Narrow-band and highly absorbing fano resonance in a cavity-coupled dielectric metasurface

Metamaterial resonance offers a flexibility in engineering the frequency and bandwidth of light absorption for a variety of optoelectronic applications such as wavelength-selective photodetection, optical sensing and infrared camouflaging etc. In this paper, we demonstrate a class of metal-dielectric thin-film cavity-coupled dielectric metasurfaces, which feature Fano resonances with both narrow bandwidth and strong light absorption. Our fabricated metasurface consists of a Si cuboid array on top of a SiO2 film backed with a metallic Cu layer. The weak coupling between electric mie mode in Si cuboid and Fabry–Perot mode within the SiO2 spacer layer yields a Fano resonance at 4.19 μm wavelength, which exhibits a strong light absorption of 65.8% and a quality (Q) factor of 112. The strongly absorbing Fano resonance is tunable within the 3–5 μm band by varying geometric parameters of the metasurface. To reveal potential application of the metasurface, the Fano resonance is applied in refractive index sensing and exhibits a sensitivity of 518.75 nm RIU−1 and a figure-of-merit (FoM) of 14.82 RIU−1. These results suggest that cavity-coupling presents an effective way in reducing the resonance bandwidth and enhancing light absorption in dielectric metamaterials, which holds promise for expanding the properties and device functionalities of metamaterials.


Introduction
Metamaterials made of periodic subwavelength units present a flexible way for manipulating light absorption properties that are not otherwise available in natural materials.With innovations in metamaterial structures and resonance modes, high efficiency light absorption has been demonstrated in a variety of spectral forms such as single-band, multi-band, or broadband spectra [1][2][3].Based on resonance-enhanced light-matter interaction, metamaterials have become a promising platform for developing non-invasive and sensitive biosensors [4,5].In addition, by breaking the time-reversal symmetry with a magnetic field, novel nonreciprocal properties such as unidirectional light absorption and scattering have been reported in magnetic metamaterials, which have added new degrees of freedom for light manipulation [6][7][8].
Narrow-band light absorption of metamaterials is especially important for emerging applications such as high-resolution optical filtering, wavelength-selective photodetection, and thermophotovoltaics etc.One common metamaterial design to realize near-perfect light absorption is the metal-insulator-metal (MIM) structure [9].Though wavelength-selective light absorption is readily achievable at resonance in such MIM metamaterials, their quality (Q) factors are often less than 20 as resulted from the large Ohmic loss in metals [10][11][12][13], which presents a bandwidth limitation in consideration of spectral resolution in many applications.
To reduce the resonance bandwidth, dielectric metamaterials have been developed by using transparent materials without metals.Metasurfaces made of micro and nanopillars of different materials such as Te, Si, Ge and TiO 2 have been fabricated [14][15][16][17], which exhibited sharp resonance in reflection or transmission spectrum with a Q factor up to 728.These dielectric metasurfaces enable an agile control over the phase of light, and have been applied in a number of applications such as metalens [18], hologram [19] and molecular fingerprint sensing [20], etc.These lossless dielectric metasurfaces, however, intrinsically do not absorb light, limiting their applications in cases involving optoelectronic and photothermal conversions such as photodetection and thermal management etc.One strategy for achieving both high Q factor and strong light absorption in dielectric metamaterial is to incorporate absorptive dielectric material in a structure with two spectrally overlapped modes at the critical coupling condition [21].Destructive interference of the two degenerate modes leads to suppression of radiative loss and enhancement of light absorption within the lossy dielectric material.Using simultaneously excited electric and magnetic dipoles, strong absorption of over 70% were demonstrated in dielectric metasurfaces made of Ge and Si nanopatches, however their Q factors were still limited to less than 50 [22,23].A Howes et al further improved the Q factor to 170 by taking advantage of the unique dispersion of SiC at midinfrared wavelengths [24].Recently, J Yu et al extended the design concept to the case of nonorthogonal-mode system by using two quasi bound state in the continuum (QBIC) modes [25].Besides the approach of using two degenerate mie modes, coupling between a mie mode and a cavity mode represents another approach, which holds potential for realizing larger Q factor.V Mylnikov and J Lu et al demonstrated lasing and enhanced photodetection response by using Fabry-Perot-enhanced Mie resonances in GaAs nanocylinder [26] and silicon nanopillar [27], respectively.Very recently, J Yu et al reported a narrow-band absorbing resonance with Q factor up to 282 by using an all-dielectric structure, whose resonance absorption is restricted to the near-infrared wavelengths as limited by bandgap of the used semiconducting Ge film [28].In addition, by using special modes of optical anapole and Wood anomaly in metal-dielectric disk arrays, R Li and J Chen et al have revealed strongly absorbing resonances with bandwidths of a few nanometers in theory at visible and near-infrared wavelengths [29,30].In this paper, we present a metal-dielectric scheme for coupling dielectric metasurface with an Fabry-Perot thin-film cavity, which opens up a pathway for obtaining high Q and strongly absorbing resonance in the mid-infrared region without material bandgap limitation.A Fano resonance with 65.8% absorption efficiency and a high Q factor of 112 (1627 in simulation) is observed at 4.19 μm wavelength, and is tunable in the midinfrared band by varying the geometrical structure parameters.These results indicate that cavity-coupled dielectric metasurface offers an effective way for obtaining both high Q factor and strong resonance absorbance, which holds promise for high spectral resolution applications.

