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[Keisuke Watanabe](https://orcid.org/0000-0002-4285-2135), [Hemam Rachna Devi](https://orcid.org/0000-0002-9667-2690), [Masanobu Iwanaga](https://orcid.org/0000-0002-8930-6940), [Tadaaki Nagao](https://orcid.org/0000-0002-6746-2686)

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[Vibrational Coupling to Quasi‐Bound States in the Continuum under Tailored Coupling Conditions](https://mdr.nims.go.jp/datasets/6dea684a-cb2a-4d0f-a6fc-7cef9b37dbc2)

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Vibrational Coupling to Quasi‐Bound States in the Continuum under Tailored Coupling ConditionsRESEARCH ARTICLEwww.advopticalmat.deVibrational Coupling to Quasi-Bound States in theContinuum under Tailored Coupling ConditionsKeisuke Watanabe,* Hemam Rachna Devi, Masanobu Iwanaga, and Tadaaki NagaoPhotonic resonance modes can be spectrally coupled to the vibrational modesof molecules in the mid-infrared regime through interactions betweenlocalized electric fields and nearby molecules. According to recent studies,radiative loss engineering of coupled systems is a promising approach fortailoring coupling conditions and enhancing the molecular signals. However,this strategy has only been realized using the localized surface plasmonresonances of metal nanostructures, which suffer from increased ohmic lossin the mid-infrared region and face serious limitations in achieving highquality (Q) factors. In this study, silicon-based metasurfaces formed onsilicon-on-insulator wafers are adopted to achieve high Q factors and tune thecoupling conditions between the quasi-bound states in the continuum (qBICs)and molecular vibrations. The coupling between the resonance mode andpolymethyl methacrylate molecules is tailored from weak to strong couplingregimes by simply changing the structural asymmetry parameter and utilizingthe intrinsically high Q factors of the qBIC modes. In addition, the optimalasymmetry parameter that maximizes the enhanced molecular signal isidentified, opening a route toward realizing highly sensitive surface-enhancedinfrared spectroscopy using complementary metal–oxide–semiconductorcompatible all-dielectric materials.K. WatanabeInternational Center for Young Scientists (ICYS)National Institute for Materials Science (NIMS)1-1 Namiki, Tsukuba, Ibaraki 305-0044, JapanE-mail: watanabe.keisuke@nims.go.jpH. R. Devi, T. NagaoInternational Center for Materials Nanoarchitectonics (MANA)National Institute for Materials Science (NIMS)1-1 Namiki, Tsukuba, Ibaraki 305-0044, JapanM. IwanagaResearch Center for Electronic and Optical MaterialsNational Institute for Materials Science (NIMS)1-1 Namiki, Tsukuba, Ibaraki 305-0044, JapanT. NagaoDepartment of Condensed Matter PhysicsGraduate School of ScienceHokkaido UniversityKita 10, Nishi 8, Kita-ku, Sapporo 060-0810, JapanThe ORCID identification number(s) for the author(s) of this articlecan be found under https://doi.org/10.1002/adom.202301912© 2023 The Authors. Advanced Optical Materials published byWiley-VCH GmbH. This is an open access article under the terms of theCreative Commons Attribution License, which permits use, distributionand reproduction in any medium, provided the original work is properlycited.DOI: 10.1002/adom.2023019121. IntroductionResonantly coupled systems between pho-tonic resonators and molecules are char-acterized by spectral variations resultingfrom light–matter interactions.[1–3] Pho-tonic nanostructures are advantageous ow-ing to their strong near-field confinementat the nanoscale, which enables stronginteractions with nearby molecules.[4] Ifthe coupling rates between the resonatorsand molecules are sufficiently higher thanthe constituent damping rates, the coupledsystem reaches a strong coupling regimeand forms a newly hybridized or polari-ton state,[5] exhibiting mode splitting in thespectra. Compared to coupling with elec-tronic transitions,[6–8] which has attractedsignificant attention over the past decade,vibrational transitions have much smallertransition dipole moments.