 Φ Φ 2 + sinh 2 Ψ Ψ 2 (4.
Ψ = 𝛿 2 -𝛿 1 = 2𝜋𝑑 𝜆 ( 𝑛 1 𝜅 1 𝑐 1 - 𝑛 2 𝜅 2 𝑐 2 ) (4.17)
Assuming that the studied medium in the form of a layer and the substrate are transparent, that is, that the transmission coefficients are approximately equal to 1, then the relationship describing the second-order nonlinear susceptibility for the nonlinear medium is given in form [4.5 -4.6]:

𝐼 2𝜔 (𝜃) = ( 128𝜋 5 𝑛 2𝜔 2 cos 2 𝜃 2𝜔 𝜆 𝜔 2 𝑐 ) (𝜒 𝑒𝑓𝑓 (2) 𝐼 𝜔 𝑑) 2 ( sin 2 Φ + sinh 2 Ψ Φ 2 + Ψ 2 ) (4.18)
Φ and Ψ are phase angles and can be described as:

Φ = 2𝜋𝑑 𝜆 𝜔 (𝑛 𝜔 cos 𝜃 𝜔 -𝑛 2𝜔 cos 𝜃 2𝜔 ) (4.19) Ψ = 2𝜋𝑑 𝜆 𝜔 ( 𝑛 𝜔 𝜅 𝜔 cos 𝜃 𝜔 - 𝑛 2𝜔 𝜅 2𝜔 cos 𝜃 2𝜔 ) (4.20)
where 𝐼 𝜔 and 𝐼 2𝜔 are the intensities of fundamental and generated second harmonic waves, respectively, 𝜆 𝜔 is fundamental wavelength beam, 𝑑 is the thickness od studied medium, 𝜃 𝜔 and 𝜃 2𝜔 are angles of fundamental and generated second harmonic wave, respectively, 𝑛 𝜔 and 𝑛 2𝜔 describe indexes of refraction at fundamental and generated second harmonic wavelength, respectively, 𝜅 𝜔 and 𝜅 2𝜔 are extinction coefficients of fundamental and generated second harmonic wavelength, respectively.

Kubodera -Kobayashi

The Kubodera-Kobayashi model [4.7] is used to calculate 𝜒 (3) . This model consist in directly comparing the maximum amplitude of the light intensity generated third harmonic by diagnosed ___________________________________________________________________________ Waszkowska Karolina | Study and diagnostic of the physicochemical properties of new -conjugated (metallo)supramolecular architectures for nonlinear optics. 100 medium with the maximum amplitude of the light intensity obtained in the measurement of 1 mm of silica which is used as a reference material:

𝜒 (3) = 𝜒 𝑆𝑖𝑙𝑖𝑐𝑎 (3)
𝐿 𝑆𝑖𝑙𝑖𝑐𝑎 𝑐𝑜ℎ = 𝜆 𝜔 6 • |𝑛 3𝜔 -𝑛 𝜔 | (4.22)
where 𝜆 𝜔 is the wavelength of the fundamental beam, while 𝑛 3𝜔 and 𝑛 𝜔 are refractive indexes of the reference material for the fundamental beam and the generated third harmonic, respectively.

When the optical absorption is not negligible, the relation ( 4) includes the linear absorption coefficient  and takes the form:

𝜒 (3) = 𝜒 𝑆𝑖𝑙𝑖𝑐𝑎 (3) ( 2 𝜋 ) ( 𝐿 𝑆𝑖𝑙𝑖𝑐𝑎 𝑐𝑜ℎ 𝑑 ) √ 𝐼 3𝜔 𝐼 𝑆𝑖𝑙𝑖𝑐𝑎 3𝜔 ( 𝛼𝑑 2 1 -𝑒𝑥𝑝 (- 𝛼𝑑 2
)

) (4.23)

Reintjes

The Reintjes model [4.9] was the first model in which attempts were made to explain the phenomena that is responsible for the formation of so-called Maker's fringes [4.10 -4.11]. In this model, it is assumed that the wave propagates in a homogeneous, nonconductive, nonmagnetic, nonlinear medium. To express the intensity of the third harmonic generation, it is necessary to solve the wave equation in such a medium: where 𝑐 is speed of light and 𝑃 ⃗ 𝑁𝐿 is nonlinear polarization of medium. This model also assumes that:

∇ ⃗ ⃗ × ∇ ⃗ ⃗ × 𝐸 ⃗ + 𝑛 2 (3𝜔) 𝑐 2 𝜕 2 𝐸 ⃗ 𝜕𝑡 2 = - 4𝜋 𝑐 2 𝜕 2 𝑃
𝐸 ⃗ = 1 2 {𝐸 1 𝑒𝑥𝑝[-𝑖(𝜔 1 𝑡)]𝑒 1 + 𝐸 3 𝑒𝑥𝑝[-𝑖(𝜔 3 𝑡)]𝑒 3 + 𝑐. 𝑐. } (4.25)
as well as:

𝑃 ⃗ 𝑁𝐿 = 1 2 {𝑃 1 𝑁𝐿 𝑒𝑥𝑝[𝑖(𝑘 1 𝑧 -𝜔 1 𝑡)]𝑒 1 + 𝑃 3 𝑁𝐿 𝑒𝑥𝑝[𝑖(𝑘 3 𝑧 -𝜔 3 𝑡)]𝑒 3 + 𝑐. 𝑐. } (4.26)
Acquire that 𝐸 𝑖 = 𝐴 𝑖 𝑒𝑥𝑝(𝑖𝑘 𝑖𝜔 𝑧) then equation ( 4.25) takes form:

𝐸 ⃗ = 1 2 {𝐴 𝜔 𝑒𝑥𝑝[𝑖(𝑘 1 𝑧 -𝜔 1 𝑡)]𝑒 1 + 𝐴 3𝜔 𝑒𝑥𝑝[𝑖(𝑘 3 𝑧 -𝜔 3 𝑡)]𝑒 3 + 𝑐. 𝑐. } (4.27)
where 𝐴 𝜔 and 𝐴 3𝜔 denote the amplitudes of the fundamental beam field and the generated third harmonic, respectively. If we consider only the components along the 𝑧 axis, then we get the following relation:

𝜕 2 𝐸 ⃗ 𝜕𝑧 2 = 1 2 𝜕 2 𝜕𝑧 2 {𝐴 𝜔 𝑒𝑥𝑝[𝑖(𝑘 1 𝑧 -𝜔 1 𝑡)]𝑒 1 + 𝐴 3𝜔 𝑒𝑥𝑝[𝑖(𝑘 3 𝑧 -𝜔 3 𝑡)]𝑒 3 + 𝑐. 𝑐. } (4.28) therefore: 𝜕 2 𝐸 ⃗ 𝜕𝑧 2 = ∇ 2 𝐴 𝜔 + 𝑖𝑘 𝜔 𝜕𝐴 𝜔 𝜕𝑧 𝑒𝑥𝑝[𝑖(𝑘 1 𝑧 -𝜔 1 𝑡)] - 1 2 𝐴 𝜔 𝑘 𝜔 2 𝑒𝑥𝑝[𝑖(𝑘 1 𝑧 -𝜔 1 𝑡)] + ∇ 2 𝐴 3𝜔 + +𝑖𝑘 𝜔 𝜕𝐴 3𝜔 𝜕𝑧 𝑒𝑥𝑝[𝑖(𝑘 3 𝑧 -𝜔 3 𝑡)] - 1 2 𝐴 3𝜔 𝑘 3𝜔 2 𝑒𝑥𝑝[𝑖(𝑘 3 𝑧 -𝜔 3 𝑡)] + 𝑐. 𝑐. (4.29)
Moreover, second expression on the left side of the equation ( 4.24) can be written as: According to the general expression of polarization, we can write:

𝑛 2 (3𝜔) 𝑐 2 𝜕 2 𝐸 ⃗ 𝜕𝑡 2 = 1 2 𝑛 2 (3𝜔) 𝑐 2 𝜕 2 𝜕𝑡 2 {𝐴 𝜔 𝑒𝑥𝑝[𝑖(𝑘 1 𝑧 -𝜔 1 𝑡)] + 𝐴 3𝜔 𝑒𝑥𝑝[𝑖(𝑘 3 𝑧 -𝜔 3 𝑡)] + 𝑐. 𝑐. } = = 1 2 𝑛 2 (3𝜔) 𝑐 2 {𝐴 𝜔 𝜔
𝑃 𝑁𝐿 (3) (𝜔) = ∑ {𝜒 (3) (𝜔; 𝜔 1 ; … ; 𝜔 2 )𝐸 ⃗ 1 (𝜔 1 ) … 𝐸 ⃗ 3 (𝜔 3 )} 𝜔=𝜔 1 +⋯+𝜔 3 (4.35)
In the case of the THG technique, the polarization then takes form: we can replace:

𝑃 𝑁𝐿 = 1 4 𝜒 (3) 𝐴 𝜔 3 [𝑒𝑥𝑝(𝑖𝑘 𝜔 𝑧)] 3 (
𝜔 2 𝑘 = 𝜔 2 𝑐 𝑛𝜔 = 𝜔𝑐 𝑛 = 2𝜋𝑐 2 𝜆 (4.39)
As a result we get following expression:

𝜕𝐴 3𝜔 𝜕𝑧 = 𝑖 𝜋 2 𝜆 3𝜔 𝑛 3𝜔 𝜒 (3) 𝐴 𝜔 3 𝑒𝑥𝑝[-𝑖∆𝑘𝑧] = 𝑖 3𝜋 2 𝜆 𝜔 𝑛 3𝜔 𝜒 (3) 𝐴 𝜔 3 𝑒𝑥𝑝[-𝑖∆𝑘𝑧] (4.40)
where 𝑛 3𝜔 denotes refractive index for 3𝜔, and ∆𝑘 describes phase shift vector for the process of third harmonic. By integrating equation (4.40) between 0 and L we get relation:

𝐴 3𝜔 = ∫ 𝑖 3𝜋 2 𝜆 𝜔 𝑛 3𝜔 𝜒 (3) 𝐴 𝜔 3 𝑒𝑥𝑝[-𝑖∆𝑘𝑧]𝑑𝑧 = 3𝜋 2 𝜆 𝜔 𝑛 3𝜔 𝜒 (3) 𝐴 𝜔 3 [ 1 -𝑒𝑥𝑝(-𝑖∆𝑘𝐿) ∆𝑘 ] 𝐿 0 (4.41)
However, the intensity of the wave can be expressed as:

𝐼 𝑖𝜔 = 𝑛 𝑖𝜔 𝑐 2𝜋 |𝐴 𝑖𝜔 | 2 (4.42)
Thus, the intensity of the generated third harmonic with the amplitude described by equation (4.41) takes the form: or written as:

𝐼 3𝜔 = 𝑛 3𝜔 𝑐 2𝜋 ( 3𝜋 2 𝜆 𝜔 𝑛 3𝜔 ) 2 ( 2𝜋 𝑛 𝜔 𝑐 ) 3 𝐼 𝜔 3 |𝜒 (3) | 2 | 1 -𝑒𝑥𝑝(-𝑖∆𝑘𝐿) ∆𝑘 | 2 (
𝐼 3𝜔 = 576𝜋 6 𝑛 3𝜔 𝑛 𝜔 3 𝜆 𝜔 2 𝑐 2 𝐼 𝜔 3 |𝜒 (3) | 2 𝐿 2 | sin ( ∆𝑘𝐿 2 ) ∆𝑘𝐿 2 | 2 (4.44)
where 𝐼 𝜔 and 𝐼 3𝜔 designate the fundamental and harmonic light intensities, respectively, and |𝜒 (3) | describes the electronic contribution of the third order nonlinear susceptibility of the nonlinear medium. In the case where the sample is not absorbing, the intensity of the third harmonic depends on the phase shift, that means: The Kajzar -Messier model can be considered in two cases [4.12 -4.13]. The first of these is the case when the investigated sample is an isotropic medium. The propagation of the harmonic wave in a nonlinear medium takes place according to the representation of Fig. 4.2. The harmonic electric field created in a nonlinear medium with parallel faces 2 placed between two considered linear media (1 and 3) is the sum of a forced wave 𝑏 and two free waves 𝑡 and 𝑟:

ΔΨ = Δ𝑘𝐿 = ( 6𝜋Δ𝑛 𝜆 𝜔 ) 𝐿 = ( 𝜋 𝐿 𝐶 ) 𝐿 (
𝐸 2 3𝜔 = 𝐸 2𝑡 3𝜔 𝑒𝑥𝑝[-𝑖(3𝜔𝑡 -𝑘 3𝜔 2𝑓 𝑟)] + 𝐸 2𝑟 3𝜔 𝑒𝑥𝑝[-𝑖(3𝜔𝑡 -𝑘 3𝜔 2𝑓 𝑟)] + +𝐸 2𝑏 3𝜔 𝑒𝑥𝑝[-𝑖(3𝜔𝑡 -𝑘 𝜔 2𝑏 𝑟)] + 𝑐. 𝑐. (4.47)
Taking into account polarized light perpendicular to the incident plane, the third harmonic electric field is created:

𝐸 3𝑡 3𝜔 = 𝐸 2𝑏 3𝜔 𝐴𝑒𝑥𝑝(𝑖𝑘 2𝑡 3𝜔 𝑙){𝑒𝑥𝑝[𝑖(𝑘 2𝑏 3𝜔 -𝑘 2𝑡 3𝜔 )𝑙] -1} (4.48)
where:

𝐸 2𝑏 3𝜔 = 4𝜋𝑃 𝑁𝐿 (2)
∆𝜀 and nonlinear polarization is given by: 𝑃 𝑁𝐿

𝜒 (3) (𝐸 2 𝜔 ) 3 . This assumption leads to:

𝐸 2𝑏 3𝜔 = 𝜋𝜒 (3) Δ𝜀 (𝐸 2 𝜔 ) 3 = 𝜋𝜒 (3) Δ𝜀 (𝑡 12 𝜔 𝐸 𝜔 ) 3 (4.49)
Moreover, factor A is defined by:

𝐴 = 𝑁 2 3𝜔 + 𝑁 2 𝜔 𝑁 2 3𝜔 + 𝑁 3 3𝜔 ⟹ 𝑁 𝑗 𝜔,3𝜔 = 𝑛 𝑗 𝜔,3𝜔 cos 𝜃 𝑗 𝜔,3𝜔 ⋀ 𝑗 = 1,2,3 (4.50)
where the fundamental wave transmission coefficient 𝑡 12 𝜔 between medium 1 and the input surface of the nonlinear medium is determined by: where: 𝐸 𝜔 and 𝐸 2𝜔 are the amplitudes of the optical electric fields in centres 1 and 2, respectively, the indicators 𝑏 and 𝑡 refer to harmonic waves transmitted by force and free space, 𝑙 thickness of the nonlinear medium, 𝜃 𝑗 propagation angle in the middle 𝑗, ∆𝜀 = 𝜀 𝜔 -𝜀 3𝜔 describes dielectric constant dispersion, 𝑛 𝜔,3𝜔 = √𝜀 𝜔,3𝜔 denotes refractive indexes, and 𝑘 𝜔,3𝜔 is the amplitude of the wave vectors that fulfil the relation:

𝑡 12 𝜔 = 2𝑛 1 cos 𝜃 1 𝑛 1 cos 𝜃 1 + 𝑛
𝑘 2𝑏 3𝜔 = 3𝑘 2 𝜔 = 3𝜔𝑁 2 𝜔 𝑐 𝑎𝑛𝑑 𝑘 2𝑡 3𝜔 = 3𝑘 2 3𝜔 = 3𝜔𝑁 2 3𝜔 𝑐 (4.52)
Setting the boundary conditions of the electric field on interfaces 1 -2 and 2 -3 and neglecting the waves reflected on the interfaces and the air share in relation to the vacuum, we get for the outgoing harmonic field:

𝐸 3𝜔 = 1 𝜋 𝜒 (3) Δ𝜀 𝑇𝑒𝑥𝑝(𝑖Ψ 3𝜔 )(𝐸 𝜔 ) 3 [𝑒𝑥𝑝(𝑖∆ 𝑝 ) -1] (4.53)
where:

Δ 𝑝 = Ψ 𝜔 -Ψ 3𝜔 = 3𝜔𝑙(𝑁 2 𝜔 -𝑁 2 3𝜔 ) 𝑐 (4.54)
where 𝐸 𝜔 designates the incident electric field. Since Δ 𝑝 varies depending on the angle of incidence, the harmonic field will change between the maximum value of 2|𝐴| for Δ 𝑝 = (2𝑚 + 1)𝜋 (where 𝑚 = 0,1,2, … ) and the minimum value for Δ 𝑝 = 2𝑚𝜋. This change in the harmonic field causes Maker fringes during sample rotation.

The second case of Kajzar -Messier model is when we study a thin film deposited on the substrate [4.13]. In the case of a thin film deposited on the substrate and sandwiched between two media considered to be linear, we obtain the resulting electric field (see Fig. Indicators 𝑆 and 𝐹 refer to the substrate and thin film, respectively, 𝑡 1 𝜔 is the fundamental wave transmission coefficient between air and thin film, and 𝑡 3 3𝜔 the harmonic wave transmission coefficient between the substrate and air. Intensity of generated harmonic for transparent thin film is defined as:

𝐼 3𝜔 = 64𝜋 4 𝑐 2 | 𝜒 (3) Δ𝜀 | 𝑆 2 (𝐼 𝜔 ) 3 |𝑒𝑥𝑝[𝑖(Ψ 𝑆 3𝜔 -Ψ 𝐹 𝜔 )]{𝑇 1 [𝑒𝑥𝑝(𝑖ΔΨ 𝑆 ) -1] + 𝜌𝑒𝑥𝑝(𝑖𝜙)𝑇 2 [1 -𝑒𝑥𝑝(-𝑖ΔΨ 𝐹 )]} + 𝐶 𝑎𝑖𝑟 | 2 (4.56)
where:

𝜌𝑒𝑥𝑝(𝑖𝜙) = [ 𝜒 (3) Δ𝜀 ] 𝐹 [ 𝜒 (3) Δ𝜀 ] 𝑆 ⁄ (4.57)
where ∆𝜀 𝑆 and ∆𝜀 𝐹 are the dispersion of the dielectric constant in the substrate and the thin layer, respectively and are given in following form: The dispersion of the refractive index Δ𝑛 𝐴𝑖𝑟 , Δ𝑛 𝑆 and Δ𝑛 𝐹 of air, substrate and thin film, respectively, are given by:

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Δ𝑛 𝐴𝑖𝑟 = 𝑛 𝐴𝑖𝑟 𝜔 -𝑛 𝐴𝑖𝑟 3𝜔 = 1.085 • 10 -5 ⋀ Δ𝑛 𝑆 = 𝑛 𝑆 𝜔 -𝑛 𝑆 3𝜔 ⋀ Δ𝑛 𝐹 = 𝑛 𝐹 𝜔 -𝑛 𝐹 3𝜔 (4.63)
For the fundamental wave at 1064 nm the 𝜒 𝑆 (3) and 𝜒 𝐴𝑖𝑟 (3) values for silica and air, respectively, are equal to 𝜒 𝑆 (3) = 2.0 • 10 where:

𝐶 ′ = [ 𝜒 (3) Δ𝜀 ] 𝐴𝑖𝑟 [ 𝜒 (3) Δ𝜀 ] 𝑆 ⁄ (4.65)
where 𝛹 is the phase of the air proportion parameter, and 𝛼 and 𝛽 = 𝛼 + ΔΨ 𝑆 are the phase differences between the fundamental and harmonic waves for propagation in air, respectively, on the input and output sides of the sample.

SHG/THG Experiments

Experimental setup allowed for second-and third order nonlinear optical response measurements via Maker fringe technique is presented in Fig. 4.4. This technique is based on rotating sample and measuring intensity of generated harmonic in transmission manner as a function of incident angle [4.16 -4.18]. Studied samples were rotated from -75 to +75 with step 0.5 in vertical (P) and Aforementioned, the generation of the second harmonic strongly depends on the symmetry of diagnosed material. Second harmonic generation in centrosymmetric materials is possible by creating macroscopic noncentrosymmetry. This is performed by applying an external electric field forcing the orientation of molecules which have dipole moments towards the electric field line.

