Silicon based Double Fano resonances photonic integrated gas sensor

Silicon based Double Fano resonances photonic integrated gas sensor | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Article Silicon based Double Fano resonances photonic integrated gas sensor Norhan A. Salama, Shaimaa M. Alexeree, Salah S. A. Obayya, Mohamed A. Swillam This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-4067143/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 22 Oct, 2024 Read the published version in Scientific Reports → Version 1 posted 10 You are reading this latest preprint version Abstract The telecommunication wavelengths play a crucial role in the development of photonic integrated circuit (PIC). The absorption fingerprints of many gases lie within these spectral ranges, offering the potential to create miniaturized gas sensor for (PIC). In this work, we present novel double Fano resonances within the telecommunication wavelength range, based on silicon metasurface for selective gas sensing applications. Our proposed design comprises periodically coupled nanodisk and nano-bar resonators mounted on a quartz substrate. We show that the Fano resonances can be precisely tuned across the wavelength range from (𝜆=1.52𝜇m) to (𝜆=1.7𝜇m) by adjusting various geometrical parameters. Furthermore, we optimize the sensor for double detection of carbon monoxide (CO), with an absorption fingerprint at ~ 1.566 𝜇m, and nitrous oxide (N 2 O), with an absorption fingerprint at ~ 1.67𝜇m. The sensor exhibits exceptional refractometric sensitivity to CO of 1,735 nm/RIU with an outstanding FOM of 11,570. In addition, the sensor shows a sensitivity to N 2 O of 194 accompanied by a FOM of 510. The structure reveals absorption losses of 7% for CO and 3% for N 2 O. The outstanding FOM and absorption losses provide selectivity for the sensing material. Our proposed design holds significant promise for the development of highly sensitive double detection refractometric photonic integrated gas sensor. Metasurfaces metamaterial double Fano resonance CO gas sensor N2O gas sensor optical gas sensor Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Figure 8 1. Introduction Design of smart, compact, and low-cost gas sensors is in growing demand in modern society, as they play a crucial role in environmental monitoring 1 , industrial safety 2 , food safety 3 , disease diagnosis 4 , and medical applications 5 . In particular, detecting carbon monoxide (CO) and carbon dioxide (CO2) are of pivotal importance as serious pollutant greenhouse gases that threaten human and animal health. CO and CO 2 have colorless and odorless gases that can’t be perceived by human senses. CO introduces significant harmful effects on human health as compared to CO 2 . For instance, it reduces the blood’s ability to carry oxygen 6 , and causes a headache, dizziness, weakness, and respiration rate depravity 7 . Moreover, CO is responsible for the formation of tropospheric ozone 8 , 9 . CO is generated as a byproduct of the incomplete combustion of fusil fuel and organic material in industrial processes, transportation, and residential applications. Other kinds of gases are useful for medical applications, such as nitrous oxide (N 2 O). N 2 O is used as an anesthetic in dental surgery and ambulances. However, the overdose of N 2 O causes dissociative anesthesia and a lack of oxygen levels in the body 5 . In addition, N 2 O has an adverse impact on climate change and ozone layer degradation 10 . Various techniques are employed for gas sensing applications, such as semiconductor, electrochemical, and on-chip optical gas sensors. Other techniques, such as the quantum cascade laser spectrometer is utilized for CO detection in the stratosphere and troposphere, showing high sensitivity down to 1– 2 ppbV with a time resolution of 1 s 11 . This method is compatible with onboard aircraft and balloons. The charge transfer effect 12 and the electrical resistance changes of metal oxide-based sensors 13 are also employed for CO detection. Despite the advantages of high sensitivity and cost-effectiveness, these methods suffer from low chemical specificity, poor scalability, and limited longevity. On-chip optical gas sensors are alternative approaches to tackling the aforementioned limitations. The idea behind on-chip optical sensors is based on enhancing light-matter interaction through the creation of confined hotspots of evanescent fields of nano/ micro-structures 14 , 15 . There are two main platforms for optical sensors, namely the refractive index (RI) sensor and the absorption sensor. The absorption sensors take advantage of their high sensitivity and selectivity. However, their rack size and high cost deployed them for on-site applications. On the contrary, RI sensors have the advantages of high sensitivity, portability, and low cost, but at the expense of selectivity. However, Swillam et al 16 have demonstrated the possibility of detecting the dispersion of both the real and imaginary parts of the targeted substance using the RI sensors. The dispersion of the complex refractive index is a unique feature of each substance. The complex refractive index can be extracted from the shift of the resonance wavelength and the energy losses due to absorption across the spectral range. For this purpose, a single micro‑ ring resonator (MRR) has been proposed, providing multiple resonances over the operating wavelength range and enabling the determination of the dispersion of the complex refractive index. This highlights the importance of selecting the working wavelength to coincide with the absorption fingerprints of the sensing material for selective application. Near and MID-IR spectral regions are of pivotal importance for sensing applications, as most molecules have unique fingerprints within these ranges 17 . The telecommunication wavelength range in near IR is the best choice for photonic integrated circuit (PIC) applications. Silicon (Si) photonics offer exceptional performance, such as high-speed data transmission, miniaturization, high sensitivity, and scalability 18 . Moreover, the advancement in fabrication technologies for nano/microstructures and the complementary metal oxide semiconductor (CMOS) process position Si as the best candidate for sensing applications 19 . To date, the realization of optical gas sensors is mainly based on plasmonic platforms. For example, functionalized plasmonic Au-CuO nanocomposite film has been employed for carbon monoxide sensing demonstrating sensitivity to a concentration down to 50ppm 20 . Au-YSZ (yttrium stabilized with zirconium) has been used for detecting CO in the visible range (𝜆=600nm) at high temperature \(\sim400 C^\circ\) 21 . Integrated chemical microsensor and SPR has been employed to detect different concentrations of CO by measuring the corresponding small phase differences of SnO 2 22 . Superficial plasmonic resonance based on Kretschmann configuration has been proposed for CO concentration measurement by intensity interrogation 8 . Despite the undisputed advantages of highly sensitive small designs of plasmonic sensors, the severe inherent dissipation losses engendered by using the noble metals act as major obstacles. This is apart from CMOS incompatibility and the material cost 23 . Owing to these limitations, the optical gas sensors are still in the early stages and need further investigations to overcome the aforementioned challenges. Thanks to the optical metasurfaces, the dissipation losses of the plasmonic devices have been greatly enhanced demonstrating exquisite sensitivity and quality factor accompanied with the low cost and the ease of fabrication 24 , 25 . Dielectric metasurfaces (DM) are further breakthrough that served as an optimum solution to the efficiency and cost problems 26–28 . Metasurfaces are structures consisting of subwavelength 2D nanoantennas that can be adequately designed introducing phase discontinuity across the surface 29 . For the dielectric metasurfaces, the underline physics is associated with the first and second Mie scattering resonances of the subwavelength resonators. The dielectric resonators demonstrate a strong response to both the electric and magnetic fields allowing full phase coverage from 0 to 2π 23 . For sensing applications, some spectral features should be considered; the sharpness of the resonance wavelength that is expressed by the quality factor and the spectral shift “sensitivity” introduced by the change of the refractive index of the surrounding medium. Fano resonance is one of the most intriguing phenomena that is widely exploited for sensing applications 30 - 31 . Fano spectral line is characterized by the presence of a dip and peak of the transmission or reflection spectrum showing a high-quality factor 32,33 . Fano resonance results from the coupling of two oscillators with different damping rates. At resonance, the undamped oscillator shows an abrupt π phase shift, while the strongly damped oscillator shows a slow phase change introducing a broad spectral line. Fano spectral resonance has been realized in various configurations such as photonic crystals 34,25 , microcavities 35 , dielectric cylinders 36 , dielectric spheres 37 , and metasurfaces 31 . The periodic configurations such as the photonic crystals and metasurfaces demonstrate narrower spectral lines compared to the single resonators. This phenomenon positioned metasurface, as an easy fabrication material, at the forefront of the sensing applications 32 . Numerous structure designs have been investigated for gas sensing applications based on the Fano resonance perspective. For example, a side-coupled upright rectangular cavity with a metal-dielectric-metal (MDM) waveguide has been investigated for CH 4 and H 2 sensing applications. The structure demonstrates a plasmonic Fano resonance with sensitivity up to 846 nm/RIU and a Q-factor of 1.7 38 . Further study, plasmonic microcavities have been proposed utilizing the doped silicon as a new approach to induce a plasmonic effect with mitigated plasmonic losses. The structure shows sensitivity up to 6000 nm/RIU and FOM of 385 providing limited insertion losses 35 . The same approach is used for aluminum-doped zinc oxide (AZO) metasurfaces that are used for H 2 gas sensing showing a redshift ~ 13 nm within 10 min for H 2 concentration 4% 39 . On the other hand, structures based on all-dielectric high index material such as the periodic “Lucky knot” shaped nanostructure 40 , split bar resonator 41 , and periodic unit cells of coupled rectangular bar and ring resonators 42 , coupled nano-bar with nanodisk 43 , coupled nano-ellipse with nano-bar 44 , are employed for sensing applications for different materials. All-dielectric structures show enhanced quality factors reaching up to 980 in some cases 41 , however with less sensitivity than their plasmonic counterparts. In this work, we present a tunable double Fano resonant metasurface based on all-dielectric silicon operating around the telecommunication wavelength (𝜆=1.55𝜇m) for selective gas sensing applications in PIC. The proposed design comprises periodic cells of coupled silicon nanodisk and silicon nano-bar resonators. The Fano resonances can be precisely tuned across the range from (𝜆=1.52𝜇m) to (𝜆=1.7𝜇m) by adjusting the different geometrical parameters including the radius, the gap distance between resonators, and the nano-bar width. Furthermore, the sensor is optimized for double selective detection of carbon monoxide (CO) and nitrous oxide (N 2 O). Our work is categorized into five sections; initially, we define the structure geometry and the simuation setup. Secondly, we study the double Fano resonance mechanism showing the near-field coupling effect between the bright mode of the nano-bar resonator and the dark mode of the nanodisk/nano-bar resonator. The generated Fano resonances are derived from the destructive and constructive interference between the bright mode of the nano-bar and the dark mode of either the nanodisk or the nano-bar. At first Fano resonance (FR1), the generated mode is primarily influenced by the excitation of the dark mode of the nanodisk resonator, while at the second Fano resonance (FR2), the generated mode is