[9] Nevertheless,by utilizing an enhanced energy exchangerate between the collective dipole resonanceof high-density molecular vibrations andthe single resonance mode,[10] strongcoupling between plasmonic nanostructures and molecularvibrations,[11–14] including polymethyl methacrylate (PMMA)molecules,[15,16] has been reported quite recently. The key chal-lenge in achieving a strong coupling regime is to reduce thedamping rate of the nanostructure compared to the coupling rateg with the molecules. Thus, it is important to precisely controlthe losses in the structure. However, an elaborate structural de-sign is required, and the variable range of losses is limited bythe large ohmic loss and collisional damping of metals. In thisrespect, dielectric nanostructures have advantages in terms oflow material losses and wide tunability of radiative quality (Q)factors.[17] In particular, dielectric metasurfaces at quasi-boundstates in the continuum (qBICs) have recently attracted world-wide attention[18–22] and can control their radiative losses sim-ply by changing their asymmetry parameters,[23,24] thus offeringgreat potential for the extensive tuning of the coupled systemfrom weak to strong coupling regimes.Another advantage of loss engineering is that it favors molec-ular sensing based on surface-enhanced infrared absorption(SEIRA) spectroscopy. Identification of a small number ofmolecules in the mid-infrared range has conventionally been re-alized by utilizing the interactions between molecular vibrationsand strongly localized electric fields in plasmonic platforms.[25,26]Recently, loss engineering for maximizing molecularAdv. Optical Mater. 2024, 12, 2301912 2301912 (1 of 8) © 2023 The Authors. Advanced Optical Materials published by Wiley-VCH GmbHhttp://www.advopticalmat.demailto:watanabe.keisuke@nims.go.jphttps://doi.org/10.1002/adom.202301912http://creativecommons.org/licenses/by/4.0/http://crossmark.crossref.org/dialog/?doi=10.1002%2Fadom.202301912&domain=pdf&date_stamp=2023-10-27www.advancedsciencenews.com www.advopticalmat.deabsorption at the vibrational modes has been reported asanother strategy.[27–31] The ratio of radiative to nonradiativeintrinsic loss rates originating from metallic nanostructures canbe controlled by changing the structural parameters, resulting ina large vibrational signal under optimum conditions.[32,33] Thismethod provides significant enhancement without requiringprecise nanofabrication, such as a few nanometer gaps.[30] De-spite their highly desirable features, the feasibility of enhancingmolecular signal strengths with all-dielectric materials has notyet been explored and demonstrated.In this study, we theoretically and experimentally demonstratethe enhancement of molecular signal strength by engineeringthe coupling conditions between the qBIC modes of silicon meta-surfaces and the vibrations of PMMA molecules. The structuralasymmetry parameters of the asymmetric pair-rod arrays are se-lected such that the Q factors of the qBIC modes vary indepen-dently while maintaining the resonance wavelengths. The cou-pling conditions of the qBIC-PMMA system are readily tunedfrom weak to strong coupling regimes by simply changing theasymmetry parameters, whereas the upper limits of the Q fac-tors are determined by the leakage losses into the high-index sub-strate of the silicon-on-insulator (SOI) wafer. We also show theexistence of an optimum asymmetry parameter that maximizesthe molecular signal, as explained by temporal coupled mode the-ory. These conditions are significantly affected by the downwardleakage losses when the oxide layer thickness of the SOI wafer ischanged. To the best of our knowledge, this is the first report toshow that the loss engineering of all-dielectric metasurfaces canincrease the molecular vibrational signals, providing a means forhighly sensitive surface-enhanced infrared spectroscopy withoutusing metals.2. Results and Discussion2.1. Structure and CharacteristicsFigure 1a shows the proposed silicon metasurface with asymmet-ric pair-rod arrays on an SOI wafer with 400-nm thick silicon anda 2000-nm thick buried oxide (BOX) layer. The period of array P is3900 nm, the primitive silicon rod length L is 2625 nm, the rodsheight w is 985 nm, and the distance between the centers of thepair-rod is 1825 nm. The qBIC condition arises from symmetrybreaking of the unit structure of the metasurface that satisfies theBIC condition with ideally infinite Q factors, even inside the lightcone.