Design and fabrication
Our designed structure is depicted in figure 1(a), consisting of a Si cuboid array on top of a SiO 2 spacer layer and a metallic Cu film.The Si cuboids form a lossless dielectric metasurface, while the SiO 2 and Cu films form a Fabry-Perot cavity.The Cu film is chosen as the reflective ground plane for our convenience in fabrication, and it can be replaced with other noble metals.Mie mode excited within the Si cuboid couples with the underlying thin-film cavity, leading to a narrow-band Fano resonance with enhanced light absorption.Analytically, mie resonances in the Si cuboid can be described with the dielectric resonator theory [31].Under perfect magnetic wall boundary, standing-wave resonances are present within the Si cuboid, which can be classified as electric modes TE m,n,q+δ and magnetic modes TM m,n,q+δ , where m, n and q are the mode orders, and δ is a parameter describing the field fringing effect.For TE m,n,q+δ electric modes, their electric fields are in plane within the x-y plane, and the magnetic fields are out of plane along z direction.For TM m,n,q+δ magnetic modes, their magnetic fields are in x-y plane, while the electric fields are along z direction [32].Resonance wavelength of the electric or magnetic mode is given by where a, b and h are dimensions of the Si cuboid and ε r is the permittivity of Si. k 0 and α z are wavenumber and decay coefficient in vacuum, and k z is the wavenumber component in z-axis direction.The parameter g = 1 for TE m,n,q+δ electric modes and g = ε r for TM m,n,q+δ magnetic modes.Among above different orders of modes, we focus on the TE 1,2,δ mode, which is often termed toroidal dipole in literature [33].Magnetic fields of the TE 1,2,δ mode form strongly localized vortices.Due to its small radiative loss and high Q factor, we choose the TE 1,2,δ mode in our metasurface design and couple it to an underlying metal-dielectric film cavity.The Fabry-Perot resonance within the SiO 2 cavity is given by where k is the wavenumber in SiO 2 layer, which has a thickness of d. j is the reflection phase on SiO 2 /air and SiO 2 /Cu interfaces.By using equations (1) and (2), the TE 1,2,δ electric mode and the cavity mode can be designed at similar frequencies.Their coupling could lead to a narrow-band Fano resonance as well as an enhanced light absorption in the Cu metal.For a qualitative calculation on the resonance absorption properties, we used a commercial numerical finite-difference time-domain (FDTD) model to calculate absorption spectrum and the resonant mode properties.Reported experimental refractive indices data are used for the Si and SiO 2 [34,35].The Cu is described by a Drude model [36] with plasma frequency of 6.38 × 10 4 cm −1 and damping frequency of 2.78 × 10 2 cm −1 .To calculate resonance at both normal and oblique incidence conditions, we used plane-wave excitation and Bloch boundary condition in the model.The three-dimensional unit-cell domain is discretized into approximately 1 × 10 6 rectangular conformal mesh elements with a minimum size of 13.7 nm.A simulation time of 5 × 10 4 fs is discretized at time step of 0.013 fs to meet the convergence condition such that light intensity within the simulation volume decays to less than 1 × 10 −6 .
In our design strategy, we used both analytical approach and numerical FDTD model.We first used equations (1) and (2) to design the frequency of the Fano resonance within our interested mid-infrared region.This analytical calculation allows us to determine approximate geometric sizes of the metasurface structure.On the basis of initial structure, we next used numerical FDTD model to calculate the resonant reflection and absorption spectra of the metasurface.The geometric sizes of the silicon cuboid and the SiO 2 film thickness were scanned and optimized for searching for both minimum bandwidth and maximum resonance absorption.Figure 1(b) shows the simulated absorption spectra of one optimized metasurface structure at normal incidence.Dimensions of the Si cuboid are a = 1 μm, b = 2.1 μm, and h = 0.6 μm.The periods are P x = 2 μm, and P y = 3 μm.Thickness of the SiO 2 layer is d = 1.2 μm.The black curve shows transmission spectrum of the Si cuboid metasurface on a SiO 2 substrate without underlying thin-film cavity.The TE 1,2,δ mode is excited at 4.28 μm.Its Q factor is 108.The blue curve shows the reflection spectrum of the SiO 2 /Cu films without top Si cuboids.The Fabry-Perot resonance appears at 4.2 μm with a broad bandwidth.For our designed Si cuboid metasurface with underlying SiO 2 cavity, as shown in the red curve, the TE 1,2,δ mode slightly blue-shifts and its bandwidth is significantly reduced as a result of the cavity-coupling.Due to the small resonance amplitude and large bandwidth of the Fabry-Perot mode, its spectral feature is barely seen in the coupled Fano resonance.Full width at half maximum (FWHM) of the Fano resonance is 2.63 nm, corresponding to a Q factor of 1627, which is about 15 times of the value for the metasurface without cavity-coupling.The resonant absorption of the cavity-coupled TE 1,2,δ mode is 96.9%. Figure 1(c) shows electric fields of the cavity-coupled TE 1,2,δ mode.Two current loops with opposite circulating directions are formed within the x-y plane, which create head-to-tail connected magnetic field vortex in y-z plane as shown in figure 1(d).Electromagnetic fields of this TE 1,2,δ mode is largely confined within lossless Si cuboid, which contributes to less optical loss and a narrow resonance bandwidth.
Figure 2 shows calculated absorption spectra of our cavity-coupled silicon cuboid metasurface as we varied the structural sizes and the incident angle.As shown in figure 2(a), as width of the silicon cuboid a increases, the Fano resonance monotonically redshifts, which is consistent with the analytical result of equation (1).Meanwhile, the absorption efficiency also changes with the silicon cuboid width.A maximal absorption of 96.9% is obtained for width of a = 1 μm.As period of the silicon cuboid varies, resonant wavelength of the Fano mode remains nearly unchanged, as shown in figure 2(b).The period affects the absorption efficiency.The maximal resonant absorption is obtainable at period of P x = 2 μm. Figure 2(c) shows the absorption spectra for different cavity thicknesses.Similarly, the SiO 2 film thickness mainly affects absorption efficiency but not frequency of the Fano mode.The optimal thickness is d = 1.2 μm according to the highest resonant absorption.Results of these size parameter variations suggest that the metasurface structure described in figure 1 is optimized for obtaining both narrow bandwidth and strong resonant absorption.In addition, as the incident angle increases from 0°to 30°, as shown in figure 2(d), the absorbing Fano resonance blueshifts from 4.28 μm to 4.02 μm.Meanwhile, its absorption decreases from 96.9% to 66.9% with degraded Q factor due to decoupling between the TE 1,2,δ mode and the Fabry-Perot mode.Therefore, our designed Fano resonance is expected to be sensitive to the incident angle.The resonances at longer wavelengths of 4.66 μm (at 10°), 4.87 μm (at 20°) and 5.13 μm (at 30°) are the TE 1,1,δ modes, whose detailed analysis will be given in next section.
To reveal wavelength tuning of the absorbing Fano resonance, we designed three sample structures as listed in table 1.For each target wavelength around the 3-5 μm infrared-transmitting window, we first designed the sample structure analytically using equations (1) and (2), and then optimized the geometric parameters with numerical FDTD model for searching both minimum bandwidth and maximum resonance absorption.Table 1 gives the detailed structure parameters of samples A-C.By varying structural parameters, the resonance wavelength is shifted from 3.57 μm to 5.14 μm.The three designed samples show small FWHMs of 2.3-2.63 nm and Q factors of 1488-2234, as calculated from the ratio of the resonance frequency to the FWHM of the  absorption peak.Meanwhile, resonant absorptions of the three samples are 90.8%-96.9%,manifesting the effectiveness of our used cavity-coupling approach for obtaining both high Q factor and strong light absorption.
In fabrication process, the Cu and SiO 2 films were sequentially deposited on a 4-inch silicon wafer by using e-beam evaporation, while the amorphous silicon layer was synthesized using magnetron sputtering.Refractive indices and thicknesses of SiO 2 and the amorphous silicon layers were measured by using an ellipsometer.The amorphous silicon cuboid array was fabricated using stepper photolithography and reactive-ion etching.During reactive-ion etching, SF 6 gas was used to selectively etching amorphous silicon on top of the SiO 2 .Top-view and cross-section images of a representative sample B are given in figure 3, as measured with a scanning electron microscope (SEM) at 5 kV electron high tension (EHT).Area of the fabricated Si cuboid array is 0.8 cm × 0.8 cm.Sizes and periods of the Si cuboids are close to our designed values with a slight deviation of less than 4%.Due to imperfection of reactive-ion etching, an about 78 nm Si residue layer remained unetched.In addition, edges of the Si cuboids are slightly rounded and the sidewalls are not ideally vertical.

