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All-Dielectric Metasurface Based on Complementary Split-Ring Resonators for Refractive Index Sensing

All-Dielectric Metasurface Based on Complementary Split-Ring Resonators for Refractive Index Sensing hv photonics Communication All-Dielectric Metasurface Based on Complementary Split-Ring Resonators for Refractive Index Sensing 1 1 2 , 3 , 4 2 , 3 , 4 Mohsen Samadi , Fatemeh Abshari , José F. Algorri , Pablo Roldán-Varona , 3 2 , 3 , 4 5 6 Luis Rodríguez-Cobo , José M. López-Higuera , José M. Sánchez-Pena , Dimitrios C. Zografopoulos 7 , and Francesco Dell’Olio * Faculty of Electrical and Computer Engineering, Tarbiat Modares University, Tehran 1411713116, Iran; samadi@physik.uni-kiel.de (M.S.); f.abshari@modares.ac.ir (F.A.) Photonics Engineering Group, University of Cantabria, 39005 Santander, Spain; algorrijf@unican.es (J.F.A.); pablo.roldan@unican.es (P.R.-V.); miguel.lopezhiguera@unican.es (J.M.L.-H.) CIBER-bbn, Instituto de Salud Carlos III, 28029 Madrid, Spain; luis.rodriguez@unican.es Instituto de Investigación Sanitaria Valdecilla (IDIVAL), 39011 Santander, Spain Department of Electronic Technology, Carlos III University, 28911 Madrid, Spain; jmpena@ing.uc3m.es Consiglio Nazionale delle Ricerche, Istituto per la Microelettronica e Microsistemi (CNR-IMM), 00133 Roma, Italy; dimitrios.zografopoulos@artov.imm.cnr.it Department of Electrical and Information Engineering, Polytechnic University of Bari, 70125 Bari, Italy * Correspondence: francesco.dellolio@poliba.it Abstract: Thanks to their lower losses and sharper resonances compared to their metallic counterparts, all-dielectric metasurfaces are attracting a quickly growing research interest. The application of such metasurfaces in the field of refractive index sensing is extremely attractive, especially due to the expected high performance and the simplicity of the sensing element excitation and readout. Herein, we report on an all-dielectric silicon metasurface based on complementary split-ring resonators Citation: Samadi, M.; Abshari, F.; (CSRRs) optimized for refractive index sensing. A quasi-bound state in the continuum (quasi-BIC) Algorri, J.F.; Roldán-Varona, P.; with an ultra-high quality factor can be excited in the near-infrared (NIR) window by violating the Rodríguez-Cobo, L.; López-Higuera, structure symmetry. By using the three-dimensional finite element method (3D-FEM), a refractive J.M.; Sánchez-Pena, J.M.; index sensor for biomedical applications with an ultra-high figure of merit (FoM > 100,000 RIU ) Zografopoulos, D.C.; Dell’Olio, F. has been designed, exploiting the quasi-BIC resonance. The proposed design strategy opens new All-Dielectric Metasurface Based on Complementary Split-Ring avenues for developing flat biochemical sensors that are accurate and responsive in real time. Resonators for Refractive Index Sensing. Photonics 2022, 9, 130. Keywords: metasurface; biosensor; bound state in the continuum https://doi.org/10.3390/ photonics9030130 Received: 17 January 2022 1. Introduction Accepted: 22 February 2022 Published: 25 February 2022 Resonant micro- and nano-photonic refractive index sensors have long been utilized for real-time, label-free analysis of chemical and biological samples, such as identifying Publisher’s Note: MDPI stays neutral target biomolecules in a biologic fluid or detecting organic liquid compounds. When target with regard to jurisdictional claims in molecules interact with light, the sensor resonance frequency shifts due to light–matter published maps and institutional affil- interaction. The frequency shift is subsequently measured and utilized to detect target iations. molecules [1–6]. The sensitivity (S = Dl /Dn) of refractive index sensors is evaluated as the res ratio of the shift in the sensor resonance wavelength to the change in the sample’s refractive index. The figure of merit (FoM = S/FWHM) normalizes the refractive index sensitivity to Copyright: © 2022 by the authors. the resonant mode spectral width (full width at the half maximum, FWHM) [5–8]. Licensee MDPI, Basel, Switzerland. Surface plasmons [9–12], photonic crystal cavities [3,13–16], and whispering gallery This article is an open access article mode resonators [2,4,17–20] have all been used to produce better sensitivities and superior distributed under the terms and sensing performance. Furthermore, biochemical sensing applications have used plasmonic conditions of the Creative Commons nanostructures that support Fano resonances [21–24]. However, despite their high sensitiv- Attribution (CC BY) license (https:// ity to the surrounding medium refractive index, they suffer from broad resonances caused creativecommons.org/licenses/by/ by high optical absorption losses in the metal, which severely limit the sensor FoM. 4.0/). Photonics 2022, 9, 130. https://doi.org/10.3390/photonics9030130 https://www.mdpi.com/journal/photonics Photonics 2022, 9, x FOR PEER REVIEW 2 of 7 resonances caused by high optical absorption losses in the metal, which severely limit the sensor FoM. Photonics 2022, 9, 130 2 of 7 Metasurfaces (MSs) are planar interfaces made of periodic arrays of sub-wavelength resonant elements used to manipulate the phase, polarization, and amplitude of light [25– 27]. They are the 2D equivalents of bulk metamaterials. Due to their lower ohmic losses and thus Metas sharper Fano reso urfaces (MSs) arenances than t planar interfh ac eir me es matd ae llic equ of periiva odlent ic as, a rray ll- sdie of ls ect ubr -ic MSs wavelen hg at ve h become more popular in recent years for sensing applications [28–34]. In this regard, a resonant elements used to manipulate the phase, polarization, and amplitude of light [25–27]. new type of MS based on the CSRR [35] was recently reported. In this MS, an ultrathin They are the 2D equivalents of bulk metamaterials. Due