Keywords: Direct laser writing, femtosecond laser, silver containing glasses, silver clusters, waveguides, new type of refractive index

chute de transmission de 80% (7dB) pour une longueur d'interaction de 5 mm est fabriqué dans un bloc de verre de 1 cm contenant de l'argent. Ces résultats sont prometteurs pour toute application de détection de surface à partir de verres à l'argent dont l'indice de réfraction peut dès lors être ajusté en amont, en vue de la gamme réfractive visée.

Résumé

L'interaction laser-matière a intéressé la communauté scientifique depuis la découverte du laser dans les années 1960. La recherche et le développement au cours des dernières années ont conduit à un nombre quasiment illimité d'applications industrielles et médicales basées sur le laser. Nettoyage laser, découpe, marquage, chirurgie des yeux au laser, ablation de tumeurs cancéreuses, imagerie médicale, le laser offre un outil polyvalent et non remplaçable dans les domaines industriels et médicaux. Plus spécifiquement, l'interaction laser-verre a été largement étudiée au cours des deux dernières décennies. Le processus de focalisation des lasers femtosecondes à l'intérieur des verres, afin de modifier leurs propriétés physico-chimiques, est appelé inscription laser directe. La technique d'inscription laser directe permet une structuration tri-dimensionnelle (3D) directe et rapide du verre, rendant possible la création de composants optiques 3D intégrés dans des matériaux transparents. Cette nouvelle technique présente de nombreux avantages par rapport à la lithographie, technique traditionnellement utilisée pour la création des composants optiques. La lithographie se limite à la structuration bidimensionnelle (2D) des matériaux et nécessite de nombreuses étapes, ce qui rend l'inscription laser directe hautement compatible pour le transfert de procédés de fabrication industrielle. De nombreuses applications pourraient être basées sur la technique d'inscription laser directe, telles que la création de capteurs miniaturisés et/ou de composants photoniques dans des puces de verre. En effet, par exemple, la technique d'inscription laser directe dans les verres a conduit à la création de Modular Photonics, une entreprise basée en Australie qui vend des micro-puces à base de verre manufacturées par la technique d'inscription laser directe pour des applications de sélection de mode, plus spécifiquement pour des besoins astronomiques. Toutefois, il reste pertinent de mener une recherche permettant de développer la compréhension et la maitrise de nouveaux processus lors de l'interaction laser-matière, ce qui constitue le fondement de cette thèse.

Cette thèse a ainsi été réalisée grâce à une collaboration entre l'Université de Bordeaux (France) et l'Université Laval à Québec (Canada), dans le cadre du Laboratoire International Appliqué (LIA) LUMAQ (Lumière Matière Aquitaine Québec). Plus précisément, elle a été réalisée entre trois laboratoires, le Centre des lasers intenses et ses applications (CELIA) et l'Institut de chimie de la matière condensée de Bordeaux (ICMCB) de l'Université de Bordeaux et le Centre d'Optique, Photonique et Laser (COPL) à l'Université Laval, Québec, Canada. Elle consistait à consacrer près de la moitié du temps de la thèse dans chaque iii université tout en travaillant sur le même projet, qui est la continuité des recherches menées dans le groupe « Short Pulse Lasers : Applications et Matériaux » (SLAM) de Lionel Canioni et le groupe « Chimie et Photonique des Matériaux Oxyde de Fluorescence », sous la direction de Thierry Cardinal à l'ICMCB. Les recherches précédentes étaient basées sur l'optimisation et la maîtrise de la synthèse des verres oxydes à base de phosphate de zinc contenant de l'argent, ainsi que sur la recherche et la compréhension des différents processus exotiques de l'interaction laser-verre après l'inscription laser directe. Ces recherches ont abouti à la création de l'entreprise « Argolight », une spin-off spécialisée dans la vente de lames de verre structurées au laser permettant l'étalonnage de fluorescence des microscopes. En outre, la NASA a utilisé un des produits Les travaux antérieurs du groupe sur les verres de phosphate de zinc contenant de l'argent ont permis d'une part de formuler et développer des verres innovants de qualité optique, et d'autre part d'induire par laser un riche éventail de propriétés induites par irradiation laser femtoseconde. En effet, de tels verres phosphate à l'argent sont des verres spéciaux et exotiques, en comparaison aux verres standards généralement utilisés par la communauté scientifique ou l'industrie manufacturière laser, pour réaliser l'inscription laser directe. L'incorporation d'ions d'argent à l'intérieur de la matrice de verre permet des réponses exotiques du verre après l'inscription laser directe, telles que : la création de très forts contrastes de fluorescence à partir de la synthèse de nouvelles espèces moléculaires de type agrégats ; l'exaltation localisée en 3D des propriétés optiques non linéaires de génération de troisième harmonique et aussi la création directe et pionnière de génération de second harmonique effective ; la fabrication localisée d'un milieu effectif verre/métal suite à la précipitation de nanoparticules métalliques d'argent à réponse plasmonique de surface. Dans ce contexte, ce projet de thèse ambitionne d'aller au-delà des avancées obtenues sur la création locale de propriétés optiques, en visant la création de nouvelles propriétés, et surtout le développement de fonctionnalités optiques. Ainsi, ce projet de thèse porte sur la création et la fonctionnalisation de nouveaux types de guides et composants optiques basés sur la photochimie de l'argent activée par irradiation laser. En particulier, le projet prévoit de créer de nouveaux types de guides d'ondes ainsi que des composants optiques intégrés, dont les propriétés ne sont pas accessibles à partir des verres standards.

Ce manuscrit de thèse est divisé en quatre chapitres. Le premier chapitre parle du fond du verre, du laser et de l'interaction laser-verre en général tandis que le deuxième chapitre concerne plus spécifiquement l'écriture laser directe dans les verres à l'argent qui présente une réponse originale. -------------------------------------------------------- ---------------------------------------------------------------------- ------------------------------------------------------------------------- More specifically, the first chapter of the project consists in introducing the glass and laser and presenting their history. The main laser-glass interaction processes are also explained in this chapter.

The second chapter is the main part of this manuscript. It takes into account the different types of modifications induced in glasses following DLW as well as a review of some previous works. Then, silver containing zinc phosphate glasses are introduced as well as the exotic laser-glass interaction they produce. Finally, the design, fabrication and characterization of optical components are presented in this chapter.

The third chapter consists of a comparison between the standard type I modification and the new type A modification reported in this manuscript. The comparison takes into consideration the morphology, the refractive index changes and the near-field guided mode profile.

The fourth and last chapter consists in introducing the writing of near-surface waveguides that do not require any additional process as well as a presentation of a pioneer refractive index sensor exhibiting the advantages of type A modification. industrial tools, the study of the laser-matter process is prerequisite. The understanding of the effect of the laser on the matter and the physical-chemical phenomena that occur during this interaction is mandatory. Every material interacts with the laser irradiation in a specific way from the other. In this chapter, we will start by presenting glass material used in this work by walking through its history, the definition, the fabrication process and some other properties while the second part will introduce the history of the laser and its functionality.

Finally, the last part highlights the interaction between femtosecond lasers and glasses. This interaction highly depends on the type of laser used as well as on the glass properties. The different physical phenomena that occur following the interaction of femtosecond lasers with glasses will be presented in detail in order to understand the core of the laser-glass interaction.

I.2. Glass I.2.1. Glass history

The oldest records of glass making are some clay tables dating from around 650 BC. They were not completely understandable as no dictionaries exist explaining the technical terms used back then (inspired from [START_REF] Zarzycki | [END_REF]). However, the oldest Nowadays, many industrial glass companies exist such as Corning, Saint-Gobain, Pilinkgton, Asahi Glass Co, etc. and they master the art of glass making.

documented

I.2.2. Definition of glass

Many definitions have been proposed by scientists over the last two decades. In 1990, Elliot suggests that glasses are materials that do not present a long distance of atom periodicity like crystals and are an amorphous solid exhibiting a glass transition [START_REF] Elliot | Physics of amorphous materials[END_REF] . Zarzycki said that a glass is a non-crystalline solid exhibiting the phenomena of glass transition [START_REF] Zarzycki | [END_REF]. The glass is a solid presenting a structure of a liquid, non-crystalline solid or simply amorphous solid taking into consideration the atom disorder based on X-ray diffraction [3]. Finally, Shelby in 1997 said that the glass is an amorphous solid with the absence of atomic order at long distance while exhibiting a glass transition zone. Every material, inorganic, organic or metal formed by any technique presenting a glass transition is a glass [4]. So eventually, we can describe the glass as a super cooled liquid in a metastable condition

I.2.2.b. Thermodynamic aspect

Is the glass transition a phase transition? In order to answer this question, we will look into the thermodynamic aspects of the glass formation and the Kauzmann paradox [START_REF] Zarzycki | [END_REF]. But first let us introduce the entropy notion. The entropy (S) defines the disorder in the system. For instance, as mentioned before in section I.2.2, the crystal exhibits an organized atomic structure on a large scale, therefore the disorder is minimum implying a low entropy. However, for the glass, the atomic disorder is much greater, therefore we have a higher entropy than the crystal.

Let's consider again a hot liquid being cooled down to form a glass or a crystal.

Kauzmann in 1948, noted that the configuration entropy of an equilibrium liquid decreases as a function of the temperature that if extrapolated below the temperature TK, it would fall below the crystal entropy (Figure I.3). That was not acceptable given that it does not fit with the third law of thermodynamics which states that the entropy of a crystal must be null at a temperature of 0K (S=0 → T=0K). This disturbing phenomenon is stopped by a coincidental intervention of the kinetic phenomenon, the glass transition. The entropy freezes at a characteristic value of the equilibrium liquid at Tg as shown in Figure I.3. Moreover, the interval between Tk and Tg is generally quite small. The glass exhibits an entropy at 0K which is not the case for the crystal (Figure I.3). This is the Kauzmann paradox.

Grest and Cohen in 1981 tried to explain the glass transition as a first order phase transition [START_REF] Grest | Liquids, Glasses, and the Glass Transition: A Free-Volume Approach[END_REF], Gibbs and Dimarzio in 1958 suggested a second order phase transition [7] when Stillinger in 1988 proposed that no phase transition was happening [START_REF] Stillinger | Supercooled liquids, glass transitions, and the Kauzmann paradox[END_REF]. Eventually, Stillinger was right. The glass transition is not a phase transition at all. It does not fulfil the Ehrenfest criteria for first or second order phase transition [START_REF] Messaddeq | The glass transition temperature versus the fictive temperature[END_REF], contrary to the crystal where the cooling process of a liquid to form a crystal is considered as a phase transition from liquid to solid state.

Figure I.3

The configurational entropy as a function of the temperature of the cooling process of an equilibrium liquid. The glass transition freezes the entropy and avoids a thermodynamic catastrophe. This is known as the Kauzmann paradox. Taken from [START_REF] Zarzycki | [END_REF] Given that the glass transition is characterized by a change in the heat capacity ∆Cp, it could be experimentally detected using the Differential Scanning Calorimetry

I.2.3. Glass formation

After chemistry and physical chemistry were developed over the years, scientists started proposing criteria and formulas about glass formation instead of recipes based on tasting their powders to form glass. More specifically, in 1926 scientists proposed criteria for glass formation that may be applicable in some cases. This subject will not be discussed in detail in this manuscript. If readers are interested in this part, they may refer to the following readings [START_REF] Zachariasen | THE ATOMIC ARRANGEMENT IN GLASS[END_REF][START_REF] Goldschmidt | Die Gesetze der Krystallochemie[END_REF][START_REF] Smekal | Mechanische Messung chemischer Bindefestigkeiten[END_REF][START_REF] Sun | FUNDAMENTAL CONDITION OF GLASS FORMATION*[END_REF][START_REF] Shelby | Introduction to Glass Science and Technology[END_REF].

We will be interested only in oxide glasses since the glasses used in this work are oxide ones. In order to form a glass, scientists have classified the oxide glasses in three categories. Glass formers, modifiers and intermediates [START_REF] Zachariasen | THE ATOMIC ARRANGEMENT IN GLASS[END_REF][START_REF] Sun | FUNDAMENTAL CONDITION OF GLASS FORMATION*[END_REF]. The optical proprieties of a glass depend on the elements forming this glass, in other words the cations and ions used to form the glass. The optical transparency for glasses is directly linked to the absorption of the glass for different wavelengths (this part inspired by [START_REF] Zarzycki | [END_REF]). Let's consider an incident light passing through a bulk glass. A quantity of light will be reflected, scattered, absorbed and the rest will be we can express the absorption coefficient as:

Glassformers
𝛼=- 1 𝑙 ln ( 𝐼 𝐼 0 ) (I-2)
Based on the transmission of the glass, the absorption coefficient could be calculated using (I-2). It is recommended to represent the absorption of the glass using the absorption coefficient in cm -1 or dB/cm and not the transmission percentage. This gives more quantitative data about the transmission of the glass. The reflected light of one facet of a glass is known as the Fresnel reflection. The percentage of reflected light depends on the refractive index change of the material. For example, silver containing zinc phosphate glass used in this work with a refractive index change of n~1.6, Fresnel reflection is calculated to be around 5% using the following formula:

𝑅 = ( 𝑛 1 -𝑛 2 𝑛 1 +𝑛 2 ) 2 (I-3)
where 𝑛 2 in this case is the glass refractive index and 𝑛 1 is equal to 1 which is the refractive index of the air.

As mentioned before, the transparency window of the glass depends on its composition and the choice of glass network former and modifier molecules.

Generally, standard oxide glasses exhibit a high transmission in the visible range and NIR but high absorption in the UV (Figure I.6). However, other type of glasses can exhibit a high transmission in the Infrared (IR) region and low transmission in the VIS such as chalcogenide [START_REF] Savage | Chalcogenide glasses transmitting in the infrared between 1 and 20 μ -a state of the art review[END_REF]. Generally, the absorption in the UV range is linked to electronic transitions due to the absorption of an electron in the valence band to be promoted in the conduction band. However, the absorption in the IR is linked to the molecular vibrations at this wavelength and the phonon energy [START_REF] Messaddeq | The glass transition temperature versus the fictive temperature[END_REF].

I.2.4. Glass making

Making glasses could be performed by many techniques. It could be formed from plasma (evaporation), from liquid (quenching technique, sol-gel) or from solids (decomposition) [START_REF] Messaddeq | The glass transition temperature versus the fictive temperature[END_REF]. In this framework, we will be interested in the melt-quenching technique which is used to form the glass. Two methods of melt-quenching techniques exist. The first one is the float glass which is an industrial technique used for the creation of large quantities of glass (which is not going to be presented herein) and the lab technique which is more of a "homemade" technique.

I.2.4.a. Lab technique

The lab technique used at ICMCB to make silver containing glasses is the melt- When rapidly quenching the liquid, the atoms do not have time to get into order and crystalize. One should note that the quenching method is performed manually; therefore the cooling process of the glass is not the same. It differs from one batch to another, from person to person. Eventually, one should note that the glass properties may differ from one glass batch to another. Afterwards, the glass is annealed at 40 °C below the glass transition Tg for at least 4h to relax the accumulated mechanical constraints. Finally, after the annealing process the glass is removed from the furnace and allowed to rest at room temperature waiting to be cut and polished.

I.2.5. Introduction to fiber optics

The previous part consisted in talking about the fabrication of bulk glasses. In this part, we will introduce fiberoptics. Bulk glasses can be shaped into fibers forming a thin glass wire that we call an optical fiber where light can propagate inside based on Total Internal Reflection (TIR). Optical fiber is generally formed in a cylindrical shape and made with low loss material such as fused silica glass. It has a centre core in which light is guided because of TIR, and is embedded in an outer cladding of slightly lower refractive index as shown in Figure I.8. Fiberoptics is responsible for most of our communication systems and internet. Thousands of kilometers of optical fiber exist underwater in the world in order to connect the world together using the internet. Optical fiber exhibits many advantages for light/information transportation. It exhibits lower signal attenuation and higher band pass compared to electric wires. This waveguiding process in fiber optics will be discussed furthermore in Chapter II at section II.3.1.a as well as the DLW process in ribbon shaped silver containing fibers in section II.6.5. In the 1960s, the laser was invented and characterized as a solution in search of a problem [17]. Scientists did not imagine the range of applications they could have access to using a laser. Nowadays lasers are everywhere. In our daily life, we use products that are related to the laser. Recently in 2016, a laser interferometry system was used to detect gravitational waves and the first observation ever of a binary black hole merger [START_REF] Abbott | Observation of Gravitational Waves from a Binary Black Hole Merger[END_REF]. In short, laser applications in the medical and industrial fields are somewhat unlimited. Research is extending the boundaries of potential applications.

Specifically for this project, the laser is used for writing photonic components inside glasses.

We can clearly see that the invention of the laser was a great achievement during the twentieth century (inspired by [17]). It all started with the discovery of the process of stimulated emission in which a beam of radiation passing through a gain medium can generate identical photons to those of the incident beam as reported by Albert Einstein in 1917. The first amplification based on the simulated emission was not achieved till 1954 by the research team of Charles Townes at Columbia University [START_REF] Gordon | Molecular Microwave Oscillator and New Hyperfine Structure in the Microwave Spectrum of N${\mathrm{H}}_{3}[END_REF]. They managed to build a microwave amplifier based on stimulated emission radiation that they called "maser". That was the beginning of the laser.

The "maser" was developed into an "optical maser" operating in the visible (Vis)

and infra-red (IR) regions in 1958 [START_REF] Schawlow | Infrared and Optical Masers[END_REF] by the same research group. Then, the race was on to demonstrate a working laser and Theodor Maiman of Hughes Laboratories won it in May 1960 [START_REF] Maiman | Stimulated Optical Emission in Fluorescent Solids. I. Theoretical Considerations[END_REF]. He managed to get a pulsed laser emitting in the red wavelength out of a ruby crystal pumped by a flash-tube. Later on, in 1961 a continuous gas laser was demonstrated by Bell Labs by Javan, Bennet and Herriott. That laser operated in the near infra-red (NIR) wavelength at 1.15µm [START_REF] Javan | Population Inversion and Continuous Optical Maser Oscillation in a Gas Discharge Containing a He-Ne Mixture[END_REF]. Following these two discoveries, the number of lasers increased significantly.

Many types of lasers were created operating at different wavelengths, different powers, different mode regimes. Currently, a huge number of lasers exist, going from solid state [START_REF] Maiman | Stimulated Optical Emission in Fluorescent Solids. I. Theoretical Considerations[END_REF], dye [START_REF] Littman | Spectrally narrow pulsed dye laser without beam expander[END_REF], semi-conductor [START_REF] Hall | Coherent Light Emission From GaAs Junctions[END_REF], gas [START_REF] Heard | Ultra-violet Gas Laser at Room Temperature[END_REF], fibre [START_REF] Fortin | Fluoride glass Raman fiber laser at 2185 nm[END_REF] , freeelectron [START_REF] Emma | First lasing and operation of an ångstrom-wavelength freeelectron laser[END_REF] to X-ray lasers [START_REF] Rocca | Demonstration of a Discharge Pumped Table-Top Soft-X-Ray Laser[END_REF] that can operate in continuous and pulsed modes. Generally, the laser is characterized by its wavelength emission, average power, operating mode (continuous or pulsed), repetition rate and pulse duration (in case of pulsed laser). A continuous laser could be transformed into a pulsed one using two techniques: Q-Switching (using saturable absorbers, electric-optic shutters,…)

allowing pulses in the nanosecond range or Mode locking (using SESAMs, acoustooptic switches, …) allowing shorter laser pulses in the pico to femtosecond range [START_REF] Svelto | Principles of Lasers[END_REF]. As shown in Figure I.9, in order to have a femtosecond laser, the insertion of a Mode locking device is a must as well as compensating for the cavity dispersion due to the presence of a large band active medium. For more information and details the reader is referred to the following reference [START_REF] Svelto | Principles of Lasers[END_REF]. Then, to have higher laser energies that are sufficient for applications demanding it such as direct laser writing, the laser presented in During this project, the lasers used for direct laser writing are mode locked lasers.

The wavelength emission is determined by the gain medium i.e. the atomic/molecular transitions between the atomic levels. Lasers could operate in wavelengths going from X-ray [START_REF] Rocca | Demonstration of a Discharge Pumped Table-Top Soft-X-Ray Laser[END_REF] to the IR regions [START_REF] Bernier | 3.77 mum fiber laser based on cascaded Raman gain in a chalcogenide glass fiber[END_REF].

Maxwell's wave equations, predicting the propagation of transversely oscillating electromagnetic waves, were the first indication of the true nature of light.

Therefore, laser light propagation is defined by the Maxwell Equations published in 1864 (inspired from [START_REF] Silfvast | Laser Fundamentals[END_REF] ). Considering the use of lasers in this project, the equations herein represent the propagation of light in a dielectric medium, in this case glasses.

∇. E = -1 ϵ 0 ∇. P (I-4)

∇. H = 0

(I-5) ∇ × H = 𝜀 0 𝑑𝐸 𝑑𝑡 + 𝑑𝑃 𝑑𝑡 + 𝐽 (I-6) ∇ × E = -𝜇 0 𝑑𝐻 𝑑𝑡 (I-7)
Using the Maxwell equations above, the general wave equation of the electric field 𝐸 could be obtained:

∇ × (∇ × E) + 1 𝑐 2 𝑑 2 𝐸 𝑑𝑡 2 = -𝜇 0 𝑑 2 𝑃 𝑑𝑡 2 -𝜇 0 𝑑𝐽 𝑑𝑡 (I-8)
where P is the polarization J current density H vector quantity of the magnetic flux 𝜀 0 permittivity in the vacuum 𝜇 0 permeability of the vacuum

The right side of the equation is called the source terms. The first term is related to the polarization changes while the second term is related to the conduction charges that are applicable in metallic materials. Given that in this work we are using glasses, the second term will not be taken into consideration; therefore the general wave equation becomes:

∇ × (∇ × E) + 1 𝑐 2 𝑑 2 𝐸 𝑑𝑡 2 = -𝜇 0 𝑑 2 𝑃 𝑑𝑡 2
(I-9)

I.3.2. Gaussian beam

As mentioned before, the laser amplification process occurs generally inside the laser cavity between two mirrors. The propagation of light back and forth between the two mirrors implies a Gaussian intensity profile for the propagating mode in the cavity which is the TEM00 (without getting into details). The mode maintains the same shape everywhere inside the laser cavity (between the two mirrors) and beyond the cavity (output of the laser) unless an optical element is introduced that distorts or changes the Gaussian profile. Generally, most of the output laser modes are TEM00 Gaussian modes which is the case also in this work.

Let's now consider a Gaussian beam propagating along the z-axis as shown in Where w0 is the beam waist,  is the wavelength of the beam and z the position along the propagating z axis.

Following propagation, the width of the Gaussian beam decreases (R<0) until it reaches its minimum waist size w0 (z=0) at the wave front curvature R= (Figure I.12). Afterwards, the beam expands and diverges (R>0) as a cone of half-angle θ 0 .

The beam is considered to be parallel to the propagation axis on a length of 2zr that is called depth of focus or the confocal parameter (Figure I.12) corresponding to the double of the Rayleigh length. One should note that the tighter we focus the beam the faster it diverges. We can conclude that the major beam intensity is restrained in a voxel corresponding more or less to the depth of focus of the beam.

Therefore, the morphology of the interaction zone is dictated by the laser's Gaussian shape. Generally, the laser beam quality is defined by the factor M 2 ≥1. In this work, the laser beams exhibit a quality factor M 2 ~1.1. The beam quality factor M 2 defines the beam illumination pattern as well as the laser propagation and transformation properties. It also indicates how the laser output beam is close to the fundamental Gaussian beam mode. The larger the value of M 2 the lower the beam quality is. For more information about the M 2 the reader is referred to the following references [START_REF] Svelto | Principles of Lasers[END_REF][START_REF] Bhowmik | measuring, and optimizing laser beam quality<[END_REF]. However, in some experiments cylindrical lenses were installed in order to change the beam shape at the focus plane i.e. change the morphology of the modified region. This part will be more detailed in section III.3.2.b. Also, beam shaping is possible using a Spatial Light Modulator (SLM) which is not used during this work for beam shaping.

I.3.3. Laser-material interaction

Laser-matter interaction could be realized using a CW or a pulsed laser. In this framework, it is realized using pulsed femtosecond lasers. In dielectric materials such as glasses, a non-linear absorption process is present when the light intensity is sufficient to generate one. Femtosecond lasers provide a high intensity of light in a short time which triggers the non-linear effects. The photons are absorbed by the atoms forming the glass matrix and then, if the energy is sufficient, the electrons are able to pass from the valence band to the conduction band. Therefore we have photoionization. More specifically, the electrons gain enough kinetic energy to move freely in the glass matrix. The process is shown in Figure I.13 for dielectric materials. The energy absorbed by the electrons should be higher than the band gap Eg between the valence and the conduction band. In dielectric materials, the Eg is generally higher than the energy of one photon; therefore, in order for the electrons to pass to the conduction band, the non-linear absorption process is a must. Moreover, the non-linear absorption process confines the deposited energy in a 3D interaction voxel allowing the creation of sub-micrometre structures [START_REF] Royon | Femtosecond laser induced photochemistry in materials tailored with photosensitive agents[END_REF]. Inspired from [START_REF] Chris | Laser-induced breakdown and damage in bulk transparent materials induced by tightly focused femtosecond laser pulses[END_REF][START_REF] Bérubé | Étude des changement structuraux photo-induits dans le verre à l'aide des imulstions femtosecondes et application à l'inscription de composants photoniques[END_REF].

Multi-Photon Ionization (MPI) refers to the absorption process of the energy of two

or more photons by an electron in the valence band to pass to the conduction band.

