Rami Zegadi
email: ramizegadi@univ-setif.dz

Nathalie Lorrain

Loїc Bodiou

Mohammed Guendouz

Lahcene Ziet

Joël Charrier

Enhanced Mid-Infrared gas absorption spectroscopic detection using Chalcogenide or porous germanium waveguides

Keywords: Mid-Infrared detection, Integrated optical sensors, Power factor, Design, Ridge and slot waveguides, Chalcogenide and Porous germanium materials

Different integrated photonic sensors are investigated for the detection in the mid-infrared region of the two gases namely carbon dioxide (CO 2 ) and methane (CH 4 ). The three studied structures are ridge waveguides, based both on chalcogenide films (ChG) or porous germanium (PGe) and slot waveguides based on ChG. Waveguide dimensions are optimized to obtain the highest power factor between guided light and gas while maintaining a single mode propagation in the mid-infrared wavelength range. The achievable power factor is 1% in case of ChG ridge-waveguide, 45% for PGe-ridge, and 58% in case of ChG-slot. Extremely low limits of detection (LOD), 0.1 ppm for carbon dioxide at λ= 4.3 μm and 1.66 ppm for methane at λ= 7.7 μm are obtained for a ChG slot waveguide, due to the large gas absorption coefficients in the mid-infrared spectral range. For porous germanium waveguides, low LOD values are also computed: 0.12 ppm for CO 2 at λ= 4.3 μm and 1.89 ppm for CH 4 at λ= 7.7 μm. These results show that the proposed structures could achieve competitive performance required for generic spectroscopic detection on a chip for environment and health sensing.

Introduction

In recent years, chemical sensing has emerged as an important application for integrated photonics outside of optical communication. The detection of noxious and flammable gases becomes necessary at from both domestic and industrial point of views. Gas sensors can be used to detect different types of gases and have therefore found applications in various fields in particular chemistry, health, biology, agriculture and environment [START_REF] Majhi | Recent advances in energy-saving chemiresistive gas sensors: A review[END_REF]. The mechanism of detection can depend on thermal, chemical, mechanical, electrical or optical properties of functional materials [START_REF] Meng | Electrically-Transduced Chemical Sensors Based on Two-Dimensional Nanomaterials[END_REF]. Nevertheless, high-end spectroscopic systems often require laboratories that would use free space configurations to measure the absorption spectra of gas molecules inside a measurement chamber. These systems could be considered cumbersome and expensive, which is considered as the first disadvantage [START_REF] Huang | Silicon-on-sapphire waveguides design for mid-IR evanescent field absorption gas sensors[END_REF][START_REF] Hu | Silicon photonic platforms for midinfrared applications[END_REF][START_REF] Han | On-chip mid-infrared gas detection using chalcogenide glass waveguide[END_REF][START_REF] Tombez | Methane absorption spectroscopy on a silicon photonic chip[END_REF][START_REF] Gutierrez-Arroyo | Optical characterization at 7.7 µm of an integrated platform based on chalcogenide waveguides for sensing applications in the mid-infrared[END_REF][START_REF] Pi | Design of a mid-infrared suspended chalcogenide/silica-on-silicon slotwaveguide spectroscopic gas sensor with enhanced light-gas interaction effect[END_REF][START_REF] Koompai | Analysis of Si3N4 waveguides for on-chip gas sensing by optical absorption within the mid-infrared region between 2.7 and 3.4 µm[END_REF][START_REF] Gutierrez-Arroyo | Theoretical study of an evanescent optical integrated sensor for multipurpose detection of gases and liquids in the Mid-Infrared[END_REF]. The second major disadvantage of these sensors comes from their size, which impedes on-field deployment. Integrated optical sensors are a promising alternative to avoid these drawbacks [START_REF] Kumari | Silicon-on-nitride slot waveguide: a promising platform as mid-IR trace gas sensor[END_REF]. With their immunity to electromagnetic interference, low power consumption, compactness, lightweight, and remote sensing ability, these sensors are adequate tools to detect different types of gases. In addition, the response time with high sensitivity, low Limit of Detection (LOD) and large reusability make them indispensable for the realization of lab-on-chip systems that are both cheap and portable.

The mid-infrared (Mid-IR), which is defined as the wavelength range of the electromagnetic spectrum between 2 and 20 μm, contains absorption peaks for a wide variety of gases including H 2 O, CO, CO 2 , NO, NO 2 , CH 4 [START_REF] Huang | Silicon-on-sapphire waveguides design for mid-IR evanescent field absorption gas sensors[END_REF][START_REF] Frish | Progress toward mid-IR chip-scale integrated-optic TDLAS gas sensors[END_REF][START_REF] Khonina | Evanescent Field Ratio Enhancement of a Modified Ridge Waveguide Structure for Methane Gas Sensing Application[END_REF][START_REF] Dettenrieder | Toward the Required Detection Limits for Volatile Organic Constituents in Marine Environments with Infrared Evanescent Field Chemical Sensors[END_REF]. For example, carbon dioxide (CO 2 ) displays strong absorption features around 4.3 μm and methane (CH 4 ) exhibits two strong absorption at 7.7 and 3.3 μm [START_REF] Gordon | The HITRAN2016 molecular spectroscopic database[END_REF]. The challenge is then to design highly sensitive sensors of lab-onchip size that can be integrated into embedded circuitry for controlling systems.