One of this method is the corona poling technique [4.20]. In this method, the sample is heated to change the orientation of molecules, while at the corona point a high voltage, about 4 -8 kV, is used. Applied at this point the electric field accelerates the free electrons which ionizing the environment. Produced in this way ions, which have the same sign as the applied electric field, are orienting towards the surface of the material, where they forming an internal electric field along which the molecules are orienting. When high voltage is turned off, orientation remains suspended for particular time, depended on the chemical properties of the system. In the case of polymeric materials, it is important that the applied temperature have to be less than the glass transition temperature 𝑇 𝑔 of the material. describes orientation of dipole moment in polymer matrix. This technique, like any other, has advantages and disadvantages. First of all, the corona poling system is easy to use and has a fast charging process. Moreover, the main advantage is the ability to achieve macroscopic noncentrosymmetry in guest-host systems, thanks to which it is possible to obtain the SHG effect.

On the other hand, the forced orientation of the dipole moments in molecules is achieved for an indefinite period of time, depending on the properties of the material. Due to the fact that the corona poling method is based on reducing the absorbance of a given material, in order to estimate the relaxation time, the absorption spectrum should be regularly measured after using this technique. Besides, other disadvantages of this method include the formation of surface roughness (not always), which has a direct impact on optical loss. According to Ref. [4.21], the ordering parameter in the corona poling method had value around f = 0.3, where the parameter f assumes a value from 0 to 1 depending on the degree of orientation. Considering that each molecule has different properties, the ordering parameter consists mainly of: dipole moment, absorption, guesthost concentration, isotropy, and other properties. One of the methods to determine this parameter is to measure the absorption spectrum of the thin film before and after the application of the corona poling method.

Z-scan Technique

During self-focusing of the intense Gaussian beam in the nonlinear medium, beam distortion occurs. The resulting distortion is measurable, and the information obtained allows us to extract the 𝑛 2 value of the medium. In 1989, M. Sheik-Bahae [4.22] developed a method that focuses the laser beam on a thin sample. Light passing through a small hole is then detected in a distant field.

When scanning the sample along the 𝑧 direction through the lens focus, the far field aperture transmittance is measured, hence the name of the technique: Z-scan. To understand the Z-scan method, let's use a material that has a positive 𝑛 2 and is located far from the lens. If the studied sample is thin, the intensity transmitted by the sample is low, whereas the energy passed through the hole is constant. As the sample approaches the focus, the intensity increases. When the intensity reaches a sufficiently high value, a positive lensing effect can be obtained. This effect causes, when scanning the sample, at a distance with 𝑧 < 0 in front of the focus, the beam approaching the focus, which results in spreading in a distant field. Therefore, the aperture transfer function decreases. Another situation occurs when focusing at a distance of 𝑧 > 0. The added lensing effect reduces the beam divergence, and hence the aperture transmittance increases. Near 𝑧 = 0, the lensing effect has little effect on the beam, as a result the iris transmittance returns to a low intensity value. As a result of the described phenomenon, a typical curve is obtained. An extraordinary useful feature of the Z-scan technique is that the nonlinear index sign is immediately obvious from the data.

Nonlinear optical properties were investigated by Z-scan technique [4.23 -4.24] as well using frequency-doubled beam from pulsed Nd:YAG laser (Ekspla, PL2250) in transmission manner presented in Fig. An extremely useful property of the Z-Scan technique is that the sign of the nonlinear absorption coefficient and the nonlinear refractive index is immediately obvious from the recorded transmittance curves. Besides, the analysis of this data is quick and simple, making it a good technique for studying new nonlinear materials. Moreover, in contrast to, for example, the third harmonic generation, thanks to the Z-scan we are able to determine both the real and the imaginary part of the nonlinear susceptibility 𝜒 (3) . Among other advantages is the simplicity of the methodsingle beam, there is no difficult alignment other than keeping the beam right in the centre of the aperture. However, the disadvantages of the technique include the fact that a very high quality Gaussian beam 𝑇𝐸𝑀 00 is required to achieve absolute measurements, as well as thermal effects during the Z-scan experiment can cause a contribution to third-order NLO susceptibility determined from this technique, for example from thermal heating induced by laser beam pulse on the sample with time. The difference between the maximum and minimum transmission ("peak-valley") is called Δ𝑇 𝑝-𝑣 , where is negative in the "peak-valley" configuration and positive in the "valley-peak" configuration (Fig. 4.10). Δ𝑇 𝑝-𝑣 value is given from:

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∆𝑇 𝑃-𝑉 = 0,406 ΔΦ 0 √2 (1 -𝑆) 0,25 (4.66)
where (1 -𝑆) 0,25 is a parameter connected to the diameter of aperture placed before photomultiplier, and 𝑆 is defined by: ___________________________________________________________________________ Waszkowska Karolina | Study and diagnostic of the physicochemical properties of new -conjugated (metallo)supramolecular architectures for nonlinear optics. 117

𝑆 = 1 -𝑒𝑥𝑝 (- 2𝑟 𝑎 2 𝑤 𝑎 2 ) (4.67)
where 𝑟 𝑎 corresponds to radius of the aperture, and 𝑤 𝑎 corresponds to radius of the laser beam at the position of aperture. This relation (4.67) is applied when the distance between aperture and nonlinear medium is large and the radius of Gaussian beam does not change while passing through the medium. Moreover, in equation ( 4.66) ΔΦ 0 describes the electric field nonlinear phase change,

given in following form:

ΔΦ 0 = 𝑘Δ𝑛 0 𝐿 𝑒𝑓𝑓 (4.68)
In equation ( 4.68) Δ𝑛 0 is determined by following relation:

Δ𝑛 0 = 𝛾′𝐼 0 (4.69)
and 𝐿 𝑒𝑓𝑓 is described as: and 𝐸 is the energy of laser beam measured by powermeter, 𝜏 is the pulse duration (30 ns). Now, including this relation in (4.71), we obtain:

𝐿 𝑒𝑓𝑓 = 1 -𝑒 -𝐿𝛼 0 𝛼 0 ( 4
∆𝑇 𝑃-𝑉 = 1,624𝛾′𝐿 𝑒𝑓𝑓 𝐸(1 -𝑆) 0,25 𝜆√2𝑤 0 2 𝜏 (4.73)
Transforming this equation with respect to 𝛾′, we achieve:

𝛾′ = 𝜆√2𝑤 0 2 𝜏 1,624𝐼 0 𝐿 𝑒𝑓𝑓 𝐸(1 -𝑆) 0,25 ∆𝑇 𝑃-𝑉 (4.74)
The above relation shows the relationship between the non-linear refractive index and the experimentally determined Δ𝑇 𝑝-𝑣 parameter. Finally, the real value of 𝜒 (3) is determined from the following relation:

𝑅𝑒(𝜒 (3) ) = 4𝑛 0 2 𝜀 0 𝑐 3 𝑛 2 (4.75)

Open Aperture Z-scan

Open aperture Z-scan (OA), where all transmitted light is measured, allows to determine nonlinear absorption. We identify two types of nonlinear absorption: saturable absorption (SA) and reverse saturable absorption (RSA), which are determined during measurements in which we receive the transmission in the form of "peak" or "valley", respectively. In this case, the distribution of the intensity and the nonlinear phase shift at the output of the sample is given by the following relation: where 𝐿 𝑒𝑓𝑓 and 𝐼 0 are given in the same conditions as described in relations (4.70) and (4.72), respectively. Determination the imaginary part of third order nonlinear susceptibility 𝜒 (3) is calculated using following expression: nonlinear absorption [4.22]. In case of impact of the nonlinear absorption during experiment of CA Z-Scan, the calculation of the nonlinear refractive index is completed using divided Z-Scan, where ∆𝑇 𝑃-𝑉 is taken directly form divided Z-Scan.

𝑇(𝑧, 𝑆 = 1) = 1 √𝜋𝑞 0 (𝑧, 0) ∫ 𝑙𝑛[1 + 𝑞 0 (𝑧, 0)𝑒𝑥𝑝(-𝜇 2 )]𝑑𝜇 +∞ -∞ (
𝐼𝑚(𝜒 (3) ) = 𝑛 0 2 𝜀 0 𝑐𝜆 3𝜋 𝛽 (4.78)

Spectroscopy Characterization

Atomic Force Microscopy

Atomic Force Microscopy (AFM) was first developed in 1986 by G. Binnig [4.25] and shortly after the discovery it became a leading technique in surface analysis, even on a molecular and atomic scale. AFM is a method that allows to observe the shape of the surface of the object under study in three dimensions at the nanometre scale This technique is used to image the surface of any material, regardless of its transparency, hardness or conductivity. Atomic force microscopy has many advantages over other techniques, including electron microscopy techniques. The main advantage is its versatility in the field of measurement, for example in the air or fluid environment, not in a high vacuum, which allows the imaging of samples in their home state.

The typical atomic force microscope system is shown in Fig. 4.14 [4.26]. The most crucial element of this microscope is a sharp probe, most often V-shaped, placed near the end of an elastic cantilever. By scanning all surface of sample, the deflections of the cantilever are monitored, which allows obtaining a three-dimensional image of the topography of the sample in high resolution.

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Due to the fact that all measurements made by using the AFM are based on the physical interaction between the probe and the sample, the shape of the probe is important to determinate these interactions. In addition to the radius of curvature at the tip of the probe, the geometry of all parts that can interact with the sample is of great importance, especially when imaging or plummeting. There are many different surface imaging modes available in AFM technique. Imaging may take place in contact mode, intermittent mode and also in non-contact mode [4.27]. These modes provide a range of different information about the surfaces to be tested. Contact Mode Imaging means that the probe always stays in contact with the sample. As a result, the impact of the probe -the sample takes place in the repulsive are, as illustrated in Fig. 4.15. This is the simplest AFM operating mode and was originally used to scan the surface. There are two variations of this technique: the mode in continuous and variable power. In the constant mode, a feedback mechanism is used to maintain the deflection and thus the contact force mode of the cantilever. As the cantilever tilts, the height changes in the z-axis direction to restore the original deflection or "set point". The position change in the z-axis direction is monitored, while the information obtained in the x and y position functions is used to create a topographic image of the sample surface. In the case of imaging the force of a variable, the feedback mechanisms are turned off so that the distance in the z-direction remains unchanged and the deviation is monitored in order to obtain a topographic image. This mode can only be used on samples that are relatively smooth, generally providing better resolution than constant mode.

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The contact mode is usually chosen for imaging a hard and relatively flat surface due to the ease of use. However, there are a few drawbacks. Transverse force may occur when the probe moves to ___________________________________________________________________________ Waszkowska Karolina | Study and diagnostic of the physicochemical properties of new -conjugated (metallo)supramolecular architectures for nonlinear optics. 125

the edge of the sample, which may damage the probe or the sample itself. Also, friction forces between the probe and the sample can lead to reduced image resolution. In addition, the relatively high forces with which the probe cooperates with the sample can cause sample deformation, which underestimates the height of the surface, and also increases the contact area between the probe and the surface. The contact area determines the resolution limit.

In order to combat the limitations of imaging in the contact mode, as mentioned earlier, the Intermittent Contact Mode (Tapping Mode) is used. In this mode, the cantilever can oscillate at a value close to the resonant frequency. When oscillations occur close to the surface of the sample, the probe will repeatedly couple to the surface, limiting the vibration amplitude. During surface scanning, the oscillation amplitude of the cantilever changes as different topographies are encountered. By using a feedback mechanism to change the height in the axis from the piezoelectric table and maintain a constant amplitude, the image of surface topography can be obtained in a similar manner as in the case of imaging in the contact mode. In this way, the probe scans the surface, and the occurrence of lateral forces is significantly reduced compared to the contact mode.

While surfaces with different mechanical and adhesive properties are scanned, the frequency of vibrations will change, causing the phase signal to shift between the frequency at which the cantilever actually oscillates. This phenomenon has been used to obtain phase images in addition to topographic images, which may show changes in the material properties of the surface being tested. Although the qualitative data provided by phase images is useful, it is difficult to extract quantitative information from them, because they are a complex result of many parameters, such as adhesion, scanning strength, load force, topography, flexibility and other.

In the Non-contact Mode, the image is oscillated, similar to the intermittent mode, but with a much smaller amplitude. When the probe approaches the surface of the sample, long-range interactions, such as van der Waals interactions or electrostatic forces, occur between atoms in the probe and sample. This results in a detectable shift in the cantilever oscillation frequency. Detecting the phase shift between oscillation frequencies allows the positioning angle to be set in the z-axis direction to keep the cantilever in contact with the surface by feedback. Because the probe is not in contact with the surface of the sample in the repulsion zone, the impact surface is minimized, potentially allowing a higher surface resolution. As a result, in this mode it is an image that can best achieve true atomic resolution while testing the appropriate surface in the right conditions. However, in practice, obtaining high quality images is more difficult to produce than in intermittent mode.

During air imaging, all but the most hydrophobic surface areas will have a significant layer of water that can be larger than the van der Waals force range.

Ellipsometry

Ellipsometric spectroscopy is used to study the change in polarization of the electromagnetic wave reflected from the tested medium. The way in which the polarity changes depends on the optical parameters and the thickness of the material being tested. The name ellipsometry comes from the fact that a linearly polarized electromagnetic wave after reflection is elliptically polarized. This technique is very well known, among others in 1889 P. Drude was the first to investigate the optical properties of metals using an ellipsometer [4.29]. The scheme of the operation setup of the UVISEL Horiba Jobin Yvon ellipsometer is shown in Fig. 4.17. The xenon lamp operating in the spectrum 190 nm to 2100 nm, acting as a light source, is characterized by the fact that the outgoing light is monochromic and then linearly polarized by a polarizer and then reflected from the sample.

The reflected beam goes to a photoelastic modulator, which allows to induce a modulated phase shift of the reflected beam. This photoelastic modulator is a fused silica bar exhibiting isotropic behaviour without applying stress, acting as a birefringence modulator. After the beam passes to the analyser, which transforms the polarization ellipse, and then moves to the detector. The coefficients (Ψ, Δ) determined during the measurement of ellipsometry are defined as the ratio of the amplitude reflection coefficients for both polarizations p-and s-:

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Ψ = tan -1 (|𝜌|) = tan -1 ( |𝑟 𝑝 | |𝑟 𝑠 | ) = tan -1 [( 𝑅 𝑝 𝑅 𝑠 ) 1 2 ⁄ ] (4.83)
While ∆ equals [4.30]:

∆= arg(𝜌) = { tan -1 [𝐼𝑚(𝜌)/𝑅𝑒(𝜌)] 𝑓𝑜𝑟 𝑅𝑒(𝜌) > 0 tan -1 [𝐼𝑚(𝜌)/𝑅𝑒(𝜌)] + 180° 𝑓𝑜𝑟 𝑅𝑒(𝜌) < 0, 𝐼𝑚(𝜌) ≥ 0 tan -1 [𝐼𝑚(𝜌)/𝑅𝑒(𝜌)] -180° 𝑓𝑜𝑟 𝑅𝑒(𝜌) < 0, 𝐼𝑚(𝜌) < 0 (4.84)
It can be noticed that both dependencies correspond to the relationship defined by 𝑁 ≡ 𝑛 -𝑖𝜅 (4.15), in which we express the refractive index and the extinction coefficient. These constants are determined from experimental data by using appropriate models, depending on the characteristics of the investigated material [4.30]. In this work, the most important aspect is the determination of the refractive indices of the thin layers under study for strictly defined

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wavelengths, that is: 1064 nm, which corresponds to the wavelength, 532 nm, which corresponds to the generated second harmonic wavelength, and 355 nm corresponds to the generated third harmonic, in order to calculate nonlinear susceptibilities using the Herman-Hayden and Reintjes models described in subsection 4.1.

Literature

Sample Preparation

A total of four porphyrin complexes have been purchased from Sigma-Aldrich company: platinum(II) 2,3,7,8,12,13,17,18-

Surface Characterization

The thickness of guest-host systems was measured by profilometer (Dektak 6M) and found as 1650 In connection with the nonlinear optical properties of SHG and THG guest-host thin films, it is very important that these samples are optically transparent for the wavelength of the pumping beam 1064 nm, which means that the samples do not absorb laser radiation in any way. On the other hand, it can be observed that the absorbance at 532 nm (corresponding to SHG) and 355 nm (corresponding to THG) is significant. This means that the signal that is generated is absorbed to some extent at the same time. Therefore, when calculating the properties of SHG and THG, it is necessary to take into account the effects of absorption -that is, the absorption coefficients for these wavelengths. The determined values of these coefficients are included in Tab. 5.2. case of 2D plots, the maximum photoluminescence (PL) is located in the same wavelength, but with a much lower intensity. Generally, platinum is more emissive than palladium, hence more intense emission and longer lifetime were observed for the PtOEP sample. In this way, the approximately excitation and emission wavelengths for which maximum is located, were determined, and their values are presented in Tab. 5.3. The studies of the second, as well as third harmonics, were carried out using the experimental setup presented in subchapter 4.2. The THG and SHG studies for the PdOEP sample are briefly presented in [5.5], which show the influence of the matrix polymer (PMMA, PVK, P1VN) on the nonlinear optical response. In this manuscript, we focused on the differences resulting from the use of selected substituents in the complexes of the studied porphyrins. Generally, obtained guest- host metalloporphyrin thin films with PMMA did not show the SHG effect, thus it was necessary to use corona poling technique to orient the molecules in the polymer matrix in one direction.

Spectroscopic Studies

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Moreover, from the polarization plots, no difference in SHG signal intensity was observed between the applied polarization (see except for the FeOEP sample, which is strongly polar.

This means that the remaining samples, in combination with the polymer matrix, form an isotropic system in which NLO response is independent on the direction. By comparing the SHG intensity of the signal between the studied samples (see Fig. 5.12), it was noticed that the strongest NLO response was obtained with the FeOEP sample, due to the fact that this sample has nonplanar structure and moreover is more polar than the rest of the studied porphyrins. On the other hand, RuOEP also has a nonplanar structure, however the FeCl substituent is more electronegative than RuCO, therefore the RuOEP sample has a weaker SHG signal intensity than FeOEP. The remaining porphyrin samples PtOEP and PdOEP have planar structure, besides they are from the same group of the periodic table where the sum of dipoles is equal to zero, therefore these samples are characterized by a weaker SHG signal than nonplanar structures, and the intensity does not differ much between these samples. On the other hand, Fig. obtained NLO graphical responses, the highest  (2) values were obtained for the FeOEP sample.

Due to the fact that the H-H model contains parameters characterizing the sample and parameters depending on the polarization, the calculated values of  (2) in this case are higher, and the calculation error determined from the total differential is not too large. For better contrast, the calculated values are visualized graphically in the form of histogram in Fig. 5.14. In the case of THG studies, there are no structure constraints, thus corona poling was not required to obtain a third-order nonlinear optical response. Fig. 5.15 shows the third harmonic signal for all investigated metalloporphyrins in s-polarized laser beam. The third-order nonlinear optical response was also unaffected by the applied polarization, the signal for s-and p-polarized wave is almost identical. In the case of the samples, also no huge difference between the signal was noticed.

Third Harmonic Generation

Therefore, the values of the third-order (𝜒 (3) ) nonlinear susceptibilities were estimated using theoretical models and Reintjes (subsection 4.1.5).

Z-Scan Results

The investigations of nonlinear refraction and nonlinear absorption were carried out by using Z-Scan experimental alignment shown in Fig. 4.9 in subsection 4. and excitation laser wavelength 532 nm is close to resonance, which may mean that above the absorbance value of 1.0, the effect is saturated, that is why with dilution the effect becomes stronger. Moreover, the PdOEP sample is characterized by strong linear absorption at 532 nm, and in this case also the saturable absorption effect should occur during the Z-scan measurement, however we noticed opposite situation. Therefore, it is necessary to perform calculations on molecular orbitals to understand behavior in those studied samples. The best way to compare the Z-scan results for these samples is to compare them at the lowest concentration. From the calculated real and imaginary parts of the nonlinear susceptibility, the total values of  (3) was determined and are shown in Tab. 5.7 with comparison of  (3) values determined from THG method in p-polarized laser beam. It can be noticed that, as in the case of the THG method, the FeOEP sample seemed to have the highest values of nonlinear susceptibility, and in the case of the Z-scan method, the values for this sample are lower than the other PtOEP and PdOEP.