to their lower ohmic losses and thus sharper slot is etched Fano r in a silicon layer on a st esonances than their metallic andardequivalents, glass substra all-dielectric te. In the NIR MSs window, the MS have become mor shows e popular two m in ult recent ipolaryears resonance for sensing s. Meapplications anwhile, an asym [28–34m ]. e In try this in regar the st d,ruct a neuw re type of th ofe MS based on the CSRR [35] was recently reported. In this MS, an ultrathin slot is etched slotted CSRR can be used to trigger a quasi-BIC with an ultra-high Q-factor thanks to the in a silicon layer on a standard glass substrate. In the NIR window, the MS shows two vanishing radiation losses for a small degree of asymmetry. Quasi-BIC modes have multipolar resonances. Meanwhile, an asymmetry in the structure of the slotted CSRR can already been exploited in many application domains, including nonlinear optics and be used to trigger a quasi-BIC with an ultra-high Q-factor thanks to the vanishing radiation sensing [36–38]. losses for a small degree of asymmetry. Quasi-BIC modes have already been exploited in In our study, by examining the sensitivity of the quasi-BIC mode to the superstrate many application domains, including nonlinear optics and sensing [36–38]. medium refractive index, we assessed the CSRR-MS sensing capacity. By exploiting the In our study, by examining the sensitivity of the quasi-BIC mode to the superstrate non-radiative nature of the quasi-BIC mode, exceptionally high-quality factors and FoMs medium refractive index, we assessed the CSRR-MS sensing capacity. By exploiting the can be produced, allowing for the design of highly accurate biological and chemical non-radiative nature of the quasi-BIC mode, exceptionally high-quality factors and FoMs sensors. can be produced, allowing for the design of highly accurate biological and chemical sensors. 2. Metasurface 2. Metasurface Figure 1 shows the proposed sensing device. A periodic array of circular slots is fully Figure 1 shows the proposed sensing device. A periodic array of circular slots is etched in a silicon layer of thickness h, deposited on a glass substrate to form the CSRR- fully etched in a silicon layer of thickness h, deposited on a glass substrate to form the MS. Each unit cell of the periodic structure has one circular slot, whose structural CSRR-MS. Each unit cell of the periodic structure has one circular slot, whose structural parameters are shown in the inset of Figure 1. The slot width, the inner diameter, the parameters are shown in the inset of Figure 1. The slot width, the inner diameter, the distance between neighboring slots in the x-direction, the pitch of the periodic square distance between neighboring slots in the x-direction, the pitch of the periodic square array, array, and the size of the silicon gaps are identified as s, w, g, p, and t, respectively. In and the size of the silicon gaps are identified as s, w, g, p, and t, respectively. In addition, an addition, an asymmetry parameter tx is introduced in order to break the structure asymmetry parameter t is introduced in order to break the structure symmetry and excite symmetry and excite the quasi-BIC resonance, reducing the arc length in one half of the the quasi-BIC resonance, reducing the arc length in one half of the CSRR structure. The CSRR structure. The depth of the slots etched in the silicon layer is equal to h. depth of the slots etched in the silicon layer is equal to h. Figure 1. A three-dimensional schematic illustration of the CSRR metasurface. In a silicon layer with Figure 1. A three-dimensional schematic illustration of the CSRR metasurface. In a silicon layer with a thickness of h, the periodic split rings are etched. The unit cell (marked by a yellow dashed square) a thickness of h, the periodic split rings are etched. The unit cell (marked by a yellow dashed square) is shown in the inset. is shown in the inset. The transmission spectra of the MS have been computed using the 3D-FEM. The silicon layer is assumed as deposited on a glass substrate with a refractive index of n = 1.52, and a y-polarized plane wave irradiates the MS in the z-direction (see Figure 1). We assume h = 232 nm, s = 25 nm, w = 496 nm, g = 240 nm, and t = 100 nm, which are identical to the values in [35]. The refractive index dispersion of silicon is considered [39]. Photonics 2022, 9, 130 3 of 7 All these geometrical features are compatible with the technological constraints typically imposed by e-beam lithography, having a resolution below 5 nm [40]. We assume that the metasurface is top illuminated by a sub-pm linewidth laser source operating in the NIR, whose emission frequency can be precisely tuned in a narrow range of a few hundreds of pm by a piezoelectric transducer. A standard detector operating in the NIR can be used for measuring the transmitted power. 3. Simulation Results The MS has been simulated by 3D-FEM. In our simulations, we consider a 1-m-thick glass substrate with the silicon layer on the top. We assume that the Si layer is patterned by a periodic array of 25-nm-wide circular slots. The slots and the 1-m-thick volume above the silicon layer are filled with superstrate media of various refractive indices (n in the range 1.31–1.33). The size of each unit cell including one circular slot was p = 786 nm and periodic boundary conditions were used along x and y directions. Two ports were added on the top and the bottom domains and a y-polarized plane wave was incident onto the MS from the top port. The maximum mesh size for the glass substrate, the silicon layer, and the superstrate media was approximately (l/7.6), (l/17.45), and (l/6.65) nm, respectively. First, we estimated the MS transmission spectra by assuming that the MS was sym- metric (t = 0) and that the etched slots, as well as the volume above the Si layer, were