Photonic integrated circuits operating in the Mid-IR range have already been implemented using the mature technology offered by III-V and group IV semiconductors. These devices have taken advantage of the Mid-IR transparency of silicon (2-8 µm) [START_REF]Mid-infrared integrated photonics on silicon: a perspective[END_REF], germanium (2-14 µm) [START_REF] Mashanovich | Germanium mid-infrared photonic devices[END_REF][START_REF] Marris-Morini | Germanium-based integrated photonics from near-to mid-infrared applications[END_REF], and gallium arsenide (2-16 µm) [START_REF] Ivanov | Metamorphic InAs(Sb)/InGaAs/InAlAs nanoheterostructures grown on GaAs for efficient mid-IR emitters[END_REF] to integrate passive components at chip level [START_REF] Gutierrez-Arroyo | Optical characterization at 7.7 µm of an integrated platform based on chalcogenide waveguides for sensing applications in the mid-infrared[END_REF][START_REF] Mashanovich | Germanium mid-infrared photonic devices[END_REF][START_REF] Singh | Mid-infrared materials and devices on a Si platform for optical sensing[END_REF][START_REF] Chang | Low-loss germanium strip waveguides on silicon for the mid-infrared[END_REF][START_REF] Sieger | Toward On-Chip Mid-Infrared Sensors[END_REF]. Other materials such chalcogenide glasses (ChG) could also be used. They are amorphous semiconductors and contain elements such as tellurium, selenium or sulphur covalently bonded with As, Ge, Sb, and Ga [START_REF] Wang | Optically reconfigurable metasurfaces and photonic devices based on phase change materials[END_REF]. They can be doped with rare earth ions [START_REF] Vighnesh | optical, thermal, mechanical, morphological & radiation shielding parameters of Pr3+ doped ZAlFB glass systems[END_REF] and processed as fibers, thin films or integrated waveguides displaying a broad transparency extending towards the mid-IR, up to 12 µm, 15 µm and 20 µm respectively for sulphide, selenide and telluride glasses [START_REF] Gutierrez-Arroyo | Optical characterization at 7.7 µm of an integrated platform based on chalcogenide waveguides for sensing applications in the mid-infrared[END_REF]. Mid-IR supercontinuum generation and sensing have been demonstrated using ChG fibers [START_REF] Starecki | Mid-IR optical sensor for CO2 detection based on fluorescence absorbance of Dy3+: Ga5Ge20Sb10S65 fibers[END_REF][START_REF] Petersen | Mid-infrared supercontinuum covering the 1.4-13.3 μm molecular fingerprint region using ultra-high NA chalcogenide step-index fibre[END_REF]. Integrated Mid-IR chalcogenide devices have been fabricated on different substrates such as silicon (Si) [START_REF] Lin | Demonstration of high-Q mid-infrared chalcogenide glass-on-silicon resonators[END_REF], calcium fluoride (CaF 2 ) [START_REF] Mere | Polarization-independent angletolerant mid-infrared spectral resonance using amorphous germanium high contrast gratings for notch filtering application[END_REF], sulphide glass (As 2 S 3 ) [START_REF] Demetriou | Refractive index and dispersion control of ultrafast laser inscribed waveguides in gallium lanthanum sulphide for near and mid-infrared applications[END_REF], sodium chloride (NaCl) [START_REF] Kanou | Mid-infrared spectroscopic analysis of saccharides in aqueous solutions with sodium chloride[END_REF], lithium niobate (LiNbO 3 ) [START_REF] Mayer | Offset-Free Gigahertz Midinfrared Frequency Comb Based on Optical Parametric Amplification in a Periodically Poled Lithium Niobate Waveguide[END_REF] for surface enhanced infrared absorption spectroscopy (SEIRAS) [START_REF] Mayerhöfer | Structures for surface-enhanced nonplasmonic or hybrid spectroscopy[END_REF][START_REF] Takayama | MID-INFRARED NANOPHOTONICS FOR BIOCHEMICAL SENSING: A REVIEW[END_REF] or directly integrated with Quantum Cascade Laser (QCL) chips [START_REF] Hillbrand | Coherent injection locking of quantum cascade laser frequency combs[END_REF]. The feasibility of chemical-biological sensing in gas and liquid environment exploiting Mid-IR sensing based on undoped chalcogenides [START_REF] Han | On-chip mid-infrared gas detection using chalcogenide glass waveguide[END_REF][START_REF] Su | Monolithic on-chip mid-IR methane gas sensor with waveguide-integrated detector[END_REF]and on the luminescence from rare-earth doped chalcogenide integrated platforms have been proposed and demonstrated [START_REF] Ari | Rare-earth-doped chalcogenide glasses for mid-IR gas sensor applications[END_REF][START_REF] Shaw | Mid-wave IR and long-wave IR laser potential of rare-earth doped chalcogenide glass fiber[END_REF].

Several platforms have been studied for optical detection. These include waveguides, Mach-Zehnder interferometers, micro-ring resonators and microcavities in the near-infrared range [START_REF] Liu | Highly sensitive Mach-Zehnder interferometer biosensor based on silicon nitride slot waveguide[END_REF][START_REF] Liu | All-optical on-chip sensor for high refractive index sensing[END_REF]. The detection principle is based on the change in refractive index. In case of gas detection, the refractive index variation is very small and, therefore, these refractive index changes are not the most reliable parameters to exploit. On the contrary, the detection of gases by absorption and consequent reduction of the transmitted intensity in the guiding structures is particularly interesting in the Mid-IR range. The key point of volume absorption in gas sensors is based on the increased interaction of light and gas infiltrated into the pores, which has to be maximized. The use of ridge and slot waveguides should maximize the power factor ratio value. Moreover, the use of integrated waveguide made of porous materials could also enhance the light-gas interaction [START_REF] Azuelos | Optimization of porous silicon waveguide design for micro-ring resonator sensing applications[END_REF].