Moreover, as mentioned before, for these concentrations the NLO signal for the sample PtOEP becomes supersaturated, hence the large values of the NLO parameters occurred. Furthermore, the third harmonic generation method is distinguished by the fact that nonlinear susceptibility has only electronic contribution, and the Z-scan method is more accurate due to the contribution of nonlinear refraction (electronic element) and nonlinear absorption (molecular element), hence the 3) values determined from the Z-scan method are higher than the  the THG method. Besides, it is important that nonlinear studies are performed under similar conditions. In the case of thin layers, it is difficult to obtain samples of the same thickness with the same concentration, but the Z-scan method allows us to perform research for the same concentration of solutions. Moreover different wavelengths of laser source have been used in those experiments: THG -1064 nm and Z-Scan -532 nm.

 (

Conclusions

Summarizing, the above work presents the research on nonlinear optical and spectroscopic properties of selected porphyrin complexes PtOEP, RuOEP, FeOEP and PdOEP as a models

for nonlinear optical research in supramolecular assemblies. The studies were performed on samples in state of thin films obtained by the spin-coating method and in solutions.

Photoluminescence studies were carried out on thin films. During the excitation of the samples with a length corresponding to the maximum of the absorption peak, the investigated samples emit red light, and the lifetime time is very short, which indicates a fluorescence decay. Moreover, studies of the second and third order nonlinear optical properties were carried out using the second and third harmonic generation method, respectively. The results presented show that the samples have a strong nonlinear response for thin films due to chemical structure of studied metalloporphyrins.

In addition, third-order nonlinear effects were investigated with the Z-scan technique, which allows the simultaneous measurement of nonlinear refraction and nonlinear absorption for different solution concentrations. All four samples have strong nonlinear saturable or reverse saturable absorption as well as positive or negative nonlinear refractive index. Each of these samples has unique spectroscopic and nonlinear optical properties. These interesting properties of porphyrin complexes result in them being of the most promising candidates for applications based on nonlinear optics, inter alia in data storage, as optical limiters and also appear to be ideal candidates for Q-switching.

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| Study and diagnostic of the physicochemical properties of new -conjugated (metallo)supramolecular architectures for nonlinear optics. 158

CHAPTER 6: TRIPLE STRANDED HELICATES

Motivation in this work is using self-assembly instead of mononuclear complexes and investigate influence of two metals on NLO properties. The work reported herein was devoted to study linear, photoluminescent and nonlinear optical properties of some selected metallo-supramolecular triplestranded helicates and in particular to evaluate the influence of the metal cations over one period used during the self-assembly process such as iron(II), cobalt(II), nickel(II), zinc(II), on such physical properties. The determination of first and second-order hyperpolarizability of a molecule is often used to understand the affinity between the molecular structure and NLO properties.

Therefore we present also the quantum chemical calculation of electronic delocalization through a -conjugated molecular system. To explain the origin of the NLO phenomena occurring in the investigated supramolecular systems -calculations predicting: HOMO (Highest Occupied Molecular Orbital) and LUMO (Lowest Unoccupied Molecular Orbital), first and second-order hyperpolarizabilities were performed. The calculations of HOMO and LUMO are very important aspects to consider the molecular reactivity. The results presented below were published in [6.1].

Sample Preparation

The metal complexes in this research are triple stranded helicates which are resulting from the selfassembly process of three ligands based on iminopyridine fragments and two metal cations, as previously reported [6.2] and synthesized by Dr. Abdelkrim El-Ghayoury and Dr. Yohan Cheret.

The metal cations being Fe 2+ (HelFe), Co 2+ (HelCo), Ni 2+ (HelNi) and Zn 2+ (HelZn). In the first order thickness of obtained thin films have been measured using profilometer (Dektak 6M, Veeco). Layers are thinner than 1 micron, and their exact values are given in Tab. 6.1.

Surface Characterization

Afterwards, the photographs of the samples were taken with an optical microscope (Fig. 6.2). In addition to the different colors, some defects in the structure of the layer can also be seen, which were examined in detail using AFM microscope. Typical AFM images analyzed by Gwyddion software are presented in Fig. 6.3. Measurements were carried out in the range 1 m  1 m. It was observed that films are quite homogenous and smooth, although some surface irregularities have been observed. The surface roughness was then measured and calculated. However, the unevenness is not significant -it is at the level of several hundred picometers, in the case of the HelFe sample almost one nanometer. This is important when measuring the second and third harmonics to obtain a periodic symmetric signal which is not affected by structure defects. The obtained values are located in Tab. Absorption spectra (Fig. 6.5) of the studied thin films were measured by using UV-Visible spectrophotometer in the range 300-1000 nm. Cobalt(II), nickel(II) and zinc(II) exhibit one strong absorption band located at max = 355 nm that can be assigned to the * and n* interligand charge transfer ( 1 ILCT) transitions. In the case of HelFe helicate, in addition to the band located at max = 331 nm, the absorption spectrum exhibits a band located in the visible region which is assigned to metal to ligand charge transfer transition ( 3 MLCT) as commonly observed for iron(II)

Spectroscopic Studies

N-heterocyclic ligands [6.3 -6.4] due to d-d transitions in iron(III) complexes. Note that the absorbance at 1064 nm, that constitutes the fundamental wavelength of laser beam at SHG and THG measurements, is negligible. We also noted, that at wavelength corresponding to THG, which is 355 nm, the absorbance is significant which means that simultaneous THG generation is somewhat absorbed. For this reason, the calculations associated with THG experiment have included the absorption coefficient. On the other hand, in case of SHG wavelength, which is 532 nm, absorbance is not negligible for HelFe helicate, therefore for this material the calculations was performed by including the absorption coefficient as for THG. Moreover, with the appearance of linear absorption for a wavelength of 532 nm, we should also expect nonlinear absorption. The exact max with absorption coefficients for 532 nm (which corresponds to SHG) and 355 nm (which corresponds to THG) are presented in Tab. 6.2. emission signal was recorded. This is due to the fact that the photoluminescence was carried on thin films containing only 10% of the studied material with the result that both absorption and emission for these compounds are not high intense. 3D photoluminescence spectra shows the intensity for a given emission wavelength as a function of the excitation wavelength. These PL spectra were carried out in the excitation wavelength range 310 nm to 340 nm and emission wavelength range from 350 nm to 500 nm for HelFe, HelCo and HelNi, sample containing zinc(II) was measured in excitation wavelength range from 310 nm to 390 nm and emission wavelength range from 400 nm to 500 nm. As we observed, the strongest enhancement of PL intensity was located near resonant region during excitation by UV light. However it was noted, that PL spectra is determined by asymmetrical shape which is caused by concentration of the samples. By determining the excitation and emission wavelengths for which the highest intensity occurs, the luminescence decay time was then measured using additional pulse diodes with wavelengths close to excitation wavelengths, which are presented on Fig. 6.7. The lifetime was measured in room temperature, and achieved results were fitted by double-exponential function

𝑦 = 𝑦 0 + 𝐴 0 𝑒 -𝑡 𝑇 1 ⁄ + 𝐴 1 𝑒 -𝑡 𝑇 2 ⁄ [ 6

Second Harmonic Generation

The measurements of the second, as well as third harmonic effects, were carried out using the experimental setup presented in subchapter 4.2. Y-cut quartz crystal was used as reference materials. Measurements were performed for vertical and horizontal polarization of fundamental laser beam. In this work, we focused on the differences in NLO effects resulting from the use of selected metal cations in the triple stranded helicates. According to the structural properties of guest-host systems, it was necessary to use the corona poling technique to obtain the second ___________________________________________________________________________ Waszkowska Karolina | Study and diagnostic of the physicochemical properties of new -conjugated (metallo)supramolecular architectures for nonlinear optics. 167 harmonic signal. SHG responses showed that the signal is not much dependent on polarization configuration (Fig. 6.8 -6.11). The strongest signal of the generated second harmonic was obtained for the HelNi thin film. Additionally, Fig. 6.12 shows the dependence of the intensity of the generated second harmonic as a function of the laser energy made at Częstochowa University of Technology, presented in subsection 4.2 in Fig. 4.6. In this method, also the strongest response was obtained for the HelNi sample. the fact that in the case of these supramolecular systems which are triple stranded helicates, when forming a guest-host system with polymer matrix, the system takes the form of an isotropic medium and the nonlinear response is independent on direction of polarized incident laser light.

Moreover, outstanding differences were not noticed between the  (2) values depending on the metal cation, due to the fact that metal cations are from over one period, and in fact their contribution to NLO properties is small. The highest values were obtained for the HelNi sample. For better contrast, the calculated values are visualized graphically in the form of histogram in Fig. 6.13. In the case of THG studies, there are no structure constraints, thus corona poling was not required to obtain a third-order nonlinear optical response. Fig. 6.14 shows the third harmonic signal for all investigated triple helicates in s-polarized laser beam. Additionally, Fig. 6.15 presents the dependence of the intensity of the generated third harmonic as a function of the laser energy made at Częstochowa University of Technology, presented in subsection 4.2 in Fig. 4.6. As it was mentioned previously, due to the high absorbance 355 nm, it is necessary to take into account the absorption coefficient in the calculations, the values of which are presented in Tab.

6.2. Basically, THG response is independent from polarization of fundamental beam, however slight differences between calculated values of  (3) calculated by using Kubodera-Kobayashi and Reintjes model have been observed (see Tab. 6.5). This is due to small changes in the laser energy when changing polarization with a half-wave plate. Likewise SHG measurements, there was no significant difference observed for THG with the included metal cation, from the same reason.

Z-Scan Results

Analysis of nonlinear absorption and nonlinear refraction have been performed using Z-Scan experimental alignment shown in Fig. 4.9 in subsection 4.4. The triple stranded helicates were dissolved in acetonitrile forming solution with percentage concertation form 0.5% to 0.2%.

However, due to the fact that in the following calculations the value of the molar concentration is needed, instead of the percentage, the following calculations were made, in which the percentage concentration corresponds to the molar concentration, i.e. 0.5% corresponds to 2.3 mM, 0.4% corresponds to 2.2 mM, 0.3% corresponds to 1.65 mM and 0.2% corresponds to 1.1 mM. The measurements were carried out for different laser energies from 0,5 to 2,0 J. Only the HelFe sample allowed for obtaining nonlinear absorption because it absorbs at 532 nm. Furthermore, HelFe sample showed no response in close aperture Z-scan. Achieved responses from OA and CA Z-scan are presented in Fig. 6.17. According to the fact that acetonitrile is characterized by quite high nonlinearity during the CA Z-scan measurement [6.6], its impact was taken into account in the calculations, where the third-order NLO susceptibility of the ACN is subtracted from the NLO susceptibility of the solution. From the data obtained during the measurement of nonlinear absorption for sample HelFe, the NLO absorption cross section 𝜎 was calculated, which determines the efficiency of a single molecule in the ground state to approach the excited state during the multiphoton absorption process, using the appropriate relation [6.7 -6.8]:

𝜎 = ℏ𝜔𝛽 𝑁 𝐴 𝜌 (6.1)
where: ℏ -Planck's constant, 𝑁 𝐴 -Avogadro's number, 𝜌 -concentration of solution [mole per volume]. The calculation results are presented in Tab. 6.6.

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| Study and diagnostic of the physicochemical properties of new -conjugated (metallo)supramolecular architectures for nonlinear optics. 174 HelNi is characterized by the highest total value of refractive index. Moreover, as previously mentioned, absorption coefficient  have been calculated only for HelFe complex from saturable absorption response (𝛽 < 0), due to linear absorption properties at 532 nm. We have to take into account that  (3) calculated from THG has only electronic contribution, as well as in Z-scan electronic and molecular. Besides, aforementioned, measurements were provided for different type of samples -in third harmonic generation experiments were carried out on thin films and in Z-scan technique we used liquid solutions. Furthermore, experiments were carried out in different laser ___________________________________________________________________________ Waszkowska Karolina | Study and diagnostic of the physicochemical properties of new -conjugated (metallo)supramolecular architectures for nonlinear optics. 175

wavelength (1064 nm for THG and 532 nm for Z-scan). However, as in the case of THG studies, the parameters obtained using Z-scan proved to be the best for the HelNi sample, although they are not significantly different from the other helicates. The calculated values of the nonlinear refractive index and the nonlinear absorption coefficient are given in Tab. 6.6 is shown schematically with the graphs in Fig. 6.18.

Table 6.6: Calculated values of NLO refractive index n2, NLO absorption coefficient , NLO absorption cross section , real and imaginary part of third order NLO susceptibility Re( (3) ), Im( (3) ) of studied triple stranded helicates. Moreover, the value of the third-order nonlinear susceptibility composed of the real and the imaginary parts was calculated. The results for individual samples and their concentrations are presented in Tab. 6.7. The results were also compared with the THG values obtained experimentally. However, it should be taken into account that both experiments were not carried out under the same conditions, i.e. a different laser wavelength was used, as well as a different method (thin layer and solution). However, it can be seen that, as in the case of THG, the highest values were obtained for the HelNi sample.

 [mM] n2  10 -19 [m 2 W -1 ]   10 -12 [mW -1 ]   10 -54 [m 4 s] Re( (3) )  10 -21 [m 2 V -2 ] Im( (3) )  10 -21 [m 2 V -2 ] HelFe 2.3 - - 3

Quantum Chemical Calculations

The initial geometrical parameters of the metallohelicates were obtained from Single Crystal X-ray Diffraction refinement data [6.9]. The optimization of the molecular geometries leading to energy minima was achieved by using density functional dispersion-corrected DFT-D3 theory calculations using B3LYP/6-31+G(d,p) basis set and the UV-vis absorption spectra were computed applying b3lyp/6-31++g(d,p) methodology without dispersion-correction implemented in the GAUSSIAN 09 program package [6.10] noncovalent interactions. Therefore dispersion-corrected DFT provides a unique tool for the analysis of complex aromatic systems [6.11]. The modelled structures were used to calculate HOMO-LUMO energies, frequency-dependent first and second hyperpolarizabilities. It should be mentioned that the empirical dispersion correction mainly affects the geometry of the molecule but is not effective for the other calculated parameters. The frequency-dependent (-2,,) and (-3,,,) parameters at considered  = 0.04282 a.u. (=1064 nm wavelength) were calculated using GAMESS [6.12] program by B3LYP/lanl2DZ basis set. Analyzing the values of the position of the absorption maximum max calculated theoretically and determined experimentally presented in Tab. 6.8, one can notice a bathochromic shift of the experimental spectra in relation to the theoretical ones. Which may be related to both the calculation method and the fact that the experimental spectra were made in the solid phase. The highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) are validity parameters to study the specific movements of electron transfer in molecules (see Tab. hyperpolarizability is also very important. In the present case, the dipole moments, μ (expressed in Debye units) for investigated complexes are very small which is due to the geometry of the molecule. The obtained results, both experimental and theoretical, suggest quite a good secondorder nonlinear response (Tab. 6.10). All atoms and molecules (except S-state atoms) have one or more not disappearing permanent multipole moments. In the case of microcircuits with octahedral symmetry, there is a need to define higher-order multipoles and a hexadecapole system, the moment of which is determined by the fourth-rank tensor. The Tab. 6.9 shows the diagonal components of mulipole moments for the tested molecules. With the high octahedral symmetry all other, except hexadecapole moment, mullipole moments should be zero. In this case the also quadrupole moments-second rank tensor (determined by the charge distribution (see Fig. 6.20)

have high values for all molecules and can play a crucial role in the obtained high hyperpolarizabilities. The Fig. 6.20 shows the charge distribution for HelZn resulting from the natural electrical properties of the system from which we can notice a positive and negative regions of the potential. The positive charges lie closer to the metal cationic center (blue region) the potential becomes positive in this region and their influence on the potential is greater while negative charges (orange region) is located at the ends and in the center of the molecule.

It is known that even in symmetrical systems, the process of polarization occurs under the influence of an external electric field, which gives rise to induced dipoles or dipoles of higher order. In the first approximation, the induced dipole moment D ind is proportional to the external electric field higher than the one for urea (static first hyperpolarizability for urea molecule  (-2;,) = 30.90 ×10 -32 esu) [6.14]. We can easily find a correlation between the parameters characterizing the electronic properties presented in Tab. 6.8 -6.9 and the obtained second order hyperpolarizabilities (see Tab. 6.11).

As mentioned earlier, the HOMO-LUMO energy gap for HelFe is smallest than for HelZn hence the highest value of the second-order hyperpolarizability for HelFe is obtained. Decreasing the value of the energy gap increases the charge transfer within the molecule. As you can see from the Tab. 6.11 the second order hyperpolarizability of compound HelFe (=24167.288×10 -36 esu) is one order higher than for HelZn (=3855.040×10 -36 esu). We also compared our hyperpolarizabilities  values with reported by Leupacher et al. [6.15] of methylene blue (=32.00×10 -36 esu) employing THG measurements and the value of  for HelFe is three order higher. It should be noted that the determined theoretical values of  and  are significantly higher than the values of NLO susceptibilities calculated from the experimental data. It should be taken into account that the experiment was carried out on thin layers with only 10 wt% of the studied material in relation to the polymer matrix. Moreover, guest-host systems has the disadvantage that losses of NLO response occur and are strongly dependent on the concentration of the material relative to the polymer.

Conclusions

Triple stranded helicates: HelFe, HelCo, HelNi and HelZn were synthesized and their corresponding thin films were prepared successfully using well-known spin-coating technique.

Sample Preparation

Spectroscopic Studies

Spectroscopic studies of thin films of pyrene-based complexes were performed on the spectrometer in the range 1100-300 nm and the results are shown in Fig. 7.9. Due to the fact that the samples have a very high molar mass, and the concentration of the solutions from which the thin films were deposited is not too large, due to the limitations of the material possessed, the optical absorption is not intense. In general, these modified pyrene-based complexes are characterized by strong intramolecular metal-ligand - stacking in modular systems [7.1] which correspond to the absorption peaks in Fig. 7.9. It can also be noticed that the samples above 500 nm are completely optically transparent, which means that for the wavelength of 1064 nm corresponding to the wavelength of the laser light source, during the measurement of the generation of the second and third harmonics, no absorption occurs, as well as the generated SHG with a wavelength of 532 nm is not simultaneously absorbed. In general, due to the fact that the probability of multi-photon processes, in this case of two-photon absorption (TPA), is many orders of magnitude smaller than that of single-photon processes, when measuring the Z-scan with excitation 532 nm, simultaneous absorption of two photons may be unlikely. In addition, TPA is also influenced by the intensity of the laser beam and the aforementioned concentration. It can also be seen from Fig. 7.9 that the absorption peaks are in the shorter wavelength direction, and their values are given in Tab. 7.2. In the case of Zn[2]C and Cd[2]C, the maximum absorption peaks are probably below 300 nm, however due to the very strong absorption of the glass substrate below this wavelength, the signal was not recorded. Moreover, it was observed that in the case of third harmonic generation (THG), the absorption is not negligible, which means that it has an influence on the size of the THG effect, as a reason of the signal generated is absorbed to some extent. Therefore, for this wavelength of 355 nm, the linear absorption coefficients  were determined, and their values are given in Tab. 7.2.