filled with a fluid, as typical for chemosensors and biosensors. In this calculation, we assumed that the fluid had a refractive index n = 1.33 and neglected the fluid optical absorption. The symmetric MS supports two strong resonances at l = 1545 nm and l = 1610 nm, 1 2 Photonics 2022, 9, x FOR PEER REVIEW 4 of 7 as shown in Figure 2a. The size of the silicon gap (t) has small effect on these multipolar resonances, as revealed in prior research [35]. (a) (b) (c) Figure 2. (a) Transmission spectrum of the symmetric MS (tx = 0). (b) Electric field (Ey) distribution Figure 2. (a) Transmission spectrum of the symmetric MS (t = 0). (b) Electric field (E ) distribution x y relevant to the quasi-BIC resonant mode at the top of the asymmetric MS (tx = 10 nm) irradiated in relevant to the quasi-BIC resonant mode at the top of the asymmetric MS (t = 10 nm) irradiated in the the z-direction by a y-polarized plane wave. (c) Transmission spectrum of the asymmetric MS (tx = 10 z-direction by a y-polarized plane wave. (c) Transmission spectrum of the asymmetric MS (t = 10 nm). nm). In addition to the resonances mentioned above, symmetry breaking allows the de- scribed CSRR-MS to support an ultra-high quality factor quasi-BIC mode. We decreased Figure 3. Dependence of the resonance wavelength on n, i.e., the refractive index of the aqueous medium inside the etched slots and above the Si layer. The CSRR-MS is asymmetric, with tx = 10 nm. The sensitivity of the quasi-BIC mode to changes in the superstrate medium −1 refractive index (S = λres/n) was computed and found to be S = 155 nm RIU . In addition to S, we considered the figure of merit (FoM), defined as FoM = S/FWHM, where FWHM is the full width at half maximum of the transmission drop at resonance wavelength. For example, for the quasi-BIC mode at = 1608.7 nm, we estimated a FWHM of 0.4 pm, −1 resulting in an ultra-high FoM of 387.500 RIU . Although the archived value of S is comparable to that reported for other all-dielectric metasurfaces [34] and worse than that Photonics 2022, 9, x FOR PEER REVIEW 4 of 7 Photonics 2022, 9, 130 4 of 7 (a) (b) the arc length in one half of the CSRR structure by introducing an asymmetry parameter t = 10 nm to violate the structure in-plane inversion symmetry and trigger the quasi-BIC mode, as shown in [35]. The in-plane electric field (E ) of the quasi-BIC resonant mode was calculated at the top surface of the asymmetric CSRR MS (t = 10 nm) and plotted in Figure 2b. The transmission spectrum of the asymmetric MS in the narrow wavelength ranging from 1605 nm to 1610 nm is shown in Figure 2c, considering again n = 1.33 and k = 0 (k is the extinction coefficient of the superstrate medium). The quasi-BIC resonance occurs at l = 1608.7 nm. res To study the asymmetric MS performance as a refractive index sensor, we varied (c) the refractive index n of the fluid inside the etched slots and above the Si layer in the Figure 2. (a) Transmission spectrum of the symmetric MS (tx = 0). (b) Electric field (Ey) distribution range from 1.31 to 1.33. Then, the transmission spectrum in each case was calculated to relevant to the quasi-BIC resonant mode at the top of the asymmetric MS (tx = 10 nm) irradiated in investigate the sensitivity of the quasi-BIC mode to n. Figure 3 shows the outcome of our the z-direction by a y-polarized plane wave. (c) Transmission spectrum of the asymmetric MS (tx = 10 numerical calculations. The dependence of the resonance wavelength on n is almost linear, nm). as demonstrated in the linear fit of the dashed line in Figure 3. Figure 3. Dependence of the resonance wavelength on n, i.e., the refractive index of the aqueous Figure 3. Dependence of the resonance wavelength on n, i.e., the refractive index of the aqueous medium inside the etched slots and above the Si layer. The CSRR-MS is asymmetric, with tx = 10 nm. medium inside the etched slots and above the Si layer. The CSRR-MS is asymmetric, with t = 10 nm. The The sens sensitivity itivity of t of the h quasi-BIC e quasi-BIC mod mode to changes e to chang in the es in t superstrate he supe medium rstrate med refractive ium −1 index refract(iS ve ind = l e/ x n()Swas = λres computed /n) was compute and found d an to d be found S = 155 to be nm S = 15 RIU5 nm . In RIU addition . In add to Si,tion we res consider to S, we considered the ed the figure of fig merit ure o (FoM f mer ), defined it (FoM), def as FoM ine= d S a/ s FWHM FoM = ,Swher /FWH eM FWHM , wheris e FW theH full M width at half maximum of the transmission drop at resonance wavelength. For example, is the full width at half maximum of the transmission drop at resonance wavelength. For for example the quasi-BIC , for the quasi-BI mode at C = mode at 1608.7 nm,= 1608.7 nm, we estimatedwe estim a FWHMated of 0.4 a pm, FWHM resu o lting f 0.4 p in an m, −1 ultra-high FoM of 387.500 RIU . Although the archived value of S is comparable to that resulting in an ultra-high FoM of 387.500 RIU . Although the archived value of S is reported for other all-dielectric metasurfaces [34] and worse than that obtainable with some comparable to that reported for other all-dielectric metasurfaces [34] and worse than that plasmonic sensors [41], we stress that the main performance parameter is the FoM, whose value exceeds 10 . We evaluated the effect of a nonzero value of k on the quasi-BIC resonance and the FWHM. We calculated the transmission spectra of the asymmetric CSRR MS (t = 10 nm) for a constant superstrate refractive index of n = 1.33 and different values of the superstrate extinction coefficient (k ranging from 0 to 5  10 ). The FWHM of the resonance was increased for higher k values due to larger optical losses inside the superstrate medium, leading to a low-FoM sensing device, as shown by Figure 4a. Figure 4b shows that the FWHM of the quasi-BIC mode changes non-linearly with variations