In this work, an analytical design of an evanescent optical field sensor working in the Mid-IR spectral domain is provided for detection of CO 2 , and CH 4 . The objective is to optimize the detection ratio with three different integrated optical devices based on ChG and Porous Germanium (PGe) materials with the same refractive indices as the ChG layers as a direct comparison for the large transparency windows in the Mid-IR. ChG and PGe ridge waveguides and ChG slot waveguides are explored in order to optimize sensor performance. The waveguide dimensions are therefore optimized to enhance the interaction between guided light and gas power factor while maintaining single-mode propagation in the Mid-IR. The LOD for each structure is calculated and compared to previously reported results.

Theory and proposed design

Principle of the gas detection scheme based on absorption bands in the Mid-IR.

The detection of gases depends on the absorption bands in the Mid-IR wavelength range. Each gas has one or more absorption peaks, known as the gas fingerprint. In our case for the three guiding integrated structures, the two gases studied are carbon dioxide (CO 2 ) and methane (CH 4 ). CO 2 has a high absorption peak at a wavelength of 4.3 μm while CH 4 has two absorption peaks at 3.3 and 7.7 μm [START_REF] Gordon | The HITRAN2016 molecular spectroscopic database[END_REF]. Three integrated optical structures, presented in Figure 1 Theses porosities were chosen so as to have refractive indices corresponding to those of ChG ridge waveguide based on the guiding layer material Se 4 and the confinement layer material Se 2 , and calculated using Bruggeman model for effective index [START_REF] Gutierrez-Arroyo | Theoretical study of an evanescent optical integrated sensor for multipurpose detection of gases and liquids in the Mid-Infrared[END_REF][START_REF]Optical loss study of porous silicon and oxidized porous silicon planar waveguides[END_REF]. The structural dimensions wrail, g, h, and w correspond to the width of Se4 ChG regions, width of the gap region, height of the waveguide, and the width of the waveguide, respectively. The detection mechanism consists of measuring the power in the optical output signal, which varies as a function of the absorption coefficient C (mol L -1 ). Therefore, power attenuation increases with gas concentration levels and it is also directly dependent on light-gas interaction power factor ƞ [START_REF] Butt | Silicon on silicon dioxide slot waveguide evanescent field gas absorption sensor[END_REF]. Γ sup is defined as the ratio of the evanescent field power in the air superstrate to the total guided optical power. Г 1 and Г 2 represent, respectively, the interaction field power factor between the gas to detect and the fraction of total guided optical power in the guiding and confinement layers. Г 1 and Г 2 are defined schematically in Figure 1.(b) for the porous waveguide. In order to calculate the field distribution in the waveguide, the Full Vector Mode Solver FMM (film mode matching) of FIMMWAVE was used. The distribution of the field intensity in the superstrate, guiding and confinement layers relative to the total intensity are defined respectively as [START_REF] Azuelos | Optimization of porous silicon waveguide design for micro-ring resonator sensing applications[END_REF]: Where P z is the Poynting vector along the propagation direction z, and Γ sup , Г 1 and Г 2 , obey the relation [START_REF] Azuelos | Optimization of porous silicon waveguide design for micro-ring resonator sensing applications[END_REF]:

Superstrate Γ sup

Substrate Si

1 ) ( ) ( ) ( 2 1 sup          (4)
The power factor η(λ) can be expressed by:

) ( ) ( ) ( ) ( 2 2 1 1 sup            p p ( 5
)
With p 1 and p 2 the porosities of respectively the guiding and confinement layers.

Parameters p 1 and p 2 only concern porous materials, therefore the evanescent field factor η(λ) is more important in PGe ridge waveguide compared to ChG ridge waveguide for which η(λ) =Γ sup .

The wavelength corresponding to the absorption peak of the gas under study, the light travelling through the waveguide is attenuated. The examination of the transmission spectra of the propagating light covering the peak region of this gas allows us to identify it with great selectivity and sensitivity. The principle of wave absorption is one of the most widely used in optical sensors since it is possible associate the optical power P in a guiding structure under the concentration C of a substance. It is possible to associate the optical power P in a guiding structure with the concentration of a substance C using Beer-Lambert's law [START_REF] Gutierrez-Arroyo | Theoretical study of an evanescent optical integrated sensor for multipurpose detection of gases and liquids in the Mid-Infrared[END_REF], this expression is wavelength-dependent λ and is written in the form: 0 ( ) e x p ( ) ( ) ( ) ( ) ( )

p ro p P P C L L                 (6)
P0(W) is the optical power at the waveguide input, η (%) is the interaction power factor, α (cm -1 ) corresponds to the propagation losses, L (cm) is the length of the waveguide interacting with the target molecules and ε is the molar absorption (L.mol -1 cm -1 ) which is associated with the absorption of the molecule A according to: A = C ε.

The sensitivity of the integrated optical sensor is defined as the ratio between the change in optical power and the change in concentration of the molecules to be detected. It is calculated by deriving equation ( 6) with respect to C [START_REF] Gutierrez-Arroyo | Theoretical study of an evanescent optical integrated sensor for multipurpose detection of gases and liquids in the Mid-Infrared[END_REF]:

0 ( ) ( ) ( ) e x p ( ) ( ) ( ) ( ) ( ) p r o p dP S L P C L L dc                    (7)
For this expression, the condition α >> ηεC is accomplished for low concentration to be measured. Equation [START_REF] Gutierrez-Arroyo | Optical characterization at 7.7 µm of an integrated platform based on chalcogenide waveguides for sensing applications in the mid-infrared[END_REF] reveals that the sensitivity is directly proportional to η and, therefore, can be improved by maximizing its value.