influenced by the excitation of the dark mode of nano-bar resonator. Thirdly, we study the different geometrical parameters effect on the double Fano resonance. This section is classified into three sub-sections; first, we show that the double Fano resonance effect is realized for the radius geometrical parameters between (r = 200nm) to (r = 210nm). The nanodisk radius geometry greatly influences the FR1 causing a significant red shift up to orders of tens of nanometers, while causing a minor red shift, a few nanometers, to FR2. Then, we investigate the effect of the gab distance between the resonators demonstrating the exhibition of opposite spectral shifts upon increasing the gap distance showing a blue shift for FR1 and a red shift for FR2, resulting in increasing the spectral difference between the two resonances reaching up to ~ 66nm. It is worth noting that increasing the spectral difference between FR1 and FR2 is of special importance for sensing applications to avoid the spectral interference with the sensing signals. Next, we demonstrate the effect of the width (w) of the nano-bar that, in contrast to increasing the radius of the nanodisk, greatly influences the (FR2) showing a significant red shift upon increasing the width (w), while slightly influences the (FR1). The quality factor (Q-factor) of each tuning parameter is calculated achieving a significant Q-factor of 15,712. Finally, the sensor is optimized with the geometrical parameters of (r = 205nm, G = 180nm, w = 333nm) for selective detection of both carbon monoxide (CO), which possesses an absorption fingerprint approximately at 1.56 𝜇m, and nitrous oxide (N 2 O), that possesses an absorption fingerprint approximately at 1.67 𝜇m. The sensor achieves an outstanding sensitivity of 1,736 nm/RIU for CO detection accompanied by exceptional FOM of 11,570 and exhibits significant losses of 7% following exposure to CO gas. In addition, the sensor exhibits a detection for N 2 O with a sensitivity of 194 nm/RIU accompanied by an FOM of 510 and an absorption loss of 3% following exposure to N 2 O. The outstanding FOM and the distinct absorption losses are the crucial parameters for selectivity in refractometric sensors. Our design fabrication method has been demonstrated in ref 45 . Fabrication is started with the deposition of a 220 nm thick silicon layer on a quartz substrate using low-pressure chemical vapor deposition (LPCVD). Then, the structure is defined using the electron beam lithography (EBL) followed by the reactive ion etching. The structure is further integrated into a gas unit cell. Owing to the challenge of the required long optical path length for light-gas interaction, several approaches are proposed for achieving miniaturized gas cells with long optical path lengths. Among them, is the impressive approach of using a linear-variable optical filter (LVOF) as a gas cell 46 . The (LVOF) is composed of two face-to-face Bragg mirrors; a flat mirror and a tapered mirror. The (LVOF) acts as an array of Fabry-Pero cavities allowing multiple reflections and hence, increases the optical path length. Accordingly, we find a strong potential for integration of our design with the (LVOF) allowing a miniaturized device with on-chip scale level. Our reported design demonstrates superior performance for gas sensing applications compared to the previous studies presented in Table 1 . Table 1 Comparison between our sensor and the previously reported sensors Structure Working wavelength sensitivity Sensing material Q-factor FOM Coupled plasmonic Si microcavities 35 3.6 𝜇m 4.46 𝜇m 2,300 nm/RIU 3,860nm/RIU (CH 2 O) (N 2 O) 385 60 145 Coupled ring/nano-bar 42 1.35 𝜇m 289 nm/RIU n = 1.4 to n = 1.44 483 103 metal-dielectric-metal (MDM) waveguide 38 0.948 𝜇m 846 nm/RIU CH 4 and H 2 28 73 Periodic “Lucky knot” 40 7.3 𝜇m 986 nm/RIU Glucose at different temperature 520 33 Split bar resonator 41 1.6 𝜇m to 2𝜇m 525 nm/RIU n = 1.3 to n = 1.7 800 260 The reported design 1.566 𝜇m 1,735 nm/RIU 194 nm/RIU CO N 2 O 15,640 4,293 11,570 510 2. Design and simulation setup Initially, the schematic of periodic nanobars and periodic nanodisks with the corresponding normslized reflection spectra are presented in Fig. 1 (a-c). The design under consideration is based on periodic coupled oscillators of nano-bars and circular nanodisks as depicted in Fig. 1 d. The initial geometrical parameters of the structure are defined as; the nanobar length of (L = 900nm), the width of (w = 300nm), radius of (r = 205nm), the gap distance between the resonators of (G = 130nm), the other side gap distance of (G2 = 150nm), the pitch in x-direction of (P1 = 990nm), the pitch in y-direction of (P2 = 1050nm) and the thickness of both resonators of (t = 220nm). The structure is mounted on a quartz substrate. The optical response of each system is numerically investigated using commercial software (Lumerical) based on the finite difference time domain method (FDTD) 47 . The simulation setup is established as follows; the periodic boundary conditions are used for x and y directions, while the perfectly matched layers (PML) are used in z-direction. The structure is impinged on by a normal incident plane wave with a polarization direction parallel to the long axis of the nano-bar resonator (y-polarization). The mesh type is auto-nonuniform with an accuracy of 7. 3. The double Fano resonance mechanism Fano resonance originates from the interference between a continuum band of states with the discrete quantum optical states of coupled two resonators. The coupled resonators response could be treated as coupled harmonic oscillators model described by the following equations 42 : $${\dot{x}}_{1}-j({\omega }_{0}+j{\gamma }_{1}) {x}_{1}+j\kappa {x}_{2}=g{E}_{0} {e}^{j\omega t}$$ $${\dot{x}}_{2}-j({\omega }_{0}+\delta +j{\gamma }_{2}) {x}_{2}+j\kappa {x}_{1}=0$$ 1 , where \({x}_{1}\) and \({x}_{2}\) are the amplitudes of the collective modes of resonator 1 (bright mode) and resonator 2 (dark mode), respectively. \({\omega }_{0}\) is the central resonance frequency of the bright mode resonator. \({\gamma }_{1}\) and \({\gamma }_{2}\) are the damping rates of the two resonators expressing the radiative and the nonradiative damping. \(\kappa\) and \(\delta\) are the coupling coefficients between the resonators and the detuning of resonance frequency of oscillators 1 and 2, respectively. \(g\) is the dipole coupling strength of the bright mode with the incident electric field \({E}_{0}\) . The interaction between the bright resonance with the narrower dark resonance, that coexist at certain spectral range, leads to high quality factor Fano spectral line. Damping rates and the coupling coefficient are crucial precursors for the Fano resonance phenomenon. In our design, the nonradiative damping rates are suppressed due to utilizing an all-dielectric material. Simultaneously, the radiative damping is minimized due to the collective oscillation of the array unit cells. On the other hand, decreasing the coupling coefficient \(\kappa\) than the larger damping rate, which is dependent on the geometrical parameters, is necessary to enhance field localization and consequently increase the Q-factor. The interplay between damping rates and coupling coefficient plays a pivotal role in shaping Fano resonances and their corresponding Q-factors in metamaterials. Silicon-based circular nanodisks have been previously explored providing the possibility of introducing a Fano resonance that is controlled by the aspect ratio; the diameter and the height of the disk, enabling high directionality control 36 . The resulting resonance represents the strong coupling between the Mie-like mode and the Fabry-Pero like mode. However, a dark mode is realized when the radiation from all the modes compensates each other 33 . The nanodisk of the thickness of (t = 220nm), radius of (r = 205nm) and the periodic distance of (P = 990nm) exhibits dark mode along the range of wavelengths from 1.5–1.7𝜇m as can be observed in Fig. 1 c (red curve), consistent with 36 . Building upon the findings in 48 , the dark mode of the nanodisk can be excited by the azimuthal incidence of the near field Bessel beam generating a so-called pseudo modes, the modes that have no real optical oscillations. Axially symmetric Bessel beam offers the advantage of exciting specific polarization only i.e TM or TE mode, eliminating the potential of mode suppression caused by interference. Different theoretical approaches have been proposed for launching near-field Bessel beams such as the parallel plates waveguide 49 and metamaterial lens with gradient index 50 . In our design, we utilize a nano-bar to generate a Bessel-like mode, as visually evidenced in the 2D electric field profile of the nanobar along the dashed line near the nano-bar surface (Fig. 1 (c,i)).The nano-bar acts as a bright mode with a wide bandwidth as shown in Fig. 1 c (black curve). When the two resonators are brought in close proximity, as shown in Fig. 1 d, double Fano resonances are realized as demonstrated in Fig. 1 e. The schematic diagram presented in Fig. 1 f is an initial demonstration of the coupling mechanism between the two resonators. The dipole mode of the nano-bar (red curve)- the electric field intensity profile along the dashed line in (Fig. 1 (c,i))- excites the magnetic dark mode within the nanodisk, inducing a displaced perpendicular electric field circulating around the nanodisk. A detailed investigation of this coupling mechanism and its role in both Fano resonances (FR1 and FR2) will be presented in the following subsections. 3.1 Fano resonance at FR1 At FR1, the demonstration of the near field coupling mechanism of the nano-bar and the nanodisk, explained above, is verified showing a magnetic dipole resonance within the nanodisk, Fig. 2 a, inducing a displaced circulating electric field around the nanodisk, Fig. 2 e-g. The magnetic and the electric field profiles are characterized by field distribution following the Bessel function, showing a maximum magnetic field intensity at the center accompanied by a minimum electric field intensity at the same position, as depicted in Fig. 2 d and Fig. 2 h. In the gap distances between the resonators, the electric and magnetic fields are almost equal to zero. The overall electric and magnetic field distribution demonstrates a spatial Fano resonance. Our numerical study aligns with the analytical solution for the near-field Bessel beam excitation of spherical nanoparticles presented in ref 51,48 . From Fig. 2 b-c and Fig. 2 f-g, distinct magnetic and electric phase shifts are observed in the frequency domain between the peak (𝜆=1.548 𝜇m) and dip (𝜆=1.5483𝜇m) resonances.The magnetic field exhibits an abrupt change in orientation, transitioning from outward for the peak resonance to inward for the dip resonance. Similarly, the electric field circulates in opposite directions for the peak and dip resonances, as shown in Fig. 2 f and Fig. 2 g. 3.2 Fano resonance at FR2 At FR2, the nano-bar bright mode excites the magnetic dark mode within the nanodisk as well as the magnetic dark mode within the nano-bar with different strength, Fig. 3 a and Fig. 3 d. Simiarly to FR1, the out of plane magnetic resonance within the nanodisk, Fig. 3 b and Fig. 3 c, results in a displaced circulating electric field around the nanodisk, Fig. 3 f and Fig. 3 g. In addition, a strong electric field confinement is generated between the the nano-bar and the nanodisk and on the edge of the nano-bar facing the nanodisk, Fig. 3 e and Fig. 3 h. The electric field vector profile demonstrates the induced circulating electric field around the nano-bar, Fig. 3 f-g. 4. The geometrical parameters effect on the double Fano resonances Now, we show the effect of the geometrical parameters of the structure; radius of the nanodisk, the gap distance between both resonators and the width of the nanobar resonator, in terms of the reflection spectrum, the resonance wavelengths, the spectral difference between the two resonances and the quality factor (Q-factor). We demonstrate the ability of the structure for tuning the Fano resonance positions at will. The Q-factor is defined as \(\left(Q=\frac{{\lambda }_{res}}{FWHM}\right)\) where \({\lambda }_{res}\) is the resonance wavelength and (FWHM) is the full width at half maximum. 