of the superstrate extinction coefficient (k). While the value of FWHM is nearly constant for k < 10 , a sharp increase was observed for larger k values. Photonics 2022, 9, x FOR PEER REVIEW 5 of 7 obtainable with some plasmonic sensors [41], we stress that the main performance parameter is the FoM, whose value exceeds 10 . We evaluated the effect of a nonzero value of k on the quasi-BIC resonance and the FWHM. We calculated the transmission spectra of the asymmetric CSRR MS (tx = 10 nm) for a constant superstrate refractive index of n = 1.33 and different values of the superstrate −6 extinction coefficient (k ranging from 0 to 5 × 10 ). The FWHM of the resonance was increased for higher k values due to larger optical losses inside the superstrate medium, leading to a low-FoM sensing device, as shown by Figure 4a. Figure 4b shows that the FWHM of the quasi-BIC mode changes non-linearly with variations of the superstrate −6 extinction coefficient (k). While the value of FWHM is nearly constant for k < 10 , a sharp Photonics 2022, 9, 130 5 of 7 increase was observed for larger k values. (a) (b) Figure 4. (a) Resonance relevant to the quasi-BIC mode for several values of k. (b) FWHW of the Figure 4. (a) Resonance relevant to the quasi-BIC mode for several values of k. (b) FWHW of the quasi-BIC quasi-BIC mod mode e vs. k vs. . k. Since the values of k are below 10 for several applications involving, for example, −6 Since the values of k are below 10 for several applications involving, for example, organic liquid compound detection [42], we expect a modest degradation of the FoM organic liquid compound detection [42], we expect a modest degradation of the FoM (reduction factor < 2) due to the nonzero values of k when applications involving fluids (reduction factor < 2) due to the nonzero values of k when applications involving fluids having k < 10 @ 1.6 m are considered. −6 having k < 10 @ 1.6 µm are considered. 4. Conclusions 4. Conclusions We report on the design of a refractive index sensor with an ultra-high figure of 5 1 merit (>10 RIU ) based on all-dielectric metasurfaces that support a quasi-BIC mode. We report on the design of a refractive index sensor with an ultra-high figure of merit 5 Our 3D −1 numerical simulations showed that the ultra-narrow quasi-BIC resonance in the (>10 RIU ) based on all-dielectric metasurfaces that support a quasi-BIC mode. Our 3D complementary split-ring resonator metasurface structure can attain a sensitivity value of numerical simulations showed that the ultra-narrow quasi-BIC resonance in the 1 1 155 nm RIU and an outstanding FoM of 387,500 RIU , when k = 0. This high value of FoM complementary split-ring resonator metasurface structure can attain a sensitivity value of is obtained with a value of t (the geometrical asymmetry parameter) equal to 10 nm, which −1 −1 155 nm RIU and an outstanding FoM of 387,500 RIU , when k = 0. This high value of FoM is feasible from a technological point of view. Considering new biomedical applications, the is obtained with a value of tx (the geometrical asymmetry parameter) equal to 10 nm, proposed technique offers new paths of research on light–matter interactions. In addition, which is feasible from a technological point of view. Considering new biomedical cluster analysis could be utilized to enhance the resolution of chemosensors and biosensors applications, the proposed technique offers new paths of research on light–matter developed according to the approach discussed here [43,44]. interactions. In addition, cluster analysis could be utilized to enhance the resolution of Author Contributions: Conceptualization, M.S. and F.D.; methodology, M.S., F.A. and F.D.; software, chemosensors and biosensors developed according to the approach discussed here [43,44]. M.S. and F.A.; validation, J.F.A., P.R.-V., L.R.-C. and D.C.Z.; investigation, M.S., F.A. and J.F.A.; writing—original draft preparation, M.S. and F.D.; writing—review and editing, all authors; supervi- Author Contributions: Conceptualization, M.S. and F.D.; methodology, M.S., F.A. and F.D.; sion, D.C.Z. and F.D.; project administration, J.M.L.-H. and J.M.S.-P.; funding acquisition, J.M.S.-P. software, M.S. and F.A.; validation, J.F.A., P.R.-V., L.R.-C. and D.C.Z.; investigation, M.S., F.A. and and F.D. All authors have read and agreed to the published version of the manuscript. J.F.A.; writing—original draft preparation, M.S. and F.D.; writing—review and editing, all authors; supervision, Funding: D. This C.Z. and work F is.D. part ; project adm of the projects inistrati PID2019-107270RB-C21 on, J.M.L.-H. and J.M and .SPID2019-109072RB-C31, .-P.; funding acquisition, funded by MCIN/AEI/10.13039/501100011033 and FEDER “A way to make Europe”, PDC2021- J.M.S.-P. and F.D. All authors have read and agreed to the published version of the manuscript. 121172-C21, funded by MCIN/AEI/10.13039/501100011033 and European Union “Next generation Funding: This work is part of the projects PID2019-107270RB-C21 and PID2019-109072RB-C31, EU”/PTR, TeDFeS Project (RTC-2017-6321-1 funded by MCIN/AEI/10.13039/501100011033 and funded by MCIN/AEI/10.13039/501100011033 and FEDER “A way to make Europe”, PDC2021- FEDER “A way to make Europe”), and project S2018/NMT-4326, funded by the Comunidad de 121172-C21, funded by MCIN/AEI/10.13039/501100011033 and European Union “Next generation Madrid and FEDER Program. J.F.A. received funding from Ministerio de Ciencia, Innovación y EU”/PTR, TeDFeS Project (RTC-2017-6321-1 funded by MCIN/AEI/10.13039/501100011033 and Universidades of Spain under the Juan de la Cierva-Incorporación grant. Institutional Review Board Statement: Not applicable. Informed Consent Statement: Not applicable. Data Availability Statement: Not applicable. 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All-Dielectric Metasurface Based on Complementary Split-Ring Resonators for Refractive Index Sensing