Sensitivity is also useful to determine the optimum waveguide length L opt , which is found at the maximum of the S function and depends on the propagation loss. So, propagation loss α is also important in determining the optimal length of the guide L opt , allowing the maximum sensitivity S to be obtained. The expression for calculating the optimal transducer interaction length L is given by [START_REF] Gutierrez-Arroyo | Theoretical study of an evanescent optical integrated sensor for multipurpose detection of gases and liquids in the Mid-Infrared[END_REF]:

opt 1 L= ε (λ )η (λ )C (λ )+ α (8)
If the previously imposed condition (α >> ηεC) is fulfilled, L opt depends essentially on α and can be approximated as, L ≈ 1⁄α. This equation reveals the impact of waveguide propagation losses on the sensor performance.

The minimum resolvable concentration C min or LOD is given by the following expression [START_REF] Gutierrez-Arroyo | Optical characterization at 7.7 µm of an integrated platform based on chalcogenide waveguides for sensing applications in the mid-infrared[END_REF]:

0 p ro p o p t m in opt S N R N E P B -ln 1 - P e x p ( -α L ( λ ) ) C= ε ( λ ) η ( λ ) L ( λ )     (9)
The LOD (Cmin) is physically limited by the photodetector specifications, such as signal-to-noise ratio (SNR), noise equivalent power (NEP and bandwidth (B). The employed value of the photodetector are P 0 (W) = 1 mW, SNR equal to 10, -

N E P = 5 × 1 0 W /H z , and B = 5 K H z [START_REF] Gutierrez-Arroyo | Theoretical study of an evanescent optical integrated sensor for multipurpose detection of gases and liquids in the Mid-Infrared[END_REF]. The Signal to Noise Ratio (SNR) is fixed equal to 10 for this calculation. This SNR value is unfavorable considering the coupling loss at the waveguide input and output So, this SNR value was not dependent on the performance of the QCL.

Optimization of transducer dimensions

To achieve the best sensing performance, the power factor η has to be maximized through waveguide dimension (w, g, h, and w rail ) optimization. These waveguiding structures were designed using a commercial software (FIMMWAVE, Photon Design) to obtain the geometrical dimensions, width (w or w rail ) and height (h), allowing single mode propagation at wavelengths of 4.3 µm or 7.7 µm, while maximizing the power factor. All the simulations were performed when the waveguides are singlemode.

For the fabrication of these integrated devices, the chalcogenide thin films are subsequently deposited onto silicon substrates by RF magnetron sputtering. The multilayered structure was made of a -thick lower confinement layer and a low thick guiding layer while galvanostatic etching of germanium substrate is performed in a two electrode electrochemical cells with a Pt wire counter to fabricate porous germanium layers by using an electrolyte which is a volumic mixture of hydrofluoric acid ad anhydrous ethanol. Then, integrated waveguides of different widths were then fabricated using a classical i-line photolithographic process or by e-beam process according to device dimensions followed by a dry etching procedure at low pressure combining reactive ion etching (RIE) and inductively coupled plasma (ICP) etching.

Moreover, n inherent feature of porous germanium material is its open pore network. This can be used to modify the properties of optical devices in-situ, by filling the pores with other molecules. The pores are several nanometers in diameter to allow the infiltration of gas.

Optimization of the ridge waveguide dimensions at wavelengths of 4.3μm and 7.7μm

Silicon and germanium are transparent materials in the wave range [2-15μm]. Moreover, the refractive index n of these materials do not vary in the studied wavelength range [START_REF] Němec | Optical properties of (GeSe2)100-x(Sb2Se3)x glasses in nearand middleinfrared spectral regions[END_REF][START_REF]Refractive index of silicon and germanium and its wavelength and temperature derivatives[END_REF].

For the simulation and for both studied wavelength, single mode ridge waveguides with refractive indices of n 1 = 2.69 and n 2 = 2.49, respectively for the guiding layer (ChG guiding layers in the case of ChG materials and PGe in the case of porous materials with a porosity p 1 = 0.42) and the lower confinement layer (in the case of ChG materials and PGe in the case of porous materials with porosity a p 2 = 0.47) were considered. A refractive index n 0 =n air = 1 is used for the superstrate as the presence of CH 4 or CO 2 at low concentration is not supposed to significantly affect the refractive index of air. The evolution of Γ sup as a function of the geometrical parameters (w, h) of ChG waveguide, which allow single mode propagation is presented in Figure 2.(a) and 2.(b) at λ= 4.3 μm and at λ= 7.7 μm, wavelengths of interest for CO 2 and CH 4 , respectively. As TM polarization represents an optimization in the sensor design by maximizing the power factor [START_REF] Gutierrez-Arroyo | Theoretical study of an evanescent optical integrated sensor for multipurpose detection of gases and liquids in the Mid-Infrared[END_REF], only the results for this polarization are reported. Figure 2.(a) shows that the value of Γ sup for the detection of CO 2 is maximum for waveguide widths w between 6.1 μm and 9.1 μm and for waveguide height h between 1.3 μm and 1.6 μm. A value of Γ sup = 1% is obtained for the optimal dimensions of the waveguide of w = 7.9 μm and h = 1.4 μm.

For the detection of CH 4 , Figure 2.(b) shows that the value of Γ sup is maximum (1%) for waveguide widths w between 12 μm and 15 μm and for guide height h between 2.4 μm and 2.7 μm. The optimal dimensions of the waveguide are w = 14.4 μm and h = 2.4 μm. The TM polarization gives a larger evanescent field factor Γ sup , hence its choice for this type of material.