4.1 The radius parameter of the nanodisk effect First, we study the effect of varying the radius of the nanodisk (r), while keeping the gap distance fixed at \((G=130nm)\) and the nanobar width fixed at (w=300nm). Figure 4 a shows the reflection behavior of various nanodisk radius parameters (r) ranging from (r=190nm) to (r=210nm). The structure of (r=190nm) shows the emergence of Fano resonance at the spectral region of (FR2) only. By increasing the radius to (r = 195nm), a transparency window is realized with a high dispersive nature that is considered an obstacle for sensing applications. Further increasing of the nanodisk radius shows the formation of significant double Fano resonances at FR1 and FR2. Increasing the radius (r) of the nanodisk from (r = 195nm) to (r=210nm) causes a substantial red shift in the first Fano resonance (FR1) and a minor red shift in the second Fano resonance (FR2) as shown in Fig. 4 b. Hence, the spectral gap distances between the two resonances (d𝜆) decrease as demonstrated in Fig. 4 c. The radius effect emphasizes that the FR1 is primarily attributed to the excited dark mode inside the nanodisk as previously explained. Further radius increasing than (r = 210nm) diminishes the resonance at FR2. Figure 4 d illustrates the calculated Q-factors for various radius parameters, revealing a maximum value of 7,674 for r = 200nm at FR1 and 7,960 for r = 210nm at FR2. Aiming to operate within the telecommunication wavelength (𝜆=1.55 𝜇m), we select the structure with a radius of (r = 205 nm) that exhibits an operating wavelength of (𝜆=1.548 𝜇m) and Q-factor of 5,160 at FR1 for further investigations. 4.2 The gap distance parameter effect Next, we investigate the influence of varying one gap distance (G) between the nanodisk and the nano-bar resonators, while keeping the other gap fixed at (G2 = 150 nm) on the reflection behavior as shown in Fig. 5 . Increasing the G distance leads to opposing shifts: blue shift for FR1 and redshift for FR2 as depicted in Fig. 5 a and Fig. 5 b. Consequently, the spectral gap distance (d𝜆) between FR1 and FR2 widens with increasing G as illustrated in Fig. 5 c. For G = 150nm, the Fano resonance at both FR1 and FR2 disappears due to symmetry as may be observed from Fig. 5 a ( red curve). In addition, G exerts a substantial influence on the modulation depth that is enhanced as G increases beyond 150nm showing a notable enhancement up to (~ 90%) for (G = 180 nm) as depicted from Fig. 5 a and Fig. 5 e. Additionally, the calculated Q-factors are noteworthy for G values between 160 nm and 180 nm, with FR1 exhibiting exceptional Q-factors of 25,784 for (G = 160 nm) and 15,459 for (G = 180 nm). However, the structure of (G = 160 nm) suffers from the limitation of the small modulation depth of 35% as may be observed in Fig. 5 e. Therefore, the structure of (G = 180 nm) is the more suitable choice for further investigation. 4.3 The nano-bar width parameter effect Further investigation is performed for the structure of different nanobar resonator widths. In contrast to increasing the nanodisk radius, increasing the nano-bar width causes a substantial redshift to FR2 and a minor redshift to FR1, as can be observed from Fig. 6 a and Fig. 6 b. Increasing the nano-bar width provides the advantage of increasing the spectral gap (d𝜆) between FR1 and FR2 as illustrated in Fig. 6 c.The calculated Q-factors of FR1 retain at high values reaching up to 15,711 for the structure of (w = 340 nm), while the Q-factors of FR2 varies having its maximum 3,463 for the structure of (w = 340 nm) as shown in Fig. 6 d. 5. Double Fano resonance application in gas sensing Many gas molecules posses unique absorption fingerprints within the telecommunication wavelength range. For selective gas sensing applications, we excite the specific Fano resonance at a wavelength precisely matching the gas’s spectral fingerprint. This optimal alignment induces a remarkable spectral shift accompanied by significant losses due to absorption, highlighting the gas molecules’ unique spectral signatures. Carbon monoxide (CO) and nitrous oxide (N 2 O) gases are significant greenhouse gases that contribute to climate change and environmental degradation 9,10 . The accurate and efficient detection and monitoring of these gases are crucial for mitigating their adverse impacts.CO and N 2 O possess distinct absorption fingerprints in the telecommunication wavelength range at (~𝜆=1.57𝜇m) and (~𝜆=1.67𝜇m), respectively. The absorbance of both gases at temperature (T = 298 K), pressure (P = 1atm), effective path length (l = 5m) and gas mole-fraction (X = 0.01) are computed using Spectraplot tool based on HITRAN database and presented in Fig.7 52,53 . Using the absorbance data, the dispersive real and the imaginary parts of the complex refractive index of CO and N 2 O are calculated using the Krammers-Kronig relation 54 : $$n\left({{\lambda }}_{0}\right)= n\left({{\lambda }}_{1}\right)+p\frac{\left({{\lambda }}_{1}^{2}-{{\lambda }}_{0}^{2}\right)}{\pi } \underset{0}{\overset{\infty }{\int }}\frac{{\lambda }\text{k}\left({\lambda }\right)\text{d}{\lambda }}{\left({{\lambda }}_{1}^{2}-{{\lambda }}^{2}\right)\left({{\lambda }}_{1}^{2}-{{\lambda }}^{2}\right)}$$ 2 Where \(p\) is the Cauchy principal value of integral, \(n\left({{\lambda }}_{1}\right)\) is the known refractive index of the gas at wavelength ( \({{\lambda }}_{1}\) ) and \(\text{k}\left({\lambda }\right)\) extinction coefficient that is calculated from the absorption coefficient \({\alpha }\left({\lambda }\right)\) as follows: $$\text{k}\left({\lambda }\right)=\frac{4\pi {\alpha }\left({\lambda }\right)}{\lambda }$$ 3 Leveraging the unique optical properties of double Fano resonances, we have developed our design for the detection of both CO and N 2 O gases. The structure is optimized with parameters; r = 205nm, G = 180nm, and w = 333nm, enabling the realization of double Fano resonance at 𝜆=1.5667𝜇m and 𝜆=1.674𝜇m. The normalized reflection spectra of the sensor for both CO and N 2 O with respect to the vacuum (n = 1) are presented in Fig. 8 . The sensor’s key features that contribute to the design selectivity are the sensitivity accompanied by high figures of merits and the absorption losses. The sensor sensitivity is calculated as the ratio of the spectral shift of the Fano resonance to the change of the refractive index after the exposure to the gas sensing material ( \(S=\frac{\varDelta \lambda }{\varDelta n}\) ). The figure of merit (FOM) is defined as the ratio between the sensitivity and (FWHM) of the Fano resonance. The sensor exhibits an exceptional sensitivity to CO of (S CO = 1,735 nm/RIU) and boasts an ultrahigh FOM of (11,570). Meanwhile, it exhibits a sensitivity of (S N2O = 194 nm/RIU) with an acceptable FOM of (510). The sensor's sensitivity performance for N 2 O detection is lower than its performance for CO, but it is still good enough to be useful for many applications. Furthermore, the absorption losses, which are expected to amplify due to the sensor's operation within the absorption band, are calculated as the normalized change in FWHM of the Fano resonance following exposure to the gas sensing material: \((L=\frac{{FWHM}_{g}-{FWHM}_{0}}{{FWHM}_{0}}\) ) where \({FWHM}_{g}\) and \({FWHM}_{0}\) are the full width at half maximum for the gas and free space, respectively. The calculated absorption losses reveal values of ( \({L}_{CO}=7\%\) ) for CO and \({(L}_{N2O}=3\%)\) for N 2 O. These significant absorption losses provide valuable information about the gas sensing material and its concentration. Therefore, absorption losses are crucial for qualitative and quantitative refractometric sensing applications. Conclusion This study reports the development of a selective gas sensor based on double Fano resonance operating at telecommunication wavelengths for photonic integrated circuit applications. The sensor design employs an all-dielectric silicon metasurface consisting of coupled nanodisk and nanobar resonators. Each Fano resonance can be tuned independently by adjusting the geometrical parameters, including the nanodisk radius, the gap between the nanodisk and the nano-bar, and the nano-bar width. Leveraging Fano resonance at the absorption band of the sensing material holds promise for selective gas sensing applications in terms of figures of merit (FOM) and absorption losses. We demonstrate the feasibility of this approach by developing a sensor design capable of detecting both carbon monoxide (CO) and nitrous oxide (N 2 O) gases at wavelengths of 1.566 µm and 1.674 µm, respectively. The sensor exhibits remarkable sensitivities of 1,750 nm/RIU for CO and 194 nm/RIU for N 2 O, accompanied by exceptional FOM of 11,570 and 510, respectively. These exceptionally high FOMs underscore the sensor's outstanding selectivity potential. Furthermore, the absorption losses, evident from the increased FWHM, are identified revealing values of 7% for CO and 3% for N 2 O. These distinct absorption losses highlight the proposed design's potential as a highly sensitive and selective gas sensor. Additionally, the sensor's compatibility with CMOS technology and its low-cost fabrication process make it an attractive candidate for practical applications. Materials and methods Finite difference time domain (lumerical software) has been used for simulating the optical response of the proposed structures to incident plane waves. Matlab software has been used for calculating Krammers Kronig relation. Declarations Data availability: The datasets used and/or analysed during the current study available from the corresponding author on reasonable request. Acknowledgment: We declare no financial support. Conflict of interests: the authors declare no competing interests. Contributions: N.S has designed the proposed structure. N.S has performed the theoretical modelling and numerical simulations. N.S has written the manuscript. S.A has contributed to the technical discussion regarding the gas sensing application. S.O has contributed to the technical discussion regarding metasurface physical concepts and related design issues presented in the paper. M.S has contributed to the technical discussion regarding metasurface physical concepts and related design issues presented in the paper. All the authors have revised and edited the manuscript. References Mi, G., Horvath, C., Aktary, M. & Van, V. Silicon microring refractometric sensor for atmospheric CO_2 gas monitoring. Opt. 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Transf. 200 , 249–257 (2017). Gordon, I. E. et al. The HITRAN2016 molecular spectroscopic database. J. Quant. Spectrosc. Radiat. Transf. 203 , 3–69 (2017). Lucarini, V., Saarinen, J., Peiponen, K.