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hv photonics Communication All-Dielectric Metasurface Based on Complementary Split-Ring Resonators for Refractive Index Sensing 1 1 2 , 3 , 4 2 , 3 , 4 Mohsen Samadi , Fatemeh Abshari , José F. Algorri , Pablo Roldán-Varona , 3 2 , 3 , 4 5 6 Luis Rodríguez-Cobo , José M. López-Higuera , José M. Sánchez-Pena , Dimitrios C. Zografopoulos 7 , and Francesco Dell’Olio * Faculty of Electrical and Computer Engineering, Tarbiat Modares University, Tehran 1411713116, Iran; samadi@physik.uni-kiel.de (M.S.); f.abshari@modares.ac.ir (F.A.) Photonics Engineering Group, University of Cantabria, 39005 Santander, Spain; algorrijf@unican.es (J.F.A.); pablo.roldan@unican.es (P.R.-V.); miguel.lopezhiguera@unican.es (J.M.L.-H.) CIBER-bbn, Instituto de Salud Carlos III, 28029 Madrid, Spain; luis.rodriguez@unican.es Instituto de Investigación Sanitaria Valdecilla (IDIVAL), 39011 Santander, Spain Department of Electronic Technology, Carlos III University, 28911 Madrid, Spain; jmpena@ing.uc3m.es Consiglio Nazionale delle Ricerche, Istituto per la Microelettronica e Microsistemi (CNR-IMM), 00133 Roma, Italy; dimitrios.zografopoulos@artov.imm.cnr.it Department of Electrical and Information Engineering, Polytechnic University of Bari, 70125 Bari, Italy * Correspondence: francesco.dellolio@poliba.it Abstract: Thanks to their lower losses and sharper resonances compared to their metallic counterparts, all-dielectric metasurfaces are attracting a quickly growing research interest. The application of such metasurfaces in the field of refractive index sensing is extremely attractive, especially due to the expected high performance and the simplicity of the sensing element excitation and readout. Herein, we report on an all-dielectric silicon metasurface based on complementary split-ring resonators Citation: Samadi, M.; Abshari, F.; (CSRRs) optimized for refractive index sensing. A quasi-bound state in the continuum (quasi-BIC) Algorri, J.F.; Roldán-Varona, P.; with an ultra-high quality factor can be excited in the near-infrared (NIR) window by violating the Rodríguez-Cobo, L.; López-Higuera, structure symmetry. By using the three-dimensional finite element method (3D-FEM), a refractive J.M.; Sánchez-Pena, J.M.; index sensor for biomedical applications with an ultra-high figure of merit (FoM > 100,000 RIU ) Zografopoulos, D.C.; Dell’Olio, F. has been designed, exploiting the quasi-BIC resonance. The proposed design strategy opens new All-Dielectric Metasurface Based on Complementary Split-Ring avenues for developing flat biochemical sensors that are accurate and responsive in real time. Resonators for Refractive Index Sensing. Photonics 2022, 9, 130. Keywords: metasurface; biosensor; bound state in the continuum https://doi.org/10.3390/ photonics9030130 Received: 17 January 2022 1. Introduction Accepted: 22 February 2022 Published: 25 February 2022 Resonant micro- and nano-photonic refractive index sensors have long been utilized for real-time, label-free analysis of chemical and biological samples, such as identifying Publisher’s Note: MDPI stays neutral target biomolecules in a biologic fluid or detecting organic liquid compounds. When target with regard to jurisdictional claims in molecules interact with light, the sensor resonance frequency shifts due to light–matter published maps and institutional affil- interaction. The frequency shift is subsequently measured and utilized to detect target iations. molecules [1–6]. The sensitivity (S = Dl /Dn) of refractive index sensors is evaluated as the res ratio of the shift in the sensor resonance wavelength to the change in the sample’s refractive index. The figure of merit (FoM = S/FWHM) normalizes the refractive index sensitivity to Copyright: © 2022 by the authors. the resonant mode spectral width (full width at the half maximum, FWHM) [5–8]. Licensee MDPI, Basel, Switzerland. Surface plasmons [9–12], photonic crystal cavities [3,13–16], and whispering gallery This article is an open access article mode resonators [2,4,17–20] have all been used to produce better sensitivities and superior distributed under the terms and sensing performance. Furthermore, biochemical sensing applications have used plasmonic conditions of the Creative Commons nanostructures that support Fano resonances [21–24]. However, despite their high sensitiv- Attribution (CC BY) license (https:// ity to the surrounding medium refractive index, they suffer from broad resonances caused creativecommons.org/licenses/by/ by high optical absorption losses in the metal, which severely limit the sensor FoM. 4.0/). Photonics 2022, 9, 130. https://doi.org/10.3390/photonics9030130 https://www.mdpi.com/journal/photonics Photonics 2022, 9, x FOR PEER REVIEW 2 of 7 resonances caused by high optical absorption losses in the metal, which severely limit the sensor FoM. Photonics 2022, 9, 130 2 of 7 Metasurfaces (MSs) are planar interfaces made of periodic arrays of sub-wavelength resonant elements used to manipulate the phase, polarization, and amplitude of light [25– 27]. They are the 2D equivalents of bulk metamaterials. Due to their lower ohmic losses and thus Metas sharper Fano reso urfaces (MSs) arenances than t planar interfh ac eir me es matd ae llic equ of periiva odlent ic as, a rray ll- sdie of ls ect ubr -ic MSs wavelen hg at ve h become more popular in recent years for sensing applications [28–34]. In this regard, a resonant elements used to manipulate the phase, polarization, and amplitude of light [25–27]. new type of MS based on the CSRR [35] was recently reported. In this MS, an ultrathin They are the 2D equivalents of bulk metamaterials. Due to their lower ohmic losses and thus sharper slot is etched Fano r in a silicon layer on a st esonances than their metallic andardequivalents, glass