Measurement results and analysis
To measure absorption spectra of our metasurface samples, Fourier transform infrared (FTIR) reflection spectroscopy is utilized.Incident IR light is focused on samples with an 8-inch focal length off-axis parabolic mirror.The reflected light is collected with a second off-axis parabolic mirror and then is measured with a mercury cadmium telluride (MCT) detector.The sample and the MCT detector positions are controlled with two co-axial motorized rotation stages, which allow the incident angle to be varied from 15°to 75°.Since light transmission is zero in our sample structure with metal ground plane, absorption spectra is readily obtained by subtracting the reflection from unit. Figure 4(a) shows our measured and simulated absorption spectra of the sample B at an incident angle of 15°.As shown in experimental red curve, cavity-enhanced TE 1,2,δ electric resonance is observed at 4.19 μm wavelength, close to the simulation result as given by the black curve.The slight redshift of the resonance as compared with calculated result is due to imperfect fabrications including the sidewall geometrical deviations and the residue unetched silicon layer as revealed in figure 3. The Q factor and bandwidth of the measured Fano resonance are 112 and 37.5 nm, while the simulated ones are 1627 and 2.63 nm.There is an extra spectral dip at 4.88 μm, which appears at oblique 15°incidence angle but not at normal incidence.This mode corresponds to our calculated resonance at 4.754 μm as shown in figure 4(b).It is the fundamental TE 1,1,δ electric dipole mode with strong magnetic field in z-direction, which couples with incident light only at oblique incident angle.In addition, there is also a spectral dip feature observed at 6.14 μm,  which is attributed to impurity defect absorption of SiO 2 .In our above measured spectra, besides the Fabry-Perot cavity mode existing between the SiO 2 /Cu and Si/SiO 2 interfaces, no other light interference effects are observed.Also since the period of our sample is less than the resonance wavelength, light scattering from diffraction orders is also not present within our measured wavelength range [37].
Our above measured Q factor of the cavity-coupled TE 1,2,δ mode is one order of magnitude less than the theoretical value.The discrepancy likely originates from fabrication imperfection and inaccuracy of modelled material properties.Figure 5 shows our calculated absorption spectra of sample B by considering geometry imperfection and optical loss of the Si cuboid.For silicon cuboids with imperfect sidewall geometry and the 78 nm Si residue layer as revealed in SEM image in figure 3, Q factor of the calculated Fano resonance reduces to 956 as revealed in blue spectrum.On the other hand, as optical loss is considered for silicon with a refractive index of 3.2+0.014i[38], our calculated Q factor of the Fano resonance is only 134 as shown in the black spectrum, which suggests that optical loss of silicon plays an even more significant role in affecting Q factor of the cavity-coupled TE 1,2,δ resonance.As the geometry imperfection and optical loss of silicon are both considered as shown in green spectrum, the calculated Q factor of the metasurface further reduces to 129, very close to our experimental value of 112.These simulated results indicate that deviation of optical properties of silicon is likely a major factor accounting for the discrepancy between experiment and theory.As for the second TE 1,1,δ mode at 4.88 μm (4.754 μm in theory), its measured absorption is much less than the simulated value as evident in figure 4(a).This discrepancy is also due to fabrication imperfection and inaccuracy of modelled material properties as supported by the comparison results in figure 5.
To have better understanding on above observed narrow-band Fano resonance, we used a coupled oscillator model to illustrate coupling properties between the TE 1,2,δ electric mode and the Fabry-Perot mode in our designed metasurface.The TE 1,2,δ mode is represented by a harmonic oscillator with resonance frequency ω 1 and damping rate γ 1 , while the Fabry-Perot mode is represented by a second oscillator with resonance frequency ω 2 and damping rate γ 2 .The two oscillators have a coupling coefficient of ν 12 .Under external driving fields of a 1 e iωt and a 2 e iωt , motion equations of the two oscillators are written by [39] g w n g w n By assuming the displacements as x 1 = c 1 e iωt and x 2 = c 2 e iωt , amplitudes of two oscillators c 1 and c 2 can be solved as With expressions of amplitudes c 1 and c 2 , absorption spectrum of the coupled oscillators is obtained as We fitted the experimental spectrum with the coupled oscillator model.As shown as black dotted curve in figure 6, result of the coupled oscillator model is in good agreement with the measured spectrum.The fitting parameters are ω 1 = 71.63THz, γ 1 = 0.56 THz, ω 2 = 51.14THz, γ 2 = 