[34] In our study, asymmetry is added by varying the lengthsof the upper and lower rods in the unit cell, whose asymmetryparameter is expressed as:𝛼 = 2ΔLL(1)Figure 1b shows a representative scanning electron mi-croscopy (SEM) image of a metasurface fabricated using electron-beam lithography and deep silicon etching (see ExperimentalSection). As an example, we simulate the field strength |E|2 atthe qBIC resonance wavelength (𝛼 = 0.2) for the xy-plane at halfthe height of the silicon rods (𝛼 = 0.2) using the finite-differencetime-domain (FDTD) method. Figure 1c shows the strongly lo-calized electric field intensity at the sidewalls of the silicon rods,which induces a strong interaction with the coupled molecules.The white arrows indicate the existence of anti-parallel displace-ment currents in the upper and lower rods, which give rise toa net electric component in the x-direction. Consequently, theqBIC resonance mode (nonzero 𝛼) can be excited in free-spaceusing a normally incident x-polarized plane wave. We also cal-culate the spatially averaged |E|2 spectrum (𝛼 = 0.2) for the xy-plane at the center of the silicon nanostructures (lower panel onFigure 1c). At the peak wavelength, the near-field intensity is res-onantly enhanced by the qBIC resonance.The distinctive feature of the asymmetric pair-rod structure isthat the linewidths can be independently tuned, while the reso-nance peak wavelengths remain almost constant when varying𝛼, which allows for easy control of the coupling conditions withmolecular vibrations. Figure 1d shows the simulated transmis-sion spectra of bare silicon metasurfaces with different 𝛼. Boththe resonance peak amplitudes and line widths increase withparameter 𝛼 while maintaining the peak positions. In the ex-periment, the transmission spectra of a 3 mm × 3 mm samplewere acquired at normal incidence using Fourier-transform in-frared spectroscopy. The experimental results in Figure 1e are al-most in good agreement with the simulation, except for the slightblueshifts of the qBIC modes, which can be attributed to fabrica-tion imperfections such as the shrinkage of the rod corners.To analytically illustrate the experimental variations in thelinewidths ( = 𝜆c/Qtotal, where 𝜆c is the resonance mode of a qBICmode) of metasurfaces with different 𝛼, the total Q factor Qtot isdecomposed into the radiative (Qr) and other nonradiative Q fac-tors (Qnr) as:Q−1tot = Q−1r + Q−1nr = Q−1r + Q−1abs + Q−1scat (2)Here, Qabs−1 and Qscat−1 are the material absorption and scatter-ing losses due to surface roughness, respectively. To investigatethe loss mechanisms produced by the asymmetric cladding lay-ers of SOI wafers in the vertical direction, we calculate the Q fac-tors and decompose the contributions from the three directionsas follows:[35,36]Q−1 =P (t)𝜔0U (t)=Ptop (t) + Pbottom (t) + Pin (t)𝜔0U (t)= Q−1top + Q−1bottom + Q−1in (3)where U(t) is the modal electromagnetic energy, and P(t) is theradiation power absorbed in the calculation boundary. P(t) isthen separated into radiation in the in-plane direction (Pin(t)),upward direction (Ptop(t)), and downward direction (Pbottom(t)),whose boundaries are positioned approximately at 𝜆/4 aboveand below the silicon surface. In the calculation, Bloch boundaryconditions are used in the x- and y- directions; therefore, themodel is considered to have an infinite array size, and henceQin−1 = 0. In this case, Qr−1 = Qtop−1 + Qbottom−1. The extinctioncoefficients k of c-Si and SiO2 are assumed to be zero for thecalculations to separate Qr and Qnr (see S1Supporting Informa-tion for a nonzero k). The calculated Q factors superimposedon the experimental results are shown in Figure 2. The QtopAdv. Optical Mater. 