This photoionization rate highly depends on laser intensity. The multiphoton ionization rate is given by [START_REF] Chris | Laser-induced breakdown and damage in bulk transparent materials induced by tightly focused femtosecond laser pulses[END_REF][START_REF] Stuart | Laser-induced damage in dielectrics with nanosecond to subpicosecond pulses[END_REF][START_REF] Lenzner | Femtosecond Optical Breakdown in Dielectrics[END_REF]:

𝑃(𝐼) = 𝜎 𝑘 𝐼 𝑘 (I-16)
where 𝜎 𝑘 is the multiphoton absorption coefficient for absorption of k photons and I is the laser intensity. In order to have photoionization, a minimum number k of photons is required to satisfy the relation 𝑘ℎ ̅ 𝑤𝐸 𝑔 . Therefore, the total energy absorbed is related to the number of photons. In the case of silver containing zinc phosphate glasses that are used in this work, the band gap is between 4.5 eV and 4.8 eV depending on the concentration of silver ions inside the glass [START_REF] Bourhis | Photostructuration par laser infrarouge femtoseconde de verres photosensible de phosphate de zinc, d'argent et de gallium[END_REF]. When using a 1030 nm laser which exhibits a photon energy of 1.2 eV, a four-photon absorption process is required in order to achieve ionization.

Tunneling ionization refers to an electron passing through a short barrier and becoming free. The electric field generated by the laser intensity eliminates the Coulomb potential wells that bind a valence electron to its atom. When the field is very strong, the Coulomb potential well is eliminated and the electron passes through the short barrier and becomes free [START_REF] Stuart | Laser-induced damage in dielectrics with nanosecond to subpicosecond pulses[END_REF] as shown in Figure I.14.a This type of nonlinear process prevails for strong laser fields and low laser frequency (high ). However, it could simultaneously occur with the Multi-Photon Ionization process in other cases. Keldysh proposed a parameter to express the transition between the two processes known as the Keldysh parameter [START_REF]Concerning the theory impact ionization in semiconductors[END_REF]:

𝛾 = 𝑤 𝑒 [ 𝑚𝑐𝑛𝜀 0 𝐸 𝑔 𝐼 ] 1/2 (I-17)
where w is the laser frequency, c velocity of light, n refractive index change of the medium, 𝜀 0 permittivity in the vacuum, Eg band gap, m and e reduced mass and charge of the electron and I the laser intensity. When the Keldysh parameter is higher than 1 (>1), the MPI dominates the process while when it is lower (<1), the tunneling ionization dominates. However, when it is around 1 (~1), the intermediate regime [START_REF] Stuart | Nanosecond-to-femtosecond laser-induced breakdown in dielectrics[END_REF], we have a mix of both MPI and tunneling ionizations. In our framework,  is estimated to be higher than 1 (~1.3) which puts us in the MPI process regime.

Avalanche ionization refers to a two-step process. A free electron in the conduction band absorbs photons until its energy exceeds the Eg of the material. An electron with higher energy than the band gap E>Eg can collide and excite another electron in the valence band to the conduction band as shown in Figure I.14.b. This process will continue as long as the pulse is increasing the number of free electrons in the focal volume [START_REF] Stuart | Laser-induced damage in dielectrics with nanosecond to subpicosecond pulses[END_REF].

▪ Plasma generation

The three previously mentioned non-linear effects contribute to ionize the material resulting in the creation of high density electronic plasma in the vicinity of the focal volume. This is due to the high density of electrons generated. The electron density distribution could be described by the following equation [START_REF] Bérubé | Étude des changement structuraux photo-induits dans le verre à l'aide des imulstions femtosecondes et application à l'inscription de composants photoniques[END_REF]:

𝑑𝑛 𝑒 𝑑𝑡 = 𝑊 𝑃𝐼 + 𝛼 𝐶 𝐼𝑛 𝑒 (1 + ∑ 𝛽 𝑗 𝐼 𝑗 𝑘-1 𝑗=1 ) (I-18)
where 𝛼 𝐶 is the avalanche ionization coefficient, 𝑛 𝑒 electron density and 𝛽 𝑗 the cold avalanche which was not introduced in this manuscript. If readers are interested in further details, they are referred to [START_REF] Gaier | Hole-assisted energy deposition in dielectrics and clusters in the multiphoton regime[END_REF][START_REF]Femtosecond laser-matter interactions[END_REF][START_REF] Chichkov | Femtosecond, picosecond and nanosecond laser ablation of solids[END_REF] . The first term of the left part of the equation indicates the contribution of the photo-ionization process while the second term is linked to the avalanche ionization effect. The creation of plasma could be linked to both processes or only to photo-ionization [START_REF] Couairon | Filamentation and damage in fused silica induced by tightly focused femtosecond laser pulses[END_REF]. The morphology and the type of modifications in the material following laser-matter interaction are directly linked to the electron density distribution in the plasma. In fact, the threshold of modification is associated to a certain value of the electron density and the

I.3.4. Effects of laser parameters

Laser-matter interaction is a two-way process. The interaction response depends on the matter used i.e. glass, metals, soft tissues, etc. as well as the laser parameters.

In this framework, we are working on glasses, changing one laser parameter could sometimes make a lot of difference as we are going to see in this part.

▪ Wavelength:

The laser wavelength is an important parameter in laser-glass interaction. If the glass exhibits a band gap in the UV, in order to have a non-linear process, a green laser for instance or Infra-Red (IR) laser must be used. However, a laser operating in the UV could be used but the interaction with the glass will be a linear one.

Therefore, the non-linear processes are not present. Moreover, the wavelength used can define the number of photons absorbed to defy the glass band gap. For the same glass, using different wavelengths can generate two-photon absorption or four-photon absorption for example. If a glass exhibiting a band gap of 4.6 eV when irradiated using a 1030 nm laser, a four-photon absorption process occurs; however using a 515 nm implies a two-photon absorption process. For instance, Hernandez-Rueda et al. investigated the influence of the laser wavelength on the written waveguides in fused silica [START_REF] Hernandez-Rueda | The influence of femtosecond laser wavelength on waveguide fabrication inside fused silica[END_REF] by using lasers from the UV to the IR range.

It was concluded that using shorter wavelengths leads to smaller written features, lower thresholds and narrower energy range for waveguide fabrication [START_REF] Hernandez-Rueda | The influence of femtosecond laser wavelength on waveguide fabrication inside fused silica[END_REF].

▪ Repetition rate, heat accumulation and laser writing regimes

As mentioned before, a laser can operate in continuous mode (CW) or in pulsed The number of pulses per second is determined by the laser repetition rate. For example if a laser is operating at 𝜏=250 kHz, it delivers 250 000 pulses per second.

During this work, femtosecond lasers are used exhibiting short pulses of hundreds of femtoseconds which is equivalent to 10 -15 s as we are going to see in the following chapters. accumulation effects with variable repetition rates. They also found that the radius of the structures produced increased as a function of the repetition rate i.e. number of pulses in borosilicate glass [START_REF] Eaton | Heat accumulation effects in femtosecond laser-written waveguides with variable repetition rate[END_REF]. What is more interesting in this work was the numerical model of cumulative heating that was proposed. A finite differential method was applied to laser conditions to investigate the physical processes [START_REF] Zhang | Heat accumulation during high repetition rate ultrafast laser interaction: Waveguide writing in borosilicate glass[END_REF].

The laser pulses were modeled as periodic heat sources appearing as delta functions in time since the electron heating and the electron-phonon coupling time (<1ps) is much shorter than the thermal diffusion time of the glass in this case (>0.1µs). The laser energy distribution was modeled as a spherical Gaussian mode:

𝐸(𝑟) = 𝐸 0 𝑒 (-𝑟 2 𝑤 0 2 ) ⁄ (I-19)
where r is the radial distance and w0 is the 1/e radius at the focused laser beam waist. And the model was based on the radial component of the 3-D heat diffusion equation that was solved numerically:

𝜕 𝜕𝑟 (𝑟 2 𝜕𝑇 𝜕𝑟 ) = 𝑟 2 𝐷 𝜕𝑇 𝜕𝑡 (I-20)
where T(r,t) is the temperature and D is the thermal diffusivity of the glass.

The results of the numerical model for different repetition rates are shown in Figure I. [START_REF] Abbott | Observation of Gravitational Waves from a Binary Black Hole Merger[END_REF]. The horizontal black dashed line presents the annealing temperature of the glass used. This is the temperature where the glass melts and starts sustaining modifications. Three repetition rates were taken into consideration, 100kHz, 500kHz and 1MHz [START_REF] Zhang | Heat accumulation during high repetition rate ultrafast laser interaction: Waveguide writing in borosilicate glass[END_REF]. For the 100kHz repetition rate, we can observe that the glass temperature is increasing roughly above the annealing temperature after receiving the first pulse. However, afterwards the temperature decreases well below the annealing temperature before the next pulse arrives. The glass has sufficient time to cool down before the next pulse. The time between two pulses is lower than the thermal diffusion of the glass 𝑇 < 𝐷. So on the one hand, we do not have a cumulative thermal effect or more specifically we have minimum heat accumulation.

On the other hand, for the 500kHz and 1MHz repetition rates, we clearly see that we have a cumulative effect of pulses i.e. cumulative thermal effect (heat accumulation). After the first pulse, the glass temperature increases above the annealing temperature and the second pulse arrives quickly so the glass does not have time to cool down and the temperature continues to build up. For the 1MHz, the thermal cumulative effect is more significant due to the fast repetition rate i.e.

shorter time intervals between two consecutive pulses, the glass has no time to cool down before the following pulse. The time between two pulses is higher than the thermal diffusion of the glass 𝑇 > 𝐷 which leads to thermal modification volumes much larger than the laser focus plane [START_REF] Eaton | Heat accumulation effects in femtosecond laser-written waveguides with variable repetition rate[END_REF][START_REF] Zhang | Heat accumulation during high repetition rate ultrafast laser interaction: Waveguide writing in borosilicate glass[END_REF].

▪ Polarisation:

Laser polarisation during laser-glass interaction could sometimes affect the results.

It has been reported by Stalmashonak et al. that reshaping metallic nanoparticles

(NPs) into non-spherical ones depends on laser polarisation [START_REF] Stalmashonak | Transformation of silver nanospheres embedded in glass to nanodisks using circularly polarized femtosecond pulses[END_REF]. The MPI was found to be significantly higher for a linear polarization compared to a circular one in fused silica and sapphire as reported by Temnov et al [START_REF] Temnov | Multiphoton ionization in dielectrics: comparison of circular and linear polarization[END_REF]. Moreover, the polarization was found to strongly affect the creation of nanogratings in glasses, in which the nanogratings are only formed with linear polarization [START_REF] Bhardwaj | Optically produced arrays of planar nanostructures inside fused silica[END_REF]. In the waveguides field, it has been reported by an Australian research team that using a circular polarisation increases the transmission i.e. deceases the propagation losses of photo-written waveguides [START_REF] Ams | Study of the influence of femtosecondlaser polarisation on direct writing ofwaveguides[END_REF].

▪ Numerical Aperture

The numerical aperture (NA) of the focusing objective determines the size of the beam at the focus plane, therefore determining the area of the irradiated zone. The beam waist at the focus plane for a NA<0.7 is given by:

𝑤 0 = 0.518 𝜆 0 𝑁𝐴 (I-21)
When for a high NA i.e. NA>0.7, it is given by: 𝑤 0 = 0.61 𝜆 0 𝑁𝐴

(I-22)
where 𝜆 0 is the wavelength in the free space and NA the numerical aperture of the focusing objective. So, one can conclude, that using a higher NA objective i.e.

focusing the beam tighter, leads to the creation of smaller structures and vice versa.

It was reported that increasing the NA of the focusing objective used drastically decreases the modification threshold in glasses [START_REF] Schaffer | Micromachining bulk glass by use of femtosecond laser pulses with nanojoule energy[END_REF][START_REF] Ashcom | Numerical aperture dependence of damage and supercontinuum generation from femtosecond laser pulses in bulk fused silica[END_REF] ))

(I-23)
where 𝑃 𝑎𝑣𝑔 is the laser average power after the objective, 𝑇 the time between two pulses, 𝑘 the Gaussian constant estimated to be 0.93 assuming that the pulse profile is a Gaussian one and not square, 𝑇 0 the pulse duration and 𝑤 0 the beam waist.

I.4. Conclusion

This chapter covers the theoretical approach of laser-glass interaction in general. It starts by introducing the glass and its characterizations, the laser and eventually the process of femtosecond laser-glass phenomena.

We first start by introducing the history of glass that dates back to 650 BC, then by defining the glass itself as well as the glass transition phase. Even though in the beginning of time, forming glasses was based on some recipes, nowadays the glass industry is a vast one and glass is considered as an easy product to make. The ease of making it, the optical window transparency in different wavelengths and the fact that it could be shaped into fibers makes the glass a very attractive platform for photonic and sensing applications.

Secondly, the laser is introduced and more specifically the laser-glass interaction process. It is based on a non-linear process that allows the interaction of a laser with a transparent substrate glass. The different timeline of physical processes was presented following laser-glass interaction as well as the plasma generation around the interaction voxel. We saw different glass responses for different laser parameters, which highlights the effect of laser parameters in the interaction process. Finally, we defined two inscription regimes based on the heat accumulation process that were classified as athermal and thermal regimes.

The broad points regarding glass, lasers and basic laser-glass interactions were covered allowing to tackle the main theme of this work where we will be introducing

II.2.1. Type I modification origins

For the direct laser writing of photonic components such as waveguides, one is usually interested in type I modification due to the smooth nature of the index change associated with this type. Therefore, in this manuscript we will be interested generally in type I modification. Over all, type I refractive index change (∆n) is associated to the formation of color centers [START_REF] Streltsov | Study of femtosecond-laser-written waveguides in glasses[END_REF][START_REF] Chan | Modification of the fused silica glass network associated with waveguide fabrication using femtosecond laser pulses[END_REF][START_REF] Little | Mechanism of femtosecond-laser induced refractive index change in phosphate glass under a low repetition-rate regime[END_REF] and/or the change in the glass density [START_REF] Schaffer | Bulk heating of transparent materials using a high-repetition-rate femtosecond laser[END_REF][START_REF] Chan | Structural changes in fused silica after exposure to focused femtosecond laser pulses[END_REF][START_REF] Dekker | Annealing dynamics of waveguide Bragg gratings: evidence of femtosecond laser induced colour centres[END_REF][START_REF] Zhao | Temperature dependence of femtosecond laser induced refractive index change in Nd3+-doped phosphate glass[END_REF]. Color centers result from a defect in the glass lattice implying the absence of an atom from the place it would normally occupy in the glass lattice. The electrons are trapped in such defects, which lends a certain absorption band and color to the material. Thus, laser irradiation could create enough color centers that the ∆n could be correlated to the Kramers-Kronig mechanism [START_REF] Streltsov | Study of femtosecond-laser-written waveguides in glasses[END_REF]. The formation of color centers has been observed in many glasses such as phosphate [START_REF] Little | Mechanism of femtosecond-laser induced refractive index change in phosphate glass under a low repetition-rate regime[END_REF] and borosilicate [START_REF] Little | Structural changes in BK7 glass upon exposure to femtosecond laser pulses[END_REF]. Some groups have suggested that the presence of color centers produces a metastable change in the polarizability associated with a change in the molar refraction of the material [START_REF] Abdel-Baki | Factors affecting optical dispersion in borate glass systems[END_REF]. The change in polarizability is caused by a variation in the concentration of ionic bonds that results from the capture of free electrons by defects in the network structure that occur during irradiation [START_REF] Messaddeq | Light-induced relief gratings and a mechanism of metastable light-induced expansion in chalcogenide glasses[END_REF]. This change in polarizability may induce a decrease [START_REF] Little | Mechanism of femtosecond-laser induced refractive index change in phosphate glass under a low repetition-rate regime[END_REF][START_REF] Messaddeq | Study of the photosensitivity of GeS binary glasses to 800nm femtosecond pulses[END_REF] or increase [START_REF] Couairon | Filamentation and damage in fused silica induced by tightly focused femtosecond laser pulses[END_REF] of the ∆n mainly on the material in which it is induced. Generally, color centers are not stable and they disappear after thermal annealing.

However, the change in the glass density is due to the local heating of the glass and restructuration during the cooling process following laser passage. In the laser focal spot, due to the absorption of the laser energy, the glass is heated to a temperature higher than Tg, therefore it melts [START_REF] Chan | Structural changes in fused silica after exposure to focused femtosecond laser pulses[END_REF] and following the laser passage, it cools down at a different speed and process from the initial nonirradiated glass resulting in a change in the density of the material creating a change of ∆n of the material. The ∆n created could be positive or negative based on the material irradiated [START_REF] Fletcher | Direct femtosecond laser waveguide writing inside zinc phosphate glass[END_REF]. Several groups have noticed that the magnitude of the index variation is related to the cooling rates of the material, which confirms the link between the index change and the thermal processes that occur during laser irradiation [START_REF] Streltsov | Study of femtosecond-laser-written waveguides in glasses[END_REF]. Moreover, the change in the glass density i.e. the photoinduced ∆n could also be related to the ion exchange following laser irradiation as observed by Kanehira et al. [START_REF] Kanehira | Ion exchange in glass using femtosecond laser irradiation[END_REF] and others [START_REF] Arriola | Low bend loss waveguides enable compact, efficient 3D photonic chips[END_REF]. Obviously, several parameters play an important role in the determination of the sign and the magnitude of the refractive index variation in the glass going from the laser parameters to the glass composition. This part will be more detailed in Chapter III II.3. State of the art:

II.3.1. Waveguides
Over the past two decades, many research groups created waveguides inside glasses using the direct laser technique since the first demonstration by Davis et al.

in 1996 [START_REF] Davis | Writing waveguides in glass with a femtosecond laser[END_REF]. The inscription of waveguides in glasses is the basic application that builds up for the creation of integrated optical circuits. Two different writing configurations are possible, longitudinal and transverse in which the sample is translated respectively along and perpendicularly to the beam propagation axis.

The longitudinal writing configuration [START_REF] Fletcher | Direct femtosecond laser waveguide writing inside zinc phosphate glass[END_REF] results in intrinsically symmetric, round waveguides and their size is determined by the focal spot of the laser beam.

However, their length is limited by the focal length of the focusing objective.

Furthermore, the transverse writing provides much more versatility and flexibility in creating complex 3D geometries. The disadvantage could be producing a strong asymmetry in the waveguide cross section resulting sometimes in elliptical waveguides. Certain methods were introduced to overcome this problem. Some research groups use a slit placed before the microscope objective [START_REF] Ams | Slit beam shaping method for femtosecond laser direct-write fabrication of symmetric waveguides in bulk glasses[END_REF]. Others use cylindrical telescope lenses [START_REF] Cerullo | Femtosecond micromachining of symmetric waveguides at 1.5 µm by astigmatic beam focusing[END_REF][START_REF] Bérubé | Femtosecond laser direct inscription of mid-IR transmitting waveguides in BGG glasses[END_REF] and some use a spatial light modulator (SLM) [START_REF] Salter | Adaptive slit beam shaping for direct laser written waveguides[END_REF] to reduce the asymmetry and create circular waveguides.

Waveguides were written in fused silica glasses [START_REF] Hernandez-Rueda | The influence of femtosecond laser wavelength on waveguide fabrication inside fused silica[END_REF][START_REF] Hirao | Writing waveguides and gratings in silica and related materials by a femtosecond laser[END_REF][START_REF] Shah | Waveguide writing in fused silica with a femtosecond fiber laser at 522 nm and 1 MHz repetition rate[END_REF], phosphate glasses [START_REF] Chan | Waveguide fabrication in phosphate glasses using femtosecond laser pulses[END_REF][START_REF] Fletcher | Direct femtosecond laser waveguide writing inside zinc phosphate glass[END_REF][START_REF] Little | Mechanism of femtosecond-laser induced refractive index change in phosphate glass under a low repetition-rate regime[END_REF], Borosilicate glasses [START_REF] Zhang | Heat accumulation during high repetition rate ultrafast laser interaction: Waveguide writing in borosilicate glass[END_REF][START_REF] Mauclair | Ultrafast laser writing of homogeneous longitudinal waveguides in glasses using dynamic wavefront correction[END_REF], fluoride glasses [START_REF] Bérubé | Femtosecond laser-induced refractive index modifications in fluoride glass[END_REF], chalcogenide glasses [START_REF] Mcmillen | Ultrafast laser fabrication of low-loss waveguides in chalcogenide glass with 0.65  dB/cm loss[END_REF][START_REF] Bérubé | Femtosecond laser direct inscription of surface skimming waveguides in bulk glass[END_REF] and other glasses as well. Depending on the glass transmission widows, waveguides operating from the visible [START_REF] Chan | Waveguide fabrication in phosphate glasses using femtosecond laser pulses[END_REF][START_REF] Fletcher | Direct femtosecond laser waveguide writing inside zinc phosphate glass[END_REF][START_REF] Bérubé | Femtosecond laser-induced refractive index modifications in fluoride glass[END_REF] to the IR [START_REF] Bérubé | Femtosecond laser direct inscription of mid-IR transmitting waveguides in BGG glasses[END_REF][START_REF] Nandi | Femtosecond laser written channel waveguides in tellurite glass[END_REF][START_REF] Osellame | Waveguide lasers in the C-band fabricated by laser inscription with a compact femtosecond oscillator[END_REF][START_REF] Ródenas | Three-dimensional mid-infrared photonic circuits in chalcogenide glass[END_REF] (up to 3.85 µm) region were written using direct laser writing. Moreover, low loss waveguides in the order of 0.1 dB/cm (Borosilicate glasses, Fused silica glasses and chalcogenide glasses) [START_REF] Zhang | Heat accumulation during high repetition rate ultrafast laser interaction: Waveguide writing in borosilicate glass[END_REF][START_REF] Will | Optical properties of waveguides fabricated in fused silica by femtosecond laser pulses[END_REF][START_REF] Tong | Optical loss measurements in femtosecond laser written waveguides in glass[END_REF] and even lower to 0.027dB/cm in Gorilla glass [START_REF] Lapointe | Making smart phones smarter with photonics[END_REF] were reported, paving the way for a bigger scale of material processing and optical/photonic circuits in needed cases as well as for industrial transfer. However, the lowest propagation losses of 0.027dB/cm [START_REF] Lapointe | Making smart phones smarter with photonics[END_REF] has not been reported/reproduced by any research team to date. One can say that the DLW losses could be comparable to silicon based ultra-low loss waveguides processed with lithography technique exhibiting losses of 0.0008dB/cm [START_REF] Lee | Ultra-low-loss optical delay line on a silicon chip[END_REF] and 0.026dB/cm [START_REF] Li | Ultralow-loss, high-density SOI optical waveguide routing for macrochip interconnects[END_REF] for example.

Finally, based on the creation of waveguides using DLW, many optical components were created like couplers, splitters, waveguide lasers etc. The following part will briefly discuss some of the significant work done over the past years based on waveguides written in glasses. But before, a small overview of the waveguiding theory is presented. The rays exhibiting a propagation angle 𝜃 smaller than the critical angle given  𝑐 ̅ by,

 𝑐 ̅ = 𝑐𝑜𝑠 -1 (𝑛 2 𝑛 1 )
⁄ could be guided inside the waveguide. The light propagates inside the waveguide as a form of a mode that could be determined using the selfconsistency condition. Modes are fields that maintain the same transverse spatial distribution and polarization all along the waveguide along the propagation axis.

Assuming that a monochromatic light is propagating inside a planar waveguide with an angle 𝜃 smaller than the critical angle  𝑐 ̅ , we impose the self-consistency condition that a wave reproduces while propagating to determine the propagating modes. In one round trip, the different optical path distance that occurs is given by: 𝐴𝐶 ̅̅̅̅ -𝐴𝐵 ̅̅̅̅ = 2𝑑𝑠𝑖𝑛𝜃 while 𝑑 is the waveguide width (Figure II.4). Every time the light bounces on the interface core-cladding a phase shift occurs presented by ∅ 𝑟 .

For self-consistency, the phase shift between two waves should be zero or a multiple of 2, therefore:

2𝜋 𝜆 2𝑑𝑠𝑖𝑛𝜃 -2∅ 𝑟 = 2𝜋𝑚 (II-1)
The reflection phase ∅ 𝑟 is as a function of the propagation angle 𝜃. It depends also on the polarization of the incident wave, TE (Transvers Electric) or TM (Transvers Magnetic). Let's consider a TE wave propagating inside the waveguide (the electric field is in the x direction) the self-consistency condition is given by:

𝑡𝑎𝑛 ( 𝜋 𝑑 𝜆 𝑠𝑖𝑛𝜃 -𝑚 𝜋 2 ) = √ 𝑠𝑖𝑛 2 𝜃 𝑐 ̅̅̅ 𝑠𝑖𝑛 2 𝜃 -1 (II-2)
The solution of (II-2) is a graphical one as shown in The previous explanation was the case of a planar dielectric waveguide in 1 dimension (1D). However, an optical fiber is a 3D medium. Therefore cylindrical coordinates are to be taken into consideration to write the Helmholtz equation. In that case, the fiber is characterised by a Characteristic equation expressed using

Bessel functions instead of a self-consistency equation. Also, the solution of the characteristic equation could be a graphical one (similar to the self-consistency condition) allowing to determine the fiber parameters. This part will be briefly presented later in the manuscript (section II.3.3). For more details, the reader is invited to read chapter 9 of the following reference [START_REF] Saleh | Fundamentals of Photonics[END_REF].

In a more general and simple way, the waveguiding process in fibers that are dielectric waveguides is based on total internal reflection (TIR) as shown in Figure The photo-written waveguides could be considered as an optical fiber with an infinite cladding which is the glass. The ∆n is given by:

∆𝑛 = 𝑛 1 -𝑛 2 𝑛 1 (II-3)
An incident light beam into the fiber/waveguide could be guided if it makes an angle  with the fiber axis that is smaller than

 𝑐 ̅ with  𝑐 ̅ = 𝑐𝑜𝑠 -1 (𝑛 2 𝑛 1 ) ⁄ . An
acceptance angle  𝑎 is required so the light is guided with:  𝑎 = 𝑠𝑖𝑛 -1 𝑁𝐴 where 𝑁𝐴 is the numerical aperture of the fiber/waveguide as given by:

𝑁𝐴 = √𝑛 1 2 -𝑛 2 2 (II-4)
The acceptance angle/the numerical aperture determines the cone of acceptance of the fiber/waveguide as shown in Figure II.7. The guided rays inside the fiber exit while diverging according to the acceptance angle i.e. numerical aperture. The acceptance angle 𝜃 a of an optical fiber. The rays within the acceptance cone are guided inside the fiber by total internal reflection. The numerical aperture is given by: NA=sin𝜃 𝑎 . Taken from [START_REF] Saleh | Fundamentals of Photonics[END_REF].