550 THz, a 1 = 335.4THz 2 , a 2 = 3.8 × 10 −6 THz 2 , and ν 12 = 5 × 10 −6 THz 2 .The coupling coefficient ν 12 is much smaller than the damping rates of the two oscillators, which indicates that the narrow-band Fano resonance results from a weak coupling between the TE 1,2,δ electric mode and the Fabry-Perot mode [40].In addition, the driving force a 2 for the Fabry-Perot mode is significantly smaller than a 1 for the TE 1,2,δ electric mode, suggesting that coupling of the Fano resonance with external field is primarily through the TE 1,2,δ electric mode.It is also worthy to note that, though here we chose the TE 1,2,δ mode for constructing the narrow-band and highly absorbing Fano resonance, the cavity-coupling mechanism is applicable to other mie modes in dielectric metasurfaces.
We next studied polarization properties of the narrow-band Fano resonance mode.Figure 7(a) shows absorption spectra of the sample B at different polarizations while keeping the incident plane as y-z plane and the incident angle at 15°.The state of incident polarization is described with an angle relative to the s-polarization with electric field in x direction.As polarization angle increases from 0°to 90°, resonance of the cavity-coupled TE 1,2,δ mode becomes weaker and varnishes at p-polarization in y direction.In the meantime, a second mode starts to emerge at 4.025 μm, and its resonant intensity increases with polarization angle.Figure 7(b) shows magnetic fields of this resonance mode at 4.025 μm.A magnetic dipole in x direction is excited, suggesting the resonance is the TM 1,1,δ fundamental magnetic mode excited at p-polarization.Its electric fields have major components perpendicular to the silicon cuboid along z direction, as shown in figure 7(c).For an arbitrary polarization with direction between s and p polarizations, the TE 1,2,δ mode and the TM 1,1,δ mode are excited simultaneously.Therefore, the cavity-coupled Fano resonance is best excited at s-polarization.To demonstrate static tuning of the Fano resonance, we measured absorption spectra of samples A-C with different structural parameters.As shown in figure 8, Fano resonances occur at 3.71 μm, 4.19 μm, and 5.03 μm for samples A-C, respectively.Their absorption efficiencies are between 65% and 87%.Therefore, by varying the geometric dimensions, the narrow-band absorbing Fano resonance can be flexibly designed and tuned as required in many applications.As compared with theoretical results, our measured Fano resonance wavelengths have slight deviations of 2.2%-3.8%,as caused by fabrication imperfections of Si cuboid arrays and an oblique incident angle of 15°used in experiment.
As benefiting from the cavity-enhanced Q factor of the Fano resonance, our structure could be applied to high-resolution infrared sensing.Here, we take refractive index sensing as an example, which plays an important role in chemical and biomolecular monitoring [41].In experiment, we deposited SiO 2 film on top of our metasurface sample as the analyte.In order to access the sensing properties for a bulk refractive index change, we gradually increased thickness of the SiO 2 analyte film.1800 nm SiO 2 by using e-beam evaporation technique.The SiO 2 film covers the Si cuboid resonators, which yields a refractive index change of Δn = 0.4.Figure 9(b) shows reflection spectra of the sample B as the SiO 2 film thickness increases.Resonance wavelength of the TE 1,2,δ mode shows a red shift as the analyte thickness increases from 0 to 1800 nm.From these resonance shifts, the sensitivity S and figure-of-merit (FoM) can be obtained according to the definitions of S = Δλ/Δn and FoM = S/dλ [42], where the Δλ is the wavelength shift, dλ is the FWHM bandwidth of the resonance.As shown in figure 9(c), the sensitivity and FoM both increase with the SiO 2 analyte film thickness and nearly saturate at the thickness of 1800 nm, close to the situation of a bulk refractive index change.The maximum sensitivity and FoM are 518.75nm RIU −1 and 14.82 RIU −1 , respectively.
Several reported sensing properties of all-dielectric metasurfaces are listed in table 2 for comparison [43][44][45][46].Our metasurface sample exhibits improved sensing performance as resulted from higher Q factor and strongly enhanced near-field of the Fano resonance.As the measured Q factor of our metasurface sample is about one order of magnitude less than the theoretical limit, a large room can be expected for sensing performance improvement of our proposed cavity-coupled dielectric metasurface by optimizing the fabrication or by using other mie mode with narrower bandwidth such as magnetic quadrupole or anapole mode [47,48].Finally, since resonance frequencies of the mie mode and Fabry-Perot mode primarily depend on geometric sizes of the optical structure, our demonstrated narrow-band absorbing Fano resonance could be extended to other wavelengths in the visible and far-infrared spectral regions.