2024, 12, 2301912 2301912 (2 of 8) © 2023 The Authors. Advanced Optical Materials published by Wiley-VCH GmbH 21951071, 2024, 6, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/adom.202301912 by Cochrane Japan, Wiley Online Library on [28/02/2024]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons Licensehttp://www.advancedsciencenews.comhttp://www.advopticalmat.dewww.advancedsciencenews.com www.advopticalmat.deFigure 1. Silicon metasurfaces at qBICs. a) Schematic of a silicon metasurface fabricated on an SOI wafer composed of two parallel asymmetric rodswith an asymmetry parameter 𝛼 = 2ΔL/L. b) Representative SEM image of fabricated silicon metasurface (𝛼 = 0.2). c) Simulated cross-sections of the|E|2 profiles at the resonance peak wavelength (upper) and the spatially averaged |E|2 spectrum (lower) in the xy-plane at half the height of the siliconmetasurface (𝛼 = 0.2). The white cones indicate the displacement current distributions. d) Simulated and e) Experimental transmission spectra. Thedashed lines indicate the approximate peak positions of the qBIC modes. The spectra are vertically shifted for clarity in (e). The qBIC modes were excitedby vertically incident x-polarized light. The right panel in (e) shows the SEM images of the measured metasurface with 𝛼 = 0, 0.06, 0.12, 0.18, 0.24, and0.30 from top to bottom.is well fitted by the well-known relationship that holds for theasymmetry parameter 𝛼 added to the nanostructure:[23]Qr = Q0𝛼−2 (4)The fitting line gives a constant value Q0 of 22.7, signifyingthat the radiative component of the external medium, particularlyin the upward direction of the metasurfaces, originates from theqBIC modes. Although SiO2 has a small absorption around theresonance wavelength in our work,[37] the relation Qnr >Qbottom isfulfilled for all values of 𝛼. This implies that the limiting factor ofthe total Q factors is neither the absorption loss nor the scatteringloss, but the leakage loss into the bottom oxide layer of the SOIwafer.[38] This significantly limits the total Q factors, especially fora small 𝛼. The existence of leakage losses is also evident from thefield intensity for the cross-section in the yz-plane (Figure 2b) atthe center of the pair-rod. The total Q factor, Qtot, was calculatedusing Equation (2), with Qnr as the fitting parameter, agreed wellwith the experimental Qtot. This result suggests that our analyti-cal model is sufficient for explaining the experimental Q factorsobtained for silicon metasurfaces using SOI wafers. It may benoted that the downward leaky losses can be reduced if the BOXlayer is sufficiently thick to optically separate the confined qBICmode from the bottom silicon substrate, as discussed later.2.2. Coupling between qBIC Modes and PMMA MoleculesNext, a 111-nm PMMA layer was spin-coated onto a bare meta-surface to characterize the coupling between the qBIC mode andAdv. Optical Mater. 2024, 12, 2301912 2301912 (3 of 8) © 2023 The Authors. Advanced Optical Materials published by Wiley-VCH GmbH 21951071, 2024, 6, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/adom.202301912 by Cochrane Japan, Wiley Online Library on [28/02/2024]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons Licensehttp://www.advancedsciencenews.comhttp://www.advopticalmat.dewww.advancedsciencenews.com www.advopticalmat.deFigure 2. Effect of leakage losses into the high-index substrate of SOI wafer. a) Q factors of metasurfaces with different 𝛼. Qtop (blue dots) and Qbottom(green line) represent Q factors that contribute to upward and downward radiations, respectively, calculated by FDTD. Qtop is fitted to Equation (4)(dashed line). Qnr (orange line) is determined so that the experimental Qtot (purple dots) is fitted with the theoretical Qtot (black line), which is calculatedby summing all the loss contributions above. b) Simulated |E|2 profile (left) and Ex profile (right) in the yz-plane at the center of the unit cell for themetasurface with 𝛼 = 0.2.the C═O stretching mode of PMMA. For the simulation, thedispersive dielectric constant of the PMMA molecules was mod-eled as a single-oscillator Lorentz permittivity whose parameterswere experimentally determined using an infrared spectro-scopic ellipsometer (see the Experimental Section). Figure 3a,bcompares simulation and experimental spectra, respectively.Although there was a slight detuning between the qBIC modesand the C═O stretching modes of the PMMA absorption in theexperiment, it was in good agreement with the simulation. Splitpeaks centered at the wavelengths of the C═O mode appearedwhen 𝛼 was large. The amplitudes of the split modes increasedwith 𝛼; however, the split modes 𝜆+ and 𝜆− were nearly constant(Figure 3c). Note that the middle peak in the spectrum with atriple lineshape, especially when 𝛼 is small, may be attributedto intrinsic uncoupled PMMA molecules and/or intermolecularinteractions for high molecular density.