-E. & Vartiainen, E.M. Kramers–Kronig Relations in Optical Materials Research. (Springer-Verlag Berlin Heidelberg, 2005). Additional Declarations No competing interests reported. Cite Share Download PDF Status: Published Journal Publication published 22 Oct, 2024 Read the published version in Scientific Reports → Version 1 posted Editorial decision: Revision requested 28 Jun, 2024 Reviews received at journal 25 Apr, 2024 Reviews received at journal 11 Apr, 2024 Reviewers agreed at journal 31 Mar, 2024 Reviewers agreed at journal 30 Mar, 2024 Reviewers invited by journal 29 Mar, 2024 Editor assigned by journal 26 Mar, 2024 Editor invited by journal 26 Mar, 2024 Submission checks completed at journal 26 Mar, 2024 First submitted to journal 10 Mar, 2024 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-4067143","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":284411112,"identity":"06351f2b-bd66-4d90-8596-a7d7ad1b4066","order_by":0,"name":"Norhan A. Salama","email":"","orcid":"","institution":"National Institute of Laser Enhanced Sciences, Cairo University","correspondingAuthor":false,"prefix":"","firstName":"Norhan","middleName":"A.","lastName":"Salama","suffix":""},{"id":284411113,"identity":"71cd6b5b-b800-4cbf-adc1-03f9b2874330","order_by":1,"name":"Shaimaa M. Alexeree","email":"","orcid":"","institution":"National Institute of Laser Enhanced Sciences, Cairo University","correspondingAuthor":false,"prefix":"","firstName":"Shaimaa","middleName":"M.","lastName":"Alexeree","suffix":""},{"id":284411114,"identity":"4a663033-0455-4f51-853a-21e50b9a5d01","order_by":2,"name":"Salah S. A. Obayya","email":"","orcid":"","institution":"Zewail City of Science, Technology and Innovation","correspondingAuthor":false,"prefix":"","firstName":"Salah","middleName":"S. A.","lastName":"Obayya","suffix":""},{"id":284411115,"identity":"a1e0cddb-f493-4d1e-8812-4a4817b0d63f","order_by":3,"name":"Mohamed A. Swillam","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA8klEQVRIiWNgGAWjYLCChAILBgb2BiQRHoJaDCSAqg5AeWzEaGEAaZFIIFKLbgP7M4kHBhLyujMfP5P4UVGbuF2+gfHB2zbcWswO8JhJAB1muO12mplkz5njiTvbGJgN5+LXwnYDqIVx2+0EM2nGtmOJG44xsEnz4tXC/gykxX7bzePfpBn/gbWw/8avhcEMpCVx2w0eoC0NNWBbmPFqOcxj/gOoJXnbmZxiy55jB4x3tiU2S845h0fL8fbHhj8qbGy3HT++8caPmjrZ7cyHD354U4ZbCwMzKvew4wYGxgY86jFBnb0BSepHwSgYBaNgJAAAyKxULGnPqZcAAAAASUVORK5CYII=","orcid":"","institution":"The American University in Cairo","correspondingAuthor":true,"prefix":"","firstName":"Mohamed","middleName":"A.","lastName":"Swillam","suffix":""}],"badges":[],"createdAt":"2024-03-10 18:32:38","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-4067143/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-4067143/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1038/s41598-024-74288-6","type":"published","date":"2024-10-22T15:57:07+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":53701145,"identity":"e1faabb2-872b-4c8f-a547-a5879f1d9746","added_by":"auto","created_at":"2024-03-29 05:23:00","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":342627,"visible":true,"origin":"","legend":"\u003cp\u003eSchematic and normalized reflection spectra of the nanobars, the nanodisks, and the coupled resonators with the dimensions of; r=205nm, L=900nm, w=300nm, G=130nm, G2=150nm, P1=990nm, P2=1050nm and t=220nm. a,b)Schematics of periodic nanobars and nanodisks, respectively. c) the normalized reflection spectrum of both the nano-bars (black curve) and the nanodisks (red curve) and their corresponding 2D electric field profiles: (i) the nano-bars (the dashed line: Bessel beam like mode plane), and (ii) the nanodisks. d)Schematic of the coupled nano-bars and nanodisks. e) The normalized reflection spectrum of the coupled resonators showing the generated double Fano resoances. f) Diagram showing the near field dipole coupling mechanism. The generated electric field (red curve) near the nano-bar excites the magnetic field inside the nanodisk, which induces a circulating electric field on the nanodisk edge.\u003c/p\u003e","description":"","filename":"Figure1.png","url":"https://assets-eu.researchsquare.com/files/rs-4067143/v1/6eeb7f09ed44860852144634.png"},{"id":53701144,"identity":"9b2d7aae-896a-48a6-9958-9fe13b7601d4","added_by":"auto","created_at":"2024-03-29 05:23:00","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":348365,"visible":true,"origin":"","legend":"\u003cp\u003eThe different H-and E-field profiles at FR1; a)the 2D cross-section of H-field profile at the peak (𝜆=1.548 𝜇m). b,c)The vector H-field profiles reveals the field direction at the peak (out-of-plane, 𝜆=1.548 𝜇m) and at the dip (in-plane, 𝜆=1.5483 𝜇m). d) the line H-field profile along the horizontal axial symmetry (the gray dashed line in Fig.a). e) the 2D cross section of E-field profie. f,g) The vector E-field profiles illustrate field circulation around the nanodisk, with opposite directions for the peak and the dip wavelengths. h) the line E-field profile along the horizontal axial symmetry plane (the gray dashed line in Fig.e).\u003c/p\u003e","description":"","filename":"Figure2.png","url":"https://assets-eu.researchsquare.com/files/rs-4067143/v1/77d36aefa2794bdee9d588a0.png"},{"id":53701147,"identity":"a7f721d9-f7ed-45b7-b0c8-66646d76f800","added_by":"auto","created_at":"2024-03-29 05:23:00","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":336482,"visible":true,"origin":"","legend":"\u003cp\u003eThe different H- and E-field profiles at FR2; a) the 2D cross section of \u0026nbsp;H-field profile at the peak wavelength. b,c) The vector H-field profiles reveals the field direction at the peak and dip wavelengths, respectively. d) the line H-field profile along the horizontal axial symmetry (the gray dashed line in Fig.a). e) the 2D cross section of E-field profile at the peak wavelength. f,g) The vector E- field profiles illustrate circulating field on both the nanobar and nanodisk. The circulation flips between the peak and dip wavelengths. h) the line E-field profile along the horizontal axial symmetry (the gray dashed line in Fig.e).\u003c/p\u003e","description":"","filename":"Figure3.png","url":"https://assets-eu.researchsquare.com/files/rs-4067143/v1/d0aacc0f6a0fed7ef0f4f238.png"},{"id":53701139,"identity":"1f8ef429-03ef-44d9-888c-d48d5250c16f","added_by":"auto","created_at":"2024-03-29 05:22:59","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":172184,"visible":true,"origin":"","legend":"\u003cp\u003eEffect of the radius parameter (r) on; a) the normalized reflection spectrum, b) the resonance wavelengths at FR1 and FR2, c) the spectral separation between FR1 and FR2, and d) the Q-factors of FR1 and FR2.\u003c/p\u003e","description":"","filename":"figure4.png","url":"https://assets-eu.researchsquare.com/files/rs-4067143/v1/45fe7acb07ea8534a799de51.png"},{"id":53701655,"identity":"c4974ee8-81fb-4ccc-bb03-c8151488af89","added_by":"auto","created_at":"2024-03-29 05:30:59","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":203642,"visible":true,"origin":"","legend":"\u003cp\u003eEffect of the (G) parameter on; a) the normalized reflection characteristics, b) the resonance wavelengths of FR1 and FR2 along the range of (G=130-200 nm), c) the spectral separation (d𝜆) between FR1 and FR2 (the open circle denotes the disappearing Fano resonance), d) the calculated Q-factor, and e) the modulation depth.\u003c/p\u003e","description":"","filename":"Figure5.png","url":"https://assets-eu.researchsquare.com/files/rs-4067143/v1/410804d02d5746ec3a3b54a2.png"},{"id":53701143,"identity":"15890337-ba03-4cdb-8bad-efe39e3fbb99","added_by":"auto","created_at":"2024-03-29 05:23:00","extension":"png","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":186637,"visible":true,"origin":"","legend":"\u003cp\u003eTEffect of nano-bar parameter width (w) on; a) The normalized reflection spectra, b) The resonance wavelengths, c) The spectral separation between FR1 and FR2, and d) The Q-factor of both resonances.\u003c/p\u003e","description":"","filename":"Figure6.png","url":"https://assets-eu.researchsquare.com/files/rs-4067143/v1/022e6fb2302751e2ef7df8c9.png"},{"id":53701148,"identity":"b2a6df01-22f9-436a-adeb-ea06b3540c1a","added_by":"auto","created_at":"2024-03-29 05:23:01","extension":"png","order_by":7,"title":"Figure 7","display":"","copyAsset":false,"role":"figure","size":92146,"visible":true,"origin":"","legend":"\u003cp\u003eThe absorbance of a)Carbon monoxide (CO) and b) Nitrous oxide (N\u003csub\u003e2\u003c/sub\u003eO) as extracted from the spectraplot simulation tool based on the HITRAN database \u003csup\u003e52,53\u003c/sup\u003e.\u003c/p\u003e","description":"","filename":"Figure7.png","url":"https://assets-eu.researchsquare.com/files/rs-4067143/v1/0e2dd5b81a54fd4b444db829.png"},{"id":53701141,"identity":"f02bc012-7142-4968-8848-5f5878f27fcb","added_by":"auto","created_at":"2024-03-29 05:22:59","extension":"png","order_by":8,"title":"Figure 8","display":"","copyAsset":false,"role":"figure","size":95616,"visible":true,"origin":"","legend":"\u003cp\u003eThe normalized reflection spectra of the gas sensor with a vacuum (n=1) as a reference towards a) CO, and b)N\u003csub\u003e2\u003c/sub\u003eO. The insets show the entire spectrum of the sensor, depicting the spectral ranges for CO and N\u003csub\u003e2\u003c/sub\u003eO sensing presented by the dashed lines, respectively.\u0026nbsp;\u003c/p\u003e","description":"","filename":"Figure8.png","url":"https://assets-eu.researchsquare.com/files/rs-4067143/v1/adc70ef6300474371b5cc782.png"},{"id":67681757,"identity":"2818f22b-44d9-40fa-a776-b2f295386b83","added_by":"auto","created_at":"2024-10-28 16:10:01","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":2703764,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-4067143/v1/1bc8d8e4-f2fb-41b0-92bd-a77bc3b30f36.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Silicon based Double Fano resonances photonic integrated gas sensor","fulltext":[{"header":"1. Introduction","content":"\u003cp\u003eDesign of smart, compact, and low-cost gas sensors is in growing demand in modern society, as they play a crucial role in environmental monitoring\u003csup\u003e1\u003c/sup\u003e, industrial safety\u003csup\u003e2\u003c/sup\u003e, food safety\u003csup\u003e3\u003c/sup\u003e, disease diagnosis \u003csup\u003e4\u003c/sup\u003e, and medical applications\u003csup\u003e5\u003c/sup\u003e. In particular, detecting carbon monoxide (CO) and carbon dioxide (CO2) are of pivotal importance as serious pollutant greenhouse gases that threaten human and animal health. CO and CO\u003csub\u003e2\u003c/sub\u003e have colorless and odorless gases that can\u0026rsquo;t be perceived by human senses. CO introduces significant harmful effects on human health as compared to CO\u003csub\u003e2\u003c/sub\u003e. For instance, it reduces the blood\u0026rsquo;s ability to carry oxygen\u003csup\u003e6\u003c/sup\u003e, and causes a headache, dizziness, weakness, and respiration rate depravity\u003csup\u003e7\u003c/sup\u003e. Moreover, CO is responsible for the formation of tropospheric ozone\u003csup\u003e8\u003c/sup\u003e,\u003csup\u003e9\u003c/sup\u003e. CO is generated as a byproduct of the incomplete combustion of fusil fuel and organic material in industrial processes, transportation, and residential applications.\u003c/p\u003e \u003cp\u003eOther kinds of gases are useful for medical applications, such as nitrous oxide (N\u003csub\u003e2\u003c/sub\u003eO). N\u003csub\u003e2\u003c/sub\u003eO is used as an anesthetic in dental surgery and ambulances. However, the overdose of N\u003csub\u003e2\u003c/sub\u003eO causes dissociative anesthesia and a lack of oxygen levels in the body\u003csup\u003e5\u003c/sup\u003e. In addition, N\u003csub\u003e2\u003c/sub\u003eO has an adverse impact on climate change and ozone layer degradation\u003csup\u003e10\u003c/sup\u003e.\u003c/p\u003e \u003cp\u003eVarious techniques are employed for gas sensing applications, such as semiconductor, electrochemical, and on-chip optical gas sensors. Other techniques, such as the quantum cascade laser spectrometer is utilized for CO detection in the stratosphere and troposphere, showing high sensitivity down to 1\u0026ndash; 2 ppbV with a time resolution of 1 s\u003csup\u003e11\u003c/sup\u003e. This method is compatible with onboard aircraft and balloons. The charge transfer effect\u003csup\u003e12\u003c/sup\u003e and the electrical resistance changes of metal oxide-based sensors\u003csup\u003e13\u003c/sup\u003e are also employed for CO detection. Despite the advantages of high sensitivity and cost-effectiveness, these methods suffer from low chemical specificity, poor scalability, and limited longevity.\u003c/p\u003e \u003cp\u003eOn-chip optical gas sensors are alternative approaches to tackling the aforementioned limitations. The idea behind on-chip optical sensors is based on enhancing light-matter interaction through the creation of confined hotspots of evanescent fields of nano/ micro-structures\u003csup\u003e14\u003c/sup\u003e,\u003csup\u003e15\u003c/sup\u003e. There are two main platforms for optical sensors, namely the refractive index (RI) sensor and the absorption sensor. The absorption sensors take advantage of their high sensitivity and selectivity. However, their rack size and high cost deployed them for on-site applications. On the contrary, RI sensors have the advantages of high sensitivity, portability, and low cost, but at the expense of selectivity. However, Swillam \u003cem\u003eet al\u003c/em\u003e\u003csup\u003e16\u003c/sup\u003e have demonstrated the possibility of detecting the dispersion of both the real and imaginary parts of the targeted substance using the RI sensors. The dispersion of the complex refractive index is a unique feature of each substance. The complex refractive index can be extracted from the shift of the resonance wavelength and the energy losses due to absorption across the spectral range. For this purpose, a single micro‑ ring resonator (MRR) has been proposed, providing multiple resonances over the operating wavelength range and enabling the determination of the dispersion of the complex refractive index. This highlights the importance of selecting the working wavelength to coincide with the absorption fingerprints of the sensing material for selective application.