For an optical fiber or perfectly circular waveguides, the parameter V allows to identify the number of modes propagating in the waveguide i.e. if the waveguide/fiber exhibit a single mode or a multimode aspect for a specific wavelength, it is given by:

𝑉 = 2𝜋 𝑎 𝜆 𝑁𝐴 (II-5)
The parameter V depends mainly on the NA i.e. ∆n and the dimension of the waveguide a, once the propagating wavelength is fixed. Single mode waveguides/fibers exist in the region where V<2.405. Beyond that region, the waveguides/fibers represent a multimode aspect [START_REF] Saleh | Fundamentals of photonics[END_REF]. Many modes other than the fundamental mode could propagate. So, in order to control the V parameter in waveguides, one could change the photo-induced ∆n and/or the dimensions of the waveguides. However, one should mention, that the photo-written waveguides are not always circular ones, especially in this project. They are elliptical. Still, one can approximate the V parameter using (II-5).

II.3.2. Depressed cladding waveguides

Actually, waveguides could be written in two ways: standard waveguides as mentioned in the previous section and depressed cladding waveguides (DCWs).

Following laser-glass interaction a smooth ∆n is produced (with the right parameters). However, the photo-induced ∆n is not always a positive one.

Sometimes it is a negative one [100] which complicates the creation of waveguides. Therefore, researchers have found a way to live with negative ∆n and started creating depressed cladding waveguides. A depressed waveguide cladding was made by writing a series of waveguides exhibiting a negative ∆n in a ring shape as shown in Figure II.9. In that case, the guiding process takes place inside the non-irradiated zone where the refractive index is higher compared to the modified region. This process eventually requires more time and more processing to the glass in order to make a waveguide. This technique was also used by other researchers to make waveguides in phosphate glasses [102] and ZBLAN glasses also [103]. The power could be partially or totally coupled from waveguide 1 (WG1) to waveguide 2 (WG2) depending on the separation distance "d" and interaction distance "L". The coupling is defined for circular cores by a coupling coefficient

given by [106]:

𝐶 = (2∆𝑛) 1/2 𝑢 2 𝐾 0 (𝑤𝑑 𝑎) ⁄ 𝑎𝑉 3 𝐾 1 2 (𝑤) (II-6)
where 𝑢 and 𝑤 are the normalized transverse parameters in the core and in the cladding, respectively. They are related to the normalized frequency by the equation:

𝑉 2 = 𝑢 2 + 𝑤 2 (II-7)
and 𝐾 𝑙 (𝑤) is the second order of Bessel function, 𝑙 is the azimuthal parameter of the LPlm propagating modes, 𝑎 the radius of the fiber, 𝑑 separation distance between the two waveguides. The parameter 𝑢 could be found by a solution of the characteristic equation of an optical fiber. For more detail, the reader is invited to the following references [START_REF] Saleh | Fundamentals of Photonics[END_REF]105,107].

The power coupled between two identical waveguides is given by:

𝑃 𝐶𝑜𝑢𝑝𝑙𝑒𝑑 = 𝑃 0 𝑠𝑖𝑛 2 (𝐶𝐿) (II-8)
where 𝑃 0 is the input power and 𝐿 the interaction distance between the waveguides.

When considering two identical waveguides, which is generally the case, a total transfer of power could occur from one waveguide to another after a specific distance called beat length calculated based on the coupling coefficient:

𝑧 𝐵 = 𝜋𝐹 𝐶 (II-9)
Where 𝐹 is given by:

𝐹 = 1 √ 1 + ( ∆𝛽 2𝐶 ) 2
(II-10)

with 𝛽 as the propagation constant and 𝐶, the coupling coefficient given by (II-6).

In this case, where the waveguides are identical, F=1 given that they exhibit the same propagation distance; therefore ∆𝛽 = 0.

Generally, the coupling coefficient and the power exchange are dictated by the waveguides parameters only. However it was found that the polarization of the guided beam could affect the coupling coefficient over a long distance of interaction in directional couplers written using DLW technique, as reported by Crespi et al. The second method is the modulated burst method where the laser source was modulated to generate a burst of laser pulses. The WBG is written with a one step process while modulating the ∆n based on the modulation of the pulse energy.

Many WBGs were created using this technique [117,118]. Given that this project will not be taking into consideration WBG manufacturing, this part will be limited Many waveguides were inscribed in phosphate and zinc phosphate glasses. Single mode waveguides were written exhibiting a ∆n=3.5x10 -3 and propagation losses estimated to be 0.95dB/cm and 0.39dB/cm for 635 nm and 1550 nm respectively [START_REF] Ams | Slit beam shaping method for femtosecond laser direct-write fabrication of symmetric waveguides in bulk glasses[END_REF]. However, it was found that the glass response following laser irradiation highly depends on the glass composition as reported by Fletcher et al. [START_REF] Fletcher | Direct femtosecond laser waveguide writing inside zinc phosphate glass[END_REF].

Indeed, the O/P ratio is responsible for the sign of the ∆n created inside the glasses As mentioned before, one of the advantages of phosphate glasses is their capacity to be doped with high concentrations of rare earth and metals. Based on the previous results on the zinc phosphate glasses as mentioned in the previous section II. 3.8, the first silver containing zinc phosphate glass was a 40P2O5-55ZnO-5Ag2O exhibiting an O/P ratio of 3.25. However, it was found that this composition was not stable for long terms and exhibited crystallization after around 65 months [START_REF] Bourhis | Photostructuration par laser infrarouge femtoseconde de verres photosensible de phosphate de zinc, d'argent et de gallium[END_REF]. So, it was necessary to add an additional compound to stabilize the glass matrix. Therefore the choice fell on gallium oxide Ga2O3, a glass former used in order to stabilize the glass matrix. Furthermore, one should mention that the introduction of ZnO and Ga2O3 did not interfere or modify the absorption bands of the glass. Both ZnO and Ga2O3 absorption bands neither overlap with the silver nor tend to promote the reduction of the silver ions inside the glass [START_REF] Bourhis | Photostructuration par laser infrarouge femtoseconde de verres photosensible de phosphate de zinc, d'argent et de gallium[END_REF]. So, silver containing zinc phosphate glasses are zinc phosphate glasses where silver was introduced into the glass network in the form of silver ions Ag + .

II.4.1. Optical properties

To study the optical properties, the absorption spectrum in the UV range was monitored in non-containing silver glasses and silver containing glasses with different silver concentrations. The O/P ratio was roughly the same while the silver concentration was changed. The non-containing silver glass starts exhibiting an absorption around 230 nm, which is attributed to the presence of defects and impurities in small quantities in the glass [START_REF] Bourhis | Photostructuration par laser infrarouge femtoseconde de verres photosensible de phosphate de zinc, d'argent et de gallium[END_REF]. However, for the silver containing glasses, the absorption band is remarkably higher and shifted towards the higher wavelengths i.e. lower energy levels. The higher the concentration of silver the more the absorption band is shifted as shown in

II.4.2. Laser-silver containing glasses interaction

The interaction between a laser and silver containing glasses exhibits an exotic response that totally differs from the standard laser-glass interaction in the literature. Following laser irradiation, photo-induced silver clusters Agm x+ are generated in the vicinity of the interaction voxel. This is based on a non-linear absorption mechanism, a pulse-to-pulse process by heat accumulation which results in the aggregation of silver atomic and ionic species. The formation of the photo-induced clusters could be explained by the following: after laser-glass interaction a reservoir of free-electrons is generated from the multiphoton process enabling the reduction of Ag + silver ions pre-existing in the glass into Ag 0 atomic states, which then aggregate with silver ions in order to form Ag

Ag specie Peak absorption [nm]

Ag α (1) 287±2

Ag 2 + 302±3 Ag α (2) 340±2 Ag 0 387±4 Ag n 442±1
Normally, the laser used for writing in such glasses is a high repetition laser, around 10 MHz emitting femtosecond pulses at 1030 nm wavelength. However, the glass is transparent at a wavelength of 1030 nm, as is shown in (Ag + +e-→ Ag 0 ) where the concentration of free electrons is at its peak. During the formation of Ag 0 , holes are trapped by silver ions Ag + : h + +Ag + →Ag 2+ and the product is assumed not to be mobile. In fact, Ag 2+ should be considered as a hole trapped in proximity of a silver ion Ag + instead of a doubly ionized silver ion. Thus, the mobility of such pair is negligible compared to the mobility of silver ions Ag + , due to its delocalization around the phosphate chains that form the glass network.

The reaction e -+Ag + +→ Ag 0 ends when the concentration of electrons vanishes. At Two conclusions could be derived from this study. In order to create silver clusters, a huge number of pulses is required as well as the right laser irradiance. The fluorescence intensity depends linearly on the irradiance while depending logarithmically on the number of pulses [START_REF] Bellec | 3D Patterning at the Nanoscale of Fluorescent Emitters in Glass[END_REF]. The second conclusion implies that a high repetition rate laser is required in order to activate and create the silver clusters. When using a low repetition rate laser, the creation of silver clusters is possible but requires a longer time of exposure which limits the writing process. A minimum number of pulses is required in order to trigger the thermal process for silver cluster creation. However, those results were not interesting for this framework given that the aim is towards the creation of optical components. Therefore no results or investigations were conducted concerning this matter. several sensors nowadays are fiber-optic based. In order to shape the glass into fibers, it all starts by making a preform that will be shaped into fibers. The glass preform in this case is a few centimetres thick and around 10 cm long, which is enough to create roughly 10 meters of optical fiber. The critical point while shaping glasses into fibers is to preserve the same characteristics of the bulk glass, trying to avoid any aggregation and crystallization of the glass during the fiber drawing process. In order to draw fibers, the preform composition used was 40P2O5-55ZnO-1Ga2O3-2Na2O-2Ag2O. The introduction of sodium (Na) in the glass composition was for poling purposes that are not addressed in this manuscript. The glass was synthetized the same way as the previously mentioned bulk glass. However, to shape the preform, the glass was casted in a specifically designed brass mold, pre- The cartography was written while changing the laser irradiance from 5.1 TW/cm 2 to 6.7 TW/cm 2 passing by 6.1 TW/cm 2 while the writing speeds were 10µm/s and 100µm/s corresponding to 1.6x10 6 and 1.6x10 5 of deposited pulses respectively.

The results show a significant absorption band at =324 nm and another weaker one at around =290 nm for all structures as shown in as mentioned before and were reported in previous works of our group [START_REF] Bellec | 3D Patterning at the Nanoscale of Fluorescent Emitters in Glass[END_REF]136,141,152]. Therefore, we confirm that the properties of the bulk glass were preserved after the drawing process and the successful creation of flat silver containing zinc phosphate fibers was achieved. modulator enabling the accumulation of N=10 5 -10 6 pulses with energies between 20 nJ and 120 nJ. A reflection type SLM is placed after the AOM in order to spatially shape the beam if needed before irradiating the glass sample. In this project, the SLM is used only as a convergence lens in order to compensate for the different focal planes and to compensate the spherical aberrations that occur when using high NA objectives [153] (the most dominant aberrations in this case given that they are proportional to NA 4 ) that occur when focusing the laser beam using a microscope objective. Generally, the microscope objective used in this case is adapted for laser focalisation under a microscope cover slide of ~170 µm with a refractive index (RI) of ~1.5. Given that our glass exhibits an RI~1.6, aberrations occur due to the refractive index mismatch. In the following work, two microscope objectives were used: 20x-0.4NA Mitutoyo, APO PLAN NIR and 20x-0.75NA Carl Zeiss. At the top, a CCD camera is placed in order to visualize the glass surface and the writing process. Bottom white and blue illuminations at 405 nm are applied. After performing DLW of waveguides, the sample was placed on the mode profile setup in order to characterize the waveguides. The mode profile setup consisted of a red diode operating at 630 nm that could be injected inside the waveguides using optical fibers. In this case a single mode HP460 fiber (core diameter 2.5 µm-NA=0.13) at 630 nm was used to inject light inside the guiding structures (waveguides, beam splitter). Then, a 100x-0,55NA Mitutoyo objective was used on the output facet to visualize the guide mode profile and conjugate it on a CCD camera. Moreover, when needed, the CCD camera was replaced by a power meter to measure the transmission losses of our waveguides. The injection fiber, the sample as well as the collecting objective were placed on separated 3 axis stages.

II.5.5. Confocal Microscope:

The photo-induced structures in silver containing glasses are sub-diffraction limited structures, therefore, imaging them using a conventional microscope is not convenient. Because they exhibit significant fluorescence intensity under UV-Blue range excitation, they are visualized using a fluorescence confocal microscope to be able to resolve them. Confocal microscopes exhibit many advantages compared to standard ones, higher resolution (up to 300 nm), imaging planes separately and the possibility of reconstructing a 3D image/video of the structures. If the reader is interested, further details can be found in reference [154].

The fluorescent images were obtained using an Olympus FLUOVIEW FV1200 confocal microscope. An oil immersion objective of 60x -1.3 NA was used to resolve the structures. Excitation wavelength was at 480 nm while the emission wavelength ranged between 500 nm and 600 nm.

II.5.6. Measuring ∆n: SID4Bio Phasics

To better characterize the written waveguides and optical components in glasses, the ∆n is a crucial parameter to especially know with respect to its sign and amplitude. During this project, the SID4Bio wave front sensor by PHASICS was used to measure and characterize the ∆n of the written structures. It provides quantitative phase imaging of the waveguides. The sensor could be placed on any microscope operating in transmission mode. The sample where the structures are written inside is placed on the microscope and is imaged using incoherent light i.e. Based on the phase contrast images and given the depth of the structures, the qualitative value of ∆n of the written structures could be ascertained. [136], which results in a higher ∆n. The same scenario applies for increasing the laser irradiance: the higher the irradiance, the greater the formation of silver clusters, as previously reported [START_REF] Bellec | 3D Patterning at the Nanoscale of Fluorescent Emitters in Glass[END_REF]. The ∆n increases from 9 Based on those results, the ∆n was properly calculated for the written structures. It was found that in that case the results do not converge with the previous results

i.e. increasing the number of pulses or the laser irradiance does not lead to a higher ∆n in all cases especially for high irradiances. This is due to the fact that high irradiances induce deeper structures in the z plane. It was found that the imaging system used SID4Bio + 100x-1.3NA oil objective is limited to a depth measurement of ~6µm. Several lines were written with the same laser conditions but spaced in the z plane by 1 µm and were imaged using the SID4Bio and a 100x- The use of a 100x-1.3NA objective with the SID4Bio is necessary in order to spatially resolve our structures. Taking into account the length of coherence, the shape of our structure in the z plane, it was found that the depth of view is around ~6 µm and after that the structures are blurry and the OPD is underestimated.

Therefore, the measurement of our imaging system in this case is limited to around for two methods: (orange) using the compensation method (black) fixed method where the depth of the structure higher than 6 µm is considered as 6 µm. Both methods converge more or less to the same values. The black shades correspond to the standard deviation of the values.

To further support our hypothesis that the photo-induced ∆n is related to the creation of silver clusters, a non-silver containing zinc phosphate (PZn) glass was irradiated using the same laser conditions and even higher irradiance. Neither fluorescence nor refractive index change were observed in this case, which indicated that the formation of silver clusters is the main and direct cause for the ∆n in silver containing glasses, in the low pulse energy regime. Moreover, the photo-induced ring shape structure was investigated using High Resolution Scanning Electron Microscopy (HRSEM) photos and Atomic Force Microscopy (AFM) A positive ∆n was observed over the whole visible (VIS)-near infrared (NIR) ranges exhibiting a maximum value, in this case of 2.5 x 10 -3 at 𝜆=365 nm. Further investigations were required to better characterize the written waveguide.

One of the advantages of writing type A waveguides is that injection of light could be possible without the need to cut and polish the side facets if they are already polished. During the writing process and while exiting the glass facet, no ablation nor damage were noticed to the glass for type A waveguides, which makes the injection of light possible. It is not the case when writing type I waveguides where when reaching the glass facet, the glass explodes and is damaged. Therefore, the polishing process is a must in order to inject light inside such waveguides. Still, to optimize the injection and characterization process of type A waveguides, the samples were always cut and polished prior to DLW.

The sample was placed on the mode profile setup and a red laser beam at 660 nm was injected inside the waveguides. The sample was excited from the side using a 405 nm before laser injection in order to visualize the structures. The first approach to write waveguides resulted in multimode waveguides in the visible and NIR range. For optical circuits and optical components, multimode waveguides are a disadvantage due to the various numbers of modes supported by the waveguide and the complexity of characterizing such waveguides. Therefore, single mode (SM) waveguides needed to be written. In order to do so, a series of waveguides were written in PZnAg1 silver containing zinc phosphate glass. The waveguides were written typically 160 µm below the surface. The DLW was performed using a 20x-0.75NA objective aiming to produce smaller waveguides.

The target was to reduce the dimensions of the waveguides as well as the ∆n.

Eventually the number of modes supported by a waveguide is linked to the dimensions and ∆n of the waveguide (II-5). To get a single mode waveguide, the laser irradiance as well as the number of pulses were optimized to get the appropriate size and ∆n. Many waveguides were written, some were multimode, some single mode. For the sake of simplicity and given that the multimode aspect was presented earlier, only one single mode will be presented.

Following DLW, the sample was cut and polished. The structures were imaged using revealed that the structure's thickness is ~100nm using HRSEM images [139] using another microscope objective but still the results are interesting. Therefore, we assume that in this case we are probably over estimating the thickness of our structures. Unfortunately, no HRSEM measurements were performed on those structures to confirm our hypothesis. But, on the other hand, using simulations, when decreasing the thickness of structures, a higher ∆n is required to support waveguiding and a higher ∆n is required to trigger the multimode aspect, as shown in Figure II.59. This is expected, since decreasing the dimensions of a waveguide decreases the 𝑉 parameter i.e. the number of guided modes. Therefore, if we are underestimating the thickness of our structures, it implies that we are underestimating the value of the photo-induced ∆n. For instance, if we estimate the structure's thickness to be 500 nm, the ∆n required to trigger the multimode aspect is 4x10 -3 , while if the thickness is 200 nm a ∆n of 2x10 -2 is required to trigger the multimode aspect. Finally, a large mismatch between the injected mode profile and the geometry of the waveguide results in injection losses estimated to be at its best at 5.22 dB as estimated by numerical simulations. The losses could be higher depending on the glass surface condition during injection (for example dust, not well polished). That is also related to the fact the waveguide is not a circular one but can be illustrated as two ellipsoids with positive ∆n spaced by ~1.85 µm. The upper bound of the overall losses is 1.2 dB/cm, estimated considering the simulated mismatch (5.22 dB), Fresnel losses of (0.43 dB) (n=1.59) and the measured insertion losses of the 7-mm waveguide. One should mention that the traditional methods for characterizing propagation losses is not highly efficient due the large mismatch between the fiber and the waveguide geometry, and the short length of the waveguide. One of the best methods to identify the propagation losses is the cutback method. It is normally used to characterize the losses in fibers. Light is injected inside a fiber roll of many meters or centimetres. The transmission is monitored while a specific length of the fiber is cut while the light injection is fixed.

The transmission increases every time a part of the fiber is cut which leads to the propagation losses per unit of length (dB/Km, dB/m, dB/cm). Unfortunately, during the project, it was not possible to have long samples up to 10 cm in order to perform the study. Therefore we limited the estimation of losses to the previously mentioned method. Further efforts are required in the future to get a more accurate evaluation of the propagation losses of such waveguides. Compared to the type I waveguides in phosphate glasses, the lowest losses were ~0. [START_REF] Schaffer | Micromachining bulk glass by use of femtosecond laser pulses with nanojoule energy[END_REF] glasses. However, one should mention that the coupling losses in both cases were not as high as in our case given that the waveguides exhibited a more circular shape. The most critical point in estimating the losses of silver-based waveguides is the power coupling/overlap between the injected mode and the elliptical waveguide shape. Numerical simulations estimate the losses to be 5.22 dB but those losses could be underestimated which makes the estimation of the propagation losses harder.

II.6.3.c. Multimode -Single mode aspect

Multimode waveguides and single mode waveguides were presented during this work. As mentioned before, a single mode (SM) waveguide is defined by the fact that the spatial movement of the injecting fiber does not excite a higher order mode. Therefore only one mode can propagate in the waveguide no matter how the injection occurs. However, for the multimode (MM) waveguides, it is not the case.

Changing the injection affects the guided mode and excites higher order modes.

The number of higher modes that could be excited in a multimode waveguide could be defined by the dimensions and the ∆n of the waveguide (V parameter in (II-5)).

Some multimode waveguides exhibit two guided modes only and others exhibit four to five guided modes for instance. However, even for a multimode waveguide, the fundamental mode could be excited. drops in the middle to 0.3 compared to 0.65 for the SM waveguide. This is probably due to the higher ∆n for the MM waveguide that results in more confining of the light inside each silver cluster plane compared to SM, where the ∆n is relatively lower and the light is less confined. This was observed for all MM and SM waveguides. As mentioned before, the waveguides behave as two highly interacting waveguides coupling light between each other, exhibiting a super mode profile as an output. In the case of a higher ∆n, the light is more confined in one plane and the interaction between them is lower. Nevertheless, all waveguides studied during this project guided light supported by both silver planes acting as one waveguide. small ∆h of 10 µm, the losses were high. Acceptable losses of around 20% (0.96 dB) were observed for Rc=50 mm and ∆h=10 µm. However, for a ∆h of 25 µm losses were significant and equivalent to losses at a ∆h of 50 µm. We believe that in that case the waveguide exhibited some defects implying higher losses. Given that the glass samples were limited in dimension to ~8 mm, the choice of Rc and ∆h were 50 mm and 40 µm respectively in order to spatially fit the component inside the 8 mm glass sample. The following parameters exhibited losses of course, but these were acceptable losses in order to demonstrate the coupling effect between type A waveguides. Following primary tests, it was found that for L=1 mm the coupling is not high enough while the 2 mm length was sufficient to observe coupling effects from one waveguide to another. Therefore, the interaction length was fixed to 2 mm and the separation distance d between two waveguides was varied from 5 to 20 µm by steps of 2.5 µm. The power transmitted by the straight waveguide Ps was normalized by dividing it by the overall sum of the guided power Ps+ Pc. Consequently, one can have a better idea of the coupling ratio. The The simulations were based on plotting the coupled power from (II-8). One can see the oscillation of the coupling ratio between 5 µm and 7.5 µm, which is typical of the coupler's behaviour. However, that was not observed in the experimental data owing to the fact that the distance step was 2.5 µm, which is too large compared to a step of 0.1 µm in simulations. Moreover, an acceptable match between the simulated and the experimental data was found. The small differences could be related to the fact that the waveguide is elliptical (𝜖=1.3) and not a circular one given that the simulations are based on LP01 circular modes interacting together. Therefore, we demonstrate the capability of creating waveguides in ribbon fibers, thus paving the way for fiber applications in spectroscopy sensing, filtering and/or fully integrated photonics. DLW in silver-containing zinc phosphate bulk glasses and ribbon fibers allows the formation of a perennial new type of waveguides which take advantage of the thermal stability and bleaching-free fluorescence of the photo-induced silver clusters up to the glass transition temperature (typically 380-400 °C here) [152,165]. Furthermore, as mentioned before such laser-induced modifications had already led to original second-order effective nonlinearities by means of direct laser poling (EFISHG), allowing for a localized second-harmonic generation that showed a significant efficiency with an effective coefficient close to the pm/V level [142,143]. In addition, a post laser irradiation thermal treatment (Tg + 20 °C) in silver-containing zinc phosphate glass had allowed the growth of silver metallic nanoparticles exhibiting an effective dielectric/metal medium bearing a plasmonic resonance response in the structured glass matrix [139]. To the best of our knowledge, combining optical and plasmonic waveguiding in the same glass sample is not achievable otherwise, which highlights the novelty and tremendous potential of these new type waveguides. Finally, one must emphasize that the creation of silver clusters is not only limited to the silver-containing zinc phosphate glasses but can also be generated in other silver containing glass matrices such as sodocalcic and borosilicate glasses, as previously reported by our group [140]. This proves the universality in terms of processes when considering tailored materials as silver-containing photosensitive glasses [START_REF] Royon | Femtosecond laser induced photochemistry in materials tailored with photosensitive agents[END_REF], and the novelty of this technique in making hybrid integrated circuits

II.7. Conclusion

Direct laser writing (DLW) in silver containing glasses induces the creation of fluorescent silver clusters Agm x+ around the interaction voxel. Their spatial distribution is dictated by the laser Gaussian beam. Those Agm x+ are responsible for a new type of refractive index change (∆n) that is compatible for waveguiding applications. This new type of ∆n totally differs from the well-known type I as it originates from the creation of the photo-induced silver clusters around the interaction voxel involving such new chemical bonds with more polarizable electron clouds than those of initial silver ions Ag + leading to a local refractive index change independent of any modification of the glass matrix itself. The photo-induced ∆n increases as a function of the laser parameters reaching a maximum value of around 8 x 10 -3 . Multimode (MM) and single mode (SM) waveguides were created inside silver containing glasses. MM waveguides in the visible and IR wavelengths exhibited dimensions of 4 x 15µm 2 with a ∆n=4.5 x 10 -3 while a SM waveguide operating at =630 nm exhibited dimensions of ~3 x 6 µm 2 , ∆n=2.5x10 -3 and propagation losses estimated to be 1.2 dB/cm. The SM waveguide mode profile consists of one mode supported by each of the two silver cluster planes acting as one supermode. The simulation of mode profiles exhibited a significant match with the experimental modes confirming that the ∆n is based on the creation of silver clusters. Following that, a 50-50 Y-beam splitter and a 50-50 coupler were written paving the way for 3D integrated optical components. Finally, the waveguiding process was demonstrated in silver containing ribbon shaped fibers by writing a 1.4 cm waveguide. These results provide unique opportunities for applications such as spectroscopy fiber sensing, filtering and/or fully integrated photonics. [START_REF] Chan | Waveguide fabrication in phosphate glasses using femtosecond laser pulses[END_REF][START_REF] Chan | Modification of the fused silica glass network associated with waveguide fabrication using femtosecond laser pulses[END_REF]166] which is due to the local heating and melting followed by a cooling process after laser passage [START_REF] Schaffer | Bulk heating of transparent materials using a high-repetition-rate femtosecond laser[END_REF], and/or the formation of color centers [START_REF] Streltsov | Study of femtosecond-laser-written waveguides in glasses[END_REF][START_REF] Chan | Modification of the fused silica glass network associated with waveguide fabrication using femtosecond laser pulses[END_REF][START_REF] Little | Mechanism of femtosecond-laser induced refractive index change in phosphate glass under a low repetition-rate regime[END_REF] (see section II.2.1). It consists of an intrinsic modification of the glass matrix itself leading to a refractive index change. Increasing the fluence of the laser, induces the creation of a type II refractive index modification which is birefringent and associated with formation of nanogratings [START_REF] Shimotsuma | Self-Organized Nanogratings in Glass Irradiated by Ultrashort Light Pulses[END_REF][START_REF] Richter | Formation of femtosecond laser-induced nanogratings at high repetition rates[END_REF][START_REF] Liang | Mechanism of nanograting formation on the surface of fused silica[END_REF]. Further increase of the fluence leads to the creation of type III modifications resulting in formation of voids or chaotic damage formation in the glass matrix.