[39]To explore the properties of the split modes in more detail, weconsidered the eigenvalues of the coupled qBIC-PMMA system,which gives two energy states as follows:[5]𝜔± =𝜔c + 𝜔m2− i2(𝛾c + 𝛾m)±12√4g2 +[(𝜔c − 𝜔m)− i(𝛾c − 𝛾m)]2(5)where 𝛾c and 𝛾m are the loss rates of the qBIC and vibrationalmodes, respectively (2𝛾c and 2𝛾m are the respective full width athalf maximum). g is the coupling rate between the qBIC and vi-brational modes. The two energy states were evaluated by observ-ing the anti-crossing behavior in structures with varied detuning( = 𝜔c − 𝜔m). Specifically, we fabricated PMMA-coated metasur-faces (𝛼 = 0.12) with scaling factors S from 0.95 to 1.05, whichallowed us to linearly tune the qBIC resonance wavelengths.Figure 3d–f compares the FDTD-simulated spectra, experimen-tal spectra, and plots of the experimental peak positions, all ofwhich showed good agreement. When there is no detuning (𝜔m= 𝜔c), Rabi splitting Ω is expressed as follows:Ω = 𝜔+ − 𝜔− =√4g2 − (𝛾c − 𝛾m)2 (6)In the experiment, Ω = 5.30 meV was obtained, as shown inFigure 3f, suggesting that the strong coupling condition[40] g >𝛾m, 𝛾c was satisfied (2𝛾m = 2.24 meV, 2𝛾c = 2.69 meV) when 𝛼= 0.12. Under this condition, the two newly formed polaritonmodes never cross each other, which is known as anti-crossingbehavior. Considering almost constant Ω = 5.30 meV and 2𝛾m =2.24 meV for all 𝛼, the coupling condition was changed by chang-ing the linewidths of qBIC modes 2𝛾c. A rough estimate indicatedthat the boundary between the strong and weak coupling regimesof 𝛼 was ≈0.27. Specifically, the strong coupling condition abovewas satisfied when 𝛼 < 0.27, and the weak coupling condition g <𝛾m, 𝛾c was satisfied when 𝛼 > 0.27. This result clearly shows thatthe coupling conditions can be tailored using the asymmetry pa-rameter 𝛼 of silicon metasurfaces. In an earlier study, changingthe radiative Q factors also affected the resonance wavelengths ofmetasurfaces.[24] In contrast, in our BIC metasurfaces, only theQ factors were changed while maintaining the resonance wave-lengths when the asymmetry parameters were changed. This pro-vides an effective means of controlling the coupling conditionswith vibrational transitions.2.3. Enhanced Molecular SignalTo predict the theoretical molecular signal strength andexplore the dominant factor of surface enhancement ef-fects in the coupled qBIC-PMMA system, we used thetemporal coupled mode theory (TCMT).[41] Figure 4a dis-plays the TCMT model of a coupled cavity-molecular sys-tem with two input ports, namely, input traveling waveAdv. Optical Mater. 2024, 12, 2301912 2301912 (4 of 8) © 2023 The Authors. Advanced Optical Materials published by Wiley-VCH GmbH 21951071, 2024, 6, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/adom.202301912 by Cochrane Japan, Wiley Online Library on [28/02/2024]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons Licensehttp://www.advancedsciencenews.comhttp://www.advopticalmat.dewww.advancedsciencenews.com www.advopticalmat.deFigure 3. Coupling between qBIC modes in silicon metasurfaces and PMMA molecules. a) Simulated transmission spectra of coupled qBIC-PMMAsystem with different 𝛼. Inset shows the chemical structure of PMMA. b) Experimental transmission spectra, and c) split modes 𝜆+ and 𝜆− as functionsof 𝛼. Dashed lines represent the respective average values. d) Simulated anti-crossing behavior in the coupled system, obtained from the metasurfaceswith different scaling factors S. e) Experimental transmission spectra. f) Experimental peak positions of the split modes (red dots) and the superimposedeigenvalues of Equation (5). Ω represents Rabi splitting. The dashed line represents the peak wavelength of the qBIC modes, and the dotted linerepresents the absorption wavelength of the PMMA molecules. The spectra are vertically shifted for clarity in (b,e). The qBIC modes were