substra all-dielectric te. In the NIR MSs window, the MS have become mor shows e popular two m in ult recent ipolaryears resonance for sensing s. Meapplications anwhile, an asym [28–34m ]. e In try this in regar the st d,ruct a neuw re type of th ofe MS based on the CSRR [35] was recently reported. In this MS, an ultrathin slot is etched slotted CSRR can be used to trigger a quasi-BIC with an ultra-high Q-factor thanks to the in a silicon layer on a standard glass substrate. In the NIR window, the MS shows two vanishing radiation losses for a small degree of asymmetry. Quasi-BIC modes have multipolar resonances. Meanwhile, an asymmetry in the structure of the slotted CSRR can already been exploited in many application domains, including nonlinear optics and be used to trigger a quasi-BIC with an ultra-high Q-factor thanks to the vanishing radiation sensing [36–38]. losses for a small degree of asymmetry. Quasi-BIC modes have already been exploited in In our study, by examining the sensitivity of the quasi-BIC mode to the superstrate many application domains, including nonlinear optics and sensing [36–38]. medium refractive index, we assessed the CSRR-MS sensing capacity. By exploiting the In our study, by examining the sensitivity of the quasi-BIC mode to the superstrate non-radiative nature of the quasi-BIC mode, exceptionally high-quality factors and FoMs medium refractive index, we assessed the CSRR-MS sensing capacity. By exploiting the can be produced, allowing for the design of highly accurate biological and chemical non-radiative nature of the quasi-BIC mode, exceptionally high-quality factors and FoMs sensors. can be produced, allowing for the design of highly accurate biological and chemical sensors. 2. Metasurface 2. Metasurface Figure 1 shows the proposed sensing device. A periodic array of circular slots is fully Figure 1 shows the proposed sensing device. A periodic array of circular slots is etched in a silicon layer of thickness h, deposited on a glass substrate to form the CSRR- fully etched in a silicon layer of thickness h, deposited on a glass substrate to form the MS. Each unit cell of the periodic structure has one circular slot, whose structural CSRR-MS. Each unit cell of the periodic structure has one circular slot, whose structural parameters are shown in the inset of Figure 1. The slot width, the inner diameter, the parameters are shown in the inset of Figure 1. The slot width, the inner diameter, the distance between neighboring slots in the x-direction, the pitch of the periodic square distance between neighboring slots in the x-direction, the pitch of the periodic square array, array, and the size of the silicon gaps are identified as s, w, g, p, and t, respectively. In and the size of the silicon gaps are identified as s, w, g, p, and t, respectively. In addition, an addition, an asymmetry parameter tx is introduced in order to break the structure asymmetry parameter t is introduced in order to break the structure symmetry and excite symmetry and excite the quasi-BIC resonance, reducing the arc length in one half of the the quasi-BIC resonance, reducing the arc length in one half of the CSRR structure. The CSRR structure. The depth of the slots etched in the silicon layer is equal to h. depth of the slots etched in the silicon layer is equal to h. Figure 1. A three-dimensional schematic illustration of the CSRR metasurface. In a silicon layer with Figure 1. A three-dimensional schematic illustration of the CSRR metasurface. In a silicon layer with a thickness of h, the periodic split rings are etched. The unit cell (marked by a yellow dashed square) a thickness of h, the periodic split rings are etched. The unit cell (marked by a yellow dashed square) is shown in the inset. is shown in the inset. The transmission spectra of the MS have been computed using the 3D-FEM. The silicon layer is assumed as deposited on a glass substrate with a refractive index of n = 1.52, and a y-polarized plane wave irradiates the MS in the z-direction (see Figure 1). We assume h = 232 nm, s = 25 nm, w = 496 nm, g = 240 nm, and t = 100 nm, which are identical to the values in [35]. The refractive index dispersion of silicon is considered [39]. Photonics 2022, 9, 130 3 of 7 All these geometrical features are compatible with the technological constraints typically imposed by e-beam lithography, having a resolution below 5 nm [40]. We assume that the metasurface is top illuminated by a sub-pm linewidth laser source operating in the NIR, whose emission frequency can be precisely tuned in a narrow range of a few hundreds of pm by a piezoelectric transducer. A standard detector operating in the NIR can be used for measuring the transmitted power. 3. Simulation Results The MS has been simulated by 3D-FEM. In our simulations, we consider a 1-m-thick glass substrate with the silicon layer on the top. We assume that the Si layer is patterned by a periodic array of 25-nm-wide circular slots. The slots and the 1-m-thick volume above the silicon layer are filled with superstrate media of various refractive indices (n in the range 1.31–1.33). The size of each unit cell including one circular slot was p = 786 nm and periodic boundary conditions were used along x and y directions. Two ports were added on the top and the bottom domains and a y-polarized plane wave was incident onto the MS from the top port. The maximum mesh size for the glass substrate, the silicon layer, and the superstrate media was approximately (l/7.6), (l/17.45), and (l/6.65) nm, respectively. First, we estimated the MS transmission spectra by assuming that the MS was sym- metric (t = 0) and that the etched slots, as well as the volume above the Si layer, were filled with a fluid, as typical for chemosensors and biosensors. In this calculation, we assumed that the fluid had a refractive index n = 1.33 and neglected