Table 1 resumes the configuration parameters of a ridge waveguide for the TM polarization and for ChG or PGe materials. w opt and h opt correspond respectively to the width and the height of the ridge waveguide that induce a maximum power factor η. As the gas will infiltrate pores of the PGe waveguide, which exhibits p 1 and p 2 porosities for the confinement and guiding layers, respectively, the values of Г 1 and Г 2 have to be taken into account in the gas and were also calculated. Compared to ChG material, the PGe material displays a substantial increase in the η factor (45 %) calculated from equation [START_REF] Han | On-chip mid-infrared gas detection using chalcogenide glass waveguide[END_REF]. The porosities in the guiding and confinement layers induced an increase in the quantity of gas in the pores which allowed a better interaction of propagated light and gas.

Optimization of the slot waveguide dimensions at wavelengths of 4.3 μm and 7.7 μm

The power factor η is optimized depending on the geometry of a slot waveguide and in particular on the dimensions of the height h and width of rail w rail of the slot waveguide and slot width g which are schematically displayed in Figure 1.(c). To achieve the best performance of the sensor, the evanescent field factor (η = Γ sup ) has to be maximized by determining the waveguide dimensions (w rail , the gap g, and h) that allow a significant fraction of light to be confined in the slot region.

A ChG slot waveguide has with a guiding layer of refractive index n 1 = 2.69 and a confinement layer n 2 = 2.49 was considered in the simulations. Air is considered yet again as superstrate (n 0 = 1) for both wavelengths 4.3 µm and 7.7 µm. In slot waveguides, only TE modes are studied. By examining these figures, it can be seen that the evanescent field factor reaches its maximum value for w rail = 800 nm and for g=30 nm. For these values, a high value of the field is confined in the slot region. Figure 3(a) shows that the variation of h does not affect w opt , which remains unchanged whatever h. W rail , on the other hand, takes on greater values with the increase of g (Figure 3(b)). As the variation of h has no impact on w, the choice of h opt = 1600 nm, for which Γ sup is slightly better, is appropriate. When w rail < w opt . (Figure 3.(a) and 3.(c)) and g < g opt (Figure 3.(c)) a major fraction of the field penetrates into the confinement region and becomes evanescent, and hence, power factor decreases. For w rail > w opt and g > g opt , evanescent field factor decreases due to the stronger confinement of field inside the high index ChG. When w rail < w opt . (Figure 3.(a) and 3.(c)) and g < g opt (Figure 3.(c)) a major fraction of the field penetrates into the confinement region and becomes evanescent, and hence, power factor decreases. For w rail > w opt and g > g opt , evanescent field factor decreases due to the stronger confinement of field inside the high index ChG.

In order to have the best sensitivity, the optimal waveguide dimension chosen are: w rail = 0.8 µm, h = 1.6µm, and g = 30 nm, for which η reach values as high as ~ 58 %.

For the wavelength of λ = 7.7 μm the same reasoning was followed. The optimal dimensions obtained are: w rail = 0.9 µm, h = 1.9 µm and g = 90 nm. The corresponding η maximum factor is about 51%.

Results and discussion

Study of the performance of a ridge waveguide with ChG material for the two wavelengths 4.3 µm and 7.7 µm

The parameters taken into consideration, obtained previously are defined in Table 1 for CO 2 and CH 4 detection at 4.3 and 7.7 µm, respectively. In both cases, the maximum value of the evanescent field factor reached ƞ = 1% for CO 2 detection and ƞ = 1 % for CH 4 detection. Sensitivity S was calculated as a function of the concentration of target molecules in the range [400 -800 ppm] and for propagation losses of 1, 3 and 6 dB/cm. Moreover, L opt and LOD were calculated according to equation ( 8) and ( 9) respectively for each wavelength and optical loss and for C = 600 ppm corresponding to the studied target molecules concentration mid-range. The output power P and sensitivity S are plotted as a function of the concentration C in Figure 4 using equations ( 6) and [START_REF] Gutierrez-Arroyo | Optical characterization at 7.7 µm of an integrated platform based on chalcogenide waveguides for sensing applications in the mid-infrared[END_REF] for different values of α prop . detection at 7.7 μm. From these sensitivity curves, it is possible to appreciate the importance of the propagation losses of the ridge waveguide on the performance of the evanescent wave sensor. Indeed, low losses and the optimal interaction associated length allow a better interaction between the propagated light and the molecules in the superstrate and induce a higher sensitivity.

For CO 2 detection and propagation losses α prop of 1 dB/cm and taking into account the optical interaction length L opt of 4.33 cm, a sensitivity (S) is equal to 1.9 nW/ppm for a LOD of 1.87 ppm. For α prop = 3 dB/cm, L opt = 1.44 cm, S is equal to 0.62 nW/ppm for a LOD of 5.63 ppm. For α prop = 6 dB/cm, a sensitivity of 0.31 nW/ppm is computed for a LOD of 11.27 ppm and L opt = 0.72 cm.

For CH 4 detection and propagation losses α prop of 1 dB/cm and L opt = 4.34 cm, a sensitivity S equal to 0.12 nW/ppm is computed for a LOD of 28.22 ppm. For α prop = 3 dB/cm and L opt = 1.45 cm, S = 0.041 nW/ppm for a LOD of 84.65 ppm.

Finally, for α prop = 6 dB/cm and L opt = 0.72 cm, S decreases to 0.02 nW/ppm for a LOD of 169.31 ppm.