Conclusions
We have designed and fabricated a Si cuboid metasurface coupled with a metal-dielectric thin film cavity.Coupling of electric TE 1,2,δ mode presented in Si cuboid and the underlying Fabry-Perot mode produced a narrow-band Fano resonance with strong absorption.Our sample structure achieved a strong absorption of 65.8% and a Q factor of 112 at 4.19 μm in experiment, while the theoretical values of absorption efficiency and Q factor approached 96.9% and 1627, respectively.By varying geometric parameters of Si cuboid and SiO 2 spacer, the Fano resonance was tuned within the 3-5 μm mid-infrared spectral range.We also applied the narrow-band Fano resonance in refractive index sensing, which showed excellent sensitivity of 518.75 nm RIU −1 and FoM of 14.82 RIU −1 .These results suggest that cavity-coupled dielectric metasurface is a compelling scheme for obtaining strong absorption and narrow bandwidth at the same time, which could be useful for a wide range of applications, including refractive index sensing, thermal management and infrared camouflaging etc.

Figure 1 .
Figure 1.(a) Schematic of a cavity-coupled Si cuboid metasurface.(b) Simulated absorption spectrum of the cavity-coupled metasurface given in red curve.The black curve shows transmission spectrum of the Si cuboid metasurface on a SiO 2 substrate without underlying cavity, and the blue curve shows reflection spectrum of the SiO 2 /Cu film cavity for comparison.(c) and (d) show the electric fields and magnetic fields for resonance mode of the cavity-coupled metasurface at 4.28 μm wavelength.