the fluid optical absorption. The symmetric MS supports two strong resonances at l = 1545 nm and l = 1610 nm, 1 2 Photonics 2022, 9, x FOR PEER REVIEW 4 of 7 as shown in Figure 2a. The size of the silicon gap (t) has small effect on these multipolar resonances, as revealed in prior research [35]. (a) (b) (c) Figure 2. (a) Transmission spectrum of the symmetric MS (tx = 0). (b) Electric field (Ey) distribution Figure 2. (a) Transmission spectrum of the symmetric MS (t = 0). (b) Electric field (E ) distribution x y relevant to the quasi-BIC resonant mode at the top of the asymmetric MS (tx = 10 nm) irradiated in relevant to the quasi-BIC resonant mode at the top of the asymmetric MS (t = 10 nm) irradiated in the the z-direction by a y-polarized plane wave. (c) Transmission spectrum of the asymmetric MS (tx = 10 z-direction by a y-polarized plane wave. (c) Transmission spectrum of the asymmetric MS (t = 10 nm). nm). In addition to the resonances mentioned above, symmetry breaking allows the de- scribed CSRR-MS to support an ultra-high quality factor quasi-BIC mode. We decreased Figure 3. Dependence of the resonance wavelength on n, i.e., the refractive index of the aqueous medium inside the etched slots and above the Si layer. The CSRR-MS is asymmetric, with tx = 10 nm. The sensitivity of the quasi-BIC mode to changes in the superstrate medium −1 refractive index (S = λres/n) was computed and found to be S = 155 nm RIU . In addition to S, we considered the figure of merit (FoM), defined as FoM = S/FWHM, where FWHM is the full width at half maximum of the transmission drop at resonance wavelength. For example, for the quasi-BIC mode at = 1608.7 nm, we estimated a FWHM of 0.4 pm, −1 resulting in an ultra-high FoM of 387.500 RIU . Although the archived value of S is comparable to that reported for other all-dielectric metasurfaces [34] and worse than that Photonics 2022, 9, x FOR PEER REVIEW 4 of 7 Photonics 2022, 9, 130 4 of 7 (a) (b) the arc length in one half of the CSRR structure by introducing an asymmetry parameter t = 10 nm to violate the structure in-plane inversion symmetry and trigger the quasi-BIC mode, as shown in [35]. The in-plane electric field (E ) of the quasi-BIC resonant mode was calculated at the top surface of the asymmetric CSRR MS (t = 10 nm) and plotted in Figure 2b. The transmission spectrum of the asymmetric MS in the narrow wavelength ranging from 1605 nm to 1610 nm is shown in Figure 2c, considering again n = 1.33 and k = 0 (k is the extinction coefficient of the superstrate medium). The quasi-BIC resonance occurs at l = 1608.7 nm. res To study the asymmetric MS performance as a refractive index sensor, we varied (c) the refractive index n of the fluid inside the etched slots and above the Si layer in the Figure 2. (a) Transmission spectrum of the symmetric MS (tx = 0). (b) Electric field (Ey) distribution range from 1.31 to 1.33. Then, the transmission spectrum in each case was calculated to relevant to the quasi-BIC resonant mode at the top of the asymmetric MS (tx = 10 nm) irradiated in investigate the sensitivity of the quasi-BIC mode to n. Figure 3 shows the outcome of our the z-direction by a y-polarized plane wave. (c) Transmission spectrum of the asymmetric MS (tx = 10 numerical calculations. The dependence of the resonance wavelength on n is almost linear, nm). as demonstrated in the linear fit of the dashed line in Figure 3. Figure 3. Dependence of the resonance wavelength on n, i.e., the refractive index of the aqueous Figure 3. Dependence of the resonance wavelength on n, i.e., the refractive index of the aqueous medium inside the etched slots and above the Si layer. The CSRR-MS is asymmetric, with tx = 10 nm. medium inside the etched slots and above the Si layer. The CSRR-MS is asymmetric, with t = 10 nm. The The sens sensitivity itivity of t of the h quasi-BIC e quasi-BIC mod mode to changes e to chang in the es in t superstrate he supe medium rstrate med refractive ium −1 index refract(iS ve ind = l e/ x n()Swas = λres computed /n) was compute and found d an to d be found S = 155 to be nm S = 15 RIU5 nm . In RIU addition . In add to Si,tion we res consider to S, we considered the ed the figure of fig merit ure o (FoM f mer ), defined it (FoM), def as FoM ine= d S a/ s FWHM FoM = ,Swher /FWH eM FWHM , wheris e FW theH full M width at half maximum of the transmission drop at resonance wavelength. For example, is the full width at half maximum of the transmission drop at resonance wavelength. For for example the quasi-BIC , for the quasi-BI mode at C = mode at 1608.7 nm,= 1608.7 nm, we estimatedwe estim a FWHMated of 0.4 a pm, FWHM resu o lting f 0.4 p in an m, −1 ultra-high FoM of 387.500 RIU . Although the archived value of S is comparable to that resulting in an ultra-high FoM of 387.500 RIU . Although the archived value of S is reported for other all-dielectric metasurfaces [34] and worse than that obtainable with some comparable to that reported for other all-dielectric metasurfaces [34] and worse than that plasmonic sensors [41], we stress that the main performance parameter is the FoM, whose value exceeds 10 . We evaluated the effect of a nonzero value of k on the quasi-BIC resonance and the FWHM. We calculated the transmission spectra of the asymmetric CSRR MS (t = 10 nm) for a constant superstrate refractive index of n = 1.33 and different values of the superstrate extinction coefficient (k ranging from 0 to 5  10 ). The FWHM of the resonance was increased for higher k values due to larger optical losses inside the superstrate medium, leading to a low-FoM sensing device, as shown by Figure 4a. Figure 4b shows that the FWHM of the quasi-BIC mode changes non-linearly with variations of the superstrate extinction coefficient (k). While the value of FWHM is nearly constant for k < 10 , a sharp increase was observed for larger k