excited byvertically incident x-polarized light.s+ = [s1+ s2+]T and output traveling wave s− = [s1− s2−]T.From the coupled mode equations, the transmission amplitudeof the transverse electric (TE)-like mode can be derived (seeS1Supporting Information) by considering the reflection coeffi-cient s1−/s1+, as follows:T = 1 −|||||s1−s1+|||||2= 1 −||||||||r −2ei2𝜃1𝜏1i(𝜔 − 𝜔c)+ 1𝜏1+ 1𝜏2+ 1𝜏nr+ g2i(𝜔−𝜔m)+ 1𝜏m||||||||2(7)Here, we assume that the coupled system couples outside themedium with an upward radiative rate of 𝜏1−1 = 𝜔cQtop−1/2 anda downward radiative rate of 𝜏2−1 = 𝜔cQbottom−1/2. The nonra-diative rate 𝜏nr−1 accounts for material absorption and scatteringlosses as 𝜏nr−1 = 𝜔cQnr−1/2 = 𝜔c(Qabs−1 + Qscat−1)/2. 𝜃1 is thephase related to the coupling coefficient between the two portsand resonance modes. In SOI wafers, the transmission spec-trum has a broad Fabry–Perot (FP) background owing to FP res-onances in the oxide layer. The interference between the broadbackground spectrum and the sharp qBIC mode explains theFano lineshape in the qBIC modes, which is expressed by thereflection coefficient r and transmission coefficient t in Equa-tion (7). Next, we define the relative transmittance Tr = T − T|𝛼 = 0Adv. Optical Mater. 2024, 12, 2301912 2301912 (5 of 8) © 2023 The Authors. Advanced Optical Materials published by Wiley-VCH GmbH 21951071, 2024, 6, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/adom.202301912 by Cochrane Japan, Wiley Online Library on [28/02/2024]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons Licensehttp://www.advancedsciencenews.comhttp://www.advopticalmat.dewww.advancedsciencenews.com www.advopticalmat.deFigure 4. TCMT analysis and enhanced molecular signal of the coupled qBIC-PMMA system. a) TCMT model of a two-port system interacting betweena metasurface (cavity) and vibrating molecules. b) Experimental relative transmittance spectra for 𝛼 = 0.18. Tr|g = 0 and Tr represent the transmittanceamplitudes of the qBIC (red) and coupled qBIC-PMMA (blue) modes at the frequency 𝜔c (dashed line). c) Transmittance difference spectra Tr − Tr|g = 0for different 𝛼. For clarity, the spectra were shifted vertically. d) Peak amplitudes T of the qBIC modes for different 𝛼 obtained experimentally (red dots)and the TCMT model (black line, Equation (7)) e) Enhanced molecular signal ΔT for different 𝛼 obtained experimentally (purple dots) and the TCMTmodel (black line, Equation (8)).obtained by subtracting the transmittance for 𝛼 = 0, to excludethe influence of the middle peak of the triple peak appearing inthe transmission of a coupled qBIC-PMMA mode, because Equa-tion (7) does not take this effect into consideration. We then de-fined the enhanced molecular signal as follows:[29,30]ΔT = Tr − Tr||g=0 (8)This expression represents the transmission difference withand without PMMA molecules at a frequency of 𝜔c as depictedin Figure 4b. Here, the Tr|g = 0 spectra were redshifted by con-sidering the increase in the refractive index of the cladding layerwhen the PMMA molecules were adsorbed on the metasurface(the extent of redshift was determined by FDTD simulation). Ex-perimentally, ΔT was determined from the transmittance differ-ence peak at a frequency 𝜔c (Figure 4c). Figure 4d,e shows theexperimental transmittance dip amplitude T and the enhancedmolecular signal ΔT, superimposed on their theoretical mod-els obtained by considering a fundamental bound on 𝜏1/𝜏2 con-strained by (1 + r)/(1 − r).[42,43] Good agreement with the experi-mental results validates the theoretical models and shows that thedependencies of the radiative losses on 𝛼 significantly change Tand ΔT. Importantly, we can determine the existence of the op-timum 𝛼, where the highest molecular vibrational signal is ob-tained. The optimum 𝛼 was ≈0.24 under the present conditions.It should be noted that we implicitly assumed here that the cou-pling strength g does not depend on the asymmetry parameter𝛼 for the calculation of ΔT using TCMT formalism. This is rea-sonable considering that the energy splitting was almost inde-pendent of 𝛼, as can be seen in Figure 3b,c. This was also truefor the FDTD simulations. The constant peak splitting indicatesthat the 𝛼-dependence of the enhanced molecular signal ΔT isnot caused by changes in g but by the radiative loss engineeringof qBIC modes.