\u003c/p\u003e \u003cp\u003eNear and MID-IR spectral regions are of pivotal importance for sensing applications, as most molecules have unique fingerprints within these ranges\u003csup\u003e17\u003c/sup\u003e. The telecommunication wavelength range in near IR is the best choice for photonic integrated circuit (PIC) applications. Silicon (Si) photonics offer exceptional performance, such as high-speed data transmission, miniaturization, high sensitivity, and scalability\u003csup\u003e18\u003c/sup\u003e. Moreover, the advancement in fabrication technologies for nano/microstructures and the complementary metal oxide semiconductor (CMOS) process position Si as the best candidate for sensing applications\u003csup\u003e19\u003c/sup\u003e.\u003c/p\u003e \u003cp\u003eTo date, the realization of optical gas sensors is mainly based on plasmonic platforms. For example, functionalized plasmonic Au-CuO nanocomposite film has been employed for carbon monoxide sensing demonstrating sensitivity to a concentration down to 50ppm\u003csup\u003e20\u003c/sup\u003e. Au-YSZ (yttrium stabilized with zirconium) has been used for detecting CO in the visible range (\u0026#120582;=600nm) at high temperature \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\sim400 C^\\circ\\)\u003c/span\u003e\u003c/span\u003e\u003csup\u003e21\u003c/sup\u003e. Integrated chemical microsensor and SPR has been employed to detect different concentrations of CO by measuring the corresponding small phase differences of SnO\u003csub\u003e2\u003c/sub\u003e\u003csup\u003e22\u003c/sup\u003e. Superficial plasmonic resonance based on Kretschmann configuration has been proposed for CO concentration measurement by intensity interrogation\u003csup\u003e8\u003c/sup\u003e.\u003c/p\u003e \u003cp\u003eDespite the undisputed advantages of highly sensitive small designs of plasmonic sensors, the severe inherent dissipation losses engendered by using the noble metals act as major obstacles. This is apart from CMOS incompatibility and the material cost\u003csup\u003e23\u003c/sup\u003e. Owing to these limitations, the optical gas sensors are still in the early stages and need further investigations to overcome the aforementioned challenges.\u003c/p\u003e \u003cp\u003eThanks to the optical metasurfaces, the dissipation losses of the plasmonic devices have been greatly enhanced demonstrating exquisite sensitivity and quality factor accompanied with the low cost and the ease of fabrication\u003csup\u003e24\u003c/sup\u003e,\u003csup\u003e25\u003c/sup\u003e. Dielectric metasurfaces (DM) are further breakthrough that served as an optimum solution to the efficiency and cost problems\u003csup\u003e26\u0026ndash;28\u003c/sup\u003e. Metasurfaces are structures consisting of subwavelength 2D nanoantennas that can be adequately designed introducing phase discontinuity across the surface\u003csup\u003e29\u003c/sup\u003e. For the dielectric metasurfaces, the underline physics is associated with the first and second Mie scattering resonances of the subwavelength resonators. The dielectric resonators demonstrate a strong response to both the electric and magnetic fields allowing full phase coverage from 0 to 2π\u003csup\u003e23\u003c/sup\u003e.\u003c/p\u003e \u003cp\u003eFor sensing applications, some spectral features should be considered; the sharpness of the resonance wavelength that is expressed by the quality factor and the spectral shift \u0026ldquo;sensitivity\u0026rdquo; introduced by the change of the refractive index of the surrounding medium. Fano resonance is one of the most intriguing phenomena that is widely exploited for sensing applications\u003csup\u003e30\u003c/sup\u003e-\u003csup\u003e31\u003c/sup\u003e. Fano spectral line is characterized by the presence of a dip and peak of the transmission or reflection spectrum showing a high-quality factor\u003csup\u003e32,33\u003c/sup\u003e. Fano resonance results from the coupling of two oscillators with different damping rates. At resonance, the undamped oscillator shows an abrupt π phase shift, while the strongly damped oscillator shows a slow phase change introducing a broad spectral line. Fano spectral resonance has been realized in various configurations such as photonic crystals\u003csup\u003e34,25\u003c/sup\u003e, microcavities\u003csup\u003e35\u003c/sup\u003e, dielectric cylinders\u003csup\u003e36\u003c/sup\u003e, dielectric spheres\u003csup\u003e37\u003c/sup\u003e, and metasurfaces\u003csup\u003e31\u003c/sup\u003e. The periodic configurations such as the photonic crystals and metasurfaces demonstrate narrower spectral lines compared to the single resonators. This phenomenon positioned metasurface, as an easy fabrication material, at the forefront of the sensing applications\u003csup\u003e32\u003c/sup\u003e.\u003c/p\u003e \u003cp\u003eNumerous structure designs have been investigated for gas sensing applications based on the Fano resonance perspective. For example, a side-coupled upright rectangular cavity with a metal-dielectric-metal (MDM) waveguide has been investigated for CH\u003csub\u003e4\u003c/sub\u003e and H\u003csub\u003e2\u003c/sub\u003e sensing applications. The structure demonstrates a plasmonic Fano resonance with sensitivity up to 846 nm/RIU and a Q-factor of 1.7\u003csup\u003e38\u003c/sup\u003e. Further study, plasmonic microcavities have been proposed utilizing the doped silicon as a new approach to induce a plasmonic effect with mitigated plasmonic losses. The structure shows sensitivity up to 6000 nm/RIU and FOM of 385 providing limited insertion losses \u003csup\u003e35\u003c/sup\u003e. The same approach is used for aluminum-doped zinc oxide (AZO) metasurfaces that are used for H\u003csub\u003e2\u003c/sub\u003e gas sensing showing a redshift\u0026thinsp;~\u0026thinsp;13 nm within 10 min for H\u003csub\u003e2\u003c/sub\u003e concentration 4%\u003csup\u003e39\u003c/sup\u003e.\u003c/p\u003e \u003cp\u003eOn the other hand, structures based on all-dielectric high index material such as the periodic \u0026ldquo;Lucky knot\u0026rdquo; shaped nanostructure\u003csup\u003e40\u003c/sup\u003e, split bar resonator\u003csup\u003e41\u003c/sup\u003e, and periodic unit cells of coupled rectangular bar and ring resonators\u003csup\u003e42\u003c/sup\u003e, coupled nano-bar with nanodisk\u003csup\u003e43\u003c/sup\u003e, coupled nano-ellipse with nano-bar\u003csup\u003e44\u003c/sup\u003e, are employed for sensing applications for different materials. All-dielectric structures show enhanced quality factors reaching up to 980 in some cases\u003csup\u003e41\u003c/sup\u003e, however with less sensitivity than their plasmonic counterparts.\u003c/p\u003e \u003cp\u003eIn this work, we present a tunable double Fano resonant metasurface based on all-dielectric silicon operating around the telecommunication wavelength (\u0026#120582;=1.55\u0026#120583;m) for selective gas sensing applications in PIC. The proposed design comprises periodic cells of coupled silicon nanodisk and silicon nano-bar resonators. The Fano resonances can be precisely tuned across the range from (\u0026#120582;=1.52\u0026#120583;m) to (\u0026#120582;=1.7\u0026#120583;m) by adjusting the different geometrical parameters including the radius, the gap distance between resonators, and the nano-bar width. Furthermore, the sensor is optimized for double selective detection of carbon monoxide (CO) and nitrous oxide (N\u003csub\u003e2\u003c/sub\u003eO). Our work is categorized into five sections; initially, we define the structure geometry and the simuation setup. Secondly, we study the double Fano resonance mechanism showing the near-field coupling effect between the bright mode of the nano-bar resonator and the dark mode of the nanodisk/nano-bar resonator. The generated Fano resonances are derived from the destructive and constructive interference between the bright mode of the nano-bar and the dark mode of either the nanodisk or the nano-bar. At first Fano resonance (FR1), the generated mode is primarily influenced by the excitation of the dark mode of the nanodisk resonator, while at the second Fano resonance (FR2), the generated mode is influenced by the excitation of the dark mode of nano-bar resonator. Thirdly, we study the different geometrical parameters effect on the double Fano resonance. This section is classified into three sub-sections; first, we show that the double Fano resonance effect is realized for the radius geometrical parameters between (r\u0026thinsp;=\u0026thinsp;200nm) to (r\u0026thinsp;=\u0026thinsp;210nm). The nanodisk radius geometry greatly influences the FR1 causing a significant red shift up to orders of tens of nanometers, while causing a minor red shift, a few nanometers, to FR2. Then, we investigate the effect of the gab distance between the resonators demonstrating the exhibition of opposite spectral shifts upon increasing the gap distance showing a blue shift for FR1 and a red shift for FR2, resulting in increasing the spectral difference between the two resonances reaching up to ~\u0026thinsp;66nm. It is worth noting that increasing the spectral difference between FR1 and FR2 is of special importance for sensing applications to avoid the spectral interference with the sensing signals. Next, we demonstrate the effect of the width (w) of the nano-bar that, in contrast to increasing the radius of the nanodisk, greatly influences the (FR2) showing a significant red shift upon increasing the width (w), while slightly influences the (FR1). The quality factor (Q-factor) of each tuning parameter is calculated achieving a significant Q-factor of 15,712. Finally, the sensor is optimized with the geometrical parameters of (r\u0026thinsp;=\u0026thinsp;205nm, G\u0026thinsp;=\u0026thinsp;180nm, w\u0026thinsp;=\u0026thinsp;333nm) for selective detection of both carbon monoxide (CO), which possesses an absorption fingerprint approximately at 1.56 \u0026#120583;m, and nitrous oxide (N\u003csub\u003e2\u003c/sub\u003eO), that possesses an absorption fingerprint approximately at 1.67 \u0026#120583;m. The sensor achieves an outstanding sensitivity of 1,736 nm/RIU for CO detection accompanied by exceptional FOM of 11,570 and exhibits significant losses of 7% following exposure to CO gas. In addition, the sensor exhibits a detection for N\u003csub\u003e2\u003c/sub\u003eO with a sensitivity of 194 nm/RIU accompanied by an FOM of 510 and an absorption loss of 3% following exposure to N\u003csub\u003e2\u003c/sub\u003eO. The outstanding FOM and the distinct absorption losses are the crucial parameters for selectivity in refractometric sensors. Our design fabrication method has been demonstrated in ref\u003csup\u003e45\u003c/sup\u003e. Fabrication is started with the deposition of a 220 nm thick silicon layer on a quartz substrate using low-pressure chemical vapor deposition (LPCVD). Then, the structure is defined using the electron beam lithography (EBL) followed by the reactive ion etching. The structure is further integrated into a gas unit cell.\u003c/p\u003e \u003cp\u003eOwing to the challenge of the required long optical path length for light-gas interaction, several approaches are proposed for achieving miniaturized gas cells with long optical path lengths. Among them, is the impressive approach of using a linear-variable optical filter (LVOF) as a gas cell\u003csup\u003e46\u003c/sup\u003e. The (LVOF) is composed of two face-to-face Bragg mirrors; a flat mirror and a tapered mirror. The (LVOF) acts as an array of Fabry-Pero cavities allowing multiple reflections and hence, increases the optical path length. Accordingly, we find a strong potential for integration of our design with the (LVOF) allowing a miniaturized device with on-chip scale level.