values. Photonics 2022, 9, x FOR PEER REVIEW 5 of 7 obtainable with some plasmonic sensors [41], we stress that the main performance parameter is the FoM, whose value exceeds 10 . We evaluated the effect of a nonzero value of k on the quasi-BIC resonance and the FWHM. We calculated the transmission spectra of the asymmetric CSRR MS (tx = 10 nm) for a constant superstrate refractive index of n = 1.33 and different values of the superstrate −6 extinction coefficient (k ranging from 0 to 5 × 10 ). The FWHM of the resonance was increased for higher k values due to larger optical losses inside the superstrate medium, leading to a low-FoM sensing device, as shown by Figure 4a. Figure 4b shows that the FWHM of the quasi-BIC mode changes non-linearly with variations of the superstrate −6 extinction coefficient (k). While the value of FWHM is nearly constant for k < 10 , a sharp Photonics 2022, 9, 130 5 of 7 increase was observed for larger k values. (a) (b) Figure 4. (a) Resonance relevant to the quasi-BIC mode for several values of k. (b) FWHW of the Figure 4. (a) Resonance relevant to the quasi-BIC mode for several values of k. (b) FWHW of the quasi-BIC quasi-BIC mod mode e vs. k vs. . k. Since the values of k are below 10 for several applications involving, for example, −6 Since the values of k are below 10 for several applications involving, for example, organic liquid compound detection [42], we expect a modest degradation of the FoM organic liquid compound detection [42], we expect a modest degradation of the FoM (reduction factor < 2) due to the nonzero values of k when applications involving fluids (reduction factor < 2) due to the nonzero values of k when applications involving fluids having k < 10 @ 1.6 m are considered. −6 having k < 10 @ 1.6 µm are considered. 4. Conclusions 4. Conclusions We report on the design of a refractive index sensor with an ultra-high figure of 5 1 merit (>10 RIU ) based on all-dielectric metasurfaces that support a quasi-BIC mode. We report on the design of a refractive index sensor with an ultra-high figure of merit 5 Our 3D −1 numerical simulations showed that the ultra-narrow quasi-BIC resonance in the (>10 RIU ) based on all-dielectric metasurfaces that support a quasi-BIC mode. Our 3D complementary split-ring resonator metasurface structure can attain a sensitivity value of numerical simulations showed that the ultra-narrow quasi-BIC resonance in the 1 1 155 nm RIU and an outstanding FoM of 387,500 RIU , when k = 0. This high value of FoM complementary split-ring resonator metasurface structure can attain a sensitivity value of is obtained with a value of t (the geometrical asymmetry parameter) equal to 10 nm, which −1 −1 155 nm RIU and an outstanding FoM of 387,500 RIU , when k = 0. This high value of FoM is feasible from a technological point of view. Considering new biomedical applications, the is obtained with a value of tx (the geometrical asymmetry parameter) equal to 10 nm, proposed technique offers new paths of research on light–matter interactions. In addition, which is feasible from a technological point of view. Considering new biomedical cluster analysis could be utilized to enhance the resolution of chemosensors and biosensors applications, the proposed technique offers new paths of research on light–matter developed according to the approach discussed here [43,44]. interactions. In addition, cluster analysis could be utilized to enhance the resolution of Author Contributions: Conceptualization, M.S. and F.D.; methodology, M.S., F.A. and F.D.; software, chemosensors and biosensors developed according to the approach discussed here [43,44]. M.S. and F.A.; validation, J.F.A., P.R.-V., L.R.-C. and D.C.Z.; investigation, M.S., F.A. and J.F.A.; writing—original draft preparation, M.S. and F.D.; writing—review and editing, all authors; supervi- Author Contributions: Conceptualization, M.S. and F.D.; methodology, M.S., F.A. and F.D.; sion, D.C.Z. and F.D.; project administration, J.M.L.-H. and J.M.S.-P.; funding acquisition, J.M.S.-P. software, M.S. and F.A.; validation, J.F.A., P.R.-V., L.R.-C. and D.C.Z.; investigation, M.S., F.A. and and F.D. All authors have read and agreed to the published version of the manuscript. J.F.A.; writing—original draft preparation, M.S. and F.D.; writing—review and editing, all authors; supervision, Funding: D. This C.Z. and work F is.D. part ; project adm of the projects inistrati PID2019-107270RB-C21 on, J.M.L.-H. and J.M and .SPID2019-109072RB-C31, .-P.; funding acquisition, funded by MCIN/AEI/10.13039/501100011033 and FEDER “A way to make Europe”, PDC2021- J.M.S.-P. and F.D. All authors have read and agreed to the published version of the manuscript. 121172-C21, funded by MCIN/AEI/10.13039/501100011033 and European Union “Next generation Funding: This work is part of the projects PID2019-107270RB-C21 and PID2019-109072RB-C31, EU”/PTR, TeDFeS Project (RTC-2017-6321-1 funded by MCIN/AEI/10.13039/501100011033 and funded by MCIN/AEI/10.13039/501100011033 and FEDER “A way to make Europe”, PDC2021- FEDER “A way to make Europe”), and project S2018/NMT-4326, funded by the Comunidad de 121172-C21, funded by MCIN/AEI/10.13039/501100011033 and European Union “Next generation Madrid and FEDER Program. J.F.A. received funding from Ministerio de Ciencia, Innovación y EU”/PTR, TeDFeS Project (RTC-2017-6321-1 funded by MCIN/AEI/10.13039/501100011033 and Universidades of Spain under the Juan de la Cierva-Incorporación grant. Institutional Review Board Statement: Not applicable. Informed Consent Statement: Not applicable. Data Availability Statement: Not applicable. 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Journal

PhotonicsMultidisciplinary Digital Publishing Institute

Published: Feb 25, 2022

Keywords: metasurface; biosensor; bound state in the continuum

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