Table of contents:

Type I refractive index change is the most communally used for the creation of optical components such as waveguides [START_REF] Fletcher | Direct femtosecond laser waveguide writing inside zinc phosphate glass[END_REF][START_REF] Ams | Slit beam shaping method for femtosecond laser direct-write fabrication of symmetric waveguides in bulk glasses[END_REF][START_REF] Will | Optical properties of waveguides fabricated in fused silica by femtosecond laser pulses[END_REF][START_REF] Osellame | Femtosecond writing of active optical waveguides with astigmatically shaped beams[END_REF][START_REF] Shah | Waveguide writing in fused silica with a femtosecond fiber laser at 522 nm and 1 MHz repetition rate[END_REF][START_REF] Salter | Adaptive slit beam shaping for direct laser written waveguides[END_REF][START_REF] Berube | Tailoring the refractive index of Ge-S based glass for 3D embedded waveguides operating in the mid-IR region[END_REF][START_REF] Lapointe | Making smart phones smarter with photonics[END_REF], integrated optical components [114, 167-169] and recently quantum photonic circuits in glasses [170,171]. However, a type I modification has been reported to exhibit a decrease in the refractive index change in some glasses such as BK7 borosilicate, ZBLAN and phosphate glasses [START_REF] Gross | Ultrafast Laser Inscription in Soft Glasses: A Comparative Study of Athermal and Thermal Processing Regimes for Guided Wave Optics[END_REF][START_REF] Little | Mechanism of femtosecond-laser induced refractive index change in phosphate glass under a low repetition-rate regime[END_REF][START_REF] Bérubé | Femtosecond laser-induced refractive index modifications in fluoride glass[END_REF]100,172,173], which complicates the creation of optical waveguides. It depends on the glass composition as well as the inscription parameters.

In silver containing glasses, silver ions embedded inside the glass matrix act as a photosensitive support for DLW. In such silver containing glasses, DLW allows the formation of fluorescent silver clusters Agm x+ in the vicinity of the laser-glass interaction voxel [START_REF] Bellec | 3D Patterning at the Nanoscale of Fluorescent Emitters in Glass[END_REF]136,141]. Those silver clusters are at the origin of a novel type of refractive index modification that we call type A (based on the Latin name of silver, Argentum), acting as an extrinsic modification from the glass matrix in 123 silver containing glasses. It allows the creation of optical waveguides as well as photonic components as was demonstrated previously in Chapter II [149,174].

In this chapter, a comparative study between the novel type A and the type I refractive index change is presented. We demonstrate that in the same glass substrate, which is a silver containing zinc phosphate glass, type A and type I refractive index changes can be induced by wisely adjusting the laser writing parameters. First, we start by investigating the type I modification in a silver containing and a non-containing silver glass. Then, in silver containing glass, we perform direct laser writing of single mode waveguides of both type A and type I. A morphology comparison between both waveguides then the refractive index mode profile, near field mode profile and losses are exploited. Finally, the advantages of the type A modifications are highlighted.

III.2. Type I modification in phosphate -zinc phosphate glasses

More specifically, phosphate glasses exhibit some challenges in the understanding of the laser-glass interaction and its control. This is due to the presence of several components in the glass composition that could affect the laser-glass interaction.

As mentioned before in section II.3.8, network modifiers are added to the glass composition to stabilize the glass matrix and/or to dope the glass with high concentrations of rare earth metals. Two writing regimes exist, athermal and thermal (section I.3.4). While writing in the athermal regime i.e. generally low repetition rate and pulse energy in the microjoule (µJ) scale, it was reported that several laser passages switch the ∆n from positive to negative in a phosphate Kigre QX glass [175]. In the thermal regime, positive and negative ∆n were observed for the same photo-induced structures where in the latter case no waveguiding could occur [START_REF] Gross | Ultrafast Laser Inscription in Soft Glasses: A Comparative Study of Athermal and Thermal Processing Regimes for Guided Wave Optics[END_REF]. Generally for the thermal regime, most of the ∆n observed were negative ones making the writing of optical waveguides complicated [START_REF] Gross | Ultrafast Laser Inscription in Soft Glasses: A Comparative Study of Athermal and Thermal Processing Regimes for Guided Wave Optics[END_REF].

Moreover, a self-organizing feature and ripple structures were observed by many research groups [START_REF] Gross | Ultrafast Laser Inscription in Soft Glasses: A Comparative Study of Athermal and Thermal Processing Regimes for Guided Wave Optics[END_REF]176] in phosphate glasses following DLW, which makes the writing of low loss waveguides nearly impossible. This indicates that the writing window of type I smooth waveguides in the thermal regime is really narrow in phosphate glasses. Moreover, it has been reported that the photo-induced ∆n in phosphate and zinc phosphate glasses highly depends on the glass composition as well as the laser parameters [START_REF] Gross | Ultrafast Laser Inscription in Soft Glasses: A Comparative Study of Athermal and Thermal Processing Regimes for Guided Wave Optics[END_REF][START_REF] Fletcher | Direct femtosecond laser waveguide writing inside zinc phosphate glass[END_REF]132,173]. Fletcher et al. investigated the effect of the ratio O/P in zinc phosphate glasses and found that a ratio O/P=3.25 is the ideal one for having positive ∆n and writing smooth waveguides [START_REF] Fletcher | Direct femtosecond laser waveguide writing inside zinc phosphate glass[END_REF]132]. To sum up, creating smooth type I modifications exhibiting positive ∆n in phosphatezinc phosphate glasses is complicated due to the multicomponent nature of the glass and requires a fine optimisation of the laser parameters and/or the glass composition.

III.3. Experimental methods

III.3.1. Glasses

The glasses used in this work are PZnAg2 with an O/P~3.37 and PZn with an O/P~3.58 (see Table II-1). In fact, PZn glass is the same glass as PZnAg2 in which the silver is replaced by Gallium. Therefore it is a non-containing-silver zinc phosphate glass. For more information about the glass synthesis process, please refer to section II.5.1.

III.3.2. Laser setup

III.3.2.a. T-pulse 200

Direct laser writing of type A waveguides was performed using the T-pulse 200 laser which is a 9.8MHz repetition laser emitting at a 1030 nm wavelength with pulse duration ~400 fs and energies in the range of 20 nJ to 120 nJ. For more detail, the setup was already presented in section II.5.3 III.3.2.b. Ti:Saphhire REGA-Coherent Direct laser writing of type I waveguides was performed using a chirped pulse amplification system (Coherent RegA) operating at a low repetition rate of 250 kHz (compared to the 9.8 MHz laser) emitting at a wavelength of 800 nm with 100 fs pulse duration using a 50x-0.55NA Nikon microscope objective. Pulse energies from 0.5 to 2.5 µJ could be obtained using this setup. A quarter-wave plate was inserted in the beam path and adjusted to obtain circularly polarized light. The glass sample was mounted on a mechanical stage (Newport XML210 and GTS30V). In order to have a circular waveguide, a cylindrical lens telescope was used (ellipticity of a/b=1/8). Type I refractive index changes were created in both silver containing zinc phosphate glass (PZnAg2) and non-containing-silver zinc phosphate glass (PZn), each glass exhibiting a different O/P ratio of 3.37 and 3.58 respectively. The laser used to perform the DLW is the Ti:Sapphire laser operating at 250 kHz while ∆n was measured using the SID4Bio wave front sensor using a 50x-0.55NA objective (for more detail, see section II.5.6). For certain parameters, a negative ∆n could be observed for the PZnAg2 glass exhibiting an O/P ratio of 3.37 while a positive ∆n is always observed for the PZn glass where the O/P ratio is 3.58 as shown in Figure indicating that changing the O/P ratio directly affects the sign of the photo-induced ∆n in zinc phosphate glasses [START_REF] Fletcher | Direct femtosecond laser waveguide writing inside zinc phosphate glass[END_REF]132]. In Figure III.2, the optical path difference (OPD) for both waveguides may not be the same magnitude, but this depends on the structures depth/thickness "e". In all cases, we are not interested in the ∆n values in this particular case (∆𝑛 = 𝑂𝑃𝐷 𝑒 ⁄ ) but rather in the profile and the sign of the ∆n. One should note that in that case, the silver ions embedded in the glass matrix (in the case of PZnAg2) do not play any role in the photo-induced modification. It is a purely type I modification (this part will be further detailed in section III.4.2). However, that was not the case for the non-containing silver zinc phosphate glass (PZn). For laser doses, i.e. pulse energy and writing speed, that are higher than the type I modification threshold, all the observed ∆n were positive. However, the ∆n profiles were not similar for all writing conditions. To better understand the different ∆n behaviours for the non-containing silver glass, a comparison between ∆n profiles for both glasses using the same laser conditions (Ep=1µJ -v=1mm/s) is shown in Figure III.5. For the PZnAg2 glass, the ∆n is a single positive peak that is surrounded by two negative ∆n peaks that are below the pristine glass. However, for PZn glass, the ∆n profile exhibits one dominating single positive ∆n peak surrounded by two small positive ∆n peaks that are above the pristine glass level. So over all, for PZn the ∆n is always positive, which is not the case for PZnAg2. The two negative peaks in PZnAg2 glass are more or less in the same spatial position of the two small positive peaks for PZn.

Comparing the behaviour of ∆n for both glasses, we see they both exhibit one main single peak that decays as the applied laser dose decreases. But, for the PZnAg2, the positive peak was surrounded by two negative ones. So when the positive peak disappears, only the negative ∆n remains. However for PZn glass, when the single positive peak disappears no more modification is observed. It could be related to the Gallium effect given that more gallium is incorporated in the PZn glass matrix or simply the difference in the O/P ratio.

Moreover, same DLW conditions were applied in an Argoglass (AG01) exhibiting an O/P ratio of 2.95 different from the glasses PZnAg2 & PZn provided by ICMCB. No positive ∆n was observed in Argoglass using the same conditions used for other glasses. The following results match with what was reported earlier, that ∆n is highly dependent of the glass composition as well as the laser irradiations in zinc phosphate glasses.

As it turns out, zinc phosphate glasses are already multicomponent glasses before the incorporation of silver ions and the ∆n highly depends on the glass composition as well as the laser parameters, which makes it complicated to confirm the response. This project does not aim at understanding and perfecting the creation of type I waveguides. Therefore our investigation stopped at this point. The type A near-field mode is an elliptical supermode that tends to be an LP01 supported by two highly interacting waveguide modes. However the type I near-field mode is a circular LP01 mode. One should not forget that the in the case of writing type I waveguides, the beam was shaped using a cylindrical lens telescope in order to obtain circular waveguides, which was not the case for type A waveguides. In terms of dimensions, they are comparable. The type A guided mode is ~3 µm x 5.5 µm compared to ~4.5 µm x 5.2 µm for the type I waveguide. For the guiding losses, type I losses were estimated to be ~4.5 dB/cm (same method used for estimating the propagation losses for type A, sectionII.6.3) which is quite high, especially compared to type A waveguides exhibiting upper losses of 1.2 dB/cm. The high losses in type I waveguides could be explained by the inhomogeneity of the glass sample as well as the defects during DLW. In addition to that, self-periodic ripples were sometimes observed for the waveguides, which is also one of the reasons for the high losses. Anyway, no further efforts were put into creating low loss type I waveguides given that this was not the aim of this project.

Yet, waveguides exhibiting low losses, lower than 0.4 dB/cm were reported by many research groups in phosphate/zinc phosphate glasses [START_REF] Ams | Slit beam shaping method for femtosecond laser direct-write fabrication of symmetric waveguides in bulk glasses[END_REF]134]. Finally, type I waveguides exhibited a heat affected zone referring to a thermal regime while the type A waveguides exhibited no heat affected zone referring to an athermal regime. Generally, thermal regimes are related to higher repetition rates compared to athermal regimes but not in this case. In fact, it depends not only on the repetition rate but also on the pulse energy. In the case of type I, the pulse energy is in the order of µJ compared to nJ in the type A. The type A modification is based on the photo-chemistry in the glass matrix whereas the type I modification is based on the melting and reconstruction of the glass matrix itself. The type A modification occurs in an extrinsic way to the glass matrix acting only on the silver ions and forming silver clusters compared to type I which is an intrinsic modification, heating the glass above the Tg, melting, reconstructing and changing the initial properties of the glass itself.

III.4.4. Flipping ∆n

As reported in section III. Otherwise, type I modifications would also exhibit be elliptical if the beam was not shaped. Another advantage for the type A modification is the possibility to write near-waveguide surfaces with no need for additional processing. This is going to be presented in detail in Chapter IV. Finally, Table III On the other hand, in silver containing glasses, wisely choosing the laser parameters and regime, either type A or type I modifications could be triggered.

The type I modification occurs in the thermal regime with high laser fluence using a low repetition laser (250 kHz) compared to an athermal regime for type A modification using with a low laser fluence using a high repetition rate laser However, to manufacture those sensors, the fiber should be tapered or a part of the cladding should be removed to reveal the sensing medium. Generally gas and chemical sensors are rather based on the absorption of the evanescent wave by the outer medium (complex part of the refractive index). However this phenomenon plays a minor role in refractive index sensors. These rather rely on the mode confinement (positive part of the refractive index) between the inner and outer medium (glass-liquid).

The Direct Laser Writing (DLW) technique is a well-established technique allowing to directly address 3D structures inside materials. More specifically, waveguides [START_REF] Fletcher | Direct femtosecond laser waveguide writing inside zinc phosphate glass[END_REF][START_REF] Lapointe | Making smart phones smarter with photonics[END_REF][START_REF] Cerullo | Femtosecond micromachining of symmetric waveguides at 1.5 µm by astigmatic beam focusing[END_REF][START_REF] Bérubé | Femtosecond laser-induced refractive index modifications in fluoride glass[END_REF]123,162,185] and optical components [124] were written embedded inside glasses using DLW. Yet just a few works were reported on written waveguides near the glass surface [START_REF] Bérubé | Femtosecond laser direct inscription of surface skimming waveguides in bulk glass[END_REF]169]. This is due to the ablation that occurs when writing near the surface given that the modification threshold decreases when approaching the glass surface [186]. The need to write near-surface optical components is to make the light interact with the outer medium in order to create miniaturized sensors in glasses. However, few works report the creation of sensors based on the DLW technique [187,188].

In the first part of this chapter, DLW of rising near-surface waveguides in silver containing glasses are reported with no need for additional processing. For the second part, the waveguides written are used to create a refractive index sensor in a ~1 cm glass chip with no need for etching or any additional process.

IV.2. Evanescent wave theory

Light propagates inside an optical fiber/waveguide as a form of mode. As mentioned before the waveguide could exhibit single mode or multimode aspects.

The propagating mode is normally confined inside the core. However, a small portion of light propagates in the cladding and decays exponentially; it is called the evanescent wave as shown in Figure IV.2. The field distribution of the evanescent wave is given by: 𝐸 = 𝐸 0 𝑒 (-𝑧𝑑 𝑝 )

(IV-1)
Where 𝐸 0 is the field distribution at the waveguide interface, 𝑧 is the length and 𝑑 𝑝 the depth penetration of the evanescent wave given by:

𝑑 𝑝 = 𝜆 2𝜋𝑛 𝑐𝑜𝑟𝑒 [𝑠𝑖𝑛 2  -( 𝑛 𝑐𝑜𝑟𝑒 𝑛 𝑐𝑙𝑎𝑑𝑑𝑖𝑛𝑔 ) ⁄ 2 ] 1/2 (IV-2)
Where  is the wavelength,  is the angle between the incident beam and the interface (propagation beam), 𝑛 𝑐𝑜𝑟𝑒 the refractive index of the core and 𝑛 𝑐𝑙𝑎𝑑𝑑𝑖𝑛𝑔 the refractive index of the cladding.

The less the mode is confined inside the core (lower ∆n), the more significant the evanescent wave is. The confinement factor is given by:

 = 𝑃 𝑐𝑜𝑟𝑒 𝑃 𝑡𝑜𝑡𝑎𝑙 = 1 - 𝑢 2 𝑉 2 (1 -𝜓 𝑙 (𝑤)) (IV-3) With 𝜓 𝑙 (𝑤) = 𝐾 𝑙 2 (𝑤) 𝐾 𝑙+1 (𝑤)𝐾 𝑙-1 (𝑤) (IV-4)
Where 𝑃 𝑐𝑜𝑟𝑒 is the power inside the core, 𝑃 𝑡𝑜𝑡𝑎𝑙 the total power injected in the fiber, 𝑢 and 𝑤 the normalized transverse parameters in the core and in the cladding respectively, 𝑉 fiber parameter given by (II-7) and 𝐾 𝑙 (𝑤) is the second order of Bessel function where 𝑙 is the azimuthal parameter of the LPlm propagating modes.

The confinement factor for the fundamental mode LP01 propagating in an optical fiber has been simulated as a function of 𝑉, the fiber parameter as depicted in Figure IV.1: the higher the V parameter the higher the confinement of the mode.

Thus, 𝑉 is proportional to the fiber radius a and to the numerical aperture NA of the waveguide, V = 2π a λ NA (II-5). So, in order to further extend the evanescent wave i.e. minimize the confinement of the propagating mode to increase the interaction with the outer medium, one can either reduce the fiber radius and/or the ∆n between the core and the cladding (to reduce 𝑉). Given that the ∆n in fiber optics are generally fixed values, researchers tend more to reduce the fiber dimensions by tapering it to enhance the sensitivity, as will be presented in section IV.3. It was found that for both fibres, the transmission is maximum when the liquid matches the RI of the surrounding polymer while the thinner taper exhibited a higher sensitivity to RI modifications.

They described the sensing mechanism as the following: the shape of the guided mode is affected by the surrounding medium i.e. the RI liquid used. If the RI of the liquid is higher than the cladding's RI (polymer in this case), the mode is ejected outside the polymer where it will be scattered by the channel and absorbed by the liquid. However, if the RI is lower, the mode propagates with no significant changes A theoretical model was suggested to be fitted with experimental results. The model is based on Fresnel's equation [START_REF] Saleh | Fundamentals of photonics[END_REF] of light bouncing inside a multimode optical fiber.

In the case of a dielectric medium, the equations could be reformulated in terms of the incident/propagation angle 𝜃, the refractive index of the core 𝑛 𝑐𝑜𝑟𝑒 and the refractive index of the surrounding medium 𝑛 𝑒𝑥𝑡 .

The amplitude reflection coefficients of perpendicular 𝑟 ⊥ and parallel 𝑟 ∥ polarization to the plane of incidence are given by: The intensity reflection coefficient of the unpolarised light can be calculated by:

𝑟 ⊥ = 𝑠𝑖𝑛𝜃 -
𝑅 = |𝑟 ⊥ | 2 + |𝑟 ∥ | 2 2 (IV-7)
As mentioned in section II.3.1.a, the waveguiding process occurs if the incident beam is lower or equal to the critical angle 𝜃 𝑐 . The injected light was approximated to a Lambertian source of light [195]; the input power of each ray is dependent of the angle 𝜃 of propagation inside the fiber and assumed proportional to cos 𝜃.

Another consideration is that the beam guided in the fiber undergoes multiple internal reflections (the case of a multimode fiber), which is related to the propagation angle 𝜃, the dimension of the sensing medium i.e. the length 𝐿 and the section 𝐷. Therefore, the number of reflections is given by:

𝑁 = 𝐿𝑡𝑎𝑛𝜃 2𝐷

(IV-8)

After immersing the fiber in the liquids, the power remaining in the fiber after the sensing medium is:

𝑃 𝑜𝑢𝑡 ∝ ∫ 𝑅 𝑛 𝑒𝑥𝑡 𝑁(𝜃) 𝑐𝑜𝑠𝜃 𝑠𝑖𝑛𝜃 𝑑𝜃 𝜃 𝑐 0 (IV-9)
The power ratio between the immersed fiber and the non-immersed one is:

𝜂 𝑅𝐼 = 𝑃 𝑜𝑢𝑡 𝑃 𝑎𝑖𝑟 = ∫ 𝑅 𝑛 𝑒𝑥𝑡 𝑁(𝜃) 𝑐𝑜𝑠𝜃 𝑠𝑖𝑛𝜃 𝑑𝜃 𝜃 𝑐 0 ∫ 𝑅 𝑛 𝑎𝑖𝑟 𝑁(𝜃) 𝑐𝑜𝑠𝜃 𝑠𝑖𝑛𝜃 𝑑𝜃 𝜃 𝑐 0 (IV-10)
Where 𝑅 𝑛 𝑒𝑥𝑡 and 𝑅 𝑛 𝑎𝑖𝑟 are the intensity reflection coefficients for the interface fiber/surrounding medium and fiber/air respectively. So, the power output of the sensor is linked to the mismatch of RI between the liquids and the guided mode.

Several RI liquids were applied to the sensing medium with RIs ranging from 1.332 where x characterizes the overlap of the mode with the different RI liquids applied on the glass and can take values between 0 and 1. It could be evaluated using the V parameter in (II-5). However V is unkown, so x was adjusted to fit the simulation and experimental data. Assuming that the Fresnel reflection coefficient is independent from θ (single mode waveguide, so θ very small), it is given by:

𝑅 𝐹𝑟 = ( 𝑛 𝑒𝑓𝑓 1 -𝑛 𝑒𝑓𝑓 2 𝑛 𝑒𝑓𝑓 1 + 𝑛 𝑒𝑓𝑓 2 ) 2 (IV-15)
So, in that case (IV-11) and (IV-12) could be written as: additional process. The conditions of DLW were optimized in order to avoid ablations of the glass when reaching the surface. First, the laser beam is focused on the surface or typically ~1 µm below the surface. The writing speed was fixed to 50 µm/s while the laser pulse energy was changed. In this chapter, we are relying on the pulse energy as our power reference given that the window for writing is so narrow. Therefore if we express the writing conditions using laser irradiance, the slight difference would be exaggerated. The DLW writing process starts while reducing the pulse energy until we reach just below ablation conditions. This pulse energy is chosen to make waveguides as it sits just below the ablation threshold allowing the creation of type A waveguides hopefully with a moderate refractive index change (∆n). One should mention that the energy window is quite narrow while writing near the glass surface. A variation of 2 to 3 nJ in the pulse energy could cause ablations. A series of 1 cm near surface waveguides were written ~5 mm from the surface in a step process where the laser is focused deeper inside the glass with each pass starting at 1µm to ~12µm. The waveguides were written Even though the NGW1 is written on the surface, it does not exhibit the highest sensitivity between the written waveguides. This is because the mode is cropped at the interface, weakly guided and weakly confined. And it is hard to monitor the transmission decrease following the deposition of the oil droplet. The farther the waveguides are from the surface, the lesser the interaction is with the outer medium, which is expected. The interaction between the waveguides and the outer medium stops at a distance of ~9 µm from the surface (Figure IV.17). The most sensitive waveguides are the ones which are ~1 µm to ~1.75 µm away from the surface exhibiting a transmission loss of ~65% (~4.8 dB) for a 4 mm oil droplet.

𝑃 𝑜𝑢𝑡 ∝ (1 -𝑅 𝐹𝑟 ) 2 ∫ 𝑅 𝑛 𝑒𝑥𝑡 𝑁 (
The mode profile of one of the most sensitive waveguides is shown in the inset of Figure IV.17. The mode profile exhibits no distortion and is totally located inside the glass. Furthermore, even the last written waveguide interacting with the outside medium ~6.5 µm away from the surface exhibits significant transmission losses of ~33% (1.73dB) showing the high sensitivity of type A waveguides. Compared to the work of Lapointe et al where the maximum transmission drop is less than 15% (0.7 dB) for an oil droplet of ~1 cm [169], our waveguides seem to be much more sensitive, up to four times more sensitive. However, one should take into consideration the distance of the waveguides to the surface in the case of Lapointe et al. In a previous work [START_REF] Lapointe | Making smart phones smarter with photonics[END_REF], a side view picture of the near-surface waveguides was shown, and it seems that the waveguides are farther than ours to the surface, which could explain the lower sensitivity. Thus, we believe that it is impossible to write type I waveguides on the surface of the glass like it is the case for type A. This is explained by the fact that the type A occurs before the type I in the pulse energy scale. The DLW in silver containing glasses targets the chemicals inside the glass i.e. silver ions and produce silver clusters. The pulse energy needed to activate the chemical reactions is significantly lower than the pulse energy needed to create type I modification (melting the glass and/or creating color centers).