\u003c/p\u003e \u003cp\u003eOur reported design demonstrates superior performance for gas sensing applications compared to the previous studies presented in Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab1\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eComparison between our sensor and the previously reported sensors\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"6\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eStructure\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eWorking wavelength\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003esensitivity\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eSensing material\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eQ-factor\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003eFOM\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eCoupled plasmonic Si microcavities\u003csup\u003e35\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e3.6 \u0026#120583;m\u003c/p\u003e \u003cp\u003e4.46 \u0026#120583;m\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e2,300 nm/RIU\u003c/p\u003e \u003cp\u003e3,860nm/RIU\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e(CH\u003csub\u003e2\u003c/sub\u003eO)\u003c/p\u003e \u003cp\u003e(N\u003csub\u003e2\u003c/sub\u003eO)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e385\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e60\u003c/p\u003e \u003cp\u003e145\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eCoupled ring/nano-bar\u003csup\u003e42\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e1.35 \u0026#120583;m\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e289 nm/RIU\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003en\u0026thinsp;=\u0026thinsp;1.4 to n\u0026thinsp;=\u0026thinsp;1.44\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e483\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e103\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003emetal-dielectric-metal (MDM) waveguide\u003csup\u003e38\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.948 \u0026#120583;m\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e846 nm/RIU\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eCH\u003csub\u003e4\u003c/sub\u003e and H\u003csub\u003e2\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e28\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e73\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003ePeriodic \u0026ldquo;Lucky knot\u0026rdquo;\u003csup\u003e40\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e7.3 \u0026#120583;m\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e986 nm/RIU\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eGlucose at different temperature\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e520\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e33\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSplit bar resonator\u003csup\u003e41\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e1.6 \u0026#120583;m to 2\u0026#120583;m\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e525 nm/RIU\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003en\u0026thinsp;=\u0026thinsp;1.3 to n\u0026thinsp;=\u0026thinsp;1.7\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e800\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e260\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eThe reported design\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e1.566 \u0026#120583;m\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e1,735 nm/RIU\u003c/p\u003e \u003cp\u003e194 nm/RIU\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eCO\u003c/p\u003e \u003cp\u003eN\u003csub\u003e2\u003c/sub\u003eO\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e15,640\u003c/p\u003e \u003cp\u003e4,293\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e11,570\u003c/p\u003e \u003cp\u003e510\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e"},{"header":"2. Design and simulation setup","content":"\u003cp\u003eInitially, the schematic of periodic nanobars and periodic nanodisks with the corresponding normslized reflection spectra are presented in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e(a-c). The design under consideration is based on periodic coupled oscillators of nano-bars and circular nanodisks as depicted in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003ed. The initial geometrical parameters of the structure are defined as; the nanobar length of (L\u0026thinsp;=\u0026thinsp;900nm), the width of (w\u0026thinsp;=\u0026thinsp;300nm), radius of (r\u0026thinsp;=\u0026thinsp;205nm), the gap distance between the resonators of (G\u0026thinsp;=\u0026thinsp;130nm), the other side gap distance of (G2\u0026thinsp;=\u0026thinsp;150nm), the pitch in x-direction of (P1\u0026thinsp;=\u0026thinsp;990nm), the pitch in y-direction of (P2\u0026thinsp;=\u0026thinsp;1050nm) and the thickness of both resonators of (t\u0026thinsp;=\u0026thinsp;220nm). The structure is mounted on a quartz substrate. The optical response of each system is numerically investigated using commercial software (Lumerical) based on the finite difference time domain method (FDTD) \u003csup\u003e47\u003c/sup\u003e. The simulation setup is established as follows; the periodic boundary conditions are used for x and y directions, while the perfectly matched layers (PML) are used in z-direction. The structure is impinged on by a normal incident plane wave with a polarization direction parallel to the long axis of the nano-bar resonator (y-polarization). The mesh type is auto-nonuniform with an accuracy of 7.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e"},{"header":"3. The double Fano resonance mechanism","content":"\u003cp\u003eFano resonance originates from the interference between a continuum band of states with the discrete quantum optical states of coupled two resonators. The coupled resonators response could be treated as coupled harmonic oscillators model described by the following equations\u003csup\u003e42\u003c/sup\u003e:\u003cdiv id=\"Equa\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equa\" name=\"EquationSource\"\u003e\n$${\\dot{x}}_{1}-j({\\omega }_{0}+j{\\gamma }_{1}) {x}_{1}+j\\kappa {x}_{2}=g{E}_{0} {e}^{j\\omega t}$$\u003c/div\u003e\u003c/div\u003e\u003cdiv id=\"Equ1\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ1\" name=\"EquationSource\"\u003e\n$${\\dot{x}}_{2}-j({\\omega }_{0}+\\delta +j{\\gamma }_{2}) {x}_{2}+j\\kappa {x}_{1}=0$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e1\u003c/div\u003e\u003c/div\u003e,\u003c/p\u003e \u003cp\u003ewhere \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({x}_{1}\\)\u003c/span\u003e\u003c/span\u003e and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({x}_{2}\\)\u003c/span\u003e\u003c/span\u003e are the amplitudes of the collective modes of resonator 1 (bright mode) and resonator 2 (dark mode), respectively. \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\omega }_{0}\\)\u003c/span\u003e\u003c/span\u003e is the central resonance frequency of the bright mode resonator. \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\gamma }_{1}\\)\u003c/span\u003e\u003c/span\u003eand \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\gamma }_{2}\\)\u003c/span\u003e\u003c/span\u003e are the damping rates of the two resonators expressing the radiative and the nonradiative damping. \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\kappa\\)\u003c/span\u003e\u003c/span\u003e and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\delta\\)\u003c/span\u003e\u003c/span\u003e are the coupling coefficients between the resonators and the detuning of resonance frequency of oscillators 1 and 2, respectively. \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(g\\)\u003c/span\u003e\u003c/span\u003e is the dipole coupling strength of the bright mode with the incident electric field \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({E}_{0}\\)\u003c/span\u003e\u003c/span\u003e. The interaction between the bright resonance with the narrower dark resonance, that coexist at certain spectral range, leads to high quality factor Fano spectral line.\u003c/p\u003e \u003cp\u003eDamping rates and the coupling coefficient are crucial precursors for the Fano resonance phenomenon. In our design, the nonradiative damping rates are suppressed due to utilizing an all-dielectric material. Simultaneously, the radiative damping is minimized due to the collective oscillation of the array unit cells. On the other hand, decreasing the coupling coefficient \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\kappa\\)\u003c/span\u003e\u003c/span\u003e than the larger damping rate, which is dependent on the geometrical parameters, is necessary to enhance field localization and consequently increase the Q-factor. The interplay between damping rates and coupling coefficient plays a pivotal role in shaping Fano resonances and their corresponding Q-factors in metamaterials.\u003c/p\u003e \u003cp\u003eSilicon-based circular nanodisks have been previously explored providing the possibility of introducing a Fano resonance that is controlled by the aspect ratio; the diameter and the height of the disk, enabling high directionality control\u003csup\u003e36\u003c/sup\u003e. The resulting resonance represents the strong coupling between the Mie-like mode and the Fabry-Pero like mode. However, a dark mode is realized when the radiation from all the modes compensates each other\u003csup\u003e33\u003c/sup\u003e. The nanodisk of the thickness of (t\u0026thinsp;=\u0026thinsp;220nm), radius of (r\u0026thinsp;=\u0026thinsp;205nm) and the periodic distance of (P\u0026thinsp;=\u0026thinsp;990nm) exhibits dark mode along the range of wavelengths from 1.5\u0026ndash;1.7\u0026#120583;m as can be observed in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003ec (red curve), consistent with\u003csup\u003e36\u003c/sup\u003e. Building upon the findings in\u003csup\u003e48\u003c/sup\u003e, the dark mode of the nanodisk can be excited by the azimuthal incidence of the near field Bessel beam generating a so-called pseudo modes, the modes that have no real optical oscillations. Axially symmetric Bessel beam offers the advantage of exciting specific polarization only i.e TM or TE mode, eliminating the potential of mode suppression caused by interference.\u003c/p\u003e \u003cp\u003eDifferent theoretical approaches have been proposed for launching near-field Bessel beams such as the parallel plates waveguide\u003csup\u003e49\u003c/sup\u003e and metamaterial lens with gradient index\u003csup\u003e50\u003c/sup\u003e. In our design, we utilize a nano-bar to generate a Bessel-like mode, as visually evidenced in the 2D electric field profile of the nanobar along the dashed line near the nano-bar surface (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e(c,i)).The nano-bar acts as a bright mode with a wide bandwidth as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003ec (black curve).\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eWhen the two resonators are brought in close proximity, as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003ed, double Fano resonances are realized as demonstrated in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003ee. The schematic diagram presented in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003ef is an initial demonstration of the coupling mechanism between the two resonators. The dipole mode of the nano-bar (red curve)- the electric field intensity profile along the dashed line in (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e(c,i))- excites the magnetic dark mode within the nanodisk, inducing a displaced perpendicular electric field circulating around the nanodisk. A detailed investigation of this coupling mechanism and its role in both Fano resonances (FR1 and FR2) will be presented in the following subsections.