The analysis of these results shows that the increase of propagation losses leads to a reduction in sensitivity and an increase of the LOD, which is undesirable. From Figure 4.(a) and 4.(b), a small variation in the output power is observed so the propagation losses do not have much influence on this parameter. Notice that the sensitivity is almost constant over the studied concentration range (Figure 4.(c) and 4.(d)). The LOD (in ppm) for CO 2 and CH 4 are 2 orders of magnitude lower than the threshold limit values (TLV) of 1000 ppm [START_REF] Dettenrieder | Toward the Required Detection Limits for Volatile Organic Constituents in Marine Environments with Infrared Evanescent Field Chemical Sensors[END_REF].

Study of the performance of a ridge waveguide made of PGe materials for the two wavelengths 4.3 µm and 7.7 µm

PGe is an interesting materiel because of its adjustable porosity, which can be modulated according to the fabrication parameters [START_REF] Bioud | Fast growth synthesis of mesoporous germanium films by high frequency bipolar electrochemical etching[END_REF]. By changing the Ge porosity, PGe refractive index can be varied between the index of air and that of Ge material), which allows the design of optical waveguiding structures.

Concentration of target molecules [ppm] S[nW/ppm]

Concentration of target molecules [µmol L -1 ]

3 dB/cm 6 dB/cm 9 dB/cm 7. For these simulations, the value of the power factor has been reached ƞ = 45.3% for CO 2 and ƞ = 44.7% for CH 4 , the initial conditions from the previous section were also taken into account. Figure 5 shows the results obtained for output power P and sensitivity S, using equations ( 6) and [START_REF] Gutierrez-Arroyo | Optical characterization at 7.7 µm of an integrated platform based on chalcogenide waveguides for sensing applications in the mid-infrared[END_REF] for different values of αprop. Expected propagation losses α prop are higher (the chosen values range from 3 to 9 dB/cm) than those used for the simulations of ChG waveguide and are mostly related to volume diffusion [START_REF] Liu | Highly sensitive Mach-Zehnder interferometer biosensor based on silicon nitride slot waveguide[END_REF].

For CO 2 detection and propagation losses α prop of 3 dB/cm with L opt = 1.40 cm, the medium sensitivity (S) is 28 nW/ppm for a LOD of 0.12 ppm. For α prop =6 dB/cm and L opt = 0.71 cm, S is 14 nW/ppm for a detection limit of 0.25 ppm. Finally, for α prop =9 dB/cm and L opt = 0.47 cm, S = 9.4 nW/ppm for a detection limit of 0.37 ppm.

For CH 4 detection and propagation losses α prop of 3 dB/cm with L opt = 1.41 cm, a sensitivity S equal to 1.8 nW/ppm is computed for a LOD of 1.89 ppm. For α prop =6 dB/cm and L opt = 0.72cm, S = 0.92 nW/ppm for a LOD of 3.78 ppm. Finally, for α prop = 9 dB/cm and L opt = 0.48cm, S = 0.62 nW/ppm for a LOD of 5.66 ppm.

The analysis of these results shows better results compared to the previous ChG waveguide due to the increased interaction between the light and the molecules which infiltrate the pores and thus increasing the power factor η(λ) and consequently enhancing the sensitivity and the decrease of the LOD.

Study of the performance of a slot waveguide for the two wavelengths 4.3 µm and 7.7 µm

It has been shown in the optimization section and Figure 3 that for this type of ChG waveguide η is equal to 58% for a wavelength λ = 4.3 µm and 51% at λ = 7.7 µm. Figure 6.(a) and 6.(c) show respectively the output power P and sensitivity S as a function of concentration of CO 2 at 4.3 μm for 3 different values of propagation loss α prop , whereas Figure 6.(b) and 6.(d) illustrate those of CH 4 at 7.7 µm.

For CO 2 detection and propagation losses α prop of 1 dB/cm with L opt = 3.88 cm, a sensitivity S equal to 100 nW/ppm is computed for a LOD of 0.034 ppm. For α prop =3 dB/cm and L opt = 1.39 cm, S is 35 nW/ppm for a detection limit of 0.1 ppm. Finally, for α prop = 6 dB/cm and L opt = 0.70 cm, we have S = 1.7 nW/ppm for a LOD of 0.19 ppm. For CH 4 detection and propagation losses α prop of 1 dB/cm with L opt =4.31 cm , a sensitivity S equal to 6.3 nW/ppm is computed for a LOD of 0.55 ppm. For α prop = 3 dB/cm and L opt = 1.44 cm, S = 2.1 nW/ppm for a LOD of 1.66 ppm. Finally, for α prop = 6 dB/cm and L opt = 0.72 cm, S = 1.1 nW/ppm for a LOD of 3.31 ppm.

In slot waveguide, the light is strongly confined in the slot region. The interaction between the target molecules and the light is then increased, improving sensitivity at the same time. The coupling losses reduce the transmitted power, which decreases the sensitivity. For ChG ridge waveguide configuration, the interaction of light with the gaseous detection medium takes place only in evanescent mode. Notice that the sensitivity of the porous material waveguide is almost comparable to the slot waveguide. The interaction of light with the gaseous environment is increased in these last two guiding structures. For the detection of CO 2 , the results reported in Table 3, show that they are better than those reported in the literature (0.26 ppm for propagation losses of 3 dB/cm) for the reference [START_REF] Gutierrez-Arroyo | Theoretical study of an evanescent optical integrated sensor for multipurpose detection of gases and liquids in the Mid-Infrared[END_REF]. For the porous germanium-based sensor, the detection limit is 0.12 ppm while for the waveguide slot the limit is 0.1 ppm for 3 dB/cm losses. For CH 4 detection, the results are comparable to those of the table items although the simulated structure was suffering from higher propagation losses.