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Second Harmonic Generation

Second and third order nonlinear effects describing the generation of the second and third harmonics, respectively, were carried out using the measuring equipment described in subsection the generated second harmonic with as a function of the polarization. It was noticed that this response has an elliptical shape, as a rule, for the polarization S, the intensity is slightly lower than for the polarization P, which should coincide with the calculated values of the second-order nonlinear susceptibility, however similarly to previously investigated supramolecular complexes, these guest-host systems takes form of isotropic medium. As mentioned in previous chapters, the generation of the third harmonic THG does not require the use of the corona poling technique. Figs. 7.26-7.32 show THG response for thin layers of pyrene-based guest-host complexes. Similarly, as previously described supramolecular compounds, no significant difference was observed between the signal versus the applied polarization, which is also noticeable when calculating the NLO parameters. Thus, the values of 𝜒 (3) were calculated using theoretical models and results are presented in Tab. 7.5. In the previous section about spectroscopic properties it was mentioned that absorption has no effect on the generation of the second harmonic, but has an effect on the generated third order nonlinear signal. Therefore, in the comparative model, the relation taking into account the absorption coefficient for the wavelength of 355 nm was used. The studies of nonlinear absorption and nonlinear refraction were performed by the Z-scan method with the excitation of laser light with wavelength 532 nm, described in the experimental section. Measurements were carried out for solutions placed in 1 mm quartz cuvettes, with a concentration of 2.0 mM, 1.5 mM, 1.0 mM and 0.

Third Harmonic Generation

Conclusions

CHAPTER 8: NANOPOROUS MEMBRANES

This chapter is devoted to the preparation of metamaterials composed of a nanoporous membrane and the studied supramolecular complex. From each type of investigated (metallo)supramolecular compounds, one of the most interesting was selected and a nanocomposite was prepared. PtOEP was selected from porphyrin complexes, HelNi was selected from triple helicates samples, and ZnTK also Zn[2]C were selected from modified pyrene-based complexes. The obtained nanocomposites were characterized by nonlinear optics studies.

Nanoporous Membranes versus Thin Films

As already mentioned in this doctoral thesis, due to the unique properties of thin films, they are used in many fields of science, from optics, through electronics, to the aviation or space industry, giving rise to many inventions. As this monograph shows, thin films are widely used in the study of nonlinear optics [8.1 -8.5]. This chapter describes the research of nonlinear optics, which was carried out not on thin films, but on alumina nanoporous membranes, in order to show their usefulness and potential use in future devices based on nonlinear optics. The NLO studies connected to nanocomposites consisting of a nanoporous membrane and the investigated compound described in [8.6 -8.7] present the SHG studies with crystals already known in nonlinear optics, KDP and Ba(NO3)2. The results presented there clearly show that the generation of the second harmonic occurs by achieving forced orientation in each separate nanopore. On the other hand, when dealing with an organic compound that does not show a second-order effect without the use of the corona poling method creating macroscopic noncentrosymmetry, when such compounds are placed in a nanoporous membrane, as in the case of dimer in the silicone membrane described in [8.8], forced orientation of the dipole moments, thanks to which it is possible to achieve the SHG effect (see Fig.

Samples Preparation

Additionally to the previously investigated thin films, nonlinear optical effects measurements have also been carried out on nanocomposites consisting of alumina Al2O3 nanoporous membranes purchased from SmartMembranes Ltd. Company (Halle, Germany), with selected supramolecular complexes. Before proceeding with the preparation of the nanocomposite, the nanoporous membrane was examined using a scanning electron microscope SEM (Fig. 8.3). Al2O3 membrane with thickness around 100 m, pore diameter  25 nm and interpore distance 65 nm (see Fig.

Porphyrin Complex Nanocomposite

Modified Pyrene-Based Complex Nanocomposite

Following the results of nonlinear optical investigations described in Chapter 7, nanocomposites containing modified-pyrene based complexes were obtained from solutions with a concentration of 2.0 mM in dimethyl sulfoxide DMSO. NLO research on the investigated nanocomposites was carried out on the basis of the SHG effect using the Maker fringe method. show the second-order nonlinear optical responses for the studied metamaterials. As in the case of the nanocomposites studied in this chapter, the nanocomposites containing modified-pyrene based supramolecular complexes show a strong dependence of the second harmonic generation in relation to the applied polarization of S and P. Moreover, the Al2O3: Zn[2]C nanocomposite is characterized by a slightly different signal shape from the previous ones studied samples. This is due to the fact that the investigated membranes do not show fully periodic distribution of nanopores, which can be seen in the SEM image of the membrane (see Fig. 8.3). There are also small places where there are no nanopores.

Besides, the measurement of the second harmonic generation on nanoporous materials is not the easiest one, due to the above-mentioned properties. However, also in this case the signal is highly polarization dependent, which could be used in modulated nonlinear optics devices.

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| Study and diagnostic of the physicochemical properties of new -conjugated (metallo)supramolecular architectures for nonlinear optics. 224

SHG Imaging

In addition to investigating the SHG effect by the Maker fringe method, the second-order nonlinear response of the nanocomposite surface was investigated using the experimental system described in Ref. [8.9]. In the above SHG images, characteristic points are marked, which either become stronger when the polarity changes from S to P, or opposite. This means that molecules can orient themselves in different directions in nanopores, which means that some places have a higher nonlinear SHG response for S polarization, while others for polarization P. In the Maker fringe method, the SHG signal is collected from a large area, which in the case of the studied nanocomposites SHG response in large area is more enhanced for the P polarization. Moreover, from the SEM image shown in Fig. 8.3a it can be seen that the nanopores are not periodically distributed, there are some "islands" of periodicity, which may also mean that for one area of the molecule they may orient themselves in another direction than for the adjacent area. Moreover, SHG imaging measurements were also performed before and after corona poling. The results are shown in Fig. 8.15. On the obtained microscope images, characteristic points are marked, which are not enhanced after the corona poling method. The conclusion of this experiment is that the corona poling of these nanocomposites does not affect the generated SHG signal.

Conclusions

This chapter presented studies of the nonlinear optics of nanocomposites with selected supramolecular compounds previously studied in this thesis. From each type of investigated compounds, one of the most interesting complexes was selected and introduced into a nanoporous alumina Al2O3 membrane from solutions. From the complex porphyrins, platinum octaethylporphyrin PtOEP was selected, with a concentration of 0.4 mM in CHCl3 chloroform, from triple helicates compounds, a compound with nickel cations HelNi with a solution concentration of 2.0 mM in acetonitrile ACN was selected, while modified pyrene-based complexes represented trefoil knot with zinc metal ZnTK and [2]catenane with zinc metal Zn[2]C with concentrations of 2.0 mM solutions in dimethyl sulfoxide DMSO. Nonlinear optical studies were carried out on the basis of the Maker fringe method, examining the generation of the second harmonic SHG. Overall, the investigations achieved the SHG signal without applying the symmetry breaking method previously used in thin film studies. This macroscopic symmetry is achieved due to the forced orientation of the dipole moments in the nanopores of the membrane. This is an important action when using metamaterials in devices based on photonics and nonlinear optics.

Moreover, it was noticed that the SHG signal is characterized by similar shape for each nanocomposite and the intensity is more or less at a similar level. This is most likely the result of the properties of the membrane, the significant distribution of nanopores, as well as their diameter.

As a perspective for further work, it seems interesting to produce nanocomposites with different nanoporous membranes, i.e. with the arrangement of the nanopores, the diameter of the nanopores, the thickness of the membrane, etc. Moreover, the SHG imaging on the surface of nanocomposites studies showed that the orientation of the molecules in the nanopores can go in different directions and that the corona poling technique has no effect on the enhancement of the SHG response. Due to the fact that the obtained nanocomposites are neither crystals nor thin films, the 𝜒 (2) calculations for these samples were not provided on the basis of the theoretical Step 4: Membrane with the material in nanopores……………………………………………...217

LIST OF FIGURES

  The second chapter describes what the title supramolecular compounds are. The chapter began with the history of the development of supramolecular chemistry. Then, the most important features and assumptions were presented, and examples of chemical structures that are classified in supramolecular chemistry are presented as well. Their applications in everyday life and in ___________________________________________________________________________ Waszkowska Karolina | Study and diagnostic of the physicochemical properties of new -conjugated (metallo)supramolecular architectures for nonlinear optics. 4

Figure 1 . 1 :

 11 Figure 1.1: The nucleus and the electron cloud are shifted relative to each other under the

Figure 1 . 2 :

 12 Figure 1.2: Geometry of generated second harmonic and energy level diagram described SHG

  Study and diagnostic of the physicochemical properties of new -conjugated (metallo)supramolecular architectures for nonlinear optics.15

Figure 1 . 3 :

 13 Figure 1.3: Geometric representation of the propagation of the fundamental and second

Figure 1 . 4 :

 14 Figure 1.4: Interaction geometry during the third harmonic generation process and energy level

1 . 5 .

 15 Waszkowska Karolina | Study and diagnostic of the physicochemical properties of new -conjugated (metallo)supramolecular architectures for nonlinear optics.20 Third-order nonlinear optical susceptibility tensor (3)

Figure 1 . 5 :

 15 Figure 1.5: Schematic representation of two processes that can take place during interaction of

  Waszkowska Karolina | Study and diagnostic of the physicochemical properties of new -conjugated (metallo)supramolecular architectures for nonlinear optics. already mentioned, light propagation in free space is described by classical physics, while light absorption and emission is described by quantum mechanics. During the interaction between the electromagnetic wave and the system of molecules with energy levels E1 and E2 in thermodynamic equilibrium, a number of different processes can occur, what is schematically illustrated in Fig. 1.6.

Figure 1 . 6 :

 16 Figure 1.6: Interaction of the electromagnetic field with a two-level system.

  1.6) [1.12]. The energy of the electromagnetic radiation absorbed by the molecule is strictly defined, that means molecule can only receive certain specific energy values. These energy values correspond to energy levels of the ___________________________________________________________________________ Waszkowska Karolina | Study and diagnostic of the physicochemical properties of new -conjugated (metallo)supramolecular architectures for nonlinear optics. 26

  1.68) ___________________________________________________________________________ Waszkowska Karolina | Study and diagnostic of the physicochemical properties of new -conjugated (metallo)supramolecular architectures for nonlinear optics. 27

Figure 1 . 7 :

 17 Figure 1.7: Transmission in a medium of thickness 1.

Figure 1 . 8 :

 18 Figure 1.8: Numerous processes of multiphoton absorption.

Figure 1 . 9 :

 19 Figure 1.9: Schematic illustration of self-focusing (𝒏 𝟐 > 𝟎) and self-defocusing (𝒏 𝟐 < 𝟎)

  Study and diagnostic of the physicochemical properties of new -conjugated (metallo)supramolecular architectures for nonlinear optics.35

Figure 2 . 1 :

 21 Figure 2.1: NaCl as an examples of material with ion-ion interactions (a) and chemical structure

Figure 2 . 2 :

 22 Figure 2.2: Schematic structures of 12-crown-4-Lithium complex (LiSCN) and [Ru(BPy)3] 2+ .

Fig

  Fig. 2.3.

Figure 2 . 3 :

 23 Figure 2.3: Schematic example of dipole-dipole interaction.

  2.5). Hydrogen bonds are ubiquitous in supramolecular chemistry.___________________________________________________________________________Waszkowska Karolina | Study and diagnostic of the physicochemical properties of new -conjugated (metallo)supramolecular architectures for nonlinear optics. 44

Figure 2 . 4 :

 24 Figure 2.4: Schematic examples of strong and weak hydrogen bonds.

Figure 2 . 5 :

 25 Figure 2.5: Schematic example of double helix DNA structure.

Figure 2 . 6 :

 26 Figure 2.6: Schematic example of Halogen bond interaction (red bond).

  1 . A molecule with a momentary dipole moment can excite it in a neighbouring molecule, as a result of which both molecules can temporarily attract or repel one another. The averaging of repulsive and attractive forces gives an attractive impact proportional to distance between molecules 𝑟 -6[2.25]. Fig.2.7 presents an schematic example of van der Waals interaction.

Figure 2 . 7 :

 27 Figure 2.7: Schematic example of van der Waals interactions.

Fig. 2 .

 2 8 presents schematic examples of - and cation- interactions in typical chemical structures.

Figure 2 . 8 :

 28 Figure 2.8: Schematic examples of complexes with face to face - stacking (a) and cation-

Figure 2 . 10 :

 210 Figure 2.10: Schematic illustration of molecular recognition process.

Figure 2 . 11 :

 211 Figure 2.11: Scheme describing the formation of a supramolecule in guest-host interaction.

Figure 2 . 12 :

 212 Figure 2.12: Schematic example of guest-host supramolecular complex.

Figure 2 . 16 :

 216 Figure 2.16: Schematic example of cyclodextrin complex.

  Waszkowska Karolina | Study and diagnostic of the physicochemical properties of new -conjugated (metallo)supramolecular architectures for nonlinear optics. 55

Figure 2 . 17 :

 217 Figure 2.17: Schematically representation of rotaxanes.

Figure 2 . 18 :

 218 Figure 2.18: Schematic exemplary supramolecular calixarene structure with a C60 molecule in

Figure 2 . 19 :

 219 Figure 2.19: The schematic exemplary illustration of a supramolecular protein: on the left -

Figure 2 . 20 :

 220 Figure 2.20: Schematic example of triple metallo-helicate.

  characteristic in visible and near infrared (NIR) spectral areas, resistance to photobleaching or to flash and long luminescence time decays. Drug transport systems are another very important application of metal organic frameworks [2.100 -2.102].

Figure 2 . 21 :

 221 Figure 2.21: The structure of MOF-5 [2.96].

Figure 2 . 22 :

 222 Figure 2.22: Schematic example of supramolecular structure with porphyrin ring.

  phosphorescence. The processes leading to these phenomena related to light absorption are best illustrated by the Jabłoński diagram (Fig.3.1).

Figure 3 . 1 :

 31 Figure 3.1: Jabłoński diagram.

  ___________________________________________________________________________Waszkowska Karolina | Study and diagnostic of the physicochemical properties of new -conjugated (metallo)supramolecular architectures for nonlinear optics. 80spectrum of an excited molecule. The law of S. Wawiłow is connected with Kasha's rule, which

Figure 3 . 2 :

 32 Figure 3.2: Simplified Jabłoński diagram illustrating the fluorescence lifetime.

  ___________________________________________________________________________Waszkowska Karolina | Study and diagnostic of the physicochemical properties of new -conjugated (metallo)supramolecular architectures for nonlinear optics. 82

  3.3). The difference between them determines the value of the energy gap. A large energy break is associated with insulators. Partial filling of the energy band can lead to a situation where the value of the energy gap is zero. Metals are characterized by having empty levels directly above double-occupied valence levels. Due to the zero energy gap they are conductors of electric current. The Fermi level is particularly interesting in metals because there are ways to change its position on the energy scale, which is done by injecting electrons or by causing a shortage of electrons in the material.___________________________________________________________________________Waszkowska Karolina | Study and diagnostic of the physicochemical properties of new -conjugated (metallo)supramolecular architectures for nonlinear optics. 83

Figure 3 . 3 :

 33 Figure 3.3: Valence bands (highest occupied by electrons) and conduction bands (empty). The

3 . 4 .

 34 These configurations are classified in terms of structure limitation in three perpendicular directions, where coordinate reference orientation depends on the ___________________________________________________________________________ Waszkowska Karolina | Study and diagnostic of the physicochemical properties of new -conjugated (metallo)supramolecular architectures for nonlinear optics. 84

Figure 3 . 4 :

 34 Figure 3.4: Division of low-dimensional structures in terms of their general shapes and level of

Figure 3 . 5 :

 35 Figure 3.5: Spin coating technique.

  ___________________________________________________________________________Waszkowska Karolina | Study and diagnostic of the physicochemical properties of new -conjugated (metallo)supramolecular architectures for nonlinear optics. 88

Figure 3 . 6 :

 36 Figure 3.6: Types of layer growth: A) Volmer -Weber island growth; B) Frank -Van der Merwe

Figure 3 . 7 :

 37 Figure 3.7: Schematic of forming island film on the substrate.

Figure 3 . 8 :

 38 Figure 3.8: Diagram showing the basic features of the vapor deposition system.

  Waszkowska Karolina | Study and diagnostic of the physicochemical properties of new -conjugated (metallo)supramolecular architectures for nonlinear optics. 92

Figure 3 . 9 :CHAPTER

 39 Figure 3.9: Experimental setup for Pulsed Laser Deposition technique.

  𝐼 2𝜔 and 𝐼 𝑄𝑢𝑎𝑟𝑡𝑧 2𝜔 are the maximum amplitudes of SHG of the investigated material and quartz, respectively, 𝜒 𝑄𝑢𝑎𝑟𝑡𝑧 (2) = 1.0 𝑝𝑚 • 𝑉 -1 [4.2] is nonlinear optical susceptibility of quartz and 𝐿 𝑄𝑢𝑎𝑟𝑡𝑧 𝑐𝑜ℎ = 21𝜇𝑚 is the coherent length of the reference material:

  Kurtz and Perry, of expressing the intensity of generated second harmonic by taking into account the absorption of the material at fundamental and generated second harmonic wavelengths. Model of Herman and Hayden assumes that the wave equation is solved for a homogeneous, nonmagnetic and nonlinear medium in the form of a thin film deposited on a transparent substrate: Maker fringes form as the sample rotates relative to the direction of the fundamental beam. Measurement of the ___________________________________________________________________________ Waszkowska Karolina | Study and diagnostic of the physicochemical properties of new -conjugated (metallo)supramolecular architectures for nonlinear optics. 96 𝑑 𝑖𝑗 (𝑖 = 1 -3; 𝑗 = 1 -6) for a nonlinear medium usually consists in measuring the complex arrangement of the substrate layer, as presented in Fig. 4.1.

Figure 4 . 1 :

 41 Figure 4.1: Three-layer scheme of the second harmonic generation system with a nonlinear

  1,0) or 𝑒υ = (cos 𝜃 , 0, -sin 𝜃) for 𝜐 = 𝑆 or 𝜐 = 𝑃, and 𝑘 ⃗ 1 = ( 𝜔 𝑐 ) (sin 𝜃 , 0, cos 𝜃), therefore in P-polarized fundamental beam, the fields of generated second harmonic in these three areas (see Fig. 4.1) are described as: ___________________________________________________________________________ Waszkowska Karolina | Study and diagnostic of the physicochemical properties of new -conjugated (metallo)supramolecular architectures for nonlinear optics. 97

  d is a film thickness, 𝐼 3𝜔 and 𝐼 𝑆𝑖𝑙𝑖𝑐𝑎 3𝜔 are THG intensities of the sample and the silica, respectively, 𝜒 𝑆𝑖𝑙𝑖𝑐𝑎 (3) = 2 • 10 -22 𝑚 2 • 𝑉 -2 [4.8], 𝐿 𝑆𝑖𝑙𝑖𝑐𝑎 𝑐𝑜ℎ = 6,7𝜇𝑚 is the coherent length of silica:

  Study and diagnostic of the physicochemical properties of new -conjugated (metallo)supramolecular architectures for nonlinear optics. 104

Figure 4 . 2 :

 42 Figure 4.2: Propagation of a harmonic wave in a nonlinear medium placed between two linear

Figure 4 . 3 :

 43 Figure 4.3: Thin film deposited on a substrate and placed between two linear media.

  horizontal (S) polarized fundamental laser beam. Parameters of apparatus used in this experiment are located in Tab. 4.1. As a light source is used pulsed Nd:YAG laser (Ekspla, PL2250) with a pulse duration of 30 ps with a power of several J, generating wavelength 1064 nm and frequency ___________________________________________________________________________ Waszkowska Karolina | Study and diagnostic of the physicochemical properties of new -conjugated (metallo)supramolecular architectures for nonlinear optics. 110 of 10 Hz. The fundamental beam of light exiting the laser passes through the beam splitter and then reflect to the photodiode. Then the light beam reaches the half-wavelength plate (𝜆 2 ⁄ ) and the Glan polarizer, which allow changing the polarization, and thus -the energy of the incident beam. The focusing lens with a focal length of 25 cm allows the beam to focus in such a way that its axis of rotation is near the focus. Then the beam reaches the sample placed on a rotational table,which permits to rotate the sample with high precision. The selective filter cuts off the fundamental wavelength transmitted at 1064 nm and allows the recording of the generated harmonic beam and keep only the wavelength of the harmonic generated: for SHG 532 nm, for THG 355 nm. This filter is placed before the photomultiplier tube, which records the generated harmonic signal.