\u003c/p\u003e \u003cdiv id=\"Sec4\" class=\"Section2\"\u003e \u003ch2\u003e3.1 Fano resonance at FR1\u003c/h2\u003e \u003cp\u003eAt FR1, the demonstration of the near field coupling mechanism of the nano-bar and the nanodisk, explained above, is verified showing a magnetic dipole resonance within the nanodisk, Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003ea, inducing a displaced circulating electric field around the nanodisk, Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003ee-g. The magnetic and the electric field profiles are characterized by field distribution following the Bessel function, showing a maximum magnetic field intensity at the center accompanied by a minimum electric field intensity at the same position, as depicted in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003ed and Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003eh.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eIn the gap distances between the resonators, the electric and magnetic fields are almost equal to zero. The overall electric and magnetic field distribution demonstrates a spatial Fano resonance. Our numerical study aligns with the analytical solution for the near-field Bessel beam excitation of spherical nanoparticles presented in ref \u003csup\u003e51,48\u003c/sup\u003e. From Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003eb-c and Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003ef-g, distinct magnetic and electric phase shifts are observed in the frequency domain between the peak (\u0026#120582;=1.548 \u0026#120583;m) and dip (\u0026#120582;=1.5483\u0026#120583;m) resonances.The magnetic field exhibits an abrupt change in orientation, transitioning from outward for the peak resonance to inward for the dip resonance. Similarly, the electric field circulates in opposite directions for the peak and dip resonances, as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003ef and Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003eg.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec5\" class=\"Section2\"\u003e \u003ch2\u003e3.2 Fano resonance at FR2\u003c/h2\u003e \u003cp\u003eAt FR2, the nano-bar bright mode excites the magnetic dark mode within the nanodisk as well as the magnetic dark mode within the nano-bar with different strength, Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003ea and Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003ed. Simiarly to FR1, the out of plane magnetic resonance within the nanodisk, Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003eb and Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003ec, results in a displaced circulating electric field around the nanodisk, Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003ef and Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003eg. In addition, a strong electric field confinement is generated between the the nano-bar and the nanodisk and on the edge of the nano-bar facing the nanodisk, Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003ee and Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003eh. The electric field vector profile demonstrates the induced circulating electric field around the nano-bar, Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003ef-g.\u003c/p\u003e \u003c/div\u003e"},{"header":"4. The geometrical parameters effect on the double Fano resonances","content":"\u003cp\u003eNow, we show the effect of the geometrical parameters of the structure; radius of the nanodisk, the gap distance between both resonators and the width of the nanobar resonator, in terms of the reflection spectrum, the resonance wavelengths, the spectral difference between the two resonances and the quality factor (Q-factor). We demonstrate the ability of the structure for tuning the Fano resonance positions at will. The Q-factor is defined as \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\left(Q=\\frac{{\\lambda }_{res}}{FWHM}\\right)\\)\u003c/span\u003e\u003c/span\u003e where \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\lambda }_{res}\\)\u003c/span\u003e\u003c/span\u003e is the resonance wavelength and (FWHM) is the full width at half maximum.\u003c/p\u003e \u003cdiv id=\"Sec7\" class=\"Section2\"\u003e \u003ch2\u003e4.1 The radius parameter of the nanodisk effect\u003c/h2\u003e \u003cp\u003eFirst, we study the effect of varying the radius of the nanodisk (r), while keeping the gap distance fixed at\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\((G=130nm)\\)\u003c/span\u003e\u003c/span\u003e and the nanobar width fixed at (w=300nm). Figure\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003ea shows the reflection behavior of various nanodisk radius parameters (r) ranging from (r=190nm) to (r=210nm). The structure of (r=190nm) shows the emergence of Fano resonance at the spectral region of (FR2) only. By increasing the radius to (r\u0026thinsp;=\u0026thinsp;195nm), a transparency window is realized with a high dispersive nature that is considered an obstacle for sensing applications. Further increasing of the nanodisk radius shows the formation of significant double Fano resonances at FR1 and FR2. Increasing the radius (r) of the nanodisk from (r\u0026thinsp;=\u0026thinsp;195nm) to (r=210nm) causes a substantial red shift in the first Fano resonance (FR1) and a minor red shift in the second Fano resonance (FR2) as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003eb.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eHence, the spectral gap distances between the two resonances (d\u0026#120582;) decrease as demonstrated in Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003ec. The radius effect emphasizes that the FR1 is primarily attributed to the excited dark mode inside the nanodisk as previously explained. Further radius increasing than (r\u0026thinsp;=\u0026thinsp;210nm) diminishes the resonance at FR2. Figure\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003ed illustrates the calculated Q-factors for various radius parameters, revealing a maximum value of 7,674 for r\u0026thinsp;=\u0026thinsp;200nm at FR1 and 7,960 for r\u0026thinsp;=\u0026thinsp;210nm at FR2.\u003c/p\u003e \u003cp\u003eAiming to operate within the telecommunication wavelength (\u0026#120582;=1.55 \u0026#120583;m), we select the structure with a radius of (r\u0026thinsp;=\u0026thinsp;205 nm) that exhibits an operating wavelength of (\u0026#120582;=1.548 \u0026#120583;m) and Q-factor of 5,160 at FR1 for further investigations.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec8\" class=\"Section2\"\u003e \u003ch2\u003e4.2 The gap distance parameter effect\u003c/h2\u003e \u003cp\u003eNext, we investigate the influence of varying one gap distance (G) between the nanodisk and the nano-bar resonators, while keeping the other gap fixed at (G2\u0026thinsp;=\u0026thinsp;150 nm) on the reflection behavior as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e. Increasing the G distance leads to opposing shifts: blue shift for FR1 and redshift for FR2 as depicted in Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003ea and Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003eb. Consequently, the spectral gap distance (d\u0026#120582;) between FR1 and FR2 widens with increasing G as illustrated in Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003ec. For G\u0026thinsp;=\u0026thinsp;150nm, the Fano resonance at both FR1 and FR2 disappears due to symmetry as may be observed from Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003ea ( red curve). In addition, G exerts a substantial influence on the modulation depth that is enhanced as G increases beyond 150nm showing a notable enhancement up to (~\u0026thinsp;90%) for (G\u0026thinsp;=\u0026thinsp;180 nm) as depicted from Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003ea and Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003ee. Additionally, the calculated Q-factors are noteworthy for G values between 160 nm and 180 nm, with FR1 exhibiting exceptional Q-factors of 25,784 for (G\u0026thinsp;=\u0026thinsp;160 nm) and 15,459 for (G\u0026thinsp;=\u0026thinsp;180 nm). However, the structure of (G\u0026thinsp;=\u0026thinsp;160 nm) suffers from the limitation of the small modulation depth of 35% as may be observed in Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003ee. Therefore, the structure of (G\u0026thinsp;=\u0026thinsp;180 nm) is the more suitable choice for further investigation.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec9\" class=\"Section2\"\u003e \u003ch2\u003e4.3 The nano-bar width parameter effect\u003c/h2\u003e \u003cp\u003eFurther investigation is performed for the structure of different nanobar resonator widths. In contrast to increasing the nanodisk radius, increasing the nano-bar width causes a substantial redshift to FR2 and a minor redshift to FR1, as can be observed from Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003ea and Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003eb. Increasing the nano-bar width provides the advantage of increasing the spectral gap (d\u0026#120582;) between FR1 and FR2 as illustrated in Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003ec.The calculated Q-factors of FR1 retain at high values reaching up to 15,711 for the structure of (w\u0026thinsp;=\u0026thinsp;340 nm), while the Q-factors of FR2 varies having its maximum 3,463 for the structure of (w\u0026thinsp;=\u0026thinsp;340 nm) as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003ed.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e"},{"header":"5. Double Fano resonance application in gas sensing","content":"\u003cp\u003e \u003c/p\u003e\u003cdiv class=\"BlockQuote\"\u003e \u003cp\u003eMany gas molecules posses unique absorption fingerprints within the telecommunication wavelength range. For selective gas sensing applications, we excite the specific Fano resonance at a wavelength precisely matching the gas’s spectral fingerprint. This optimal alignment induces a remarkable spectral shift accompanied by significant losses due to absorption, highlighting the gas molecules’ unique spectral signatures.\u003c/p\u003e \u003c/div\u003e \u003cp\u003e\u003c/p\u003e \u003cp\u003eCarbon monoxide (CO) and nitrous oxide (N\u003csub\u003e2\u003c/sub\u003eO) gases are significant greenhouse gases that contribute to climate change and environmental degradation\u003csup\u003e9,10\u003c/sup\u003e. The accurate and efficient detection and monitoring of these gases are crucial for mitigating their adverse impacts.CO and N\u003csub\u003e2\u003c/sub\u003eO possess distinct absorption fingerprints in the telecommunication wavelength range at (~𝜆=1.57𝜇m) and (~𝜆=1.67𝜇m), respectively. The absorbance of both gases at temperature (T = 298 K), pressure (P = 1atm), effective path length (l = 5m) and gas mole-fraction (X = 0.01) are computed using Spectraplot tool based on HITRAN database and presented in Fig.7\u003csup\u003e52,53\u003c/sup\u003e. Using the absorbance data, the dispersive real and the imaginary parts of the complex refractive index of CO and N\u003csub\u003e2\u003c/sub\u003eO are calculated using the Krammers-Kronig relation\u003csup\u003e54\u003c/sup\u003e:\u003c/p\u003e\u003cdiv id=\"Equ2\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ2\" name=\"EquationSource\"\u003e\n$$n\\left({{\\lambda }}_{0}\\right)= n\\left({{\\lambda }}_{1}\\right)+p\\frac{\\left({{\\lambda }}_{1}^{2}-{{\\lambda }}_{0}^{2}\\right)}{\\pi } \\underset{0}{\\overset{\\infty }{\\int }}\\frac{{\\lambda }\\text{k}\\left({\\lambda }\\right)\\text{d}{\\lambda }}{\\left({{\\lambda }}_{1}^{2}-{{\\lambda }}^{2}\\right)\\left({{\\lambda }}_{1}^{2}-{{\\lambda }}^{2}\\right)}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e2\u003c/div\u003e\u003c/div\u003e\u003cp\u003e\u003c/p\u003e \u003cp\u003eWhere \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(p\\)\u003c/span\u003e\u003c/span\u003eis the Cauchy principal value of integral, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(n\\left({{\\lambda }}_{1}\\right)\\)\u003c/span\u003e\u003c/span\u003e is the known refractive index of the gas at wavelength (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({{\\lambda }}_{1}\\)\u003c/span\u003e\u003c/span\u003e) and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\text{k}\\left({\\lambda }\\right)\\)\u003c/span\u003e\u003c/span\u003e extinction coefficient that is calculated from the absorption coefficient \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\alpha }\\left({\\lambda }\\right)\\)\u003c/span\u003e\u003c/span\u003e as follows:\u003c/p\u003e\u003cdiv id=\"Equ3\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ3\" name=\"EquationSource\"\u003e\n$$\\text{k}\\left({\\lambda }\\right)=\\frac{4\\pi {\\alpha }\\left({\\lambda }\\right)}{\\lambda }$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e3\u003c/div\u003e\u003c/div\u003e\u003cp\u003e\u003c/p\u003e \u003cp\u003eLeveraging the unique optical properties of double Fano resonances, we have developed our design for the detection of both CO and N\u003csub\u003e2\u003c/sub\u003eO gases. The structure is optimized with parameters; r = 205nm, G = 180nm, and w = 333nm, enabling the realization of double Fano resonance at 𝜆=1.5667𝜇m and 𝜆=1.674𝜇m. The normalized reflection spectra of the sensor for both CO and N\u003csub\u003e2\u003c/sub\u003eO with respect to the vacuum (n = 1) are presented in Fig.