Finally, type A waveguides are based on two sub-wavelength waveguides highly interacting together guiding one single supermode. It is well known that subwavelength waveguides exhibit a greater evanescent wave and sensitivity [182,199] compared to normal waveguides. This could also be one of the reasons that type A waveguides exhibit a high sensitivity compared to type I waveguides.

Eventually, given that few works have been reported on this subject, one can only assume the hypothesis. In our case, this could be explained by the fact that these two waveguides are so close to the surface, even one of them has a part cropped by the glass interface.

Compared to deeper waveguides, those waveguides exhibited losses up to 50% and the third where the RI is higher than glass, 𝑛 𝑒𝑥𝑡 > 𝑛 𝑔𝑙𝑎𝑠𝑠 . The first region is where the light is guided by total internal reflection (TIR) inside the waveguide with a slight augmentation of the transmission (~2-4%) observed that could be correlated to the fact that the oil drops are lowering the Fresnel reflection coefficient between the propagating mode and the outer medium. This leads to the fact that for deeper waveguides, the whole mode is confined/located inside the glass and no part of the mode is evading it. The second region is where 𝑛 𝑒𝑥𝑡 ~𝑛𝑤𝑎𝑣𝑒𝑔𝑢𝑖𝑑𝑒 , a large portion of light is ejected outside the waveguide given that the critical angle 𝜃 𝑐 is now much lower. The third is for 𝑛 𝑒𝑥𝑡 > 𝑛 𝑔𝑙𝑎𝑠𝑠 , where light is no longer guided by TIR but by many internal Fresnel reflections. One can see that the simulations fit the experimental results. The first resonance i.e. the increase of the transmission for 𝑛 𝑒𝑥𝑡 ≤ 𝑛 𝑔𝑙𝑎𝑠𝑠 was also seen in simulations as well as the experiment, which was not observed by the previous suggested models.

For the second region where 𝑛 𝑒𝑥𝑡 ~𝑛𝑤𝑎𝑣𝑒𝑔𝑢𝑖𝑑𝑒 , when the RI of the oil matches the core's (𝑛 𝑒𝑥𝑡 ~𝑛𝑤𝑎𝑣𝑒𝑔𝑢𝑖𝑑𝑒 ), the mode should be completely ejected outside the waveguide and the transmission should drop to 0% theoretically. Experimentally, it is not the case for our sensor. This could be explained by the following hypothesis.

When the mode is propagating in the waveguide, it is well confined due to the ∆n, and a small portion of the light travels outside as an evanescent wave. However, when immersing the waveguide totally in a liquid exhibiting the same RI as the core, the refractive index difference is almost null and the mode starts to get ejected outside the waveguide from both sides. But, in this case, the waveguide is immersed only from the top side, which means that only the upper part of the mode interacting with the oil will be ejected while a small part of light (lower part of the waveguide) will still be guided inside the written waveguide. A certain distance is required in order to eject the totally mode from the waveguide, which we did not achieve in our case. This was supported by the fact that increasing the oil droplet's size caused the transmission to drop also (see Figure IV.18). In this case the total interaction distance was ~5 mm which was not enough to eject the entire mode outside the waveguide. Therefore, the transmission does not drop to zero in our case when the RI of the oil matches the RI of the waveguide (more specifically, the effective refractive index of the propagating mode). A rough calculation where we assumed that half of the mode is ejected outside the waveguide and that the interaction zone with the mode exhibits a square intensity distribution resulted in transmission dropping to 93.5% (compared to 70% for the experiment) for a 4 mm droplet of oil. In order to increase the exactitude of such calculations, one should consider the real shape of the mode and the real intensity distribution interaction with the liquid, which will not be taken into consideration in this case. For the third region where 𝑛 𝑒𝑥𝑡 > 𝑛 𝑔𝑙𝑎𝑠𝑠 and based on Lumerical simulations, no waveguiding should occur. In fact, as mentioned before, the mode is no longer guided due to In addition, it was found that wisely tuning the laser writing regime could trigger either type A or type I modifications in silver containing glasses. Writing using a 250 kHz laser with µJ pulses (thermal regime in this case) induces a thermal effect and a change in the glass matrix itself corresponding to an intrinsic type of modification compared to an athermal regime using a 9.8 MHz laser and nJ pulses where the type of modification is purely based on the aggregation of the silver ions Ag + pre-existing in the glass matrix. A comparison between the two types shows that the type I exhibits a noticeable thermal affected zone, exhibiting a positive region that is surrounded by a negative one acting as a cladding while the guiding process occurs in the positive region (circular mode profile 4.5 x 5.2 µm 2 due to the circular beam shaping). Type A modification showed smaller waveguides with no presence of an affected thermal zone with an elliptical mode profile of 3 x 5.5 µm 2 .

The photo-induced type A modification is always a positive one, which was not the case for type I modification that flips its sign as a function of the laser parameters and the glass composition. This makes DLW of optical waveguides in zinc phosphate glasses more complicated. Furthermore, it was found that the type A modification occurs well before the type I modification on the pulse energy scale putting the type A modification in the region of the low pulse energy regime.

Taking advantage of the low pulse energy regime, near-surface and on surface waveguides were written in silver containing zinc phosphate glass for the first time with no special needs such as reinforced glass or any compensation methods.

Based on near-surface waveguides, an RI sensor was created that could exhibit a double resonance presenting the opportunity to create two sensing regions when the waveguide is around 1 µm from the surface. A new improved theoretical method was also introduced that fits the experimental results and was able to

Perspectives

Many perspectives arise from such interesting work and a lot of work is required such as transposing the RI sensor into a ribbon shaped silver containing fiber. The only difficulty that one could face for this work is having a really flat top surface of the fiber (±500 nm) in order to write a near-surface waveguide without problems.

For instance, aviation companies demand a technology to detect the level of fuel in airplane fuel tanks. Writing such near-surface waveguides in silver containing ribbon shaped fibers could be one solution to be able to detect in real time the level of fuel in airplane fuel tanks.

Moreover, given that the type A modification exhibits a smooth quality and subwavelength spatial resolution, this could be used for the creation of WBGs in the visible range. It could be performed either by modulating the laser beam to create a modulation of the ∆n, or by writing a waveguide and then overlapping gratings on top of it. This part was performed during the PhD project but not yet characterized.

One perspective that could be a very important and interesting one is studying the opto-optical effect.

▪ Opto-Optical effect

▪ Waveguide laser

Given that under UV-Blue excitation a significant fluorescence intensity in the visible range is emitted by the silver clusters, we tried to create a waveguide laser (WGL) based on the fluorescent emission. A type A waveguide was written using DLW in silver containing glasses and was mounted on the transmission setup. A 532 nm laser was injected inside the waveguide simultaneously with a 394 nm laser diode inside the waveguide using a microscope objective (instead of an optical fiber). Given that the fluorescence emission peak is mainly centred in the green region (~532 nm), one would expect an amplification of the green laser following excitation of the silver clusters. However, unfortunately this was not the case.

Following the injection of a 394 nm laser diode and exciting the silver clusters, a sudden 33% decrease of transmission was observed, as shown in A.4. Calculating the laser fluence, irradiance and energy deposited per voxel (Chapter III)

The average power, after the microscope objective was used, was measured for all parameters used for DLW for both lasers, the T-pulse and the Ti:Sapphire laser.

Then, the pulse energy was extracted using the following equation:

𝐸 𝑝 = 𝑃 𝑎𝑣𝑔 𝑇 (A-1)
where 𝑃 𝑎𝑣𝑔 is the averaged power measured after the microscope objective and 𝑇 is the repetition rate of the laser used.

Then the laser fluence (J/cm 2 ) is calculated using the following equation: where 𝐸 𝑛𝑜𝑟𝑚 is the electric field of the normal mode and 𝐸 𝑑𝑖𝑠𝑡𝑜 the electric field of the distorted mode. In that case, only the electric field was taken into consideration without the magnetic fields.

In the second region where the RI of the oil matches the RI of the waveguide (𝑛 𝑜𝑖𝑙 ~ 𝑛 𝑤𝑎𝑣𝑒𝑔𝑢𝑖𝑑𝑒 ), (more specifically it tends to match the effective refractive index of the propagating mode in the fiber), a theoretical drop to 0% should occur. That is why in our model, the transmission drops to 0 at a RI of 1.604. The reason why the experimental transmission does not drop to 0% is explained above in Chapter IV.

The third region of the theoretical model is where the RI of the oil is higher than the RI of the glass (𝑛 𝑜𝑖𝑙 > 𝑛 𝑔𝑙𝑎𝑠𝑠 ). The simulations were based on the Fresnel Reflection coefficient for a TE mode and fitted to the experimental results using the following equations (similar to the previous suggested models): In addition, a comparitive study between type A and type I waveguides is presented, showing that finely tuning the laser parameters allows the creation of either type A or type I modification inside silver containing glasses. Finally, based on type A near-surface waveguides, a highly sensitive refractive index sensor is created in a 1 cm glass chip, which could exhibit a pioneer demonstration of double sensing refractive ranges. The waveguiding properties observed and reported in the bulk of such silver containing glasses were transposed to ribbon shaped fibers of the same material.

Those results pave the way towards the fabrication of 3D integrated circuits and fiber sensors with original fluorescent, nonlinear and plasmonic properties that are not accessible using the standard type I modification.

  d'Argolight pour équiper le microscope de fluorescence de la Station spatiale internationale pour le SpaceX SPX CRS 11 -Falcon 9.

  photo-induits autour du voxel d'interaction. Ce type de ∆n, basé sur de nouvelles espèces chimiques, implique de nouvelles liaisons chimiques avec des nuages d'électrons plus polarisables que ceux des ions argent, Ag + , initiallement présents dans le verre, ce qui donne accès à un changement d'indice de réfraction local permanent, indépendamment de toute modification de la matrice de verre ellemême, c'est-à-dire une modification extrinsèque à la matrice vitreuse. Le ∆n photoinduit augmente en fonction des paramètres d'irradiation et atteint une valeur maximale d'environ 8x10 -3 . Des guides d'ondes multimodes et monomodes ont été créés à l'intérieur des verres à l'argent. Les guides multimode (MM) et monomodes (SM) ont été réalisés à partir de la photochimie induite de l'argent : un guide d'onde multimode (MM) dans les longueurs d'onde visible et infrarouge présentait des dimensions transverses typiques de ~415 µm 2 avec un ∆n = 4.510 -3 ; un guide d'onde monomode (SM) à la longueur d'onde 𝜆 = 630 nm présentait des dimensions de 36 µm 2 , ∆n = 2.5x10 -3 et des pertes de propagation dont la borne supérieure a été estimée à plus 1.2 dB/cm. Le profil de mode de guide d'onde SM est un mode guidé par chacun des deux plans des agrégats d'argent agissant comme un supermode. La simulation des profils de mode, conjointement à des études de microscopie corrélative, nous a permis de montrer une correspondance significative avec les modes expérimentaux d'une part, et d'autre part de confirmer que le ∆n est vraiment basé sur la création des agrégats d'argent dans les verres d'argent. Après cela, un séparateur 50%-50% de faisceau de géométrie Y et un coupleur 50%-50% ont été écrits pour une longueur d'onde 𝜆= 630nm, ouvrant la porte à la réalisation de composants optiques 3D intégrés et de circuits photoniques intégrés. Finalement, le processus de guidage d'onde a été démontré dans des fibres en forme de ruban contenant de l'argent en inscrivant un guide d'onde de 1,4 cm de long. Ces résultats offrent des opportunités uniques pour des applications telles que la détection fibrée, le filtrage, et/ou la photonique totalement intégrée.

Figure I. 1 : 9 Figure I. 2 : 14 Figure I. 6 : 15 Figure I. 7 :

 192146157 Figure I.1: The atomic arrangement of a A2O3 lattice of a (a) crystal (b) glass. The crystal exhibits atomic order compared to the disorder exhibited by the glass compound [5]. .............................................................................................. 9

Figure I. 9 : 24 Figure I. 14 : 35 Figure II. 1 : 42 Figure II. 4 : 45 Figure II. 5 : 47 Figure II. 6 : 48 Figure II. 7 : 65 Figure II. 22 : 88 Figure II. 41 :

 9241435142445547648765228841 Figure I.9: Schematic presentation of a pulsed laser oscillator. ...........................19

  exhibiting a glass transition region with atomic disorder. Compared to the atomic structure of crystals (Figure I.1.a), glass exhibits a non-organized atomic structure (Figure I.1.b). Nowadays, we have many categories of glasses: oxide glasses, metallic glasses, fluorinated glasses, chalcogenide glasses and organic glasses. In this project, we will be working on oxide glasses, more specifically zinc phosphate glasses.

Figure I. 1 :

 1 Figure I.1: The atomic arrangement of a A2O3 lattice of a (a) crystal (b) glass. The crystal exhibits atomic order compared to the disorder exhibited by the glass compound [5].

Figure I. 2 :

 2 Figure I.2: Volume variation as a function of the temperature while cooling a liquid to form a crystal or a glass. Adapted from [1].

(

  DSC). Comparing to another reference sample, the DSC output curve allows us to see the glass transition i.e. the differential heat capacity therefore detecting the glass transition temperature Tg. A DSC curve is shown in Figure I.4. The Tg can be detected when the step change in heat capacity attains half the value of the total step change [10] (Figure I.4). Moreover, the DSC curve allows the detection of the temperature where the crystallisation effect starts at Tx and the peak of crystallisation at Tc. One should note that the Tg highly depends on the glass composition and its viscosity in the liquid state. Finally, in order to correctly measure Tg we should start by cooling the equilibrium state i.e. cooling the liquid [10].

Figure I. 4

 4 Figure I.4 Possible Differential Scanning Calorimetry (DSC) curve of a cooled liquid. Tg is the glass transition temperature, Tx the temperature of formation of the first crystal, and Tc the crystallisation temperature. The DSC curve taken from [11].

  transmitted (Figure I.5). The coefficient of absorption is given by the Lambert-beer law as: 𝐼 = 𝐼 𝑜 𝑒 (-𝛼𝑙) (I-1) where I is the light transmitted, 𝐼 0 the initial incident light, 𝛼 is the absorption coefficient while l is the length of the sample as shown in Figure I.5. So, from (I-1)

Figure I. 5 :

 5 Figure I.5 : Schematic presentation of an incident light on a glass sample. Io is the incident light, IR the reflected light, IA the light absorbed, IT the transmitted light and IS the scattered light.

Figure I. 6 :

 6 Figure I.6:Absorption spectrum of a Silica glass in the visible and near infrared region.A high transmission is shown in the visible range.

quenching technique shown in Figure I. 7 .

 7 It starts by choosing and weighing the corresponding mix of powders to form the glass. Then the powders are placed in a platinum crucible where they will be heated up to the melting temperature TL (1200°C) in a furnace during 12h. At that temperature, the mixed powders will be transformed into melted liquid (Figure I.7). Then the crucible is removed from the furnace and quenched rapidly to form glass and to avoid any crystallisation process.

Figure I. 7 :

 7 Figure I.7: Schematic representation of the melting-quenching process.

Figure I. 8 :

 8 Figure I.8: Schematic presentation of a cylindrical optic fiber with inner core and outer cladding

I. 3 . 1 .

 31 Definition of laser LASER stands for "Light Amplification by Stimulated Emission of Radiation". It is based on the stimulated emission process introduced by Einstein in 1917. Basically, a laser is composed of a pump source, active/gain medium and a cavity as shown in Figure I.9. The amplification process of light takes place inside the laser cavity, more specifically in the gain medium. It is achieved by a stimulated emission process from an atomic or molecular system with transitions in an inverted population (i.e. the upper energy level is more populated than the lower).

Figure I. 9 :

 9 Figure I.9: Schematic presentation of a pulsed laser oscillator.

Figure I. 9

 9 for example could be amplified using an external amplifier as shown in Figure I.10.

Figure I. 10 :

 10 Figure I.10: Schematic presentation of a laser beam (input beam) amplified using an external amplifier. Taken from [29].

Figure I. 11 .

 11 Figure I.11. It is characterized by the intensity profile, the beam waist, Rayleigh range, the depth of focus, the beam divergence and the beam wave front curvature.

Figure I. 11 :

 11 Figure I.11: Intensity profile distribution of a Gaussian beam as function of r.

Figure I. 12 :

 12 Figure I.12: Schematic presentation of a propagating Gaussian beam.

Figure I. 13 :

 13 Figure I.13: Schematic presentation of the multi-photon absorption process. In this case, an electron in the valence band absorbs 3 photons to pass to the conduction band.

Figure I. 14 :

 14 Figure I.14: Schematic presentation of the photo-ionization processes during laserglass interaction. (a) Multi-photon ionization (MPI): An electron absorbs two or more photons to be promoted in the conduction band (b) Tunneling ionization where the electron passes through a barrier to be promoted the conduction band (c) Avalanche ionization where an electron in the conduction band absorbs two or more photons, then collides and promotes an electron from valence band to the conduction band.Inspired from[START_REF] Chris | Laser-induced breakdown and damage in bulk transparent materials induced by tightly focused femtosecond laser pulses[END_REF][START_REF] Bérubé | Étude des changement structuraux photo-induits dans le verre à l'aide des imulstions femtosecondes et application à l'inscription de composants photoniques[END_REF].

  deposited energy is proportional to the electron density. In other words, the electron density distribution in the material i.e. the shape of the plasma dictates the morphology of the modified region. This was proved by Couairon et al. They compared the morphology of a modified region in fused silica glass with the numerical simulation of electron density distribution and they found a significant match [43] as shown in Figure I.15.

Figure I. 15 :

 15 Figure I.15: (a) Scanning electron microscopy image of a track damage obtained by focusing femtosecond pulses inside fused silica (b) Numerical simulation electron density (c) Computed intensity counterplots. The comparison between experiment and simulations shows a good match of the morphology. Figure taken from [43].

Figure I. 16 :

 16 Figure I.16: Timeline of physical phenomena involved during laser-matter interaction. Inspired from [33].

  mode. When the laser is operating in continuous mode, it has no repetition rate because it is emitting light all the time, non-stop as shown in Figure I.17.a However, a pulsed laser emits pulses spaced by a certain time depending on its repetition rate (Figure I.17.b). The pulses exhibit a pulse duration 𝑇 0 and are separated by a period of T which is determined by the laser repetition rate 𝜏 = 1 𝑇 ⁄ .

Figure I. 17 :

 17 Figure I.17: Schematic presentation of the temporal evolution of the power of a (a) continuous laser (b) pulsed laser.

Figure I. 18 :

 18 Figure I.18: Numerical simulations of the heat accumulation process inside glass following laser irradiation for different repetition rates, 100kHz, 500kHz and 1MHz. A heat accumulation process starts taking place at the 500kHz repetition rate [48].

Figure I. 19 :

 19 Figure I.19: Comparison between athermal and thermal regimes. For the athermal regime, low repetition rate laser, the pulses are well spaced in time so that the temperature does not have time to build up in the material. However for the thermal regime, high repetition rate laser, the pulses are close in time and the temperature builds ups.

  as shown in Figure I.20.Therefore, when using a high NA, objective pulse energy of nJ can produce modifications in glasses. This is expected since it increases the laser irradiance interacting with the glass. The laser irradiance is defined by the quantity of power per surface area of the beam spot size. Having the same amount of power in a tighter surface area (smaller beam spot size) increases the irradiance/laser dose deposited in the glass. Taking into account (I-23), we can see that decreasing the beam waist increases the laser irradiance in the glass. In this work, we consider the laser irradiance to be:

Figure I. 20 :

 20 Figure I.20: Modification threshold dependence as a function of the numerical aperture of the microscope objective used in borosilicate glass [54].

II. 2 II. 3 44 II. 3 . 2 II. 4 69 II. 4 . 3

 23443246943 photo-induced refractive index change by femtosecond laser writing. Finally, Chapter IV the last chapter will address the direct laser writing of near-surface waveguides as well as the creation of a refractive index sensor.

Figure II. 1 :

 1 Figure II.1: Schematic presentation of the Direct Laser Writing (DLW) process.

Figure II. 2 :

 2 Figure II.2: Map of the modification thresholds in fused silica for the four regions/three types of modification as a function of the pulse energy and the numerical aperture. Adapted from [64].

Figure II. 3 :

 3 Figure II.3: The refractive index changes/modification classified as function of the irradiance. Pictures for every type of modification, waveguides, nanogratings and voids.

II. 3

 3 .1.a. Theory of waveguiding This part is inspired from [98, 99]. Let's consider a planar dielectric waveguide surrounded by a lower refractive index medium as shown in Figure II.4. The light propagates inside the waveguide by the Total Internal Reflection (TIR) principle. The inner part of the waveguide is called the core while the outer part is called the cladding. Light propagates inside the waveguide's core while making angles 𝜃 with the z axis (Figure II.4) following many multiple internal reflections (Figure II.4).

Figure II. 4 :

 4 Figure II.4: Schematic of guided and unguided rays in a planar dielectric waveguide. The rays exhibiting a propagation angle 𝜃 lower than  𝑐 ̅ = 𝑐𝑜𝑠 -1 (𝑛 2 𝑛 1 ) ⁄ are only guided. Taken from [99].

Figure II. 5 .

 5 The selfconsistency condition allows to determine the number of propagating modes in a waveguide as well as the propagation angles for different modes (in case the waveguide is multimode). No more details are presented in this manuscript concerning that matter but if readers are interested, they are referred to chapter 8 of the following reference[START_REF] Saleh | Fundamentals of Photonics[END_REF].

Figure II. 5 :

 5 Figure II.5: Graphical solution of (II-2) to determine propagation angles 𝜃 of the mode of a planar dielectric waveguide. (a)The right side (RHS) and left side (LHS) of the equation are plotted as a function of sin𝜃. The intersection points marked by filled circles determines the propagation angles 𝜃. On the other hand, each intersection of the tan function (LHS) corresponds to a mode. In this example, the waveguide can support up to 9 modes. Taken from [99]. (b) RHS (orange dashed line) and LHS (black full line) of (II-2) is plotted for a planar waveguide exhibiting a single mode aspect with ∆n=2x10 -3 , dimensions of 5µm at a wavelength of 630nm.

II. 6 .

 6 The ∆n between the core and the cladding is enough to confine light inside the core. The ∆n could be a step-index or a gradient one. In this case, we are only considering the step-index case given that the photo-written waveguides almost exhibit a step index ∆n between the pristine glass and the irradiated zone.

Figure II. 6 :

 6 Figure II.6: Schematic presentation of the way light rays propagate inside a multimode step-index optical fiber. Taken from [99].

Figure II. 7 :

 7 Figure II.7: The acceptance angle 𝜃 a of an optical fiber. The rays within the acceptance cone are guided inside the fiber by total internal reflection. The numerical aperture is given by: NA=sin𝜃 𝑎 . Taken from[START_REF] Saleh | Fundamentals of Photonics[END_REF].

  Figure II.8: (a) Top View phase contrast image of a type I waveguide written in silver containing zinc phosphate glass under white light illumination (b) Optical Path Difference (OPD) profile associated to the waveguide. A negative OPD is observed.

Figure II. 9 :

 9 Figure II.9: Tranverse view of a depressed cladding waveguide (DCW) (a) composed of 54 DCW distributed over 2 rings (b) composed of 212 DCW distributed over 4 rings. Taken from [101]

Figure

  Figure II.10: Schematic presentation of two close waveguides interacting along a distance "L" and separated by a distance "d". The power is coupled between them.

[

  108] and shown in Figure II.11.

Figure II. 11 :

 11 Figure II.11: Horizontal (squares) and Vertical (triangles) polarization transmission of laser written directional couplers as a function of the interaction length. First, the effect of the polarization is so slight, however when increasing the interaction distance, a bigger shift occurs indicating that the coupling effect could be altered based on the injected light polarization. Taken from [108].

Figure II. 12 :

 12 Figure II.12: Schematic presentation of the first demonstration of a directional coupler presented by Strelstov et al [109].

Figure II. 13 :

 13 Figure II.13: Schematic presentation of a 50-50 directional coupler. The light is injected in one branch and 50% of the power is coupled into the other branch. Taken from [110].

Figure II. 14 :

 14 Figure II.14: (a) Schematic presentation of the 3D coupler (b) Mode profiles of the output indicating that the light is coupled in the three branches with a ratio of 43%:28%:29%. Taken from [111].

Figure II. 15 :

 15 Figure II.15: (a) Schematic design of the 1 to 8 beam splitter with 7-Y junctions (b) Side view output of the far-field modes [113]

Figure II. 16 :

 16 Figure II.16: (a) Schematic presentation of the laser writing of the 1x3 beam splitter (b) Side view output visualization of the divided modes [114].

Figure II. 17 :

 17 Figure II.17: Schematic presentation of the PointbyPoint (PbP) process of writing a Waveguide Bragg Grating (WBG) as well as a bright field image of the top view of the WBG. Taken from [101]

Figure II. 18 :

 18 Figure II.18: (a) Top view of the Waveguide Bragg Grating (WBG). The waveguide is indicated by the black lines (b) Reflection spectrum of the written WBG (upper curve) compared to the transmission of a normal waveguide (lower curve). Taken from [115].

II. 3 . 7 .

 37 Photonic lantern Direct laser writing in glasses led also to the formation of photonic lanterns (PL) which are used for instance for astronomy purposes. PLs consist in writing multiple waveguides forming one multimode (MM) rectangular waveguide that gets separated into several single mode (SM) waveguides on the exit facet of the glass, as schematically depicted in Figure II.19.

Figure II. 19 :

 19 Figure II.19: Sketch of a photonic lantern (PL) starting by a multimode rectangular waveguide separating into several single mode waveguides. Taken from [125].

Figure II. 20 :

 20 Figure II.20: Side view bright field photos of the (a) 4x4 single mode waveguides (b) rectangular multimode waveguide. Output mode images of (c) the 4x4 single mode waveguides following the injection in the rectangular multimode waveguide (d) rectangular waveguide mode following the injection of light in the 4x4 single mode array waveguides. Taken from [125].