Figure 4 . 4 :

 44 Figure 4.4: SHG and THG experimental setup via Maker fringe method.

Figure 4 . 5 :

 45 Figure 4.5: Typical Maker fringes for reference materials.

Figure 4 . 6 : 112 4Figure 4 . 7 :

 4611247 Figure 4.6: Experimental setup measuring SHG and THG intensity relative to laser energy.

  Fig. 4.7. presents scheme of corona poling technique, while Fig. 4Study and diagnostic of the physicochemical properties of new -conjugated (metallo)supramolecular architectures for nonlinear optics. 113

Figure 4 . 8 :

 48 Figure 4.8: Orientation of dipole moment in polymer matrix during corona poling experiment.

4 . 9 .

 49 In this technique samples are usually investigated in form of liquids. This renowned technique allows in figure out nonlinear optical properties, such as nonlinear absorption and nonlinear refractive index, which are measured at the same time. Depending on the measured ___________________________________________________________________________ Waszkowska Karolina | Study and diagnostic of the physicochemical properties of new -conjugated (metallo)supramolecular architectures for nonlinear optics. 115 nonlinear effect, three modes of this technique are distinguished: open aperture, closed aperture and divided Z-scan.

Figure 4 . 9 :

 49 Figure 4.9: Z-scan experimental setup.

4 . 4 . 1

 441 Waszkowska Karolina | Study and diagnostic of the physicochemical properties of new -conjugated (metallo)supramolecular architectures for nonlinear optics.116 Closed Aperture Z-scanIn this type of Z-scan method (CA) an aperture is located in front of the photodetector that partially prevents the access of the laser beam after passing through the nonlinear medium. The aperture causes only the central area of the light cone to reach the detector. Typically, the values of normalized transmittance are in the range 0.1 < 𝑇 < 0.5. This solution makes the detector extremely sensitive to any focusing or defocusing the laser beam that may be caused by the sample.

Figure 4 . 10 :

 410 Figure 4.10: Typical closed aperture Z-scan curves for 𝑛 < 0 and 𝑛 > 0.

  .70) where 𝛼 0 denotes linear absorption of the nonlinear medium. Taking into account the relation (4.68) and (4.69) in the equation (4.66) we obtain the following relationship: the laser beam 𝐼 0 in the centre, while passing through the focal plane, is expressed by: Study and diagnostic of the physicochemical properties of new -conjugated (metallo)supramolecular architectures for nonlinear optics. 118

Figure 4 . 11 :

 411 Figure 4.11: Typical open aperture Z-scan curves for 𝛽 < 0 and 𝛽 > 0.

Figure 4 . 12 :

 412 Figure 4.12: UV-1800 (Shimadzu) spectrometer.

Figure 4 . 13 :

 413 Figure 4.13: Photograph presents spectrofluorometer Horiba FluoroMax-4.

Figure 4 . 14 :

 414 Figure 4.14: Schematic representation of the basic elements of the atomic force microscope. The

  Waszkowska Karolina | Study and diagnostic of the physicochemical properties of new -conjugated (metallo)supramolecular architectures for nonlinear optics. 124

Figure 4 .

 4 Figure 4.15: Lennard -Jones potential zones in which three most common AFM imaging

  Study and diagnostic of the physicochemical properties of new -conjugated (metallo)supramolecular architectures for nonlinear optics. 126

A

  total samples were collected and their surfaces were analyzed by two different atomic force microscopes: Bioscope II AFM -Nanoscope V controller (Veeco) [4.28] with phosphorous ndoped Si cantilever in scanning area 10  10 m 2 and by Nanosurf Easyscan 2 AFM by monolithic silicon cantilever in scanning area 1 × 1 𝜇𝑚 2 in contact mode. AFM images were then handled by Gwyddion 2.56 software. Fig. 4.16 presents photograph of Nanosurf Easyscan 2 AFM.

Figure 4 . 16 :

 416 Figure 4.16: Photograph presenting Nanosurf Easyscan 2 Atomic Force Microscopy.

Figure 4 . 17 :

 417 Figure 4.17: Scheme of the optical ellipsometry setup.

Figure 4 . 18 :

 418 Figure 4.18: Principles of ellipsometry.

Figure 5 . 1 :

 51 Figure 5.1: Chemical structures of porphyrin complexes: PtOEP, RuOEP, FeOEP and

  nm, 1200 nm, 1150 and 1430 nm for PtOEP, RuOEP, FeOEP and PdOEP respectively. The numerical values of the linear refractive index and extinction coefficients depending on the wavelength (1064 nm, 532 nm, 355 nm) are included in Tab. 5.1. Thin films topography was ___________________________________________________________________________ Waszkowska Karolina | Study and diagnostic of the physicochemical properties of new -conjugated (metallo)supramolecular architectures for nonlinear optics. 136 investigated using the atomic force microscope (AFM) in the contact mode described in Section 4.6. Fig. 5.2 shows the AFM images with a resolution of 1 × 1 𝜇𝑚 2 in two-and three-dimensional representation. It can be noticed that the surface of the samples is not very different from each other, they are as homogeneous and smooth as possible, what is very important in the nonlinear optical phenomena measurements, because any defects affect the quality and symmetry of the NLO signal, however some slight roughness and disturbances in the structure can be distinguished and they do not have a significant impact on optical research. Therefore, the average roughness was determined and for individual samples is equal to: 4.402 nm (PtOEP), 0.371 nm (RuOEP), 2.294 nm (FeOEP), 0.539nm (PdOEP). It can be noticed that the difference in surface roughness is small, which was also illustrated as the AFM surface profiles of the studied thin films in Fig. 5.3. Study and diagnostic of the physicochemical properties of new -conjugated (metallo)supramolecular architectures for nonlinear optics. 137

Figure 5 . 2 :

 52 Figure 5.2: Atomic force microscopy (AFM) images of studied metalloporphyrin thin films:

Figure 5 . 3 :

 53 Figure 5.3: Atomic force microscopy profiles of studied metalloporphyrin thin films.

Figure 5 . 4 :

 54 Figure 5.4: Normalized UV-Vis absorption spectra of investigated porphyrin complexes,

Figure 5 . 5 :

 55 Figure 5.5: Normalized emission spectra for PtOEP, RuOEP, PdOEP thin films by exciting

Figure 5 . 6 : 2 ⁄[ 5 . 4 ]Table 5 . 3 :Figure 5 . 7 :Figure 5 . 8 :

 56254535758 Figure 5.6: 3D representation of intensity of emission as a function of excitation wavelength of

Figure 5 . 9 :

 59 Figure 5.9: SHG intensities as a function of rotation angle in p-polarized laser beam (left) and as

___________________________________________________________________________

  Waszkowska Karolina | Study and diagnostic of the physicochemical properties of new -conjugated (metallo)supramolecular architectures for nonlinear optics. 144

Figure 5 . 10 :

 510 Figure 5.10: SHG intensities as a function of rotation angle in p-polarized laser beam (left) and

Figure 5 . 11 :

 511 Figure 5.11: SHG intensities as a function of rotation angle in p-polarized laser beam (left) and

Figure 5 . 12 :

 512 Figure 5.12: Comparison of SHG intensities for all studied porphyrin complexes in p-polarized

5 .

 5 13 shows the dependence of the SHG signal as a function of laser energy density, measured at Częstochowa University of Technology, which was mentioned in Chapter 4. Here, the strongest SHG signal was observed for the PtOEP sample, however, it is related to strong linear absorption samples for a wavelength of 532 nm. It can also be seen that on a logarithmic scale above the laser energy density 100 J/m 2 , the SHG signal for this sample becomes saturated. Tab. 5.4 shows the calculated second-order NLO susceptibility values for both laser beam polarizations using the Lee theoretical models (subsection 4.1.1) and. According to the Chapter 5 Porphyrin Complexes ___________________________________________________________________________ Waszkowska Karolina | Study and diagnostic of the physicochemical properties of new -conjugated (metallo)supramolecular architectures for nonlinear optics. 146

Figure 5 . 13 :

 513 Figure 5.13: SHG signal as a function of laser energy density of studied metalloporphyrin thin

Figure 5 . 14 :

 514 Figure 5.14: Histogram representing values of second-order nonlinear susceptibilities calculated

Figure 5 .

 5 Figure 5.15: THG intensities as a function of incident angle of studied porphyrin complexes in

Figure 5 . 16 :

 516 Figure 5.16: THG signal as a function of laser energy density of studied metalloporphyrin thin

Figure 5 . 17 :

 517 Figure 5.17: Histogram representing values of third-order nonlinear susceptibilities calculated via

4 .Table 5 . 6 :

 456 Powders of pure metalloporphyrin without the addition of polymer were dissolved in chloroform CHCl3 forming a solution with concentrations 0.5 mM, 0.4 mM, 0.3 mM and 0.2 mM. After introducing the solutions into 1 mm quartz cuvettes and placing them on the stage, the nonlinear absorption (OA Z-Scan) and the nonlinear refraction (CA Z-Scan) from -10 mm to 10 mm with a step of 0.1 mm were measured, where point 0 is corresponding to the focus point, by changing the energy of the laser pumping beam from 0.5 to 2.0 µJ with step 0.25 µJ. The signals recorded from OA and CA Z-Scan are shown in Fig.5.18 -5.19, from which the nonlinear absorption coefficients and the nonlinear refractive indexes were then determined. Due to the fact that chloroform is characterized by quite high nonlinearity during the CA Z-scan measurement (Fig.5.19a)[5.6], its influence was taken into account in the calculations in which the NLO susceptibility of the CHCl3 is subtracted from the NLO susceptibility of the solution. From the data obtained during the measurement of nonlinear absorption, the NLO absorption cross section 𝜎 was calculated, which determines the efficiency of a single molecule in the ground state to approach the excited state during the multiphoton absorption process, using the appropriate relation[5.7 -5.8]: -Planck's constant, 𝑁 𝐴 -Avogadro's number, 𝜌 -concentration of solution [mole per volume]. The calculation results are presented in Tab. 5Study and diagnostic of the physicochemical properties of new -conjugated (metallo)supramolecular architectures for nonlinear optics. 151 Calculated values of NLO refractive index n2, NLO absorption coefficient , NLO absorption cross section , real and imaginary part of third order NLO susceptibility Re(

Figure 5 . 18 :

 518 Figure 5.18: Normalized OA Z-scan characteristics for porphyrin complexes at different input

Figure 5 . 19 :

 519 Figure 5.19: Normalized CA Z-scan characteristics for CHCl3 and PtOEP at input laser energy

Figure 5 . 20 :

 520 Figure 5.20: Values of nonlinear refractive index (left) and nonlinear absorption coefficient

Figure 5 . 21 :

 521 Figure 5.21: Absorption spectra of 0.5 mM, 0.4 mM, 0.3 mM and 0.2 mM solutions of porphyrin

( 3 )

 3 values determined from ___________________________________________________________________________ Waszkowska Karolina | Study and diagnostic of the physicochemical properties of new -conjugated (metallo)supramolecular architectures for nonlinear optics. 155

Fig. 6 . 1 the

 61 studied triple stranded metallo-helicates. Hel-M guest-host polymeric thin films were prepared using well-known spin coating method from solutions with acetonitrile (ACN) solvent and poly(methyl methacrylate) (PMMA). The concentration of the prepared solution was 10 wt% of ___________________________________________________________________________ Waszkowska Karolina | Study and diagnostic of the physicochemical properties of new -conjugated (metallo)supramolecular architectures for nonlinear optics. 159 triple stranded helicate to polymer PMMA. Deposition were carried out on strictly cleaned 1 mm glass substrates using spin-coater (Spin200i, POLOS) at speed 2000 rpm.

Figure 6 . 1 :

 61 Figure 6.1: Schematic representation of the studied metallo-supramolecular assemblies.

Figure 6 . 2 :

 62 Figure 6.2: Photographs from optical microscope; a) HelFe; b) HelCo; c) HelNi; d) HelZn.

6 . 1 .

 61 Moreover, in Tab. 6.1 the values of the linear refractive index and the extinction coefficient for the wavelengths corresponding to the wavelength of the pumping laser (1064 nm), generation of the second harmonic (532 nm) and generation of the third harmonic (355 nm), determined by means of an ellipsometric measurement, are presented. Study and diagnostic of the physicochemical properties of new -conjugated (metallo)supramolecular architectures for nonlinear optics. 161

Figure 6 . 3 :

 63 Figure 6.3: Atomic force microscopy (AFM) images of studied triple stranded helicates thin

Figure 6 . 4 :

 64 Figure 6.4: Atomic force microscopy profiles of studied triple stranded helicates.

Figure 6 . 5 :

 65 Figure 6.5: Absorption spectra of studied triple stranded helicates.

  .5], which implies two time decays short T1 and long T2, describing transition from excited single state to ground state. The estimated values of decay times are given in Tab. 6.3. The recorded decay times are very short, first around 1.5-2.0 ns and second around 20-40 ns, which signifies that these samples show fluorescent properties.

Figure 6 . 6 :

 66 Figure 6.6: Photoluminescence spectra and 3D photoluminescence image of triple stranded

Figure 6 . 7 :

 67 Figure 6.7: Typical luminescence lifetime decays of studied thin films.

Figure 6 . 8 :

 68 Figure 6.8: SHG intensities as a function of rotation angle in p-polarized laser beam (left) and as

Figure 6 . 9 :

 69 Figure 6.9: SHG intensities as a function of rotation angle in p-polarized laser beam (left) and as

Figure 6 . 10 :

 610 Figure 6.10: SHG intensities as a function of rotation angle in p-polarized laser beam (left) and

Figure 6 . 11 :

 611 Figure 6.11: SHG intensities as a function of rotation angle in p-polarized laser beam (left) and

Figure 6 . 12 :

 612 Figure 6.12: SHG signal versus laser energy density of studied triple stranded helicate thin films.

Figure 6 . 13 :

 613 Figure 6.13: Histogram representing values of second-order nonlinear susceptibilities calculated

Figure 6 . 14 :

 614 Figure 6.14: THG intensities as a function of incident angle of studied triple stranded helicates in

  Nonetheless, the strongest responses in both experiments have been obtained for triple stranded helicate with nickel cation HelNi, however the obtained signal, as well as calculated third-order NLO values are not significantly different from other triple stranded helicates due to the fact that___________________________________________________________________________Waszkowska Karolina | Study and diagnostic of the physicochemical properties of new -conjugated (metallo)supramolecular architectures for nonlinear optics. 172 contribution of metal cations to NLO properties, likewise in SHG experiment, is small. For better contrast, the calculated values are visualized graphically in the form of histogram in Fig.6.16.

Figure 6 .

 6 Figure 6.15: THG signal versus laser energy density of studied triple stranded helicate thin films.

Figure 6 . 16 :

 616 Figure 6.16: Histogram representing values of third-order nonlinear susceptibilities calculated via

Figure 6 . 17 :

 617 Figure 6.17: CA Z-scan and OA Z-scan characteristics of ACN and triple stranded helicate

  measured. The results are shown in Fig.6.19. However, this sample behaves similar to the PtOEP sample described in Chapter 5, which, as the linear absorbance decreases, increases its nonlinear response, which means that NLO response is saturated for above concentration 0.2%. It is difficult to determine the optimal value for linear absorbance at wavelength 532 nm for which NLO___________________________________________________________________________Waszkowska Karolina | Study and diagnostic of the physicochemical properties of new -conjugated (metallo)supramolecular architectures for nonlinear optics. 176 absorption response would the strongest and signal would be not saturated. It depends primarily on the structure of the studied compound, on the solvent used, as well as on the molar (percentage) concentration.

Figure 6 . 18 :

 618 Figure 6.18: Values of nonlinear refractive index (left) and nonlinear absorption coefficient

Figure 6 . 19 :

 619 Figure 6.19: Absorption spectra of 0.5%, 0.4%, 0.3% and 0.2% solutions of HelFe in

  6.8). The HOMO-LUMO gaps of HelFe, HelCo and HelNi are significantly smaller than the energy gap value for HelZn. A small energy gap suggested that these molecules are relatively more reactive and less stable than HelZn. The connection between the electric dipole moments of an organic molecule having donor -acceptor substituent and first order___________________________________________________________________________Waszkowska Karolina | Study and diagnostic of the physicochemical properties of new -conjugated (metallo)supramolecular architectures for nonlinear optics. 179

E.

  In our case molecules have an asymmetric charge distribution and then the components of the dipole moment induced in different directions are different. The total moment induced in the system by the E field is the sum of the linear D L moment and the non-linear moments D NL .___________________________________________________________________________Waszkowska Karolina | Study and diagnostic of the physicochemical properties of new -conjugated (metallo)supramolecular architectures for nonlinear optics. 180Where: 𝐷 𝑖 𝑁 = 𝛼 𝑖𝑗 𝐸 ⃗ 𝑗 , ⃗ 𝑗 𝐸 ⃗ 𝑘 𝐸 ⃗ 𝑙 , 𝛼 𝑖𝑗 linear polarizability, 𝛽 𝑖𝑗𝑘 , 𝛾 𝑖𝑗𝑘𝑙 𝐸 ⃗ 𝑗 hyperpolarizabilities.

Figure 6 . 20 :Table 6 . 9 : 11 :

 6206911 Figure 6.20: Electrostatic charge distribution for HelZn -positive (blue) and negative (orange)

CHAPTER 7 :

 7 AFM analysis have shown that the obtained thin films are relatively smooth and homogeneous, as demonstrated by the studies of the surface roughness. UV-Visible absorption spectra of the studied complexes showed that their absorption has a large impact on the NLO response. Moreover, in___________________________________________________________________________WaszkowskaKarolina | Study and diagnostic of the physicochemical properties of new -conjugated (metallo)supramolecular architectures for nonlinear optics. 184 spectroscopic studies ultraviolet emission was observed from photoluminescence studies, and the luminescence decay time is relatively fast, indicating fluorescence like emission. NLO response of the studied metallo-supramolecular triple stranded helicates have been performed using SHG and THG Maker fringe method and Z-scan technique. The highest quadratic and cubic nonlinear optical susceptibilities have been found for helicate containing nickel metal cations HelNi, even if these values for the other samples are not significantly different from each other. For Z-scan studies, only the HelFe complex exhibit nonlinear absorption, however, the NLO refraction for this sample has not been obtained. Finally, the highest value of NLO refractive index have been found for complex HelNi, which is consistent with THG results. The theoretically evaluated energy gap of the compounds showing the high rate of electron transfer from the ground to the excited state. However, a significant reduction in the energy gap in the molecule investigated compounds causes a large increase in third-order nonlinear properties. The interligand π→π* transmetallic charge-transfer (ITCT) supports noncentrosymmetric charge density distribution resulting in the molecules possessing second order NLO properties. The NLO properties obtainedfor the metallo-supramolecular triple stranded helicates, indicate that these assemblies can be promising candidates to be used in photonics and nonlinear optical devices applications. Moreover, the experimental results achieved in this work show the proof of using metallosupramolecules in nonlinear optics, with cooperative effect in metals in centers. However, no significant difference between a nonlinear response for metals from the same period was observed which indicate future perspectives, where modification of nature of metallosupramolecular assemblies will be interesting for NLO studies. ___________________________________________________________________________ Waszkowska Karolina | Study and diagnostic of the physicochemical properties of new -conjugated (metallo)supramolecular architectures for nonlinear optics. 187 MODIFIED PYRENE-BASED COMPLEXES This work is devoted the study of the nonlinear optical properties of the new modified pyrenebased complexes. The motivation in this work are nonlinear optical studies on topologically nontrivial structures, metal-driven supramolecular architectures. This monograph compares the nonlinear responses of the two types of pyrene-based complexes, as well as the influence of the metal substituent on the nonlinear effect. The nonlinear effects in this chapter include second harmonic generation (SHG), third harmonic generation (THG), and nonlinear refraction by Z-scan method.