Figure 3 .
Figure 3. (a) Top-view and (b) cross-section view SEM images of a representative metasurface sample B.

Figure 4 .
Figure 4. (a) Measured and calculated absorption spectra of sample B at incident angle of 15°.(b) Simulated magnetic field distribution of the resonance mode at 4.754 μm.

Figure 5 .
Figure 5. Simulated absorption spectra of sample B by considering both geometry imperfection (including sidewall imperfection and unetched silicon residue layer) and silicon loss.The red curve shows the experimental absorption spectrum for comparison.

Figure 6 .
Figure 6.A coupled oscillator model fitting with the measured Fano resonance spectrum of sample B. The inset shows a diagram of the two coupled oscillators.

Figure 7 .
Figure 7. (a) Measured reflection spectra of sample B at different polarization angles.Simulated magnetic fields (b) and electric fields (c) of the resonance at 4.025 μm when incident light is p-polarization.

Figure 9 (
a) shows SEM image of sample B after depositing

Figure 8 .
Figure 8. Measured reflection spectra of metasurface samples A-C with different geometric parameters.

Figure 9 .
Figure 9. (a) Top-view SEM image of sample B coated with a 1800 nm thick SiO 2 film.(b) Measured reflection spectra of the metasurface with different top SiO 2 analyte thicknesses.The dashed line marks trace shift of the cavity-coupled TE 1,2,δ mode.(c) Sensitivity and FoM of the Fano resonance in refractive index sensing.

Table 1 .
Designed metasurface samples with optimized geometric parameters.

Table 2 .
Refractive index sensing performance of dielectric structures reported in literature and in this work.