[39,44]Finally, to explore the effect of the downward leaky losses, wecalculate the enhanced molecular signal, ΔT, for different BOXlayer thicknesses. Figure 5a shows the calculated Qbottom, which islimited by the leaky losses toward the high-index substrate. Here,the scaling factors of the metasurfaces with different BOX thick-nesses are slightly tuned such that the peak wavelengths of theqBIC modes and PMMA absorption match. As can be seen, theQbottom becomes larger ( = lower leaky losses) and follows the typ-ical 𝛼−2 dependence for the qBIC modes when the BOX layeris thicker. Figure 5b shows the calculated ΔT. The optimum 𝛼at which the maximum ΔT is obtained is shifted to a smaller𝛼, and the molecular signal strength increases when the BOXlayer is thicker. These findings reveal the importance of control-ling leaky losses and material choices. Specifically, a symmetriccladding with a small refractive index provides a higher molec-ular signal. However, a thick oxide layer produces unwanted FPresonances with a narrow peak wavelength spacing, which some-times hinders weak qBIC and vibrational modes. Therefore, BOXlayer thickness should be carefully designed depending on theresonance wavelength to be measured. Fortunately, the 2000-nmAdv. Optical Mater. 2024, 12, 2301912 2301912 (6 of 8) © 2023 The Authors. Advanced Optical Materials published by Wiley-VCH GmbH 21951071, 2024, 6, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/adom.202301912 by Cochrane Japan, Wiley Online Library on [28/02/2024]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons Licensehttp://www.advancedsciencenews.comhttp://www.advopticalmat.dewww.advancedsciencenews.com www.advopticalmat.deFigure 5. Effect of BOX layer thickness on a) Qbottom originating fromdownward leaky losses and b) enhanced molecular signal ΔT for different𝛼. All the data points are calculated using the FDTD simulation, assumingnonzero material absorptions.BOX layer in our work offered a moderate and sufficient back-ground around the resonance wavelength of the qBIC mode (seeS1Supporting Information for more details), which provided ameans for measuring the resonance dips and their enhancedmolecular signals.3. ConclusionIn this study, we have experimentally and theoretically performedvibrational coupling to the qBIC modes of silicon-based metasur-faces from weak to strong coupling regimes and demonstrated anenhanced molecular signal in infrared absorption. The couplingconditions were tuned by changing only the structural asym-metrical parameters of the asymmetric pair-rod arrays, whichwere responsible for the changes in the radiative losses. Wehave shown the existence of an optimum asymmetry at whichthe highest molecular signal is obtained, indicating surface en-hancement effects originating from the radiative loss engineer-ing of silicon-based metasurfaces. The wide tunability of radiativelosses in dielectric metasurfaces favors the optimization of thecoupling conditions of the vibrational mode, opening up poten-tial applications for highly sensitive surface-enhanced infraredspectroscopy without using metals. Although the total Q factorsof the coupled system are limited by leakage loss into the high-index bottom substrate, the use of SOI wafers allows the massproduction of sensor chips, which is a significant advantage ofusing complementary metal-oxide semiconductor compatible di-electric materials. We believe that these findings can be appliedto future research, including protein sensing,[45] identification ofsmall numbers of molecules,[46] and modification of chemical re-action rates under strong coupling[47] using all-dielectric meta-surfaces with optimized radiative losses.4. Experimental SectionFabrication: Silicon metasurfaces were fabricated from an SOI waferwith 400-nm c-Si and 2000-nm SiO2 layers. The SOI wafer was cleaned withacetone and isopropyl alcohol (IPA) for 10 min each in an ultrasonic bath.A positive resist (ZEP-520A, Zeon Chemicals) with a thickness of 100 nmwas spin-coated at 6000 rpm for 60 s onto the SOI wafer and prebaked ona hotplate at 180 °C for 3 