[ 62 ,

 62 100, 131, 132]. Many zinc phosphate glasses were fabricated and irradiated and only glasses exhibiting an O/P ratio of 3.25 exhibited positive ∆n where the others glasses exhibited negative ∆n [62, 100, 132]. Single mode waveguides at 660 nm where the ratio of O/P=3.25 was also written in zinc phosphate glasses exhibiting a ∆n=3x10 -4 [131]. Ferrer et al. also reported the laser writing of waveguides operating at 633 nm [133].

Figure II. 21 .

 21 The following results imply that the incorporation of silver in the glass influences the absorption band of the glass by shifting it to higher wavelengths. This is a typical property of the silver ions integrated into the glass matrix. So, the bandgap of the glass is shifted to lower energy levels (higher wavelengths as shown in Figure II.21) implying that the silver ions enhance the photosensitivity of the glass.

Figure II. 21 :

 21 Figure II.21: Absorption coefficient as a function of the wavelength for zinc phosphate glass and silver containing zinc phosphate glasses with different silver concentrations. The silver containing glasses exhibit a higher absorption band and are shifted to higher wavelengths compared to non-containing zinc phosphate glass. Adapted from[START_REF] Bourhis | Photostructuration par laser infrarouge femtoseconde de verres photosensible de phosphate de zinc, d'argent et de gallium[END_REF].

Figure II. 22 :

 22 Figure II.22: Absorption as a function of the wavelength for the PZnAg2 sample from UV to IR. A good transparency window is observed between 380 nm and 2700 nm.

  2+ . Based on a chain reaction, larger silver clusters Agm x+ are formed from Ag + , Ag 0 and Ag 2+ inside the glass matrix [44, 136], as schematically presented in Figure II.23. The transverse Gaussian beam profile induces the photo dissociation of the silver clusters in the centre region where the irradiance is higher [136].

Figure II. 23 :

 23 Figure II.23: Schematic presentation of the formation of silver clusters in silver containing glasses following laser irradiation.

Figure II. 24 :

 24 Figure II.24: Absorption (black) of the photo-induced silver clusters following laser irradiation exhibiting two main absorption bands around 290 and 345 nm. Fluorescence emission (orange) under blue light excitation at 405 nm.

  Figure II.22. Using a femtosecond laser induces non-linear effects i.e. four-photon absorption process in this case. This process was already explained in detail in section I.3.3.a. In addition to that, thanks to the non-linear process, structures below the diffraction limit could be created inside silver containing glasses, as it has been reported earlier by our group [136]. Static direct laser writing of silver containing glasses, i.e. laser fixed and sample fixed, results in the creation of 3D fluorescent (due to the silver cluster formation) structures exhibiting dimensions below the diffraction limit [136]. In order to have a better idea of the morphology of such structures, they were visualized using a fluorescence confocal microscope to resolve the structures as shown in Figure II.25. The confocal fluorescence images of the top view of the structures reveal a ring shape of fluorescence [136]. The fluorescence is attributed to the distribution of silver clusters; therefore, the clusters are distributed around the interaction voxel. The ring shape is due to the photo dissociation of the silver clusters created in the middle thanks to the transversal Gaussian profile of the laser beam (Figure II.25.bd). The side view photo exhibits two fluorescent lines arranged into a pipe shape corresponding more or less to the Rayleigh range (Figure II.25.c-e) [44].Eventually, one can say that the structures' morphology is dictated by the laser beam profile.

Figure II. 25 :

 25 Figure II.25: (a) Sketch of the morphology of the structures following static direct laser writing (DLW) (b) confocal fluorescence images under UV excitation (exc=405nm) of top view (xy) plane, ring shape (c) side view (xz) plane, two fluorescent lines in a pipe shape [136]. Schematic presentation of the writing process for (d) top view (xy) plane, photodissociation of the clusters in the middle (e) side view (xz) plane.

  that moment, the spatial distribution of Ag 0 corresponds to the slightly diffused distribution of pre-existing free electrons (green circle, Figure II.26.b). The absorption of the laser pulse induces and increases the temperature in the region resulting in thermal diffusion (Blue arrows, Figure II.26.b). The diffusion of Ag 0 (green arrows, Figure II.26.b) is highly activated by the temperature which allows these species to meet with Ag + ions and take a part in the following kinetic reaction: Ag 0 + Ag + → Ag2 + . The red circle (Figure II.26.b) reproduces the beginning of the reaction in the area of maximal concentration of Ag 0 . The reaction of the first stage of silver cluster formation Ag 0 + Ag + → Ag2 + ends when the concentration of silver atoms Ag 0 wears off. So, the spatial distribution of Ag2 + corresponds slightly to the spatial distribution of pre-existing Ag 0 (red circle, Figure II.26.c). The trapping process and reactions are so fast that the concentration of free electrons, holes and Ag 0 wears off before the next laser pulse. The following laser pulse destroys the silver clusters in the center by photo-dissociations where the laser pulse is so intense (Figure II.25). The next laser pulse again creates a reservoir of free electrons which triggers kinetic reactions responsible for the formation of silver clusters. The previously mentioned cycle repeats itself from one pulse to another and the non-dissociated silver clusters gathers on the periphery of the laser beam forming a ring shaped structure [33, 44, 136, 140, 141] following a train of pulses (Figure II.26.d). Thus, the fast diffusing of free electrons destroys the initial spatial charge neutrality of the electron-hole plasma inside the focal spot and creates an ambipolar electric field. It accelerates the diffusion of ions by a factor of two. Therefore, the electron-hole trapping process provides the formation of frozen charge redistribution in space and corresponding radial static electric field 𝐸 ⃗ 𝑑𝑐 (black arrows, Figure II.26.d) [140].

Figure II. 26 :

 26 Figure II.26: Scheme of the formation of silver clusters during laser-glass interaction in silver containing glasses. Taken from [140].

Figure II. 27 :

 27 Figure II.27: (a) Fluorescence pattern of a written line under 405 nm excitation; (b) four-line of electric field induced second harmonic generation (EFISHG) under 1030 nm femtosecond laser excitation (c) superposition of the fluorescence and EFISHG correlated patterns under 405 nm and 1030 nm excitation. Taken from [143].

Figure II. 28 :

 28 Figure II.28: Fluorescence intensity as a function of the laser irradiance and number of pulses for different laser repetition rates (a) 10MHz (b) 1MHz (c) 100kHz (d) 10kHz. Taken from [11].

Figure II. 29 :

 29 Figure II.29: Top view under white light illumination for different lines written using a 250 kHz laser emitting at 1030 nm with a fixed pulse energy of 0.26 µJ for three different speeds from the left to the right: 10 mm/s-5 mm/s-1 mm/s. To be compared with figure 4 in [148].

  heated at ~Tg-10 °C and annealed at Tg-40 °C for 12 hours. As first demonstrated, two glasses were drawn where one of them did not exhibit any silver integration. The idea aims to highlight the luminescence properties of the silver containing glass. Both preforms are shown in Figure II.30.a. The preform with no silver shows no luminescence under UV excitation at 𝜆=260nm [149]. The silver containing zinc phosphate glasses exhibit an absorption band at 𝜆=245nm due to the presence of silver ions Ag + resulting in fluorescence mainly around 𝜆=368nm. This fluorescence emission has been attributed to the d 10 ↔d 9 s 1 transition of Ag + ions homogenously dispersed throughout the glass matrix [150]. Thermal drawing was performed using a dedicated 3-meter-high optical fiber draw tower composed of an annular electrical furnace with a sharp temperature profile, a diameter monitor, a tension dancer and a collecting drum. The preform was slowly fed into the furnace and the temperature was gradually increased up to ~700°C under continuous oxygen gas flow (3l.min -1 ). The preform holder motion and capstan rotation velocity were controlled in real-time to produce the targeted fiber diameter.

Figure II. 30 :

 30 Figure II.30: Zinc phosphate glass under UV excitation (a) non-containing (PZG-4N) and silver containing (PZG-2N2A) preforms. PZG-2N2A only exhibiting fluorescence emission; (b) fibers and a leftover of a preform. Taken from [149].

Figure II. 30

 30 Figure II.30.b shows the rest of the drawn preform, capillaries and fiber under UV excitation. At first impression, the homogenous macroscopic luminescence under UV excitation is correlated to the homogeneous distribution of silver ions Ag + in the preform, capillaries and fiber. The comparison of the fluorescence properties of the fiber and the bulk glass implies that the fluorescence emission is fully preserved at the microscopic level also as shown in Figure II.31. This refers to the successful drawing process where neither clustering nor reduction of the Ag + occurred.

Figure II. 31 :

 31 Figure II.31: Comparison between bulk glass and fiber fluorescence emission properties (exc=245nm). A good match is found indicating that the drawing process preserved the glass properties. Taken from [149].

Figure II. 32 :

 32 Figure II.32: (a) Thermal drawing of ribbon fibers. Preform, bottom-neck preform and drawn fibers under UV excitation (exc=245nm). (b) Sketch, longitudinal and side view of the drawn ribbon fiber. A flat surface with a rectangular side view is obtained. Taken from [149].

  Figure II.33.c. The amplitude of the absorption band varies as a function of the irradiance, which is expected. Using lower irradiance results in generating less silver clusters, therefore less absorption. Those two absorption bands are typical of the silver clusters Agm x+

Figure II. 33 :

 33 Figure II.33: Top view of the ribbon fiber (a) under white illumination before DLW (b) under UV excitation (exc=405 nm) following DLW. The fluorescence of the written structures could be observed. (b) Fluorescence intensity broad band emission of the structures under UV excitation (exc=405 nm). (c) Fluorescence of the written cartography and the corresponding differential transmission spectra. A higher absorption band is observed for a higher laser irradiance. Taken from [149].

  White light is used to visualize and find the surface of the glass while the blue illumination serves to monitor and visualize the fluorescence of the silver cluster created during DLW. A 405 nm high pass filter is placed before the CCD in order to cut the blue diode at 405 nm allowing the observation of the fluorescence of silver clusters.

Figure II. 34 :

 34 Figure II.34: Schematic of the laser setup used for direct laser writing.

  white light. The sensor is based on a CCD camera with a modified Hartmann Mask placed in front. The incident incoherent light beam is diffracted by the mask into four replicas to create an interferogram on the CCD as shown in Figure II.35.

Figure II. 35 :

 35 Figure II.35: Sketch of the SID4Bio wavefront sensor working principle. The incident beam is diffracted by the modified Hartmann Mask into four replicas making an interferogram on the sensor (CCD Camera) [155].

Figure II. 36 :

 36 Figure II.36: Sketch of the light delayed by a refractive index object (n2) with a specific thickness "e" different than the surrounding medium (n1) leading to the construction of the phase image. The optical thickness i.e. optical path difference could be obtained [155].

Figure II. 37 :

 37 Figure II.37: The SID4Bio installed on a transmission microscope. The light is diffracted by the grating creating the interferogram on the CCD camera giving an output of an intensity and phase image [155].

  𝑛 𝜆 is the refractive index at wavelength ,  is the polarizability and 𝜌 is the density. The ∆n equation consists of two parts, volume changes in the glass ( The volume changes could be obtained from the cantilever based on the strain. The strain is measured by the deflection of the cantilever following laser irradiation. Furthermore, the change in polarizability was studied earlier by Hiroshi et al for fused silica and the range of values is well known [161]. So, based on the volume and the polarizability changes, the ∆n could be calculated using (II-11) [159]. It was found that the calculated values are lower than the values expected so eventually, this mechanical method is still to be calibrated and compared to an optical one [160]. During my PhD, I was somehow involved in a comparative study between different quantitative phase imaging techniques. Those techniques allow to directly measure the ∆n. More details are presented in the Appendix part A.3 II.6. Results II.6.1. Structures' morphology Previous results in the group were based mostly on static DLW in silver containing glasses trying to understand the basics of the laser-glass interaction. This project aims towards functionalizing those silver clusters, creating waveguides and optical components. In order to make waveguides, two crucial points are necessary: characterizing the morphology of the photo-induced structures and measuring the refractive index change (∆n). In order to do so, many linear photo-induced structures were written inside silver containing zinc phosphate bulk PZnAg1 glass typically 160µm below the surface (to minimize the spherical aberrations and optimize the confocal fluorescence characterization). The glass sample was translated perpendicularly to the laser beam to form linear structures as shown in Figure II.38.a. Silver clusters were created based on the non-linear absorption effect as explained earlier. These clusters are characterized by two main absorption bands, 290 nm and 345 nm resulting in a broad band fluorescence emission in the visible range as mentioned before (Figure II.24) and reported by[START_REF] Bellec | 3D Patterning at the Nanoscale of Fluorescent Emitters in Glass[END_REF] 136, 141, 152]. Therefore, the fluorescence refers to the presence of silver clusters.

Figure II. 38 :

 38 Figure II.38: (a) Schematic of the morphology of the structures following perpendicular translation to the laser beam propagation inside silver containing zinc phosphate glasses. Fluorescence confocal images of the (b.i) top view (xy) plane, and (c.i) side view (xz) plane. Schematic presentation of the writing process with (b.ii) top view and (c.ii) side view.

  photo-induced silver clusters are responsible for the positive ∆n following DLW.

Figure II. 39 :

 39 Figure II.39: (a) Fluorescence image (ex=480nm, em=550nm) of the written cartography. Writing irradiances are presented along the vertical axis while the number of pulses appears along the horizontal axis (b) Blowup of the phase image under white light illumination of the B2 structure (c) positive refractive index change (∆n) determined from the phase image of B2.

Figure II. 40 :

 40 Figure II.40: (a) Phase image under white light illumination showing one line of phase shift; (b) Line profile obtained from the phase image revealing only one positive peak of optical path different in that case for the structures instead of two peaks; (c) left column: experimental silver cluster spatial distribution for a progressive scale of irradiances; right column: simulated distribution of the silver clusters. For (i) and (v) low laser irradiance is used and a full disk of fluorescence is observed, which is not the case for higher irradiances. Taken from [140]

  x 10 -4 up to 8 x 10 -3 in this case( Figure II.41), which is to be compared to the ∆n values obtained in fused silica going from 1.3 x 10 -3 up to 1.7 x 10 -2 with type I modifications[START_REF] Ams | Study of the influence of femtosecondlaser polarisation on direct writing ofwaveguides[END_REF] 162]. In this study, the depth (length in the z plane (Figure II.38.a) of the structures) was averaged to 8 µm i.e. all the structures were considered having a depth of 8 µm.

Figure II. 41 :

 41 Figure II.41: Refractive index change variation (∆n) as a function of the number of pulses and laser irradiance. ∆n increases as a function of the laser parameters.Laser repetition rate 9.8 MHz.

Figure II. 42 :

 42 Figure II.42: Variation of the length of the structure along z as a function of the laser parameters, laser irradiance and writing speed. The dimensions increase as a function of the laser irradiance. Laser repetition rate 9.8 MHz. The shades correspond to the standard deviation of the values.

1 .

 1 3NA oil objective as shown in Figure II.43.

Figure II. 43 :

 43 Figure II.43: Top view phase image of different lines separated by 1 µm in the z plane. The seventh line becomes blurry indicating that the optical system is limited to around 6 µm in depth.

6

  µm. If the structure is deeper, the OPD is underestimated i.e. underestimating the ∆n, which explains the divergence of the value of ∆n when taking into consideration the real depth of the structure. Considering that and compensating for it (∆𝑛 = 𝑂𝑃𝐷 𝑒 𝑟𝑒𝑎𝑙 ⁄ * 𝐶 𝑐𝑜𝑚𝑝𝑒𝑛𝑠𝑎𝑡𝑖𝑜𝑛 ), the ∆n values where plotted again in Figure II.44, where 𝑒 𝑟𝑒𝑎𝑙 is the real thickness of the structures and 𝐶 𝑐𝑜𝑚𝑝𝑒𝑛𝑠𝑎𝑡𝑖𝑜𝑛 the calculated compensation coefficient. The compensation method took into consideration the Fresnel number in that case. One can see that the results make more sense i.e. increasing the number of pulses and/or laser irradiance increases the ∆n. In the first study of the ∆n as a function of the laser parameters (Figure II.41), all the structures' lengths were fixed to 8 µm. For this study, all the structures exhibiting lengths more than 6 µm where considered as having a length of 6 µm (fixed method with (∆𝑛 = 𝑂𝑃𝐷 6000) ⁄ given that our system is limited to around 6 µm of depth of field (z plane Figure II.43). The results are plotted in Figure II.44 and compared to the compensation method. We used the compensation method and took into account that all the structures exhibiting 6 µm in length (in the z plane) converge and have more or less the same values. However, not compensating for the OPD value leads to an underestimating to the ∆n value of our structures, which is not plotted in Figure II.44.

Figure II. 44 :

 44 Figure II.44: Refractive index change (∆n) as a function of the number of pulses for two methods: (orange) using the compensation method (black) fixed method where the depth of the structure higher than 6 µm is considered as 6 µm. Both methods converge more or less to the same values. The black shades correspond to the standard deviation of the values.

[

  136]. The glass sample was polished and etched using acid to reveal the structures to the surface. The HRSEM profile line exhibited a rise on the edges of the photo-induced structures with 80 nm width indicating a change in the chemical composition or a topological bump (Figure II.45.b) [136]. In order to investigate these hypotheses, an AFM image proves that the topology on the edges of the photo-induced structure does not increase (Figure II.45.c). Therefore, we can attribute the enhanced contrast in the edge of the HRSEM image to a change in chemical composition i.e. the presence of silver clusters. However, in the middle of the structure a topological modification is observed that is due to the selective acid-etching performed [136].

Figure II. 45 :

 45 Figure II.45: (a) High Resolution Scanning Electron Microscopy (HRSEM) image of the top view of a ring shape structure formed by silver clusters; (b) Line profile extracted from the HRSEM photo indicating a bump on the edges; (c) Atomic Force Microscopy (AFM) profile indicating no bumps on the sides. The bumps observed in the HRSEM are due to a change in the chemical composition and not to topological changes. Taken from [136].

Figure II. 46 :

 46 Figure II.46: (a) fluorescence; (b) HRSEM, top view of the photo-induced structures. The fluorescence spatial distribution is correlated to the HRSEM indicating that the silver clusters are responsible for the change in the chemical composition. The scale bar is 1 µm. Taken from [136].

Figure II. 47 :

 47 Figure II.47:(a) Silver clusters differential absorption spectrum as a function of the wavelength showing two main absorption bands near 290 nm and 350 nm; (b) Refractive index change (∆n) determined from the spectrum shown in (a) based on a Kramers-Kronig analysis, considering the filling factor of the silver clusters' spatial distribution. DLW parameters: 7TW/cm 2 -40 µm/s.

Figure II. 48 :

 48 Figure II.48: (a) Schematic of the direct laser writing process and the laser injection; (b) Picture of the bulk sample under UV excitation (ex=405nm) highlighting the fluorescence of the waveguide (indicated by the white arrow); (c) fluorescence image of the side view of the waveguide under UV excitation (ex=405nm); (d) near-field guided mode profile following laser injection [149].

  Figure II.49.e shows the fluorescent side view of WG1 and WG2 respectively. Then, the laser was injected inside the waveguides. Both waveguides exhibited a multimode aspect. Figure II.49.b and Figure II.49.f show one of the higher order guided mode profiles following laser injection. The UV light was filtered using a 450 HP filter. One can observe that the guided mode profile is supported by the two fluorescent planes i.e. the two planes of silver clusters, therefore providing another proof that the silver clusters are responsible for the ∆n in silver containing glasses. The 405 nm diode was turned off in order to better visualize the guided mode profile, as shown in Figure II.49.c and Figure II.49.g respectively for WG1 and WG2. Moreover, simulations were conducted using LUMERICAL software to simulate the propagation of light in such structures. The details of the simulations were presented earlier in the manuscript. Figure II.49.d and Figure II.49.h show the simulated modes. A significant match is noticed between the experimental and the simulated modes confirming once again our hypothesis. WG1 exhibited a ∆n of 4.5x10 -3 while WG2 a ∆n of 3x10 -3 . The ∆n was measured using the SID4Bio wave front sensor. Many modes were supported by those waveguides given that they exhibit relatively large dimensions of 15 µm with a relatively high ∆n.

Figure II. 49 :

 49 Figure II.49: Cross section view of fluorescence under UV side-excitation (exc=405nm) of (a) WG1, (e) WG2. Superimposed near field mode profile and fluorescence features for (b) WG1, (f) WG2. Near field mode profile for a high order propagating mode of (c) WG1, (g) WG2. Simulated mode profile using LUMERICAL for (d) WG1, (h) WG2. DLW parameters for WG1: 8 TW/cm 2 -10µm/s. For WG2: 8TW/cm 2 -20µm/s.

Figure II. 50 :

 50 Figure II.50: Near field mode profile following laser injection at 1.55 µm (a) fundamental mode, (b) higher order mode. The waveguide presented a multimode aspect. DLW parameters: 8TW/cm 2 -10 µm/s.

a

  confocal fluorescence microscope (Figure II.51.a), which provides a better resolution of silver cluster spatial distribution. As expected, the photo-induced structures consisted of two parallel planes exhibiting a full width half maximum (FWHM) of 0.55 µm (limited by confocal microscope resolution) and spaced by 1.85 µm along the y direction (Figure II.51.b). The corresponding length of the twin structure along z was measured to be around 6 µm (Figure II.51.c). However, the spacing between the two parallel fluorescent planes as well as their extent along z could both be varied from 1.8 µm to 3 µm and 4 µm to 15 µm respectively, depending on the microscope objective used as well as the laser parameters. The study of the extent along z was shown earlier as a function of the laser parameters (Figure II.42).

Figure II. 51 :

 51 Figure II.51: (a) Fluorescence confocal image of the side view of the waveguide. (b) Normalized horizontal fluorescence profile averaged along the y axis. (c) Normalized vertical fluorescence profile averaged along the z axis.

Figure II. 52 :

 52 Figure II.52: (a) Phase image of the top view of the waveguide under white illumination (b) Refractive index change (∆n) profile obtained from the phase image. DLW paramters: 9TW/cm 2 -60 µm/s.

Figure II. 53 :

 53 Figure II.53: Refractive index change (∆n) profile for different laser passages for an irradiance of 7 TW/cm 2 and a speed of writing of (a) 50 µm/s, (b) 30 µm/s, (c) 20 µm/s. A negative ∆n dip appears for lower writing speeds and for many laser passages.

Figure II. 54 :

 54 Figure II.54: Superposition of the silver cluster fluorescence spatial distribution (black), normalized topology after chemical etching (red) and silver ions concentration distribution (blue). Taken from [141]. During the development of silver containing glasses, it was observed that incorporating silver ions in the glass matrix tended to increase the refractive index of the glass, as shown in Figure II.55 [135]. Therefore, the absence of silver ions in the middle could be responsible for the negative ∆n dip observed in the middle.Furthermore, many laser passages imply more consumption of the silver ions reservoir i.e. the silver ions are no longer present in the middle, probably diffused leaving a small negative ∆n dip.

Figure II. 55 :

 55 Figure II.55: The variation of the refractive index of the non-containing and silver containing zinc phosphate glasses as function of the silver concentration incorporated in the glass matrix. The higher the concentration of silver the higher the refractive index of the glass is (from bottom to top). Data from [135].

Figure II. 56 :

 56 Figure II.56: (a) Experimental: (a.i) Near field mode profile after injecting a 630 nm laser, (a.ii) normalized horizontal mode profile intensity averaged along the z axis, and (a.iii) normalized vertical mode profile intensity averaged along the y axis. (b) Simulations: (b.i) simulated mode profile (to compare with Figure II.56.a.i), (b.ii) normalized horizontal intensity mode profile averaged along the z axis (to compare with Figure II.56.a.ii), and (b.iii) normalized vertical mode profile intensity averaged along the y axis.

Figure II. 57 :

 57 Figure II.57: Schematic model of the simulated waveguides using Lumerical Mode solutions software. The waveguides are simulated as two parallel ellipsoids with thickness "e", with a length "z" and separated by a distance "d". The color scale corresponds to the refractive index change. In this case, the glass refractive index change is 1.6 while the waveguide is 1.608 corresponding to a refractive index change (∆n) of 8x10 -3 .

Figure II. 58 :

 58 Figure II.58: Spatial superposition of the measured refractive index profile (∆n) (black), simulated near-field mode profile (blue) and experimental near-field mode profile (red). A good match is observed between the simulated and experimental modes and the ∆n distribution.

Figure II. 59 :

 59 Figure II.59: Variation of the minimum ∆n required to trigger the multimode aspect as a function of the thickness of the structures. Blue vertical line indicates the thickness measured by confocal microscope and used during simulations (~500nm) while the red line indicates the HRSEM measurement (~100nm) performed earlier in our group [139].

  Figure II.60.a shows the fundamental mode of a multimode waveguide while Figure II.60.b shows the fundamental mode of a single mode waveguide. The MM waveguide is 13 µm long while the SM waveguide is 6 µm. The transverse profiles of both modes are presented in Figure II.60.c. One can see that for the MM waveguide, the global mode is more confined. The two silver planes better confine light compared to the SM waveguide. The light intensity

Figure II. 60 :

 60 Figure II.60: Fundamental near-field mode profile of a (a) multimode (MM) waveguide, (b) single mode (SM) waveguide. (c) Near-field mode profiles of the MM and SM waveguides. DLW parameters for SM: 9TW/cm 2 -60µm/s, for MM: 10.5TW/cm 2 -20µm/s.

Figure II. 61 :

 61 Figure II.61: (a) Sketch of the Y-beam splitter dividing the input light into two equal outputs (top view), (b) top view fluorescence image of the Y-junction (ex=480nm, em=550nm), (c) output modes of the beam splitter (d) normalized intensity profile of the output modes indicating an almost equal splitting of light between both outputs. DLW parameters: 9TW/cm 2 -60µm/s.