Figure 7 . 1 :

 71 Figure 7.1: Chemical structures of PyTK, Py[2]C and PyDFP. The sixth coordination of each

Figure 7 . 2 :

 72 Figure 7.2: Atomic force microscopy (AFM) images of studied PyDFP thin film.

Figure 7 . 3 :

 73 Figure 7.3: Atomic force microscopy (AFM) images of studied PyTK thin film.

Figure 7 . 4 :

 74 Figure 7.4: Atomic force microscopy (AFM) images of studied ZnTK thin film.

Figure 7 . 5 :

 75 Figure 7.5: Atomic force microscopy (AFM) images of studied CdTK thin film.

Figure 7 . 6 :

 76 Figure 7.6: Atomic force microscopy (AFM) images of studied Py[2]C thin film.

Figure 7 . 7 :

 77 Figure 7.7: Atomic force microscopy (AFM) images of studied Zn[2]C thin film.

Figure 7 . 8 :

 78 Figure 7.8: Atomic force microscopy (AFM) images of studied Cd[2]C thin film.

  Waszkowska Karolina | Study and diagnostic of the physicochemical properties of new -conjugated (metallo)supramolecular architectures for nonlinear optics. 193

Figure 7 . 9 :

 79 Figure 7.9: UV-Vis absorption spectra of investigated modified pyrene-based guest-host thin

  occupied, there are no d-d transitions, no shift in the absorption spectrum and emission spectra in relation to samples containing metals was noticed. The exact values of the excitation and emission wavelengths determined from the 3D spectra are presented in Tab. 7.3.

Figure 7 . 10 :

 710 Figure 7.10: Photoluminescence spectra and 3D photoluminescence image of PyDFP.

Figure 7 . 11 :

 711 Figure 7.11: Photoluminescence spectra and 3D photoluminescence image of PyTK.

Figure 7 . 12 :

 712 Figure 7.12: Photoluminescence spectra and 3D photoluminescence image of ZnTK.

Figure 7 . 13 :

 713 Figure 7.13: Photoluminescence spectra and 3D photoluminescence image of CdTK.

Figure 7 . 14 :

 714 Figure 7.14: Photoluminescence spectra and 3D photoluminescence image of Py[2]C.

Figure 7 .

 7 Figure 7.15: Photoluminescence spectra and 3D photoluminescence image of Zn[2]C.

Figure 7 . 16 :

 716 Figure 7.16: Photoluminescence spectra and 3D photoluminescence image of Cd[2]C.

Figure 7 . 17 :

 717 Figure 7.17: Typical luminescence lifetime decays of studied modified pyrene-based complexes.

4. 2 .

 2 Y-cut quartz crystal was used as reference materials. Measurements were performed in vertical and horizontal polarization of fundamental laser beam. Moreover, as the resulting guest-host thin films do not show the same orientation of the dipole moments, it was necessary to use the corona poling technique to obtain the SHG signal.___________________________________________________________________________Waszkowska Karolina | Study and diagnostic of the physicochemical properties of new -conjugated (metallo)supramolecular architectures for nonlinear optics. 198

Figure 7 . 18 :

 718 Figure 7.18: SHG intensities as a function of rotation angle in p-polarized laser beam (left) and

Figure 7 . 19 :

 719 Figure 7.19: SHG intensities as a function of rotation angle in p-polarized laser beam (left) and

Figure 7 .

 7 Figure 7.20: SHG intensities as a function of rotation angle in p-polarized laser beam (left) and

Figure 7 . 21 :

 721 Figure 7.21: SHG intensities as a function of rotation angle in p-polarized laser beam (left) and

Figure 7 . 22 :

 722 Figure 7.22: SHG intensities as a function of rotation angle in p-polarized laser beam (left) and

Figure 7 . 23 :

 723 Figure 7.23: SHG intensities as a function of rotation angle in p-polarized laser beam (left) and

Figure 7 . 25 :

 725 Figure 7.25: Histogram representing values of second-order nonlinear susceptibilities calculated

Figure 7 . 26 :

 726 Figure 7.26: THG intensities as a function of incident angle of PyDFP thin film in s-polarized

Figure 7 . 27 :

 727 Figure 7.27: THG intensities as a function of incident angle of PyTK thin film in s-polarized

Figure 7 .

 7 Figure 7.28: THG intensities as a function of incident angle of ZnTK thin film in s-polarized

Figure 7 .

 7 Figure 7.29: THG intensities as a function of incident angle of CdTK thin film in s-polarized

Figure 7 .

 7 Figure 7.30: THG intensities as a function of incident angle of Py[2]C thin film in s-polarized

Figure 7 . 31 :

 731 Figure 7.31: THG intensities as a function of incident angle of Zn[2]C thin film in s-polarized

Figure 7 . 32 :Figure 7 . 34 :

 732734 Figure 7.32: THG intensities as a function of incident angle of Cd[2]C thin film in s-polarized

  5 mM dissolved in dimethyl sulfoxide (DMSO), depending on the input energy changed from 2 .0J to 0.5 J with steps of 0.25 J. The sample with the solution was placed on the stage moved in the direction of the Z axis from -10 mm to 10 mm with a step of 0.1 mm, where point 0 corresponds to the focus point. However, due to the aforementioned absorption properties, concentration of solutions and low intensity of the laser beam, the measurements of the two-photon absorption (TPA) in the open-aperture Z-scan (OA) were not achieved, while the close-aperture Z-scan (CA) has been registered successfully. Examples of the obtained CA Z-scan curves for the Zn[2]C sample with different solution concentrations and with the change of the laser beam energy are shown in Fig. 7.34. Due to the fact that solvent DMSO exhibits nonlinear refractive properties [7.6], its influence has been taken into account in the calculations, where the NLO susceptibility of the solvent is subtracted from the NLO susceptibility of the solution. The results of the calculated values of the nonlinear refractive index and the real value of the third-order nonlinear susceptibility for modified pyrene-based complexes with different concentrations are given in Tab. 7.6. Moreover, the calculated values of the nonlinear refractive index n2 depending on the concentration of the solutions are shown graphically in Fig.

Figure 7 . 35 :

 735 Figure 7.35: Values of nonlinear refractive index as a function of solution concentration of

  8.1). From the above works, conclusions were drawn regarding the advantages and disadvantages of nanoporous membranes and thin films, which are presented ___________________________________________________________________________ Waszkowska Karolina | Study and diagnostic of the physicochemical properties of new -conjugated (metallo)supramolecular architectures for nonlinear optics. 215 in Tab. 8.1. Moreover, Fig. 8.2 shows a photograph of both materials that are the subject of this subsection.

Figure 8 . 1 :

 81 Figure 8.1: SHG intensities in s-polarized and p-polarized laser beam of pSiO2: D1

Figure 8 . 2 :

 82 Figure 8.2: Photograph presenting nanocomposite consisting of a porphyrin complex with

8 . 3 )

 83 was firstly annealed for 2 hours in temperature around 200C. Then, each of the selected ___________________________________________________________________________ Waszkowska Karolina | Study and diagnostic of the physicochemical properties of new -conjugated (metallo)supramolecular architectures for nonlinear optics. 217 supramolecular samples was dissolved in an appropriate solvent, creating solutions with selected concentrations. Afterwards, the solutions were introduced into the nanoporous membranes and the prepared nanocomposites were annealed for 3h in less than 100C to evaporate solvent. The entire process of obtaining a nanocomposite is shown schematically in Fig. 8.4. Moreover, Fig. 8.5presents response during SHG experiment in pure Al2O3 nanoporous membrane. It was noted, that SHG effect is not observable in pure membrane.

Figure 8 . 3 :

 83 Figure 8.3: SEM image of nanocomposite (left); Schematic representation of a nanocomposite

Figure 8 . 4 :

 84 Figure 8.4: The process of preparing the nanocomposite. Step 1: Applying the solution to the

Figure 8 . 5 :

 85 Figure 8.5: Lack of SHG response in pure nanoporous Al2O3 membrane.

Figure 8 . 6 :

 86 Figure 8.6: Schematic illustration of Al2O3:PtOEP nanocomposite.

Figure 8 . 7 : 220 8Figure 8 . 8 :Fig. 8 . 9 .Figure 8 . 9 :

 87220888989 Figure 8.7: SHG intensities as a function of rotation angle in s-and p-polarized laser beam (left)

Figure 8 . 10 :

 810 Figure 8.10: Schematic illustration of Al2O3:ZnTK nanocomposite.

Figure 8 . 11 :

 811 Figure 8.11: Schematic illustration of Al2O3:Zn[2]C nanocomposite.

Figure 8 . 12 :

 812 Figure 8.12: SHG intensities as a function of rotation angle in s-and p-polarized laser beam

Figure 8 . 13 :

 813 Figure 8.13: SHG intensities as a function of rotation angle in s-and p-polarized laser beam

Figs. 8 .

 8 14 present the nonlinear SHG response of the Al2O3:HelNi nanocomposite surface depending on the polarization.

Figure 8 . 14 :

 814 Figure 8.14: SHG responses on the Al2O3:HelNi nanocomposite surface dependent on

  Study and diagnostic of the physicochemical properties of new -conjugated (metallo)supramolecular architectures for nonlinear optics.225

Figure 8 .

 8 Figure 8.15: SHG responses on the Al2O3:HelNi nanocomposite surface before and after

CHAPTER 1 Figure 1 . 1 :Figure 1 . 2 : 12 Figure 1 . 3 :

 111121213 Figure 1.1: The nucleus and the electron cloud are shifted relative to each other under the influence

Figure 1 . 4 : 18 Figure 1 . 5 :Figure 1 . 6 : 25 Figure 1 . 7 : 27 Figure 1 . 8 :Figure 1 . 9 : 32 CHAPTER 2 Figure 2 . 1 :

 14181516251727181932221 Figure 1.4: Interaction geometry during the third harmonic generation process and energy level

Figure 2 . 2 : 42 Figure 2 . 3 : 43 Figure 2 . 4 : 44 Figure 2 . 5 : 44 Figure 2 . 6 : 44 Figure 2 . 7 : 45 Figure 2 . 8 :Figure 2 . 9 :Figure 2 . 10 : 48 Figure 2 . 11 : 48 Figure 2 . 12 : 49 Figure 2 . 13 : 51 Figure 2 . 14 : 52 Figure 2 . 15 :

 22422343244425442644274528292104821148212492135121452215 Figure 2.2: Schematic structures of 12-crown-4-Lithium complex (LiSCN) and [Ru(BPy)3] 2+ …...42

Figure 2 . 16 :Figure 2 . 17 :

 216217 Figure 2.16: Schematic example of cyclodextrin complex………………………………………54

Figure 2 . 18 : 56 Figure 2 . 19 : 57 Figure 2 . 20 :Figure 2 . 21 :Figure 2 . 22 : 3 Figure 3 . 1 :Figure 3 . 2 :Figure 3 . 3 : 83 Figure 3 . 4 : 84 Figure 3 . 5 : 86 Figure 3 . 6 :Figure 3 . 7 :

 2185621957220221222331323383348435863637 Figure 2.18: Schematic exemplary supramolecular calixarene structure with a C60 molecule in

Figure 3 . 8 :Figure 3 . 9 : 4 Figure 4 . 1 :Figure 4 . 2 :Figure 4 . 3 :Figure 4 . 4 :Figure 4 . 5 :Figure 4 . 6 :Figure 4 . 7 : 112 Figure 4 . 8 :

 383944142434445464711248 Figure 3.8: Diagram showing the basic features of the vapor deposition system………………...91

Figure 4 . 9 :Figure 4 . 10 :Figure 4 . 11 :Figure 4 .Figure 4 . 13 :

 494104114413 Figure 4.9: Z-scan experimental setup………………………………………...………………115

Figure 4 . 14 :Figure 4 . 15 :Figure 4 . 16 :

 414415416 Figure 4.14: Schematic representation of the basic elements of the atomic force microscope. The

Figure 4 . 17 :

 417 Figure 4.17: Scheme of the optical ellipsometry setup…………………………………………127

Figure 4 . 18 : 5 Figure 5 . 1 :Figure 5 . 2 :Figure 5 . 3 :Figure 5 . 4 :Figure 5 . 5 :

 41855152535455 Figure 4.18: Principles of ellipsometry………………………………………………………...128

Figure 5 . 6 :Figure 5 . 7 :Figure 5 . 8 :Figure 5 . 9 :Figure 5 . 10 :Figure 5 . 11 :Figure 5 . 12 :Figure 5 . 13 :Figure 5 . 14 :Figure 5 . 15 :Figure 5 . 16 :Figure 5 . 17 :

 56575859510511512513514515516517 Figure 5.6: 3D representation of intensity of emission as a function of excitation wavelength of

Figure 5 . 18 :Figure 5 . 19 :Figure 5 . 20 :Figure 5 . 21 : 6 Figure 6 . 1 :Figure 6 . 2 :Figure 6 . 3 :Figure 6 . 4 :Figure 6 . 5 :Figure 6 . 6 :Figure 6 . 7 :Figure 6 . 8 :

 51851952052166162636465666768 Figure 5.18: Normalized OA Z-scan characteristics for porphyrin complexes at different input

Figure 6 . 9 :Figure 6 . 10 :Figure 6 . 11 :Figure 6 . 12 :Figure 6 . 13 :Figure 6 . 14 :Figure 6 . 15 :Figure 6 . 16 :Figure 6 . 17 :Figure 6 . 18 :Figure 6 . 19 :

 69610611612613614615616617618619 Figure 6.9: SHG intensities as a function of rotation angle in p-polarized laser beam (left) and as

Figure 6 . 20 : 7 Figure 7 . 1 :Figure 7 . 2 :Figure 7 . 3 :Figure 7 . 4 :Figure 7 . 5 :Figure 7 . 6 :Figure 7 . 7 :Figure 7 . 8 :Figure 7 . 9 :Figure 7 . 10 :Figure 7 . 11 :Figure 7 . 12 :Figure 7 . 13 :Figure 7 . 14 :

 6207717273747576777879710711712713714 Figure 6.20: Electrostatic charge distribution for HelZn -positive (blue) and negative (orange)

Figure 7 . 15 :Figure 7 . 16 :Figure 7 . 17 : 197 Figure 7 . 18 :Figure 7 . 19 :Figure 7 .Figure 7 . 21 :Figure 7 . 22 :Figure 7 . 23 :Figure 7 . 24 :Figure 7 . 25 :

 7157167171977187197721722723724725 Figure 7.15: Photoluminescence spectra and 3D photoluminescence image of Zn[2]C………..196

Figure 7 . 26 :Figure 7 . 27 :Figure 7 . 28 :Figure 7 . 29 :Figure 7 .Figure 7 . 31 :Figure 7 . 32 :Figure 7 . 33 :Figure 7 . 34 :Figure 7 . 35 : 8 Figure 8 . 1 :Figure 8 . 2 :Figure 8 . 3 :Figure 8 . 4 :

 7267277287297731732733734735881828384 Figure 7.26: THG intensities as a function of incident angle of PyDFP thin film in s-polarized

Figure 8 . 5 :Figure 8 . 6 :Figure 8 . 7 :Figure 8 . 8 : 220 Figure 8 . 9 :Figure 8 . 10 :Figure 8 . 11 :

 8586878822089810811 Figure 8.5: Lack of SHG response in pure nanoporous Al2O3 membrane……………………...218

Figure 8 . 12 :Figure 8 . 13 :Figure 8 . 14 :Figure 8 . 15 :

 812813814815 Figure 8.12: SHG intensities as a function of rotation angle in s-and p-polarized laser beam (left)

Table 1 . 1 :

 11 Relation between indices jkl.

	jk	11 22 33 23=32 13=31 12=21
	l	1	2	3	4	5	6

  Generally, instead of components of second-order nonlinear optical susceptibility tensor 𝜒 𝑖𝑗𝑘 , the notation 𝑑 𝑖𝑙 is used, where 𝜒 𝑖𝑗𝑘 = 2𝑑 𝑖𝑙 , and indices jkl are replaced by the indices presented in Tab.1.1 [1.8]. Using notation shown in tab.1.1, relation (1.41) can be written as follows:

													𝐸 𝑥 2 (𝜔)
		[	𝑃 𝑥 𝑁𝐿 𝑃 𝑦 𝑁𝐿	] = 2𝜀 0 [	𝑑 11 𝑑 16	𝑑 12 𝑑 22	𝑑 13 𝑑 23	𝑑 14 𝑑 24	𝑑 15 𝑑 14	𝑑 16 𝑑 12	]	𝐸 𝑦 2 (𝜔) 𝐸 𝑧 2 (𝜔)
			𝑃 𝑧 𝑁𝐿			𝑑 15	𝑑 24	𝑑 33	𝑑 23	𝑑 13	𝑑 14
													[
	expression:
													𝐸 𝑥 2 (𝜔)
	[	𝑃 𝑥 𝑁𝐿 𝑃 𝑦 𝑁𝐿 𝑃 𝑧 𝑁𝐿	] = 𝜀 0 [	𝜒 111 𝜒 112 𝜒 113	𝜒 122 𝜒 222 𝜒 223	𝜒 133 𝜒 233 𝜒 333	𝜒 123 𝜒 223 𝜒 233	𝜒 113 𝜒 123 𝜒 133	𝜒 112 𝜒 122 𝜒 123	]	𝐸 𝑦 2 (𝜔) 2𝐸 𝑥 (𝜔)𝐸 𝑧 (𝜔) 𝐸 𝑧 2 (𝜔) 2𝐸 𝑦 (𝜔)𝐸 𝑧 (𝜔)	(1.41)
													[ 2𝐸 𝑥 (𝜔)𝐸 𝑦 (𝜔) ]

in the coordination system (x, y, z) can be now written in following matrix

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Karolina

| Study and diagnostic of the physicochemical properties of new -conjugated (metallo)supramolecular architectures for nonlinear optics. 17 2𝐸 𝑦 (𝜔)𝐸 𝑧 (𝜔) 2𝐸 𝑥 (𝜔)𝐸 𝑧 (𝜔) 2𝐸 𝑥 (𝜔)𝐸 𝑦 (𝜔) ]

CHAPTER 2: SUPRAMOLECULAR CHEMISTRY 2.1. History of Supramolecular Chemistry

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	40

  An example of supramolecular systems is the aforementioned cyclodextrins with attached organic guests in water[2.29 -2.30]. the larger molecule is called the host and the smaller guest. The recognition of both molecules occurs due to non-covalent interactions and is very specific[2.32].

	higher state of disorder. Figure 2.9: Schematically presented mechanism of forming supramolecular complex caused by arbitrary, usually
	hydrophobic effect.
	Generally, we distinguish two main concepts of supramolecular chemistry. The first of them is
	molecular self-organization. It involves spontaneous organization into more complex systems
	without external interference. Self-organization process may also refer to individual molecules that
	spontaneously adopt a specific structure, for example folding of proteins [2.31]. Self-assembly of
	molecular systems leads to self-association of complicated supramolecular systems. Supramolecular
	association is caused by weak intermolecular interactions, and the process is based on the template
	There are two effects: enthalpic, in which the polar solvent stabilizes excluded from the cavity upon
	effect, which requires several stages to occur spontaneously. The second term is molecular
	quest binding, and entropic, in which the combination of guest and host results in less disruption
	recognition (Fig. 2.10), which means the specific of a compound coordinated by the larger structure
	in relation to the solvent structure. In hydrophobic effect, the entropy increases due to the
	-a ligand that results in a guest-host complex. The recognition consists in creating selective binding
	exclusion of the non-polar substance by water, which interacts during dissolution and enters a
	of the substrate molecule called a "guest" with a receptor, called the "host". These terms are
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	-conjugated (metallo)supramolecular architectures for nonlinear optics. -conjugated (metallo)supramolecular architectures for nonlinear optics.
	47 48

Figure 2.13: Schematic example of crown ether complex (1,10-Diaza-18-Crown-6) with potassium. 2.4.2. Cryptands

  , they are often used with transition metals and rare earth ions. An example of a complex of cryptanadium with lithium Li + is shown in Fig.2.14. Cryptands, similarly to the supramolecular compounds mentioned above, were also studied for nonlinear optics, by means of the second-order nonlinear properties of the complexes with barium Ba + , lithium Li + , nickel Ni 2+ , zinc Zn 2+ , copper Cu 2+ , as well as cadmium Cd 2+ ions[2.53 -2.54].