Conclusion

The pertinence of developing optical sensors in the Mid-IR range is based on the presence of the vibrational absorption bands of many molecules in this wavelength range, between 2 µm and 20 µm, thus enabling highly sensitive spectroscopic measurements for chemical analysis of target molecules for various applications such as health and environment. The development of new techniques for selective detection and high sensitivity in Mid-IR range is currently a focus of interest in industry and scientific research. In this context, devices designed in integrated optics have certain advantages over other types of sensors. In this paper, ridge and slot waveguides were optimized to obtain high power factor ratio to increase sensing detection rate of the proposed power field factor absorption gas sensor.

The materials chosen for the fabrication of these integrated platforms are chalcogenide glasses and porous germanium, which have a wide transparency in Mid-IR, a wide range of refractive index according to their composition and a relatively easy technological implementation.

The structure of the different types of waveguides, allows the molecules to interact with the evanescent wave in case of ChG and slot waveguide configurations. In porous waveguide configuration, the light interaction takes place not only with the evanescent wave but also with the light propagated in the guiding and confinement waveguide layers. In this last case, the porous configuration, the interaction between the light and the molecules is increased because molecules infiltrate the pores and thus increasing the interaction factor and consequently enhancing the sensitivity.

ChGs slot waveguides provide the highest sensitivity S = 35 nW/ppm for a detection limit of 0.1 ppm, for carbon dioxide at λ = 4.3 μm and S = 2.1 nW/ppm for a detection limit of 1.66 ppm for methane at λ = 7.7 μm when propagation losses α prop = 3 dB/cm are assumed. The results from the PGe ridge waveguide are comparable with those obtained with ChG slot waveguide and are the most impressive. Indeed, this PGe material has a large specific surface area which resulted in good characteristics, particularly its sensitivity and detection limit. These results indicate that the possible limit of detection represents, in some cases, one hundredth of the limit values recommended by international environmental standards [START_REF] Dettenrieder | Toward the Required Detection Limits for Volatile Organic Constituents in Marine Environments with Infrared Evanescent Field Chemical Sensors[END_REF], thus justifying the potential of these integrated sensor based on PGe or ChG materials as environmental monitoring tools. The detection could be improved by using lock-in detection by scanning over the absorption line or reference arm. The aim of the paper is to compare the performance of the three photonic structures using two types of materials for the integrated platform to improve to improve the detection of gas in the mid-infrared in term of optic power however the spectral resolution should be also improved [START_REF] Fathy | 0n-chip parallel Fourier transform spectrometer for broadband selective infrared spectral sensing[END_REF].

  , are studied: Ridge waveguides based on ChG materials (Figure 1.(a)), PGe material (Figure 1.(b)) and slots waveguides based on ChG (Figure 1.(c)). Waveguides (a) and (c) are fabricated on a Si substrate, while waveguide (b) is fabricated on a Ge substrate. The PGe layer porosities (and refractive index) of the ridge waveguide are respectively p 1 = 42% (n 1 =2.69) for the guiding layer and p 2 = 47% (n 2 =2.49) for the confinement layer.

Figure 1 .

 1 Figure 1. Types of waveguides investigated (a) ridge waveguide with ChG materials (b) ridge waveguide with PGe materials and (c) ChGs slot waveguide.

  be constant over the range of concentration.

Figure 2 .

 2 Figure 2. Evolution of the evanescent field factor of the evanescent wave Γ sup as a function of geometrical dimensions (w,h) for TM polarization: (a) 4.3 µm (CO 2 detection) and (b) 7.7 µm (CH 4 detection) for ridge waveguide based on ChG or PGe materials with similar refractive indices.

3 .

 3 Optimization of Slot waveguides for CO 2 detection at 4.3 μm. The variation of Γ sup as a function of the rail width w rail , (a) for different values of h, (b) for different values of gap g and (c) Variation of Γ as a function of g for the optimal values of w and h. The intensity profile of the proposed slot waveguide structures for g= 30nm is shown in the upper-right corner.

Figure 3 .

 3 Figure 3.(c), in the upper-right corner, shows the intensity profile of the TE polarization propagated modes for the optimal dimensions. It is highly confined in the slot region g. The variation of Γ sup with w for three different values of h and the width of the slot region g, and variation of Γ sup with g for a fixed value of w and h are shown in Figure 3.(a), 3.(b), and 3.(c), respectively.By examining these figures, it can be seen that the evanescent field factor reaches its maximum value for w rail = 800 nm and for g=30 nm. For these values, a high value of the field is confined in the slot region. Figure3(a)shows that the variation of h does not affect w opt , which remains unchanged whatever h. W rail , on the other hand, takes on greater values with the increase of g (Figure3(b)). As the variation of h has no impact on w, the choice of h opt = 1600 nm, for which Γ sup is slightly better, is appropriate. When w rail < w opt . (Figure3.(a) and 3.(c)) and g < g opt (Figure3.(c)) a major fraction of the field penetrates into the confinement region and becomes evanescent, and hence, power factor decreases. For w rail > w opt and g > g opt , evanescent field factor decreases due to the stronger confinement of field inside the high index ChG. When w rail < w opt . (Figure3.(a) and 3.(c)) and g < g opt (Figure3.(c)) a major fraction of the field penetrates into the confinement region and becomes evanescent, and hence, power factor decreases. For w rail > w opt and g > g opt , evanescent field factor decreases due to the stronger confinement of field inside the high index ChG.In order to have the best sensitivity, the optimal waveguide dimension chosen are: w rail = 0.8 µm, h = 1.6µm, and g = 30 nm, for which η reach values as high as ~ 58 %.For the wavelength of λ = 7.7 μm the same reasoning was followed. The optimal dimensions obtained are: w rail = 0.9 µm, h = 1.9 µm and g = 90 nm. The corresponding η maximum factor is about 51%.