min. Subsequently, a conductive layer (ESPACER300Z) was spin coated at 2000 rpm for 60 s. A nanopattern (3 mm× 3 mm)was prepared using electron-beam lithography (ELS-BODEN, Elionix) atan acceleration voltage of 100 kV. The samples were then developed us-ing xylene and IPA. Finally, the nanopatterns were transferred into the c-Silayer using silicon deep reactive ion etching equipment (MUC-21 ASE-SRE,Sumitomo Precision Products) with SF6 and C4H8 gases (Bosch process).The remaining resist was removed via O2 plasma ashing for 20 min.Characterization: The transmission spectra of the 3 mm × 3 mm sam-ple were acquired using a Fourier transform infrared spectrometer (Nico-let iS50R, Thermo Fisher Scientific) with a spectral resolution of 4 cm−1equipped with a liquid nitrogen-cooled mercury cadmium telluride detec-tor. The polarization direction of the incident light was polarized in the x-direction using a wire-grid polarizer. To couple the PMMA molecules withthe silicon metasurfaces, PMMA (950 A2) was spin-coated at 1500 rpmfor 60 s onto the surface and baked on a hotplate at 180 °C for 90 s. Indetermining the real and imaginary parts of the refractive index (n, k) ofthe PMMA molecules, an infrared spectroscopic ellipsometer (SENDIRA,SENTECH Instruments GmbH) was used. The absorption of the PMMAmolecules was then modeled as a permittivity, represented by the Lorentzmodel:[44]𝜀PMMA = 𝜀∞ +f0𝜔20𝜔20 − 𝜔2 − i𝜔Γ(9)where the background dielectric constant of PMMA molecules 𝜖∞ = 2.20,Lorentz resonance frequency 𝜔0 = 3.252 × 1014 rad/s, strength coefficientf0 = 0.016, and Lorentz damping rate Γ = 3.41 × 1012 rad/s.Simulation: Transmission spectra, electric field distributions, and Qfactors were acquired using a FDTD solver (ANSYS Lumerical). Blochboundary conditions were used in the x and y directions, and perfectlymatched layers were used in the ±z direction. In all simulations, an x-polarized plane wave was normally incident to the metasurfaces. The ex-act structural parameters were extracted from SEM images of the fabri-cated metasurface. The dielectric functions of Si and SiO2 were taken fromliterature by Palik.[48] For the calculation of radiative Q factors, the c-Siand SiO2 were assumed to be lossless (k = 0) to ignore the absorptionlosses Qabs−1, and their refractive indices were set to be 3.4 and 1.28,respectively, in the wavelength range of interest. To simulate the coupledqBIC-PMMA system, the dielectric function of the C═O stretching mode ofPMMA molecules was modeled using Equation (9), which was experimen-tally determined using a spectroscopic ellipsometer, as described above.Supporting InformationSupporting Information is available from the Wiley Online Library or fromthe author.AcknowledgementsThis work was financially supported by the JSPS KAKENHI Grant NumberJP22K20496. The authors thank Kazuaki Sakoda for technical support inthe sample fabrication. The fabrication of the silicon metasurfaces wasconducted at the Nanofabrication Platform and Namiki Foundry in NIMS.Adv. Optical Mater. 2024, 12, 2301912 2301912 (7 of 8) © 2023 The Authors. Advanced Optical Materials published by Wiley-VCH GmbH 21951071, 2024, 6, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/adom.202301912 by Cochrane Japan, Wiley Online Library on [28/02/2024]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons Licensehttp://www.advancedsciencenews.comhttp://www.advopticalmat.dewww.advancedsciencenews.com www.advopticalmat.deConflict of InterestThe authors declare no conflict of interest.Data Availability StatementThe data that support the findings of this study are available from the cor-responding author upon reasonable request.KeywordsBIC, metasurfaces, SEIRA, spectroscopy, strong couplingReceived: August 8, 2023Revised: September 16, 2023Published online: October 27, 2023[1] T. Tanaka, T. A. Yano, R. 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Advanced Optical Materials published by Wiley-VCH GmbH 21951071, 2024, 6, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/adom.202301912 by Cochrane Japan, Wiley Online Library on [28/02/2024]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons Licensehttp://www.advancedsciencenews.comhttp://www.advopticalmat.de