	by Charles Pedersen in 1967, who then received the 1987 Nobel Prize along with Donald Cram their coordination properties
	and Jean-Marie Lehn. The most important and interesting physicochemical properties of crown
	ethers are, first of all, their solubility in almost all known solvents, and they are also very good
	ligands for many ions, which combine relatively with weak ion-dipole interactions, but form a
	strong complex. What's more, they are used as catalysts to accelerate chemical reactions, as well as
	in environmental protection, by removing toxic heavy metal ions from water. Besides, they are
	widely researched in terms of nonlinear optics, Kerr effects, generation of higher harmonics or
	optical birefringence [2.50 -2.52]. Fig. 2.13 presents example of crown ethers.
	Similarly to crown ethers, cryptands are organic chemical compounds obtained synthetically. They
	Most often they are characterized by a strong complexing action, creating chelate compounds (i.e. those where the
	are cyclic polyethers with a regular structure, capable of selectively forming stable complexes with organic ligand is combined with the central ion by more than one coordination bond), with a
	cations, most often with alkali metals. As mentioned earlier, the first crown ether was synthesized characteristic spherical structure, resembling a so-called crypt -hence the nomenclature. Due to
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	-conjugated (metallo)supramolecular architectures for nonlinear optics. -conjugated (metallo)supramolecular architectures for nonlinear optics.
	51 52

Figure 2.14: Schematic example of supramolecular cryptanadium Li + complex. 2.4.3. Cyclophanes

	Cyclophanes belong to the group of organic compounds derived from aromatic hydrocarbons in
	which the characteristic feature is at least two carbon atoms derived from at least one aromatic
	moiety, which are connected to each other by a system of covalent bonds. The first description of
	cyclophane was presented in the journal Nature by C. J. Brown and A. C. Farthing [2.55], which
	were then examined by the previously mentioned Nobel laureate D. J. Cram. Fig. 2.15 shows an
	exemplary supramolecular structure composed of cyclophane. Apart from the photochemical and
	luminescent properties, nonlinear optical properties were also reported, including for example the
	relationship between the structure of cyclophane derivatives and the SHG response [2.56 -2.59].
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Figure 2.15: Schematic example of multi-layer chiral cyclophane. 2.4.4. Cyclodextrins

	This type of supramolecular system belongs to the group of dextrin (carbohydrates composed of
	simple sugar derivatives), forming a cyclic structure that is easily soluble in water. Due to the
	hydrophobicity of the interior, these compounds are able to form guest-host complexes with
	hydrophobic compounds. Cyclodextrins are widely used in pharmacy, where it is possible to reduce
	the doses of the drug due to the use of this compound. In addition, they are used in the hygiene
	industry where cyclodextrins are used to absorb or release odors. Current investigations present
	cyclodextrins research, inter alia, for NLO in the form of polymeric films, also as applications for
	optical limiting [2.60 -2.63]. Fig. 2.16 shows an exemplary cyclodextrin.
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	54

  2+ , magnesium Mg 2+ , iron Fe 2+ , cobalt Co 2+ , manganese Mn 2+ and copper Cu 2+ . Apart from the fact that they have a building, transport,

catalysis, storage, immunological etc. function, both peptides and proteins are widely studied in terms of physics, photonics, nonlinear optics. Some papers reported peptide nanostructures ___________________________________________________________________________ Waszkowska Karolina | Study and diagnostic of the physicochemical properties of new -conjugated (metallo)supramolecular architectures for nonlinear optics. 57 characterized by nonlinear optics through the SHG effect, as well as nanophotonics and nonlinear spectroscopy [2.71 -2.75]. In the case of proteins, very interesting work has described nonlinear effects using Rayleigh scattering, and, inter alia, second harmonic generation of chiral crystals as well as fluorescent proteins FPs [2.76 -2.79]. Fig. 2.19 presents example of supramolecular protein alkaline phosphatase [2.80].

  Kundu et al. reported in 2012 electrochemical and photophysical properties of triple-stranded helicates with Cu 2+ and Cd 2+ ions.

2.20 presents example of self-assembled triple metallo-helicate. The already known helicates include, among others, heteronuclear helicates

[2.89]

, helical circular structures

[2.90]

, as well as mixed helixes

[2.91]

. Under carefully selected experimental conditions, helicates with different structures are obtained, examples may be complexes, grid type structures or macrocyclic structures. Prior investigations have documented luminescent properties of ruthenium (II) triple-stranded helicates

[2.92]

and its potential application in medicine. Moreover, metallo-helicate built of from the same ligands, but with iron cation Fe 2+ , was investigated for its electronic and magnetic properties and its spin-crossover behavior was checked

[2.93]

. S. V. Eliseeva et al. presented luminescent and two-and three-photon ___________________________________________________________________________ Waszkowska Karolina | Study and diagnostic of the physicochemical properties of new -conjugated (metallo)supramolecular architectures for nonlinear optics. 59 cross section of binuclear helicates [2.94]. Nevertheless, N.

  (seeFig. 3.7), where 𝛾 𝑆 is the surface tension of the substrate, 𝛾 𝐹 is the surface tension of film under vacuum, and 𝛾 𝑆/𝐹 is the surface tension of substrate-film interface, and  describes island wetting angle. For the Volmer-Weber  > 0, therefore 𝛾 𝑆 < 𝛾 𝐹 + 𝛾 𝑆/𝐹 . However, for Frank -Van der Merwe growth  is equal to 0, hence 𝛾 𝑆 ≥ 𝛾 𝐹 + 𝛾 𝑆/𝐹 . According to Fig.3.7, during Stranski-Krastanov growth it is necessary assuming that there is a lattice mismatch between the deposited film and the substrate. The condition for Frank-Van der Merwe growth is initially fulfilled, however, the formation of layers causes indirect changes in the values of 𝛾 𝑆 and 𝛾 𝑆/𝐹 , which leads to the condition for Volmer-Weber growth.

	Chapter 3	Thin Films Physics

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Waszkowska Karolina | Study and diagnostic of the physicochemical properties of new -conjugated (metallo)supramolecular architectures for nonlinear optics. 90

  The difference of phase angles ΔΨ 𝑆 and ΔΨ 𝐹 in substrate and in a thin film, respectively, can be written in the form: 𝑙 𝑆 and 𝑙 𝐹 are the substrate thickness and the thin layer, respectively. Moreover, the factors 𝑇 1 and 𝑇 2 entered are determined by:

	∆𝜀 𝑆 = 𝜀 𝑆 𝜔 -𝜀 𝑆 3𝜔 = 7.753 • 10 -2 [𝐹 • 𝑚 -1 ]; ∆𝜀 𝐹 = 𝜀 𝐹 𝜔 -𝜀 𝐹 3𝜔	(4.58)
	∆Ψ 𝑆 = Ψ 𝑆 𝜔 -Ψ 𝑆 3𝜔 =	3𝜔𝑙 𝑆 𝑐	(𝑛 𝑆 𝜔 cos 𝜃 𝑆 𝜔 -𝑛 𝑆 3𝜔 cos 𝜃 𝑆 3𝜔 )	(4.59)
	∆Ψ 𝐹 = Ψ 𝐹 𝜔 -Ψ 𝐹 3𝜔 =	3𝜔𝑙 𝐹 𝑐	(𝑛 𝐹 𝜔 cos 𝜃 𝐹 𝜔 -𝑛 𝐹 3𝜔 cos 𝜃 𝐹 3𝜔 )	(4.60)
	where 𝑇 1 = (𝑡 12 𝜔 𝑡 23 𝜔 ) 3 𝑁 2 𝜔 + 𝑁 2 3𝜔 𝑁 2 3𝜔 + 𝑁 3 3𝜔	⋀ 𝑇 2 = (𝑡 12 𝜔 ) 3 𝑡 34 3𝜔 𝑁 3 𝜔 + 𝑁 3 3𝜔 𝑁 3 3𝜔 + 𝑁 4 3𝜔	(4.61)
	where 𝑁 𝑗 𝜔,3𝜔 = 𝑛 𝑗 𝜔,3𝜔 cos 𝜃 𝑗
	𝑡 12 𝜔 =	2𝑛 1 cos 𝜃 1 𝑛 1 cos 𝜃 1 + 𝑛 2 𝜔 cos 𝜃 2 𝜔
	𝑡 23 𝜔 =		2𝑛 2 𝜔 cos 𝜃 2 𝜔 𝜔 cos 𝜃 2 𝑛 2 𝜔 + 𝑛 3 𝜔 cos 𝜃 3 𝜔
	𝑡 23 3𝜔 =	2𝑛 2 3𝜔 cos 𝜃 2 3𝜔 3𝜔 cos 𝜃 2 𝑛 2 3𝜔 + 𝑛 3 3𝜔 cos 𝜃 3 3𝜔	(4.62)
	𝑡 34 𝜔 =		2𝑛 3 𝜔 cos 𝜃 3 𝜔 𝜔 cos 𝜃 3 𝑛 3 𝜔 + 𝑛 4 𝜔 cos 𝜃 4 𝜔
	𝑡 34 3𝜔 =	2𝑛 3 3𝜔 cos 𝜃 3 3𝜔 3𝜔 cos 𝜃 3 𝑛 3 3𝜔 + 𝑛 4 cos 𝜃 4

Study and diagnostic of the physicochemical properties of new -conjugated (metallo)supramolecular architectures for nonlinear optics.

108

𝜔,3𝜔

for 𝑗 = 1,2,3,4 and transmission coefficients 𝑡 𝑖𝑗 𝜔,3𝜔 for fundamental and harmonic wave between media 𝑖 and 𝑗 are given by (in polarization ss):

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  -22 [𝑚 2 𝑉 -2 ] [4.14 -4.15], 𝜒 𝐴𝑖𝑟(3) = 9.8 • 10 -26 [𝑚 2 𝑉 -2 ] [4.12]. The contribution of air relative to vacuum 𝐶 𝐴𝑖𝑟 is given in the following form:

	𝐶 𝐴𝑖𝑟 = 0.24𝐶 ′ {𝑡 23 3𝜔 𝑡 34 3𝜔 𝑒𝑥𝑝[𝑖(Ψ + 𝛼)] -(𝑡 12 𝜔 𝑡 23 𝜔 𝑡 34 𝜔 ) 3 𝑒𝑥𝑝[-𝑖(Ψ + 𝛽)]}	(4.64)

Table 4 . 1 .

 41 Parameters of setup used in SHG/THG measurements.

		Maker fringe	Laser energy dependence
	Laser	Nd:YAG	Nd:YAG
	Laser Wavelength	1064 nm	1064 nm
	Laser Energy	80 uJ	60 mJ
	Pulse duration	30 ps	12 ns
	Repetition rate	10 Hz	12 Hz

  Substituting the reflection coefficients 𝑟 𝑝 and 𝑟 𝑠 as the ratio of the electric field vectors, we obtain

	𝜌 ≡ tan Ψ 𝑒 (𝑖∆) ≡	𝑟 𝑝 𝑟 𝑠		(4.79)
	the following relationship:
	𝜌 ≡ tan Ψ 𝑒 (𝑖∆) ≡	𝑟 𝑝 𝑟 𝑠	≡ (	𝐸 𝑟𝑝 𝐸 𝑖𝑝	) ( 𝐸 𝑟𝑠 𝐸 𝑖𝑠 ⁄	)	(4.80)
	As mentioned before, 𝐸 𝑖𝑝 = 𝐸 𝑖𝑠 , therefore equation (4.82) can be simplified:
	𝜌 ≡ tan Ψ 𝑒 (𝑖∆) ≡ (𝐸 𝑟𝑝 ) (𝐸 𝑟𝑠 ) ⁄		(4.81)
	Using polar coordinates as a record of the amplitude reflectance coefficients, we get the following
	relationship:
	tan Ψ = |𝑟 𝑝 | |𝑟 𝑠 | ⁄	and	∆= 𝛿 𝑟𝑝 -𝛿 𝑟𝑠	(4.82)
	Substituting 𝑅 𝑝 = |𝑟 𝑝 |

Study and diagnostic of the physicochemical properties of new -conjugated (metallo)supramolecular architectures for nonlinear optics. 129 2 and 𝑅 𝑠 = |𝑟 𝑠 | 2 , we achieve:

Table 5 .

 5

		1: Thickness (d), roughness (RA), linear refractive index values (n) and extinction
			coefficients () of porphyrin complexes thin films.
		d [nm] RA [nm]	n1064	n532	n355	1064	532	355
	PtOEP	1650	4.402	1.497	1.511	1.560	0.004	0.003	0.058
	RuOEP 1200	0.371	1.486	1.490	1.495	0.015	0.034	0.032
	FeOEP	1150	2.294	1.462	1.466	1.469	0.073	0.049	0.062
	PdOEP	1430	0.539	1.464	1.478	1.488	0.037	0.0453	0.035

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Waszkowska Karolina | Study and diagnostic of the physicochemical properties of new -conjugated (metallo)supramolecular architectures for nonlinear optics. 138

Table 5 . 2 :

 52 Coefficients determined from absorption spectra of metalloporphyrin thin films.

	Sample	abs [nm]	 [10 3 cm -1 ] 355 nm 532 nm	Eg(Homo-Lumo)[eV]
	PtOEP	378, 519, 541	11.72	2.60	2.22
	RuOEP	402, 515, 547	5.11	2.97	2.23
	FeOEP	373, 534, 633	23.27	3.86	1.86
	PdOEP	383, 520, 555	10.61	2.00	2.17

Waszkowska Karolina | Study and diagnostic of the physicochemical properties of new -conjugated (metallo)supramolecular architectures for nonlinear optics. 140

Table 5 . 4 :

 54 Values of second-order nonlinear susceptibilities calculated by theoretical models.

		Model	s-p	 (2) [pmV -1 ]	p-p
	PtOEP	Lee Herman-Hayden	(0.033  0.002) (0.053  0.002)	(0.045  0.002) (0.059  0.005)
	RuOEP	Lee Herman-Hayden	(0.060  0.001) (0.069  0.002)	(0.073  0.002) (0.081  0.001)
	FeOEP	Lee Herman-Hayden	(0.105  0.003) (0.185  0.001)	(0.109  0.012) (0.262  0.013)
	PdOEP	Lee Herman-Hayden	(0.037  0.001) (0.047  0.002)	(0.049  0.002) (0.069  0.001)

Table 5 . 5 :

 55 Values of third-order nonlinear susceptibilities calculated by theoretical models.

		Model	s-p	 (3)  10 -22 [m 2 V -2 ] p-p
	PtOEP	Kubodera-Kobayashi Reintjes	(2.936  0.105) (10.960  0.222)	(3.765  0.121) (11.370  0.235)

RuOEP

Kubodera-Kobayashi (2.931  0.098) (3.310  0.101) Reintjes (9.335  0.136) (9.463  0.142) FeOEP Kubodera-Kobayashi (3.733  0.087) (4.277  0.086) Reintjes (13.410  0.196) (13.510  0.203) PdOEP Kubodera-Kobayashi (2.917  0.122) (3.390  0.123) Reintjes (9.510  0.158) (9.840  0.166)

Table 5 . 7 :

 57 Calculated values of NLO susceptibility  (3) obtained from Z-scan data, compared with THG results of studied porphyrin complexes.

	PtOEP	RuOEP	FeOEP	PdOEP

Table 6 . 1 :

 61 Thickness (d), roughness (RA), linear refractive index values (n) and extinction coefficients () of triple stranded helicates thin films.

		d [nm] RA [nm]	n1064	n532	n355	1064	532	355
	HelFe	820	0.984	1.522	1.528	1.540	0.004	0.014	0.038
	HelCo	820	0.154	1.436	1.458	1.481	0.001	0.008	0.037
	HelNi	660	0.157	1.426	1.443	1.464	0.072	0.069	0.067
	HelZn	680	0.061	1.435	1.465	1.498	0.083	0.069	0.056

Table 6 . 2 :

 62 Absorption peaks and values of absorption coefficients. peak in violet wavelength range positioned around 380-410 nm, which are result of ILCT transitions. During excitation at 532 nm and 577 nm sample containing iron(II) HelFe, no

		abs [nm]	 [10 3 cm -1 ] 532 nm 355 nm
	HelFe	331, 531, 577	4.49	8.49
	HelCo	327	0.35	11.22
	HelNi	328	0.50	8.40
	HelZn	348	0.12	10.94
	Photoluminescence spectra of the studied triple stranded helicates thin films on glass substrates

are presented in Fig.

6

.6. It was observed that for all samples PL spectra indicate one maximal PL ___________________________________________________________________________ Waszkowska Karolina | Study and diagnostic of the physicochemical properties of new -conjugated (metallo)supramolecular architectures for nonlinear optics. 164

Table 6 . 3 :

 63 Excitation, emission peaks and luminescence lifetimes of studied thin films.

		Excitation [nm]	Emission [nm]	T1Decay [ns]	T2Decay [ns]
	HelFe	320	380	(1.562  0.012)	(22.546  0.226)
	HelCo	325	400	(1.473  0.011)	(37.872  0.257)
	HelNi	328	393	(1.408  0.026)	(23.726  0.242)
	HelZn	380	410	(2.005  0.052)	(24.420  0.202)

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Waszkowska

Karolina

| Study and diagnostic of the physicochemical properties of new -conjugated (metallo)supramolecular architectures for nonlinear optics. ___________________________________________________________________________ Waszkowska Karolina | Study and diagnostic of the physicochemical properties of new -conjugated (metallo)supramolecular architectures for nonlinear optics. 166

Table 6 . 4 :

 64 Values of second-order nonlinear susceptibilities calculated by theoretical models.

		Model	s-p	 (2) [pmV -1 ]	p-p
	HelFe	Lee Herman-Hayden	(0.306  0.058) (0.340  0.045)	(0.444  0.036) (0.515  0.098)
	HelCo	Lee Herman-Hayden	(0.274  0.023) (0.646  0.025)	(0.381  0.074) (0.758  0.024)
	HelNi	Lee Herman-Hayden	(0.356  0.044) (0.673  0.047)	(0.472  0.063) (0.804  0.038)
	HelZn	Lee Herman-Hayden	(0.325  0.015) (0.410  0.026)	(0.449  0.024) (0.527  0.041)

Table 6 . 5 :

 65 Values of second-order nonlinear susceptibilities calculated by theoretical models.

		Model	s-p	 (3)  10 -22 [m 2 V -2 ]	p-p
	HelFe	Kubodera-Kobayashi Reintjes	(15.02  0.39) (17.95  0.20)	(15.38  0.39) (18.18  0.19)
	HelCo	Kubodera-Kobayashi Reintjes	(15.85  0.14) (16.19  0.12)	(15.45  0.14) (15.83  0.13)
	HelNi	Kubodera-Kobayashi Reintjes	(16.84  0.13) (18.32  0.36)	(17.28  0.14) (18.55  0.35)
	HelZn	Kubodera-Kobayashi Reintjes	(14.74  0.23) (16.33  0.48)	(14.98  0.26) (16.81  0.50)

Table 6 . 7 :

 67 Calculated values of NLO susceptibility  (3) obtained from Z-scan data, compared with THG results of studied triple stranded helicates.

	HelFe	HelCo	HelNi	HelZn

Table 6 . 8

 68

		HOMO	LUMO	(Eg)HOMO-LUMO	abs exp[nm]	abs th [nm]
		[eV]	[eV]	[eV]
	HelFe	-3.50	-2.18	1.32	331, 531, 577	272
	HelCo	-2.82	-2.57	0.25	327	-
	HelNi	-3.12	-1.71	1.41	328	280
	HelZn	-4.96	-1.02	3.94	348	278

: The computed quantum chemical parameters including: HOMO, LUMO, energy gap (Eg) HOMO-LUMO, UV-VIS absorption peak position spectra computed applying b3lyp/6-31++g(d,p) methodology and measured for of studied thin films.