\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e8\u003c/span\u003e. The sensor’s key features that contribute to the design selectivity are the sensitivity accompanied by high figures of merits and the absorption losses. The sensor sensitivity is calculated as the ratio of the spectral shift of the Fano resonance to the change of the refractive index after the exposure to the gas sensing material (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(S=\\frac{\\varDelta \\lambda }{\\varDelta n}\\)\u003c/span\u003e\u003c/span\u003e ). The figure of merit (FOM) is defined as the ratio between the sensitivity and (FWHM) of the Fano resonance. The sensor exhibits an exceptional sensitivity to CO of (S\u003csub\u003eCO\u003c/sub\u003e = 1,735 nm/RIU) and boasts an ultrahigh FOM of (11,570). Meanwhile, it exhibits a sensitivity of (S\u003csub\u003eN2O\u003c/sub\u003e = 194 nm/RIU) with an acceptable FOM of (510). The sensor's sensitivity performance for N\u003csub\u003e2\u003c/sub\u003eO detection is lower than its performance for CO, but it is still good enough to be useful for many applications. Furthermore, the absorption losses, which are expected to amplify due to the sensor's operation within the absorption band, are calculated as the normalized change in FWHM of the Fano resonance following exposure to the gas sensing material:\u003c/p\u003e \u003cp\u003e \u003cspan class=\"InlineEquation\"\u003e \u003cspan class=\"mathinline\"\u003e\\((L=\\frac{{FWHM}_{g}-{FWHM}_{0}}{{FWHM}_{0}}\\)\u003c/span\u003e \u003c/span\u003e)\u003c/p\u003e \u003cp\u003ewhere \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({FWHM}_{g}\\)\u003c/span\u003e\u003c/span\u003e and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({FWHM}_{0}\\)\u003c/span\u003e\u003c/span\u003e are the full width at half maximum for the gas and free space, respectively. The calculated absorption losses reveal values of ( \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({L}_{CO}=7\\%\\)\u003c/span\u003e\u003c/span\u003e ) for CO and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({(L}_{N2O}=3\\%)\\)\u003c/span\u003e\u003c/span\u003e for N\u003csub\u003e2\u003c/sub\u003eO. These significant absorption losses provide valuable information about the gas sensing material and its concentration. Therefore, absorption losses are crucial for qualitative and quantitative refractometric sensing applications.\u003c/p\u003e \u003cp\u003e\u003c/p\u003e"},{"header":"Conclusion","content":"\u003cp\u003eThis study reports the development of a selective gas sensor based on double Fano resonance operating at telecommunication wavelengths for photonic integrated circuit applications. The sensor design employs an all-dielectric silicon metasurface consisting of coupled nanodisk and nanobar resonators. Each Fano resonance can be tuned independently by adjusting the geometrical parameters, including the nanodisk radius, the gap between the nanodisk and the nano-bar, and the nano-bar width. Leveraging Fano resonance at the absorption band of the sensing material holds promise for selective gas sensing applications in terms of figures of merit (FOM) and absorption losses. We demonstrate the feasibility of this approach by developing a sensor design capable of detecting both carbon monoxide (CO) and nitrous oxide (N\u003csub\u003e2\u003c/sub\u003eO) gases at wavelengths of 1.566 µm and 1.674 µm, respectively. The sensor exhibits remarkable sensitivities of 1,750 nm/RIU for CO and 194 nm/RIU for N\u003csub\u003e2\u003c/sub\u003eO, accompanied by exceptional FOM of 11,570 and 510, respectively. These exceptionally high FOMs underscore the sensor's outstanding selectivity potential. Furthermore, the absorption losses, evident from the increased FWHM, are identified revealing values of 7% for CO and 3% for N\u003csub\u003e2\u003c/sub\u003eO. These distinct absorption losses highlight the proposed design's potential as a highly sensitive and selective gas sensor. Additionally, the sensor's compatibility with CMOS technology and its low-cost fabrication process make it an attractive candidate for practical applications.\u003c/p\u003e"},{"header":"Materials and methods","content":"\u003cp\u003eFinite difference time domain (lumerical software) has been used for simulating the optical response of the proposed structures to incident plane waves. Matlab software has been used for calculating Krammers Kronig relation.\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e\u003cstrong\u003eData availability:\u0026nbsp;\u003c/strong\u003eThe datasets used and/or analysed during the current study available from the corresponding author on reasonable\u003cstrong\u003e\u0026nbsp;\u003c/strong\u003erequest.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eAcknowledgment:\u003c/strong\u003e We declare no financial support.\u003c/p\u003e\n\u003cp\u003e\u0026nbsp;\u003cstrong\u003eConflict of interests:\u003c/strong\u003e the authors declare no competing interests.\u003c/p\u003e\n\u003cp\u003e\u0026nbsp;\u003cstrong\u003eContributions:\u003c/strong\u003e\u0026nbsp; N.S has designed the proposed structure. \u0026nbsp;N.S has performed the theoretical modelling and numerical simulations. N.S has written the manuscript. S.A has contributed to the technical discussion regarding the gas sensing application. S.O has contributed to the technical discussion regarding metasurface physical concepts and related design issues presented in the paper. M.S has contributed to the technical discussion regarding metasurface physical concepts and related design issues presented in the paper. All the authors have revised and edited the manuscript.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n\u003cli\u003eMi, G., Horvath, C., Aktary, M. \u0026amp; Van, V. Silicon microring refractometric sensor for atmospheric CO_2 gas monitoring. \u003cem\u003eOpt. Express\u003c/em\u003e \u003cstrong\u003e24\u003c/strong\u003e, 1773 (2016).\u003c/li\u003e\n\u003cli\u003eYebo, N. A. \u003cem\u003eet al.\u003c/em\u003e Silicon-on-insulator (SOI) ring resonator-based integrated optical hydrogen sensor. \u003cem\u003eIEEE Photonics Technol. Lett.\u003c/em\u003e \u003cstrong\u003e21\u003c/strong\u003e, 960\u0026ndash;962 (2009).\u003c/li\u003e\n\u003cli\u003eShaalan, N. 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Transf.\u003c/em\u003e \u003cstrong\u003e203\u003c/strong\u003e, 3\u0026ndash;69 (2017).\u003c/li\u003e\n\u003cli\u003eLucarini, V., Saarinen, J., Peiponen, K.-E. \u0026amp; Vartiainen, E.M. Kramers\u0026ndash;Kronig Relations in Optical Materials Research. (Springer-Verlag Berlin Heidelberg, 2005).\u003c/li\u003e\n\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"scientific-reports","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"scirep","sideBox":"Learn more about [Scientific Reports](http://www.nature.com/srep/)","snPcode":"","submissionUrl":"","title":"Scientific Reports","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Scientific Reports","inReviewEnabled":true,"inReviewRevisionsEnabled":true},"keywords":"Metasurfaces, metamaterial, double Fano resonance, CO gas sensor, N2O gas sensor, optical gas sensor","lastPublishedDoi":"10.21203/rs.3.rs-4067143/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-4067143/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThe telecommunication wavelengths play a crucial role in the development of photonic integrated circuit (PIC). The absorption fingerprints of many gases lie within these spectral ranges, offering the potential to create miniaturized gas sensor for (PIC). In this work, we present novel double Fano resonances within the telecommunication wavelength range, based on silicon metasurface for selective gas sensing applications. Our proposed design comprises periodically coupled nanodisk and nano-bar resonators mounted on a quartz substrate. We show that the Fano resonances can be precisely tuned across the wavelength range from (\u0026#120582;=1.52\u0026#120583;m) to (\u0026#120582;=1.7\u0026#120583;m) by adjusting various geometrical parameters. Furthermore, we optimize the sensor for double detection of carbon monoxide (CO), with an absorption fingerprint at ~\u0026thinsp;1.566 \u0026#120583;m, and nitrous oxide (N\u003csub\u003e2\u003c/sub\u003eO), with an absorption fingerprint at ~\u0026thinsp;1.67\u0026#120583;m. The sensor exhibits exceptional refractometric sensitivity to CO of 1,735 nm/RIU with an outstanding FOM of 11,570. In addition, the sensor shows a sensitivity to N\u003csub\u003e2\u003c/sub\u003eO of 194 accompanied by a FOM of 510. The structure reveals absorption losses of 7% for CO and 3% for N\u003csub\u003e2\u003c/sub\u003eO. The outstanding FOM and absorption losses provide selectivity for the sensing material. Our proposed design holds significant promise for the development of highly sensitive double detection refractometric photonic integrated gas sensor.\u003c/p\u003e","manuscriptTitle":"Silicon based Double Fano resonances photonic integrated gas sensor","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2024-03-29 05:22:52","doi":"10.21203/rs.3.rs-4067143/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Revision requested","date":"2024-06-28T06:30:19+00:00","index":"","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2024-04-25T13:14:22+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2024-04-11T08:15:20+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"2049309e-0fd2-45d5-8536-22e0e7e50341","date":"2024-03-31T16:37:58+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"64d17164-c305-4cee-8a14-28d3941e48c5","date":"2024-03-30T14:10:02+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2024-03-29T16:34:40+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2024-03-26T12:37:00+00:00","index":"","fulltext":""},{"type":"editorInvited","content":"","date":"2024-03-26T12:29:47+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2024-03-26T12:27:49+00:00","index":"","fulltext":""},{"type":"submitted","content":"Scientific Reports","date":"2024-03-10T18:22:59+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"scientific-reports","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"scirep","sideBox":"Learn more about [Scientific Reports](http://www.nature.com/srep/)","snPcode":"","submissionUrl":"","title":"Scientific Reports","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Scientific Reports","inReviewEnabled":true,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"7a5a9424-f1d1-4c23-812d-7c59155e1ab0","owner":[],"postedDate":"March 29th, 2024","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"published-in-journal","subjectAreas":[],"tags":[],"updatedAt":"2024-10-28T15:59:53+00:00","versionOfRecord":{"articleIdentity":"rs-4067143","link":"https://doi.org/10.1038/s41598-024-74288-6","journal":{"identity":"scientific-reports","isVorOnly":false,"title":"Scientific Reports"},"publishedOn":"2024-10-22 15:57:07","publishedOnDateReadable":"October 22nd, 2024"},"versionCreatedAt":"2024-03-29 05:22:52","video":"","vorDoi":"10.1038/s41598-024-74288-6","vorDoiUrl":"https://doi.org/10.1038/s41598-024-74288-6","workflowStages":[]},"version":"v1","identity":"rs-4067143","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-4067143","identity":"rs-4067143","version":["v1"]},"buildId":"qtupq5eGEP_6zYnWcrvyt","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}