Figure II. 62 :

 62 Figure II.62: Sketch of the S-bend

Figure II. 63 :

 63 Figure II.63: Normalized transmission of the S-bend waveguides as a function of the radius curvature Rc and the separation distance ∆h. Reversed injection data corresponds to backward injection in the S-bend waveguides. DLW parameters: 9.3TW/cm 2 -40µm/s.

Figure II. 64 :

 64 Figure II.64: Sketch of the coupler consisting of straight and S-bend waveguides.

  experimental and the simulated power coupling ratios are shown in Figure II.65.

Figure II. 65 :

 65 Figure II.65: Simulated and experimental normalized coupled power as a function of the separation distance between the two waveguides. DLW parameters: 9.3TW/cm 2 -40µm/s

Figure II. 66 :

 66 Figure II.66: (a) Near-field mode profiles of the output of the coupler; (b) normalized intensity of the mode profiles indicating the creation of a 50-50 coupler. DLW parameters: 10.8 TW/cm 2 -40µm/s.

Figure II. 67 :

 67 Figure II.67: (a) Cross-section view of the ribbon fiber with the guided mode in the middle; (b) blowup of the near-field mode profile; (c) horizontal mode profile; (d) vertical mode profile. The mode profile is similar to the mode profile in bulk glasses as shown in Figure II.56. DLW parameters: 10TW/cm 2 -25µm/s.

III.

  Comparative study between type A and the type I refractive index changes .............................................................................. III.1 Introduction ..................................................................... III.3 Type I modification in phosphate -zinc phosphate glasses ................................................................................................. III.3 Experimental methods ...................................................... III.3.1Glasses ............................................................................... III.3.2 Laser setup ......................................................................... III.3.2.a Introduction ......................................................................... III.3.2.b Ti:Sapphire REGA-Coherent ................................................... III.4 Results ............................................................................. III.4.1 Type I modification in silver containing and non-containing zinc phosphate glasses ......................................................................... III.4.2 Structure morphology ........................................................... III.4.3 Refractive index and mode profiles ......................................... III.4.4 Flipping ∆n ......................................................................... III.4.5 Advantages of type A ........................................................... III.5 Conclusion ........................................................................ Chapter III Comparative study between the type A and the type I refractive index changes III.1. Introduction Direct Laser Writing (DLW) in glasses generally induced three types of refractive index changes classified as a progressive scale of the laser irradiance/fluence: type I, type II and type III [64, 65] as previously mentioned in Chapter II. Type I is a smooth refractive index change caused by a variation of the glass density induced at low fluence

For

  this work, two lasers were used: the T-pulse 200 with a high repetition rate (9.8 MHz) for the DLW of type A waveguides; and a second laser, a Ti:Sapphire amplified laser with low repetition rate (250 kHz, compared to T-pulse) for the DLW of type I waveguides. The different laser parameters are summarized in Table III-1.

Figure III. 1 :

 1 Figure III.1: Schematic presentation of the laser setup used for writing type I waveguides.

III. 2 .

 2 The following results are similar to the ones reported by Fletcher et al.

Figure III. 2 :

 2 Figure III.2: Optical Path Difference (OPD) of the waveguide written in (orange) silver containing zinc phosphate glass (PZnAg2) and (black) non-containing silver zinc phosphate glass (PZn).

Figure III. 3 :

 3 Figure III.3: Various optical path difference (OPD) profiles as a function of (a) writing speed (b) pulse energy. The ∆n flips from negative to positive when increasing the pulse energy or decreasing the writing speed.

  Figure III.4 shows the different ∆n profiles measured for different laser conditions. The profiles shown are the only three possible profiles observed for different conditions. When writing with relatively high pulse energy and low writing speed, the ∆n profile consists of three positive peaks where the side peaks are related to the heat affected zone and the middle peak dominates (Figure III.4.a). Writing using relatively medium pulse energy and/or writing speed results in a single positive peak of ∆n (Figure III.4.b). When using low pulse energy even with low speed, very weak single positive ∆n peak is observed (Figure III.4.c). After that, no more modifications were observed indicating that the laser conditions are lower than the type I modification threshold.

Figure III. 4 :

 4 Figure III.4:Optical path difference (OPD) profiles of type I modification in noncontaining silver zinc phosphate glass as a function of the laser parameters. The ∆n is always positive.

Figure III. 5 :

 5 Figure III.5: Optical Path Difference (OPD) of the waveguide written in the same conditions (Ep=1µJ -v=1mm/s) in (orange) silver containing zinc phosphate glass (PZnAg2) and (black) non-containing silver zinc phosphate glass (PZn).

Figure III. 6 ,

 6 FigureIII.6, shows a comparison between the morphology and fluorescence aspects between type A and type I waveguides. One can observe that the type A waveguide exhibits smaller structures compared to the type I. A noticeable heat affected zone is present in the case of type I waveguides when compared to the non-existing one in type A modification. This indicates that the writing regime in that case is a thermal one given that the modified zone is larger than the laser focal spot size. The type I waveguide exhibited structures of ~24 µmx38 µm compared to 3 µm x 6 µm for the type A waveguide. However, the type I waveguide exhibited a more circular waveguide (which is due to the cylindrical lens telescope used) compared to an elliptical type A waveguide.

Figure III. 6 :

 6 Figure III.6: Top view white light illumination (a.i) for type I waveguide, (b.i) for typical type A waveguide. Top view fluorescence (a.ii) for type I waveguide, (b.ii) for typical type A waveguide. Side view white light illumination (a.iii) for type I waveguide, (b.iii) for typical type A waveguide. Side view fluorescence image of (a.iv) for type I waveguide, (b.iv) for typical type A waveguide.

Figure III. 7

 7 Figure III.7 Top view phase image of (a.i) type I waveguide, (b.i) type A waveguide. Refractive index profile of (a.ii) type I waveguide exhibiting one single positive ∆n peak. Inset: side view of the type I waveguide under white light illumination. (b.ii) Type A waveguide exhibiting two positive ∆n peaks. DLW conditions for type I: (Ep=0.65µJ -v=5mm/s -𝜏 𝑟𝑒𝑝 =250 kHz -NA=0.55 -160µm below the surface), type A (Ep=43nJ-v=60µm/s -𝜏 𝑟𝑒𝑝 =9.8MHz -NA=0.75 -160µm below the surface).

Figure III. 8 :

 8 Figure III.8: Near-field mode profile following the injection of a 630nm laser for (a.i) Type I waveguide (b.i) Type A waveguide. Normalized horizontal intensity of (a.ii) type I waveguide (b.ii) type A waveguide. Normalized vertical intensity of (a.iii) type I waveguide (b.iii) type A waveguide. DLW conditions for type I: (Ep=0.65µJ -v=5mm/s -𝜏 𝑟𝑒𝑝 =250 kHz -NA=0.55 -160µm below the surface), Type A (Ep=43nJ-v=60µm/s -𝜏 𝑟𝑒𝑝 =9.8MHz -NA=0.75 -160µm below the surface).

4 . 1 ,

 41 the type I ∆n flips as a function of the laser parameter (Figure III.3), which makes the DLW of waveguides more complicated in this case. However, type A modifications are always positive, exhibiting two positive peaks as long as the laser irradiance used is higher than the type A modification threshold. Figure III.9 shows that the type A OPD is constantly positive for all the laser parameters which is not the case for type I modification reducing the complication of writing waveguides. In Figure III.9, all the OPD's presented may exhibit the same amplitude for different laser parameters but one should not forget that the ∆n is calculated from the OPD using the following equation ∆n = OPD e ⁄ . Moreover, as mentioned before, the thickness of the structures changes as a function of the laser parameters (see Figure II.42). Therefore the ∆n is surely not the same for the different laser parameters. The purpose of Figure III.9 is to show that for all laser parameters, the photo-induced type A ∆n is a positive one.

Figure III. 9 :

 9 Figure III.9: Optical path difference (OPD) profiles as a function of (a) laser irradiance (b) writing speed. The type A ∆n is always positive no matter what the laser conditions are. Pulse energies: 30 nJ → 50 nJ.

Figure III. 10 :

 10 Figure III.10: Side view of a type I waveguide exhibiting negative ∆n (a) under white light illumination; (b) fluorescence image under blue excitation and emission in the visible range; (c) guided mode profile following laser injection at 630 nm. The dashed lines indicates the location of the waveguide. A small portion of light is guided on the side of the waveguide. (d) Refractive index change profile of the waveguide exhibiting a negative one. DLW parameters: 0.65µJ-25mm/s.

Figure III. 12 :

 12 Figure III.12: Different types of modification classifications as a function of a progressive scale of the laser fluence. The introduction of the new type A modification sits below the standard well known type I modification.

( 9 . 8 IV. 2 IV. 3 IV. 4

 98234 MHz). A morphology comparison between two single mode waveguides of each type shows a large heat affected zone for type I modification compared to a nonexisting one for type A. The overall waveguide dimensions are ~24 µm x 38 µm and 3 µm x 6 µm respectively for type I and type A waveguides. However, the guided mode profile dimensions are comparable given that the guiding region in the case of type I is around ~5 µm 2 exhibiting a circular mode profile compared to an elliptical one for type A (3 µm x 5.5 µm). Moreover, type I modification flips from positive to negative as a function of the laser parameters whereas the type A modification is always a positive one. Finally, we reported a new type of modification/refractive index change called type A (from the Latin name of silver, Argentum), based on the creation of the silver clusters that occur in the low pulse energy regime sitting well below the type I modification regime. This new type exhibits many advantages compared to type I: always positive ∆n for different laser parameters, smaller dimensions and occurring in the low pulse energy regime that could be used for writing near surface waveguides, paving the way for sensing applications, as will be presented in Chapter IV.Table of contents:IV. Direct laser writing of rising near-surface waveguides in silver containing glasses with no additional processing ........................ IV.I Introduction ...................................................................... Evanescent wave theory .................................................... Evanescent wave based sensors ........................................ IV.3.1 Refractive index sensors ........................................................ IV.3.1.a RI sensors using DLW ............................................................ Experimental methods....................................................... IV.4.1 Glass .................................................................................. IV.4.2 Laser setup ......................................................................... IV.5 Results .............................................................................. IV.5.1 Writing near surface waveguides ............................................ IV.5.2 RI sensor ............................................................................ IV.6 Conclusion ......................................................................... Chapter IV Direct laser writing of rising near-surface waveguides in silver containing glasses with no additional processing IV.1. Introduction In the past years, the use of fiber optics for sensing applications (gases, liquids) has attracted strong interest. Optical sensing provides in-situ, fast, selective, remote, real time and non-destructive sensing. It is generally based on the interaction of light with the outer medium. When light propagates in an optical fiber, a portion propagates in the cladding. It is called evanescent wave. Fiber sensors are based on the evanescent wave interaction with the outer medium. Many evanescent wave based fiber sensors were created in the past years for gas [179], chemical detection [180, 181] and refractive index sensing [182-184].

Figure IV. 1 :

 1 Figure IV.1: Simulations of the confinement factor  as a function of the V parameter of the fiber for an LP01 mode. The confinement of the mode increases as the V parameter increases.

Figure IV. 2 :

 2 Figure IV.2: Schematic presentation of an evanescent wave based sensor.

Figure IV. 3 :

 3 Figure IV.3: Schematic presentation of the sensor. Taken from [182].

[

  182].

Figure IV. 4 :

 4 Figure IV.4: Variation of the optical transmission for different refractive index liquids for taper thickness of (1) ~1.6 µm (2) ~700 nm. Taken from [182].

Figure IV. 5 :

 5 Figure IV.5: (a) Transverse cut of the plastic fiber. (b) Top view of the polished section. (c) Side view of the polished section. Due to the mismatch between the refractive index liquids and the fiber core, part of the beam is lost (2) by refraction in the sensing zone (3) guided by internal reflection. Taken from [183].

to 1 .

 1 471. The experimental and simulated normalized transmissions as a function of the different RI liquids used are shown in Figure IV.6. A considerable match is observed between simulations and experimental data. The sharp decrease occurs when the liquid matches the RI of the cladding n ext = n cladding (Figure IV.6). In this case, the new critical angle α c is lower than θ c ; all the rays with an incident angle θ < α c exhibit total reflection; however all the rays with an incident angle α c < θ < θ c will only be partially reflected and a part of the power will be ejected outside the fiber. A slight increase in the transmission was observed for RI values below n cladding which was not observed in simulations (Figure IV.6). This was explained by the scattering of light on the interface due to polishing irregularities [183].

Figure IV. 6 :

 6 Figure IV.6: Experimental and theoretical normalized transmission output as a function of the refractive index liquids. Taken from [183].

Figure IV. 7 : 12 )

 712 Figure IV.7: Schematic presentation of the refractive index (RI) sensor. Inset: Sketch of the optical rays in the sensing region. The refracted light represented in a dashed line only occurs when the RI of the liquid is higher than the RI of the cladding. Taken from [169].

  𝑅 𝐹𝑟 )2 ∫ 𝑅 𝑛 𝑒𝑥𝑡 𝑁(𝜃) 𝑠𝑖𝑛𝜃 𝑒 -𝜃 2 drops were placed on the near surface portion of the waveguide and the output transmission was monitored for every RI oil. The transmission of the waveguide following the deposit of an oil drop is normalized with respect to the transmission of the waveguide where no oils were deposited. The experimental and the new model exhibit a significant match as shown in Figure IV.8. According to Lapointe et al, three different regimes were observed. The first one is when the RI is lower than the 𝑛 𝑐𝑙𝑎𝑑𝑑𝑖𝑛𝑔 i.e. RI=1→1.5114. Light is guided based on the total internal reflection (TIR) exhibiting some losses due to the mismatch of the effective RI with the deposited liquids. The second region is from 1.5514 to 𝑛 𝑐𝑜𝑟𝑒 (~1.5117)where the critical angle 𝜃 𝑐 decreases drastically and all beams with a higher incident angle are ejected outside the waveguide, as also suggested by Bilro et al[183].The third region is where the RI of the liquids is higher than the 𝑛 𝑐𝑜𝑟𝑒 where the light is guided by many internal Fresnel reflections and not TIR[169].

Figure IV. 8 :

 8 Figure IV.8: Experimental and simulated normalized transmitted powers as a function of the refractive index of the liquids. The previous model of Bilro et al [183] is represented with a dashed line. Inset: Comparison between Lapointe's model [169] and Bilro's model [183]. Taken from [169].

Figure IV. 9 :

 9 Figure IV.9: Side view of (a) (b) the near-surface waveguides written in soda lime glass. (d) Gorilla glass. (c) 25µm below the surface. Near field mode profiles of the waveguides in Gorilla glass. (e)(f) 25µm below the surface. (g)(h) Nearsurface waveguide. Taken from [71]

Figure IV. 10 :

 10 Figure IV.10: Side view of the near surface waveguides using the compensation method compared to waveguides written ~150 µm below the surface without the glass cover in (a) fused silica (b) Eagle. Taken from [91].

Figure IV. 11 :

 11 Figure IV.11: (a) Side view of near-surface waveguide using the compensation method and the guided mode profile following laser injection at =488 nm. (b) Fluorescence emission of an aqueous fluorescein solution excited by the evanescent wave of the light guided (=488 nm) in the near-near-surface waveguide observed through a band pass filter 528/38 (top view) (c) Dark field image of a linear periodic assembly of AG@SiO2@FITC nanowires (top view) (d) Fluorescence emission of AG@SiO2@FITC nanowires (top view). Taken from [197].

using a 12 . 6

 126 MHz repetition rate Impulse laser by Clark-Mxr.Inc operating at 1030 nm with a pulse duration of 370 fs. The pulse energy was fixed to 28 nJ corresponding to 7.2TW/cm 2 and the writing speed to 50 µm/s. A 100 x -0.8NA Nikon microscope objective was used. The S-bend near surface waveguides exhibited an Rc=80mm and a ∆h=32µm (Figure IV.12). Ideally, the waveguide is preferred to be a double S-bend waveguide with a portion rising to the surface and the input and the output on the same level. However, due to the small dimensions of the sample and to minimize the curve losses of our waveguides, it was based only on a single S-bend as shown in Figure IV.12.

Figure IV. 12 :

 12 Figure IV.12: Sketch of the rising near-surface waveguide.

Figure IV. 13 :

 13 Figure IV.13: Side view under white light illumination of (a) 32 µm straight waveguide (b)(c)(d) rising near-surface waveguides. (e) Top view under white light illumination of a portion of a near-surface waveguide. Smooth modifications where no ablations or mini explosions were observed. DLW parameters: 28 nJ -50 µm/s.

Figure

  Figure IV.14: (a) Side view of the rising near-surface waveguide NWG1 under while light illumination. (b) Near-field mode profile following the injection of a 660 nm laser. (c) Sketch of the simulation of the waveguide where ~1 µm of the waveguide is simulated outside the glass. (d) Simulated mode profile based on the simulations shown in (c). A good match between experimental and simulated modes showing that the mode is confined more towards the glass due to the glass-air interface.

Figure IV. 15 :

 15 Figure IV.15: (a) Side view of a rising near-surface waveguide under white light illumination. (b) Near-field mode profile following the injection of a 660 nm laser. (c) Sketch of the simulation of the waveguide 2 µm away from the surface. (d) Simulated mode profile based on the simulations shown in (c). A good match between experimental and simulated modes showing that the mode is not affected.

Figure IV. 17 :

 17 Figure IV.17: Normalized transmission for all written waveguides following the deposition of a ~4 mm droplet of 1.604 Cargile oil. No interaction was observed after 7 µm spacing between the waveguide and the surface. Inset: Near-field mode profile of the most sensitive waveguide at ~2 µm below the surface. DLW parameters: 28 nJ -50 µm/s.

Figure IV. 18 :

 18 Figure IV.18: Normalized transmission as a function of the size of the droplet of a 1.604 Cargille oil for two waveguides with different distances from the glass surface. The larger the droplet the higher the losses in transmission.

( 3

 3 dB), which is probably due to the mode evading the waveguide when reaching the surface (glass-air interface). Once we match the RI of the glass which is ~1.602 in this case, the glass-air interface disappears and the mode is re-confined and reguided inside the waveguide as a normal waveguide embedded totally inside the glass (RTI reflections), thus the increase in the transmission and almost full compensation of the initial losses. Furthermore, this double resonance was not observed for the waveguides that are deeper in particular NWG3 & NWG4 which are ~3.[START_REF] Chan | Modification of the fused silica glass network associated with waveguide fabrication using femtosecond laser pulses[END_REF] µm and 6 µm from the surface respectively. Only one resonance is observed as reported by all the previous works [169, 182, 183]. The sensing process could be described as three different regions (Figure IV.4, Figure IV.6 and Figure IV.8);the first region where the RI of the liquid is lower than the glass, 𝑛 𝑒𝑥𝑡 ≤ 𝑛 𝑔𝑙𝑎𝑠𝑠 ,: the second region where the RI of the liquid is equal to the waveguide, 𝑛 𝑒𝑥𝑡 ~𝑛𝑤𝑎𝑣𝑒𝑔𝑢𝑖𝑑𝑒 ;

Figure IV. 19 :

 19 Figure IV.19: Normalized transmission as a function of different refractive index (RI) Cargille oils deposited on the glass surface for four different waveguides at different depths from the surface. DLW parameters: 28 nJ -50 µm/s.

  TIR but is guided due to several Fresnel reflections. Every time the light beam hits the upper part interacting with the oil (𝑛 𝑜𝑖𝑙 > 𝑛 𝑔𝑙𝑎𝑠𝑠 ), a part of light is ejected outside the waveguide and another part is reflected and guided. The third part was simulated and fitted to experimental results based on the Fresnel Reflection Coefficient and the RI of the oil (which is similar to the previous suggested models) as shown in Figure IV.20.

Figure IV. 20 :

 20 Figure IV.20: Experimental (full line) and simulations (dashed lines) for two different near surface waveguides at different distances from the surface. A good match between the experiment and the simulations.

Figure IV. 21 :

 21 Figure IV.21: Sketch of the evanescent wave/mode profile inside a near-surface waveguide for a refractive index (RI). (a) Lower than the cladding/glass; (b) higher than the cladding/glass; (c) equal to the cladding/glass. Inspired from [200]. Simulated mode profile for a (a.i) glass-air interface; (c.ii) glass-oil interface with a refractive index of oil matching the glass 𝑛 𝑒𝑥𝑡 ~𝑛𝑔𝑙𝑎𝑠𝑠 .

  simulate the behaviour of the double resonances for the first time. It is based on the mode shape confinement when it reaches the glass-outer medium interface as a function of the RI of the different oils, as well as the Fresnel reflection coefficients. Finally, a 1 cm highly sensitive RI sensor (80% -7 dB transmission drop for a 5 mm oil droplet) operating in the region of 1→ 1.632 refractive index was created based on type A. It exhibited the highest reported sensitivity for a DLW RI sensor and possible double sensing regions, which paves the way towards more integrated sensors in silver containing glasses.Finally, this project fulfilled expectations by producing the first waveguides that are based on the creation of silver clusters in silver containing glasses, paving the way towards a new type of optical circuits in bulks and fibers while exhibiting exotic properties not accessible using the standard type I modification, such as fluorescence, non-linearity, development of nanoparticles with plasmonic responses as well as writing near-surface waveguides with no need for any additional processing.

  The photo-induced silver clusters exhibit two main absorption bands in the UVvisible range, as shown in Figure II.24 while emitting fluorescence in the visible range. An approach tested during the project was to monitor the behaviour of the refractive index change when exciting the silver clusters under UV light. A change in the refractive index could occur due to the populated excited states of the clusters. The term opto-optical is based on the principle of changing the behaviour of light using light like, for example, the electro-optical effect where light is modulated using electrical signals. Herein, we tried to modulate light using light itself, therefore the term opto-optical effect. A 405 nm diode laser was added to the SID4Bio wave front sensor setup to excite the silver clusters from the bottom as shown in Figure A.b. In addition, a 405 nm notch filter was introduced in the microscope to eliminate the light coming from the blue diode into the CCD camera.

Figure A :

 A Figure A: The SiD4bio wavefront sensor mounted on a microscope operating (a) in white light illumination and providing top view phase image; (b) under blue (405 nm) illumination and providing top view local excited fluorescence image.

Figure B :

 B Figure B: Top view phase image under (a) white light illumination; (b) white light and blue light illumination simultaneously; (c) top view fluorescence image indicating the local excited zone by blue light illumination. (d) Subtraction phase image of "a" and "b" revealing a local change in the refractive index change

Figure C :

 C Figure C: Differential refractive index change (∆n) obtained from Figure B.d superposed with the fluorescence intensity line profile obtained from Figure B.c. The differential ∆n peaks spatially overlap with the fluorescence peaks indicating that the differential ∆n is caused by the excitation of silver clusters under blue light.

Figure D: (

  Figure D: (a) Top view of a standard type A waveguide exhibiting two lines; (b) using a blue diode and overlapping the grating with the type A waveguide to modulate the ∆n based on the opto-optical effect and creating a waveguide Bragg grating; (c) turning off the diode induces the disappearance of the grating; therefore, a standard type A waveguide.

  Figure E.a.Moreover, shutting down the blue diode resulted in a slow increase of 33% of the power, going back to the initial transmission (Figure E.b). The fast drop and the slow increase in transmission could be explained by the creation of the triplet excited state of the silver clusters. Once excited to a higher level, they probably exhibit an absorption band at ~532 nm which explains the sudden decrease and the slow increase of the waveguide transmission at 532 nm after turning off the diode. As a first approach, the following results may kill the idea of making a WGL in silver containing zinc phosphate glasses.

Figure

  Figure E: (a) Sudden decrease of 33% in the waveguide transmission following the simultaneous injection of 394 nm with the 532 nm laser. The dashed line indicates the moment the blue diode was turned on. (b) Slow increase of the waveguide transmission when the 394 nm laser is turned off once it reaches its initial value.The dashed line indicates the moment the blue diode was turned off.

Figure F :

 F Figure F: The measured ∆n profile using the four methods, (blue) TIE, (red) QWLSI/SID4Bio, (green) DHM and dashed lined RNF. All methods converge to the same ∆n profile and value. Taken from [202].

5 .

 5 Theoretical model of the refractive index sensor (chapter Chapter IV)The new theoretical model proposed during this work is divided into two parts. The first part is where the refractive index (RI) of the oil is lower than the RI of the glass (𝑛 𝑜𝑖𝑙 < 𝑛 𝑔𝑙𝑎𝑠𝑠 ). For this first part, the model is based on the spatial distribution of the mode when reaching the glass-oil medium. With a big difference in the refractive index change between the glass and the outer medium, which could be the air or the deposited oil droplets, the spatial distribution of the mode could change drastically, as shown in Figure IV.21. Therefore, the first part was simulated using Lumerical Mode solutions. Waveguides neighbouring the surface to 1 µm and 3.5 µm where simulated while changing the RI of the outer medium from 1 to 1.602. Then, the mode spatial distribution was overlapped with the normal standard mode which is totally embedded inside the glass. It measures the fraction of electromagnetic fields that overlap between the distorted mode and the normal mode. It is also the fraction of power from the distorted mode that could propagate inside the normal mode. The power overlap was simulated using the following equation:

Mot clés :

  Inscription laser directe, laser femtoseconde, verre, agrégats d'argent, guide d'ondes, nouveau type de changement d'indice.Title: Direct Laser Writing of a new type of optical waveguides and components in silver containing glassesAbstract: Direct Laser Writing (DLW) has been an exponentially growing research field over the last two decades, by providing an efficient and robust way to directly address three dimensional (3D) structures in transparent materials such as glasses using femtosecond laser pulses. It exhibits many advantages over the lithography technique which is mostly limited to two dimensional (2D) structuring and involves many fabrication steps. This competitive aspect makes the DLW technique suitable for future technological transfer to advanced industrial manufacturing. Generally, DLW in glasses induces physical changes such as permanent local refractive index modifications that have been classified under three distinct types: (Type I, Type II & Type III). In silver containing glasses with embedded silver ions Ag + , DLW induces the creation of fluorescent silver clusters Agm x+ at the vicinity of the interaction voxel. In this work, we present a new type of refractive index change, called type A that is based on the creation of the photo-induced silver clusters allowing the creation of new linear and nonlinear optical waveguides in silver containing glasses. Various waveguides, a 50-50 Y beam splitter, as well as optical couplers, were written based on type A modification inside bulk glasses and further characterized.