Table 7 .1: Thickness

 7

		d [nm] RA [nm]	n1064	n532	n355	1064	532	355
	PyDFP	365	1.270	1.512	1.533	1.555	0.009	0.004	0.003
	PyTK	330	0.667	1.505	1.511	1.518	0.041	0.011	0.005
	ZnTK	290	1.267	1.490	1.508	1.456	0.004	0.026	0.067
	CdTK	380	1.204	1.492	1.510	1.525	0.007	0.002	0.001
	Py[2]C	215	1.175	1.484	1.514	1.561	0.001	0.004	0.014
	Zn[2]C	300	1.266	1.495	1.505	1.488	0.001	0.005	0.028
	Cd[2]C	320	1.209	1.516	1.504	1.572	0.007	0.005	0.002

(d), roughness (RA), linear refractive index values (n) and extinction coefficients () of modified pyrene-based guest-host thin films.

Table 7 . 2 :

 72 Coefficients determined from absorption spectra of modified pyrene-based guest-host thin films.green light visible by the naked eye. Moreover, samples containing metals of zinc and cadmium, in both cases trefoil knot and[2]catenane, are characterized by PL emission with weaker intensity shifted towards short waves, which is entirely due to the properties of the metal. Therefore, due to the fact that zinc and cadmium occur in the same group of the periodic table and d orbitals are fully

	Sample	abs [nm]	355 [10 3 cm -1 ]
	PyDFP	360	13.95
	PyTK	310; 403	4.30
	ZnTK	308	0.74
	CdTK	307	0.43
	Py[2]C	301; 340	16.70
	Zn[2]C	301	0.61
	Cd[2]C	301	0.17
	Photoluminescence spectra of the investigated modified pyrene-based thin films are shown in Figs.
	7.10. -7.16. Basically, the PyDFP sample, which acts as a ligand, emits very intense light in the
	blue wavelength, while the pyrene trefoil knot PyTK and pyrene[2]catenane Py[2]C are
	characterized by the emission spectrum shifted towards longer wavelengths, emitting very intense

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Waszkowska Karolina | Study and diagnostic of the physicochemical properties of new -conjugated (metallo)supramolecular architectures for nonlinear optics. 194

Table 7 . 3 :

 73 Excitation, emission peaks and luminescence lifetimes of studied thin films.

		Excitation [nm]	Emission [nm]	T1Decay [ns]	T2Decay [ns]
	PyDFP	286 360	450	(18.62 ± 0.29) (16.03 ± 0.23)	(4.14 ± 0.02) (3.96 ± 0.02)
	PyTK	330 400	520	(17.73 ± 0.70) (13.85 ± 0.54)	(7.19 ± 0.02) (6.43 ± 0.07)
	ZnTK	320	400	(30.99 ± 0.17)	(3.12 ± 0.03)
	CdTK	320	400	(30.97 ± 0.16)	(2.97 ± 0.02)
	Py[2]C	365	510	(14.23 ± 0.12)	(5.56 ± 0.04)
	Zn[2]C	325	390	(29.43 ± 0.15)	(2.84 ± 0.03)
	Cd[2]C	325	390	(27.83 ± 0.23)	(1.79 ± 0.02)

  and Reintjes (subsection 4.1.5)

	Chapter 7	Modified Pyrene-Based Complexes
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	Waszkowska Karolina | Study and diagnostic of the physicochemical properties of new
		-conjugated (metallo)supramolecular architectures for nonlinear optics.
		204

Table 7 . 6 :

 76 7.35. From Tab. 7.6, it can be seen that the Py[2]C and PyTK samples have higher n2 values than PyDFP, which is the building block of these two complexes. Moreover, the zinc and cadmium cations found in these systems enhanced the effect of nonlinear refraction. The highest values, Calculated values of NLO refractive index n2, real part and total value of third order NLO susceptibility Re((3) ),  (3) of modified pyrene-based complexes in DMSO.The results for this experiment are different from the THG experiment, which only has electronic contribution to the third-order NLO phenomena (seeTab. 7.7). Due to the fact that the investigated samples have the same concentration of solutions, where as in the case of thin layer studied with the THG method, it is necessary to have the same concentration of molecules in layers, it is easier to compare the studied samples with each other. The total third order NLO susceptibility is influenced only by the real part of it as a result of the NLO refractive properties, the NLO susceptibility values determined by the THG technique do not differ significantly from the values determined from the Z-scan method, due to the lack of a molecular element, which is determined by NLO absorption. As it can be clearly seen, supramolecular compounds are characterized by an enhanced NLO signal compared with the PyDFP ligand. Moreover, the influence of the metal and the changes in the nature of the supramolecular complex by changing

	however, were observed for systems containing zinc metals ZnTK and Zn[2]C. It was also noticed
	that the NLO effect increases with the concentration of solution. In this case, absorption has no
	influence on the nonlinear refraction effect.

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Karolina

| Study and diagnostic of the physicochemical properties of new -conjugated (metallo)supramolecular architectures for nonlinear optics. 210 the spacer, have been noted, that is: in samples ZnTK and CdTK also Zn[2]C and Cd[2]C, the nonlinear response is stronger than for PyTK and Py[2]C, respectively. It also was noticed that the zinc cation is associated with stronger interactions than the cadmium cation, hence much higher values for the ZnTK sample relative to CdTK and Zn[2]C relative to Cd[2]C. In general, the presented supramolecular systems of new modified pyrene-based complexes are characterized by a high response of both the second and third order, moreover, they are characterized by strong NLO refraction with self-focusing properties, due to which they can be used, among others, in NLO devices based on self-phase modulation.

Table 7 .7: Calculated

 7

					PyDFP PyTK ZnTK CdTK Py[2]C Zn[2]C Cd[2]C
				2.0 mM	3.21	3.89	5.09	4.19	3.62	4.42	3.74
	 (3)  10 -21	[m 2 -2 ] V	Z-scan	1.5 mM 1.0 mM	3.08 2.54	3.45 3.09	3.83 3.71	4.02 3.42	3.23 3.01	3.88 3.47	3.40 3.30
				0.5 mM	2.04	2.96	3.49	3.09	2.67	3.12	2.84
			THG	2.32	3.01	4.45	3.28	5.30	3.88	3.52

values of NLO susceptibility  (3) obtained from Z-scan data, compared with THG results of studied modified pyrene-based complexes. ___________________________________________________________________________ Waszkowska Karolina | Study and diagnostic of the physicochemical properties of new -conjugated (metallo)supramolecular architectures for nonlinear optics. 211

  The samples were successfully obtained according to the synthesis described in the literature. The research on nonlinear optics has been divided into two parts: the first one uses thin layers prepared with the spin-coating method, while the second one is based on studies in solutions. Thin layers were used to study nonlinear optics of second and third harmonic generation (SHG and THG, respectively) by the Maker fringe method. However, before the research into NLO was started, the spectroscopic properties of thin films were checked. It was found that in the case of these supramolecular compounds, the absorption only affects the third order properties, which was taken into account in the subsequent determinations of the nonlinear optics parameters. The conducted studies of nonlinear optics have shown that the investigated supramolecular compounds are characterized by enhanced generation of the second and third harmonics. In addition, based on the Z-scan technique from the solution, NLO studies of the refractive index show that these complexes can be used in nonlinear optical devices, inter alia, as self-modulators. Due to the enhanced nonlinear properties of the second and third order, the most interesting compounds contain zinc cations: ZnTK and Zn[2]C. As the conclusion of this section, in this work the proof of using modified supramolecular nontrivial structures in nonlinear optics was achieved. By changing nature, spacer or substituent in supramolecular assemblies we can control NLO response.

	Chapter 7	Modified Pyrene-Based Complexes

This chapter presented mainly nonlinear optics studies on new modified pyrene-based supramolecular complexes. The research focused on two types of pyrene compounds: trefoil knot and

[2]

catenane. The ligand forming these two types of supramolecular compounds PyDFP (pyrene diformylpyridine) and PyTK (pyrene trefoil knot) with zinc ZnTK cations and cadmium cations CdTK, and Py[2]C (pyrene [2]catenane) together with zinc cations were investigated Zn[2]C and cadmium cations Cd[2]C. ___________________________________________________________________________ Waszkowska Karolina | Study and diagnostic of the physicochemical properties of new -conjugated (metallo)supramolecular architectures for nonlinear optics. 212 ___________________________________________________________________________ Waszkowska Karolina | Study and diagnostic of the physicochemical properties of new -conjugated (metallo)supramolecular architectures for nonlinear optics. 214

Table 8 . 1 :

 81 Comparison the advantages and disadvantages of guest-host thin films with nanoporous membranes.

	Chapter 8

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Waszkowska Karolina | Study and diagnostic of the physicochemical properties of new -conjugated (metallo)supramolecular architectures for nonlinear optics. 216

Table 1 . 1 .

 11 Relation between indices jkl………………………………………………………...[START_REF] Kleinman | Theory of Second Harmonic Generation of Light[END_REF]

	CHAPTER 4

Table 4 . 1 .

 41 Parameters of setup used in SHG/THG measurements…………………………….111

	CHAPTER 5

Table 5 . 1 :

 51 Thickness (d), roughness (RA), linear refractive index values (n) and extinction coefficients () of porphyrin complexes thin films……………………………………………..137

Table 5 . 2 :

 52 Coefficients determined from absorption spectra of metalloporphyrin thin films…...140

Table 5 . 3 :

 53 Values of excitation and emission wavelengths also with fluorescence lifetimes of studied metalloporphyrins…………………………………………………………………….142

Table 5 . 4 :

 54 Values of second-order nonlinear susceptibilities calculated by theoretical models….147

Table 5 . 5 :

 55 Values of third-order nonlinear susceptibilities calculated by theoretical models……149

Table 5 . 6 :

 56 Calculated values of NLO refractive index n2, NLO absorption coefficient , NLO absorption cross section , real and imaginary part of third order NLO susceptibility Re((3) ),

	Im( (3) ) of studied porphyrin complexes………………………………………………………151

Table 5 . 7 :

 57 Calculated values of NLO susceptibility  (3) obtained from Z-scan data, compared with THG results of studied porphyrin complexes………………………………………………….154

	List of Tables

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Waszkowska Karolina | Study and diagnostic of the physicochemical properties of new -conjugated (metallo)supramolecular architectures for nonlinear optics. 252 CHAPTER 6

Table 6 . 1 :

 61 Thickness (d), roughness (RA), linear refractive index values (n) and extinction coefficients () of triple stranded helicates thin films…………………………………………...162

Table 6 . 2 :

 62 Absorption peaks and values of absorption coefficients……………………………163

Table 6 . 3 :

 63 Excitation, emission peaks and luminescence lifetimes of studied thin films………...164

Table 6 . 4 :

 64 Values of second-order nonlinear susceptibilities calculated by theoretical models….170

Table 6 . 5 :

 65 Values of second-order nonlinear susceptibilities calculated by theoretical models….171

Table 6 . 6 :

 66 Calculated values of NLO refractive index n2, NLO absorption coefficient , NLO absorption cross section , real and imaginary part of third order NLO susceptibility Re(

(3)

), Im(

(3)

) of studied triple stranded helicates……………………………………………………175

Table 6 . 7 :

 67 Calculated values of NLO susceptibility  (3) obtained from Z-scan data, compared with THG results of studied triple stranded helicates………………………………………………..177

Table 6 . 8 :

 68 The computed quantum chemical parameters including: HOMO, LUMO, energy gap (Eg) HOMO-LUMO, UV-VIS absorption peak position spectra computed applying b3lyp/6-31++g(d,p) methodology and measured for of studied thin films…………………………………………...178

Table 6 . 9 :

 69 The computed several components of multipole moment (b3lyp/6-31++g(d,p))

	HelFe, HelNi, HelZn, HelCo……………………………………………………………...180

Table 6 . 10 :

 610 Frontier molecular orbitals of HelFe, HelCo, HelNi, HelZn, calculated at DFT/B3LYP/6-31G+(d,p) basis set level……………………………………………………..181

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Waszkowska Karolina | Study and diagnostic of the physicochemical properties of new -conjugated (metallo)supramolecular architectures for nonlinear optics. 253

Table 6 . 11 :

 611 Frequency-dependent: tot(-2;,) and tot(-3;,,) values at = 0.042827 a.u., =1064 nm, for HelFe, HelZn, B3LYP/lanl2DZ and comparison with experimental data (2) and

	 (3) …………………………………………………………………………………………….182
	CHAPTER 7

Table 7 . 1 :

 71 Thickness (d), roughness (RA), linear refractive index values (n) and extinction coefficients () of modified pyrene-based guest-host thin films.………………………………..191

Table 7 . 2 :

 72 Coefficients determined from absorption spectra of modified pyrene-based guest-host thin films……………………………………………………………………………………...193

Table 7 . 1 :

 71 Excitation, emission peaks and luminescence lifetimes of studied thin films………...196

Table 7 . 4 :

 74 Values of second-order nonlinear susceptibilities of modified pyrene-based guess-host thin films calculated by theoretical models……………………………………………………..201

Table 7 . 5 :

 75 Values of third-order nonlinear susceptibilities calculated by theoretical models……206

Table 7 . 6 :

 76 Calculated values of NLO refractive index n2, real part and total value of third order NLO susceptibility Re

( (3) ),  (3) of

  modified pyrene-based complexes in DMSO……………...209

Table 7 . 7 :

 77 Calculated values of NLO susceptibility  (3) obtained from Z-scan data, compared with THG results of studied modified pyrene-based complexes…………………………………….210

	CHAPTER 8

Table 8 . 1 :

 81 Comparison the advantages and disadvantages of guest-host thin films with nanoporous membranes…………………………………………………………………………………....216

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Waszkowska Karolina | Study and diagnostic of the physicochemical properties of new -conjugated (metallo)supramolecular architectures for nonlinear optics. 188

This work investigated the nonlinear optical properties of pyrene-containing compounds: pyrene trefoil knot (PyTK), containing zinc (ZnTK) and cadmium (CdTK), pyrene diformylpyridine (PyDFP), pyrene [2]catenane (Py [2]C), containing zinc (Zn [2]C) and cadmium (Cd [2]C) (Fig. 7.1), whose synthesis as well as physicochemical, crystallographic properties and computational modeling are described in [7.1 -7.4], and were synthesized in collaboration with University of Strasbourg and New York University in Abu Dhabi. DFP (diformylpyridine) is characterized by starting material as one of the building ligands of TK and [2]C supramolecular complexes, which is then combined with DAB (diaminopyridine) and with Zn(OAc)2 (zinc acetate). The [2]catenane and trefoil knot in a single pot are then formed as a result of the self-assembly process. [2]catenane is characterized by the fact that it is composed of two identical macrocycles linked together by two zinc ions Zn(II), and is also composed of one DFP and one DAB. On the other hand, trefoil knot is characterized by the fact that it is one structure composed of three crossings, and moreover is chiral. In addition to the above-mentioned physicochemical and crystallographic properties, [2]catenane and trefoil knot compounds have been studied for their applications in medicine, for example in pharmaceutical development in the diagnosis and treatment of cancer [7.5]. The following sections describe the studies of nonlinear optical effects carried out on these supramolecular complexes. A total of 7 samples were collected and dissolved with 50 mg of poly(methyl methacrylate) (PMMA) with average Mw ~ 120,000 by GPC (Sigma-Aldrich) in dimethyl sulfoxide (DMSO) forming 10% wt guest-host solution of complex to the polymer.

Subsequently, the solutions were applied to previously isopropanol vapor-cleaned glass substrates and thin layers were deposited in a vacuum-free spin-coater (Ossila) at 2000 rpm.

Surface Characterization

Thin layer thicknesses of modified pyrene-based complexes were measured using a profilometer (Dektak 6M) and their values are presented in Tab. Moreover, from the obtained results, we can notice that by changing the nature of supramolecular assemblies, by changing the spacer, we can control NLO response, which was not observable in case of triple stranded helicates. helicates samples. Moreover, no significant difference to the applied laser light polarization was noticed. In addition, the third-order NLO studies using the Z-scan method showed that the HelFe sample does not show NLO refractive properties, but is the only supramolecular complex of this group showing absorption properties, namely NLO saturable absorption, the effect of which increases with dilution of the solution. The remaining HelCo, HelNi and HelZn complexes are characterized by a self-focusing effect, where the most enhanced effect was again observed for the HelNi sample, however slightly different from the other samples. Furthermore, quantum chemical calculations were simulated to understand the NLO effects in these supramolecular complexes based on triple stranded helicates. The theoretically evaluated energy gap of the compounds showed the high rate of electron transfer from the ground to the excited state. However, a significant reduction in the energy gap in the molecule investigated compounds causes a large increase in third-order nonlinear properties. The interligand π→π* transmetallic charge-transfer (ITCT) supports noncentrosymmetric charge density distribution resulting in the molecules possessing second-order NLO properties. Moreover, the calculated theoretical values of secondand third-order hyperpolarizabilities were found to be in good agreement with the experimental response. Moreover, obtained results give proof of using supramolecular assemblies in nonlinear optics and modification of their nature will be interesting for NLO studies. Those unique NLO properties place supramolecular triple stranded helicates as one of the most promising candidates for applications based on nonlinear optics for instance as data storage materials.

Recently, a significant increase in research on metal-ligand organic coordination complexes has been noticed. This work focuses on the study of nonlinear optics in topologically nontrivial structures of two types of modified pyrene-based supramolecular complexes: trefoil knot and [2]catenane, also containing zinc or cadmium cations. Absorption studies showed a strong correlation for third-order NLO studies, however with longer wavelengths the samples were optically transparent emitting blue or green light, which had no direct impact on the generated From the above-described three types of supramolecular compounds with unique properties, one of the most interesting complexes was selected from every group, creating a metamaterial, and second-order nonlinear properties were investigated. The metamaterials studied are nanocomposites consisting of a selected supramolecular compound placed in the nanopores of the Al2O3 membrane. Each of these complexes was introduced to nanopores in the form of a solution with subsequent evaporation of the solvent: PtOEP with a concentration of 0. poling method, because the orientation of dipole moments is already arranged in nanopores.

Another quite important observation was the fact that the SHG signal, compared to thin films, is strongly enhanced and comes only from supramolecules. There is no loss in the NLO response, as is the case with thin film guest-host systems, when losses occur through the use of a polymer matrix (e.g. PMMA) where the concentration of studied material to polymer is typically 5-20%. Moreover, the obtained SHG response strongly depended on the applied laser light polarization. These unique properties of nanocomposites composed of supramolecular complexes and nanoporous membranes place them in potential applications in nonlinear optics and nanophotonics devices, including modulators. Moreover, another perspective of this research is to create a computational model of NLO parameters, such as nonlinear susceptibility, for samples consisting of a nanoporous membrane and the investigated material. Abstract : Due to extraordinary physicochemical properties of the -conjugated supramolecular assemblies in general and the metallosupramolecular architectures in particular are good candidates for nonlinear optical applications. The present work presents original studies of linear (including UVvisible absorption and photoluminescence) on three selected specific groups of metallosupramolecular complexes, as well as their potential nonlinear optical applications. Therefore, nonlinear optical properties of -conjugated metallohelicates, knots and metalloporphyrins nonlinear have been investigated. The second and third harmonic generation are provided on the basis of the well-known Maker fringe method, as well as the intensities of SHG and THG versus laser energy are examined. Furthermore, the enhanced NLO absorption and refraction responses are obtained by means of Z-scan technique.

The investigated compounds of metalloporphyrines, similarly to triple stranded helicates and modified pyrene-based molecular knots, are characterized by large enhanced nonlinear effect both during the studies with the Maker fringe technique and with the Z-scan technique. The observed NLO properties, mainly depend on the used metal cation in these metallosupramolecular architectures. Moreover, in this work we studied the influence of the incorporation of the best NLO supramolecular complexes (investigated in this thesis) in innovative nanoporous membranes on the generation of the second harmonic (SHG). Thus, metalloporphyrins, triple stranded metallohelicates and the modified pyrene-based knots were introduced into nanopores of the Al2O3 membranes. The first obtained results are very promising in terms of applications in the field of nanophotonics.