Figure 4 .

 4 Figure 4. ChG ridge waveguide-based integrated sensor transmission and sensitivity as a function of the concentration C for several values of propagation loss α prop . Evolution of the power P depending on concentration C of CO 2 at 4.3 μm (a) and of CH 4 at 7.7 μm (b). Evolution of the sensitivity S depending on concentration C of CO 2 at 4.3 μm (c) and of CH 4 at 7.7 μm (d).

Figure 4 .

 4 (a) and 4.(c) show respectively the output power P and sensitivity S as a function of concentration C for CO 2 detection at 4.3 μm, whereas Figure 4.(b) and 4.(d) illustrate those of CH 4

Figure 5 .

 5 Figure 5. Power and sensitivity of the integrated sensor as a function of the concentration C for several values of propagation loss α prop for PGe ridge waveguide. Evolution of the power P depending on concentration C of CO 2 at 4.3 μm (a) and of CH 4 at 7.7 μm (b). Evolution of the sensitivity S depending on concentration C of CO 2 at 4.3 μm (c) and of CH 4 at 7.7 μm (d).

Figure 5 .

 5 (a) and 5.(c) show respectively the output power P and sensitivity S as a function of concentration C for CO 2 detection at 4.3 μm, whereas Figure 5.(b) and 5.(d) illustrate those of CH 4 detection at 7.7 μm

Figure 6 .

 6 Figure 6. Power and sensitivity of the integrated sensor as a function of the concentration C for several values of propagation loss α prop for slot waveguide. Evolution of the power P depending on concentration C of CO 2 at 4.3 μm (a) and of CH 4 at 7.7 μm (b). Evolution of the sensitivity S depending on concentration C of CO 2 at 4.3 μm (c) and of CH 4 at 7.7 μm (d).

ppm] Concentration of target molecules [µmol L -1 ]

		400	500 Concentration of target molecules [ppm] 600 700	800	400 370	500 Concentration of target molecules [ppm] 600 700	800
		396				(a)				(b)
		385						369
	P[µW]	352 363 374	9 dB/cm 6 dB/cm 3 dB/cm 4.3 mm				P[µW]	366 367 368	9 dB/cm 6 dB/cm 3 dB/cm 7.7 mm
		341
		17.86	22.32	26.78	31.25		35.71	17.86 365	22.32	26.78	31.25	35.71
		Concentration of target molecules [µmol L -1 ]	Concentration of target molecules [µmol L -1	]
		Concentration of target molecules [ppm]
		400	500	600	700		800	400	500	600	700	800
		28			(c)	1.84
								1.61
	16 20 24 S[nW/3 dB/cm 6 dB/cm 9 dB/cm 4.3 mm			1.15 1.38
								0.92
		12
								0.69
		8
		17.86	22.32	26.78	31.25	35.71	17.86	22.32	26.78	31.25	35.71

Table 2

 2 summarizes all the results for the 3 studied structures for α prop = 3 dB/cm for CO 2 detection at 4.3 µm and for CH 4 detection at 7.7 µm. The different sensors studied are very sensitive, in particular the ChG-slot and PGe-ridge waveguides, which have very close results.

Table 2 .

 2 Comparison of the sensitivity and the detection limit for the three waveguides studied with α prop = 3 dB/cm at 4.3 μm and 7.7 µm.

	wavegui	η(%)	Sensitivity (nW/ppm)	LOD (ppm)
	de
	λ(µm)	4	7	4.3	7.7	4.3	7.7
		.3	.7
	ChG-	1	1	0.62	0.041	5.63	84.65
	ridge
	PGe-	4	4	28	1.8	0.12	1.89
	ridge	5.3	4.7
	ChG-slot	5	5	35	2.1	0.1	1.66
		8	1

Table 3 .

 3 Limit of Detection (LOD) of the integrated chalcogenide glass sensor for CO 2 and CH 4 measurement in Mid-IR.

	Reference	waveguide	Propagation	λ(µm	LOD	λ(µm)	LOD	method	Year
			loss	)	of CO 2	CH 4	of CH 4
				CO 2
	[3]	ChG-slot	2 dB/cm	4.23	2 ppm	-	-	Theoretic	2014
							al
	[4]	ChG-ridge	3 dB/cm	2.5	10 ppm	-	-	Experime	2017
							ntal
	[10]	ChG-ridge	1 dB/cm	4.3	0.26 ppm	7.7	1.9 ppm	Theoretic	2017
							al
	[8]	ChG-slot	3 dB/cm	-	-	3.31	1.7 ppm	Practical	2019
	This work	PGe-ridge	3 dB/cm	4.3	0.12 ppm	7.7	1.89ppm	Theoretic
							al
	This work	ChG-slot	3 dB/cm	4.3	0.10 ppm	7.7	1.66 ppm	Theoretic
							al

Table 3

 3 reports our LOD results, which are compared with the state of the art in this field. The values for CH 4 detection are in the same order than the state of the art but lowest limit of detection for CO 2 values so far reported in the literature are obtained in this using work ridge PGe material and slot waveguide based on ChG material.

Funding: This work was supported by the French national research agency under MID-VOC ANR project (ANR-17-CE09-0028-01). Equipment funding of Institut Foton were partly provided by the CPER Sophie, and by Exceptional National Program (PNE) of Algerian ministry of higher education and scientific research.

Author Contributions: R. Z. carried out the simulations, wrote the paper, and prepared the original draft; N.L. and J.C. proposed the research directions. All authors contributed to the organization of the paper, writing, and proofreading.

All authors read and agreed to the published version of the manuscript.

Conflicts of Interest:

The authors declare no conflicts of interest.