Table II -

 II 1: Table summarizing the theoretical molar composition and the properties of the different zinc phosphate glasses used in this work. Taken from [135]. -----63 Table II-2: Different silver (Ag) species identified following DLW in silver containing glasses as reported in [139]. -

67 Table III -

 67III 1: Table summarizing the different laser parameters for both lasers used in this chapter. -

  126 Table III-2: Table summarizing the comparison between type I and type A modification -

  Philippe Balcou and Eric Mevel and the director of the Centre d'Optique, Photonique et Laser, Réal Vallée for accepting me as a member of their great labs. Also thank you to Arnaud Royon for the interesting discussions about the PhD project. Thank you to my colleagues at ICMCB: Jean-Charles Desmoulin, Alexander Fargues, Sylvain Danto, Téa Skopak and Thierry Cardinal. Thank you to Jean-Charles Desmoulin and Sylvain Danto for providing glass samples, otherwise my project would not have been possible. Thank you for enduring my special demands! Téa Skopak, thank you for the discussions we had and for the time we spent talking. Special thanks and appreciation to Thierry Cardinal for all the financial support for my travels to Canada. Thanks also to my (ex) colleagues in COPL for the warm welcome and friendly environment: Mathieu Boivin, Cheikou Ba, Souleymane Toubou Bah, Fréderic Jobin, Frédéric Maes, JC Gauthier, Laurent Dusablon, Simon Duval, Yigit Ozan Aydin, Clément Frayssinous and Feng Liang.Also thank you to Céline, Sophie, Sonia, Cinthia, Michelle, Caroline and Carole from both universities for all the administrative help that you provided.Of course, I would like to thank my funding sponsors, the French National Research

	Acknowledgment General Introduction structured glass slides allowing the fluorescence calibration of microscopes.
	Furthermore, NASA used one of Argolight's products to equip the International
	DLW Laser-matter interaction has challenged the scientific communities since the Space Station microscope for the SpaceX SPX CRS 11 -Falcon 9. This PhD has been completed between two labs in two different countries, France Direct Laser Writing CELIA and Canada. These labs collaborating together under the umbrella of the Agency (ANR), "Investments for the Future" Idex program for the mobility grant, discovery of the laser in the 1960s. Research and development through the past CEntre des Lasers Intenses et ses Applications ICMCB Institut de chimie de la matière condensée à Bordeaux Laboratoire International Associé (LIA) LUMAQ (Lumière Matiere Aquitaine Quebec). LAPHIA for funding the contract extension. From the Canadian side, I would like to years led to almost a limitless number of industrial and medical laser-based While the previous works of the group on silver containing zinc phosphate glasses
	COPL SLAM I would like to thank the directors of LUMAQ Thierry Cardinal and Younès Centre d'optique, photonique et laser applications. Ranging from laser cleaning, cutting, welding, marking to laser-eye were mostly based on the investigation of the laser-glass response, this PhD project thank the Natural Sciences and Engineering Research Council of Canada (NSERC) Short Laser Pulses: Applications & Materials NPs Messaddeq as well as of the Centre des Lasers Intenses et ses Applications (CELIA), (CG101779), Canada Foundation for Innovation (CFI) (GF072345), and Fonds de surgery, ablating cancer tumours, medical imaging, the laser provides a versatile aims at creating and functionalizing of new type of optical components based on Nanoparticles DSC Differential Scanning Calorimetry IR and non-replaceable tool in both the industrial and medical fields. More specifically, the creation of fluorescent silver clusters. In fact, silver containing zinc phosphate Recherche du Québec-Nature et Technologies (FQRNT) (FT097991, CO201310) for InfraRed TIR their funding and for the equipment bought and used during this project. glasses are special and exotic glasses compared to the standard glasses used for laser-glass interaction has been extensively studied during the last two decades. Total Internal Reflection VIs Visible UV Ultra-Violet NIR Near InfraRed MPI Multi Photon Ionization NA Numerical Aperture 3D Three Dimensions 2D Two Dimensions ∆n Refractive Index Change SLM Spatial Light Modulator DWC Depressed Waveguide Cladding WG Waveguide WBG Waveguide Bragg Grating Fall Down 7 times … Get up 8 DLW by the scientific community. The incorporation of silver ions inside the glass The process of focusing femtosecond lasers inside glasses in order to change the On a personal note, I would like to dedicate this PhD to my parents. I would like to matrix allows exotic responses from the glass following DLW i.e. creation of silver physical-chemical properties of the glass is called Direct Laser Writing (DLW). DLW thank my friends from France and Canada who supported and helped me during clusters exhibiting properties such as fluorescence, nonlinearity and plasmon technique provides fast direct three-dimensional (3D) structuration of the glass this PhD: Christelle, Georges, Jean-Baptiste, Clément, Linh, Diaa. To the close resonance. In particular, the project intends to create new types of optical allowing the creation of 3D optical components embedded inside transparent friends, Vittorio, Jack and Georges thank you. Vittorio, I will miss our trips together components with properties that were not accessible in previous standard glasses. materials. It exhibits many advantages compared to the lithography technique man. Arthur Bagramyan: Thank you for having me as your friend and being like which is limited to the two-dimensional (2D) structuring of materials and involve family in Québec. We had awesome memories together. And Joyce, it was a The first part of the project explains the standard laser-glass interaction that is many steps, making DLW highly compatible with industrial manufacturing. Many pleasure meeting you from the first day I arrived to the lab and I am lucky to have mainly known by the scientific community as well as the state of the art of some applications could be based on the DLW technique such as the creation of you as a friend. That's enough for you. A person who stood by me, he calls himself miniaturized sensors and/or photonic components on glass chips. Indeed, for optical components manufactured in glasses. Next, the exotic response of silver
	PbP WGL "the sun", thank you very much. You helped a lot. I appreciate it. Point by Point example, the DLW technique in glasses has led to the creation of Modular Photonics containing glasses following DLW is presented in detail with a theoretical model. Waveguide Laser DFB Distributed Feedback a company based in Australia selling glass based micro-chips processed by the DLW The creation of a new type of waveguides and optical components in silver
	PL technique used for mode-selective applications, more specifically for astronomical Photonic Lantern containing glasses are presented in detail. The second part consists in
	MM SM needs. functionalizing the new type of waveguides and the creation of a refractive index Multimode Single Mode
	AOM sensor inside silver containing glasses. Acousto-Optic Modulator
	OPD QWLSI This PhD was performed in a joint collaboration between University of Bordeaux, Optical Path Difference Quadri-Wave Lateral Shearing Interferometry
	DHM France and Université Laval in Québec, Canada in the framework of the Laboratoire Digital Holographic Microscopy
	TIE HRSEM International Associé (LIA) LUMAQ (Lumière Matière Aquitaine Québec). More Transport Of Intensity High Resolution Scanning Electron Microscopy AFM Atomic Force Microscopy specifically, it was carried out between three labs: Centre des Lasers Intenses et
	FWHM ses Applications (CELIA) and Institute of Chemistry of the Condensed Matter of Full Width Half Maximum
	EFISHG LPG Bordeaux (ICMCB) at University of Bordeaux, France and Centre d'Optique, Electric Field Induced Second Harmonic Generation Long Period Grating
	FBG Photonique et Laser (COPL) at Université Laval, Québec, Canada. It consisted in Fiber Bragg Grating
	RI WL spending almost half the time of the PhD at each university while working on the Refractive Index White Light
	same project which is a continuity of research activities conducted in the
	"Shortpulse Lasers: Applications and Materials" (SLAM) research group of my
	supervisor Lionel Canioni and the group "Chimie et photonique des matériaux oxide
	de fluores", supervised by Thierry Cardinal at ICMCB. Previous work was based on
	optimizing and mastering the silver containing zinc phosphate glasses synthesis,
	investigating and understanding the exotic laser-glass process following DLW.
	Those activities led to the creation of "Argolight", a spin-off company selling laser
	xlv xlvi xlvii xlviii

I would like to thank also, Dr. Bertrand Poumellec, Dr. Shane Eaton, Prof Younès Messaddeq and Dr. Mathieu Bellec for accepting to take part in my PhD jury. It was an honor for me. To my PhD supervisors, Prof. Lionel Canioni, Prof. Réal Vallée and Dr. Yannick Petit, special thanks for choosing me for this PhD. Thank you for your support, understanding and help during the most difficult time of the PhD. Prof. Lionel Canioni, you were a real mentor during my PhD and also my personal life. I really appreciated all the discussions we had, related or not related to the PhD project. Thank you for the huge amount of trust you put in me. I also enjoyed travelling to several conferences with you. I am grateful for your contribution in teaching me new things and introducing me to the scientific community. Prof. Réal Vallée, I have always admired your way of engaging me in lab meetings so I could give more, work more and get better results. Yes, you are a picky person in science but I love that because I think it is a good quality for a scientist and it made me a better scientist. It was a pleasure to work for you, in your lab. Dr. Yannick Petit thank you for your friendly reception and the friendly environment you created during the course of the PhD. Thank you for following all of my work and for your constructive, critical remarks and observations. I learned a lot from you. I also wish to thank all my colleagues in the SLAM group and COPL. Thank you all for your help and the good times we spent together. Being a part of the SLAM group is like being a part of a family and I really liked this atmosphere. Thank you to the SLAM (ex) colleagues/friends, EungJang Lee, Marie Vangheluwe, Brice Mutelet, Allu Amarnath Reddy, Arthur Le Camus, Sophie Rouzet, Délphine Syvilay, Wendwesen Gebremichael (Wendey), Laura Loi, Inka Mannek-Honninger and Bruno Bousquet. Thank you all for the great atmosphere we had in the lab and outside the xlix lab. Thank you to Denis Boudreau, Alex Grégoire, Victor Azzi for the help and letting me use their equipment. Thank you also to Yannick Ledemi and Sandra Messadeq for the help. I would like to thank also Tigran Galstian for accepting me to assist him in his lab course. It gave me a great experience. Special thanks to Marc D'Auteuil, Stéphane Gagnon, David Hélie, Martin Blouin, Vincent Fortin and Diane Déziel. Marc, thank you for all you help in mounting my setups and finding the tools. I really appreciated the volleyball discussions we used to have. Stéphane, Stéphane... I asked you a lot of difficult and tricky tasks to do with my glasses during my PhD so thank you a lot for your help. Without your help and skills, it would have been nearly impossible for me to do it by my own. David and Diane, thank you a lot for the help provided for me before my arrival and to facilitate my arrival. Moreover, your friendly welcome is amazing and really appreciated. David thank you for the Québecois cultural introduction during the sugar shack. Martin Bernier, thank you for the warm welcome and the reputation you gave me at COPL (don't ask about it). It was really a pleasure to get to know you in Rochester and dance, to interact with you in and outside the lab (on my farewell party). Thank you! Julien, it was a pleasure playing volleyball with you, I really enjoyed it. Now the two brothers I had at COPL, JP Bérubé and Jérôme Lapointe. Guys!!! It was really a pleasure to work with you and go out together for beer and pool. Jay (Jérôme), I will miss having a beer with you buddy, working late together at night and our paths crossing late in the lab. JP, thank you for answering all my emails almost every day for almost 2 years, following my daily work, giving advice and helping me with my work. Thank you for enduring my persisting character and correcting my papers/abstracts. I hope you are not bored now that I am not around anymore. l

Table of contents: I. General background on glass and laser-matter interaction .......... 7 I.1 Introduction ............................................................................ 7 I.2 Glass ....................................................................................... 8

 of Glass transition .......................................................................... 9 I.2.2.b Thermodynamic aspect ..............................................................10 I.2.3 Glass formation ....................................................................... 12 I.2.3.a Optical properties: Transparency window .....................................13 I.2.4 Glass making ........................................................................... 15 I.2.4.a Lab technique ...........................................................................15 I.2.5 Introduction to fiber optics ........................................................

	I.2.1 Glass history ............................................................................ 8
	I.2.2 Definition of glass ..................................................................... 8
	I.2.2.a

16 I.3 The laser ............................................................................... 17 I

  .3.1 Definition of laser ..................................................................... 18 I.3.2 Gaussian beam ........................................................................ 21 I.3.3 Laser-material interaction.......................................................... 24

	I.3.3.a Non-linear absorption mechanisms in glasses ...............................24
	I.3.3.b Time scale ...............................................................................28
	I.3.4 Effects of laser parameters ........................................................ 29
	I

.4 Conclusion ............................................................................. 36

	Chapter I
	General background on glass and laser-
	matter interaction
	I.1. Introduction
	Laser-matter interaction is a broad research area with loosely defined boundaries.
	The laser is used to interact with different types of matter going from biological
	tissues, up to metals, dielectrics, plastics. It has become an essential tool in
	medical and industrial fields. In order to develop such effective and robust

  constitute the bone of the glass i.e. the main lattice and can usually

	form a glass with ordinary lab techniques (melt-quenching). Examples are Ba2O3,
	SiO2, GeO2, P2O5, As2O5 etc. Normally these types of glasses exhibit a high melting
	temperature. Therefore glass modifiers are added in order to lower it. Modifiers do
	not form glass under normal conditions and are usually added to the glass to
	weaken the glass [14]. Examples of glass modifiers are Na2O, CaO or K2O.
	Intermediates usually play a role between glassformers and modifiers. However,
	they cannot make a glass by themselves. Examples of intermediate glass
	constituents are: Al2O3, ZnO, Ga2O3, TiO2.
	I.2.3.a. Optical properties: Transparency window

  under 710 mW incident pump power in a combined pumping scheme (980 and 976 nm pump wavelengths)[120]. The mentioned results were mainly in phosphate glasses, but WGL were also manufactured in other types of glasses such as silicate [121], chalcogenide [122] and fluoride glasses[123]. Since this project will not be taking into account the creation of WGL, this part will be limited to the information provided above. If the reader wants further information, the following reference [124] is of interest.

	QX) in 2004 [119]. It consisted of a 20 mm active waveguide, optically pumped at
	975 nm by two laser diodes and two external fiber Bragg gratings to create the
	laser cavity. A maximum output power of 1.7 mW was obtained at 1.533 µm
	wavelength. Furthermore, to improve the power stability, a preliminary result was
	obtained on the feasibility of a Distributed feedback (DFB) laser configuration by

and if the reader is interested in more details, the following reference

[118]

is of interest. II.3.6. Waveguide lasers Waveguide lasers (WGL) are lasers based on the creation of waveguides in doped glasses by the direct laser writing process as reported by many research groups [119, 120]. The glasses were doped with rare earth elements like erbium Er or Ytterbium Yb while the waveguides were used as a gain medium and mainly external Bragg gratings to create the laser cavity. The first femtosecond laser written waveguide laser was manufactured in a Er:Yb doped phosphate glass (Kigre writing the Bragg gratings inside the glass substrate, in 2008 [120]. The glass was an Er:Yb doped phosphate glass (Kigre QX). A 20 mm long waveguide and a superposed Bragg grating were fabricated in a single step writing process. The laser device demonstrated operated at a 1537.627 nm wavelength and delivered a 0.36 mW maximum output

Table II -

 II Many research groups created waveguides inside such glasses aiming towards the creation of active waveguides. Active waveguides allow light amplification by being the gain medium in WGL integrated in glass chips. An optical gain at a wavelength of 1.5µm inside Er:Yb doped waveguides was reported in 2002 by Osellame et al. for the first time in Er:Yb doped phosphate glass [59]. Fletcher et al. again demonstrated the effect of the O/P ratio on the sign of ∆n created following direct laser writing but this time in Er:Yb doped zinc phosphate glasses. A waveguide exhibiting total losses Yb phosphate glass (QX, Kigre Inc) exhibiting a ∆n=8x10 -3 , 7 dB of gain, 0.4 dB/cm propagation losses in the C-band telecom wavelengths (1530-1565 nm) [134]. In 2012, Fletcher also reported 1dB/cm gain at 1534 nm in a waveguide written inside Er-Yb co-doped zinc phosphate glass with a ∆n=3x10 -3 .II.4. Silver containing zinc phosphate glassesThe glasses used in this project are silver containing zinc phosphate glasses exhibiting different silver concentrations. These glasses were developed and optimized during many years of research at ICMCB and the laser writing process took place in the SLAM group at CELIA. The detailed composition of the glasses is shown in TableII-1. 1: Table summarizing the theoretical molar composition and the properties of the different zinc phosphate glasses used in this work. Taken from [135].

	Sample	Name	[P]	[Zn]	[Ga]	[Ag]	Tg	O/P
			(%mol.)	(%mol.)	(%mol.)	(%mol.)	(5°C)
	PZnGa5.5	PZn	56	38.5	5.5	0	435	3.58
	PZnGa5.5:Ag5.5 PZnAg1 52.7 36.3	5.5	5.5	396 3.275
	PZnGa5.4:Ag8	PZnAg2 51.3 35.3	5.4	8	381	3.37

of 4.30.4 dB (including a coupling loss of 2.30.2dB, Fresnel losses of 0.3600.005dB and the Er 3+ absorption of 1.270.1 dB at 660 nm → ~0.74dB/cm) and a ∆n=1x10 -3 was reported for a 5 mm waveguide following the injection of a 660 nm laser [132]. Later on, in 2008, Osellame et al. managed to make a waveguide laser (WGL) inside Er:However, some experiments were conducted using Argolight glasses AG01 Argolight is a start-up company that was created by Arnaud Royon and Gauthier Papon who were working on the development and irradiation of silver containing zinc phosphate glasses at ICMCB and in the SLAM group. Currently, they sell microscope slides irradiated by femtosecond laser allowing the calibration of fluorescent microscopes in terms of resolution, fluorescence collection and spectral response.

Table II -

 II

2: Different silver (Ag) species identified following DLW in silver containing glasses as reported in [139].

Table III - 1 :

 III1 Table summarizing the different laser parameters for both lasers used in this chapter.

		T-pulse 200	REGA
	Repetition rate	9.8 MHz	250 kHz
	Wavelength	1030 nm	800 nm
	Pulse duration	400 fs	100 fs
	Pulse energy	0.2 nJ→120 nJ	0.5 µJ→2.5 µJ
	Fluence	0.8 J/cm 2 →4.75 J/cm 2	33 J/cm 2 →140 J/cm 2
	III.4. Results
	III.4.1. Type I modification in silver containing and non-containing zinc
	phosphate glasses

  -2 summarizes the comparison between type I & type A modifications in silver containing glasses.Table III-2: Table summarizing the comparison between type I and type A modification

	III.5. Conclusion
	Direct laser writing of type I modification/refractive index change was performed in
	Type I both silver-containing and non-silver-containing zinc phosphate glass exhibiting Type A
	different O/P ratio. Negative ∆n could be observed for the silver-containing glass
	Low repetition rate 250 kHz, µJ pulses High repetition rate 9.8 MHz, nJ pulses compared to an always positive ∆n in non-silver-containing glass which is probably
	related to the difference in the O/P ratio which was also reported by other research
	High writing speed(mm/s) groups.	Low writing speed (µm/s)
	Round waveguide due to beam shaping	Elliptical waveguide shape
	Large heat affected zone	No heat affected zone
	(Thermal regime)	(Athermal regime)
	One positive ∆n peak	Two positive ∆n peaks
	Circular mode profile	Elliptical mode profile
	Flipping ∆n as a function of DLW parameters	∆n always positive
	Additional processing for near surface	Near surface waveguides with no
	waveguides	additional processing

inscription laser directe d'un nouveau type de guides d'ondes et composants optiques dans des verres contenant de l'argent Résumé

  : L'inscription laser directe est un domaine de recherche en croissance depuis ces deux dernières décennies, fournissant un moyen efficace et robuste pour inscrire directement des structures en trois dimensions (3D) dans des matériaux transparents tels que des verres en utilisant des impulsions laser femtosecondes. Cette technique présente de nombreux avantages par rapport à la technique de lithographie, qui se limite à la structuration en deux dimensions (2D) et implique de nombreuses étapes de fabrication. Cela rend la technique d'inscription laser directe bien adaptée aux nouveaux procédés de fabrication. Généralement, l'inscription laser dans les verres induit des changements physiques tels qu'un changement permanent de l'indice de réfraction localisé. Ces modifications ont été classées en trois types distincts:(type I, type II et type III). Dans ce travail, nous présentons un nouveau type de changement d'indice de réfraction, appelé type A qui est basé sur la création d'agrégats d'argent photo-induits. En effet, dans des verres dans lesquels sont incorporés des ions argent Ag + , lors de leur synthèse, l'inscription laser directe induit la création d'agrégats d'argent fluorescents Agm x+ au voisinage du voxel d'interaction. Ces agrégats modifient localement les propriétés optiques comme la fluorescence, la non-linéarité et la réponse plasmonique du verre. Ainsi, différents guides d'ondes, un séparateur de faisceau 50-50, ainsi que des coupleurs optiques ont été inscrits en se basant sur ce nouveau type A et complétement caractérisés. D'autre part, une étude comparative entre les deux types de guides d'ondes (type A et type I) est présentée, tout en montrant qu'en ajustant les paramètres laser, il est possible de déclencher soit le type I soit le type A. Enfin, en se basant sur des guides d'ondes de type A inscrits proche de la surface du verre, un capteur d'indice de réfraction hautement sensible a été inscrit dans une lame de verre de 1 cm de long. Ce capteur miniaturisé peut présenter deux fenêtres de détection d'indice, ce qui constitue une première mondiale. Les propriétés des guides d'ondes inscrits dans ces verres massifs ont été transposées à des fibres en forme de ruban, du même matériau contenant de l'argent. Les résultats obtenus dans ce travail de thèse ouvrent la voie à la fabrication de circuits intégrés en 3D et de capteurs à fibre basés sur des propriétés optiques originales inaccessibles avec des guides d'onde de type I standard.

	Titre : L'	𝑛 𝑔𝑙𝑎𝑠𝑠 𝑐𝑜𝑠𝜃 1 -𝑛2 √ 1 -(	𝑛 𝑜𝑖𝑙 𝑛 𝑔𝑙𝑎𝑠𝑠 𝑠𝑖𝑛𝜃 1	) 2
	𝑅 =			(A-7)
		𝑛 𝑔𝑙𝑎𝑠𝑠 𝑐𝑜𝑠𝜃 1 + 𝑛2 √ 1 -(	𝑛 𝑔𝑙𝑎𝑠𝑠 𝑠𝑖𝑛𝜃 1 𝑛 𝑜𝑖𝑙	) 2
		𝑇 = (1 -𝑅 2 ) 𝑛		(A-8)

irradiance as well as the energy density deposited by voxel are presented in the Appendix part A.4. As mentioned before, even though the T-pulse laser exhibits a high repetition rate of 9.8 MHz the writing regime is an athermal one in this case compared to a thermal regime for the Ti:Sapphire laser exhibiting a low repetition rate of 250 kHz. Generally, thermal regimes are linked to high repetition rate lasers compared to the athermal regimes where low repetition rate lasers are used, which is not the case in this experiment. Given that pulse energies used in the case of the T-pulse are in the few nanoJoule (nJ) range compared to microJoule (µJ) pulses for the Ti:Sapphire and comparing the density of energy deposited by voxel between both lasers, one can easily understand why. Furthermore, calculating ∆𝑇, which is the highest temperature difference that occurs in one point induced by one laser pulse for both cases, confirms our claim. For the parameters used with the T-pulse 200, a maximum ∆𝑇=10K was calculated compared to a very high value of ∆𝑇 in the case of the parameters used with the Ti:Sapphire laser. The calculation used for the T-pulse are not completely compatible for calculating high energies provided by the Ti:Spahhire laser. Therefore we limited our calculation to the maximum pulse energy used, which is 1 µJ (see Appendix part A.4). Obviously, no heat affected zone was noticed for type A modification ,which is well expected with a low ∆𝑇 while for type I, the glass heats and melts resulting in the creation of a heat affected zone i.e. the modification zone is larger than the laser spot. Moreover, it is a challenge to have a moderate ∆n. The pulse energy threshold for glass modifications decreases as the beam approaches the glass surface [186], which makes it more complicated to make near-surface waveguides with a good value of ∆n. Previous works on near-surface waveguides reported a relatively low ∆n ~5 x 10 -4 in the case of reinforced Gorilla glass [169] and a moderate ∆n~2.9 x 10 -3 in Eagle glass , but using the compensation method [START_REF] Bérubé | Femtosecond laser direct inscription of surface skimming waveguides in bulk glass[END_REF]. For type A waveguides, there is no need for reinforced glass or compensation method to write near-surface waveguides while exhibiting a moderate ∆n of ~2.4 x 10 -3 (Figure IV.16). On one hand, one tends to reduce the ∆n to extend the evanescent wave and enhance the sensitivity of the waveguides but on the other hand, one is interested in a moderate ∆n in order to reduce the propagation losses due to the curvature of the rising near-surface waveguides (curvature losses). depending on the NA of the objective.

The laser irradiance in this case or laser intensity (TW/cm 2 ) is calculated as a function of the spot size, the laser repetition rate and the pulse duration using (I-23).

The deposited energy was calculated using equations extracted from the PhD manuscript of Gautier Papon [203] where the deposited energy is given by:

Where 𝛼 (4) =14. The deposited energy calculated for parameters used for type I modification exceeded the energy of the pulse which is not normal. The formula used in that case is not fully compatible when using high pulse energies. Therefore the energy deposited was limited to 1 µJ. Finally, those calculations are only approximate to show the large difference between the two laser parameters used.

And the energy deposited by voxel/laser dose is obtained by dividing the last term (the deposited energy) by the volume of the voxel:

𝑄 0 = 𝐸 𝐷 𝜋 3/2 𝑤 𝑁𝐿 2 𝑧 𝑁𝐿 (A-4)

From the laser energy deposited by voxel, one can calculate the highest temperature difference that occurs in one point induced by one laser pulse as given by:

Where 𝜌 is the molar density of the glass and 𝐶 𝑝 the heat capacity.