Permittivity-asymmetric qBIC metasurfaces for refractive index sensing

2.1 Environmental RI-controlled asymmetry factor in ε-qBIC metasurfaces

To construct the ε-qBIC in our metasurface, the design follows two steps. First, the unit cell is composed of two identical TiO₂ nanorods, which support a symmetry-protected BIC due to their C₂ rotational symmetry. Second, a dielectric cover layer is selectively applied to one of the rods, introducing a difference in permittivity between the surroundings of the nanorods. This breaks the C₂ symmetry and transforms the original BIC into a quasi-BIC, accompanied by a radiative resonance and a distinct electric field profile (Figure 1a and b). A more detailed discussion of the ε-qBIC origin is presented in the supplementary information (Fig. S6).

Figure 1:

The concept of environmental permittivity-asymmetric quasi-BIC metasurfaces for refractive index sensing. (a) Illustrating the unit cell of the ε-qBIC metasurfaces, consisting of two identical dielectric nanorods made of TiO₂ with periodicities P _x = P _y = 410 nm. The length l, width d, and height h of the nanobar are 320 nm, 105 nm, and 110 nm respectively. One of the resonators is encapsulated in a dielectric medium with refractive index of n_cov and the height of H. (b) Transition from BIC to ε-qBIC by adding a cladding layer on one of the nanobars, and corresponding electric field distribution of the ε-qBIC. (c) Asymmetry factor defined by α = n _env – n _cov, which is related to radiative loss γ _rad, where n _cov = 1.49 and n _env represent the refractive index of the dielectric medium covering on the one of nanorods, and the global environment of the whole ε-qBIC metasurfaces, respectively. (d) The Q factor exhibits an inverse-square dependence on the asymmetry factor, indicating that the asymmetry factor can modulate the radiative loss. (e) Spectral response under varying environmental RI, where changes in radiative loss additionally induce variations in transmittance intensity.

The asymmetry in permittivity leads to unequal dipole strengths between the two out-of-phase electric dipoles, resulting in a nonzero net dipole moment. This enables the resonance to couple to the far field and become observable in the transmission spectrum.

Specifically, the two TiO₂ nanorods have dimensions of l = 320 nm in length, d = 105 nm in width, and h = 110 nm in height, with a unit cell periodicity of P _x = P _y = 410 nm. One of the rods is fully encapsulated in a dielectric medium with refractive index n _cov, while the other remains exposed to an external medium with refractive index n _env. For example, this can be implemented using a PMMA layer (n _cov = 1.49) with height H of 300 nm as the cladding material.

The prepared metasurface is then placed in the sensing environment (Figure 1c). Unlike conventional g-qBIC designs, where the structural asymmetry, and thus the radiative loss, is fixed after fabrication, the ε-qBIC structure introduces asymmetry through the refractive index contrast between the cladding and the environment. This contrast is quantified by the asymmetry factor α = n _env − n _cov, allowing the radiative loss γ _rad to vary dynamically with the surrounding medium. This work first demonstrates in RI sensing where environmental changes are directly translated into both the asymmetry factor and the associated radiative loss. As shown in Figure 1d, the Q-factor exhibits an inverse-square dependence on the asymmetry factor (related with environment RI), consistent with the characteristic behavior of qBIC modes. This dependence is also reflected in the optical spectra: as the refractive index of the environment varies (from 1.30 to 1.39), the system exhibits not only a shift in resonance wavelength but also a change in resonance modulation depth (Figure 1e). This feature improves the linearity of the sensing signal readout, resulting in better stability over a broader wavelength range. We will return to this point later. Before that, we experimentally verify the simulation results, as discussed in the next section. In addition, it is worth noting that PMMA, while convenient for proof-of-concept demonstrations, suffers from poor durability in practical applications such as biosensing environments [38]. In particular, it is soluble in many common organic solvents such as acetone and chloroform, and is easily removed during plasma cleaning processes [39]. Moreover, although PMMA can remain stable in aqueous buffer solutions, it shows limited resistance to strong acidic or basic regeneration steps that are often required in biosensing protocols [40]. These limitations indicate that more durable polymers (e.g., SU-8 [41]) or inorganic coatings (e.g., SiO₂) should be considered for future applications.

2.2 Experimental validation of both resonance wavelength and intensity modulation in ε-qBIC metasurface

To experimentally validate the refractive index sensing capabilities of both g-qBIC and ε-qBIC metasurfaces, we performed transmittance measurements (Figure 2a) in a controlled aqueous environment using commercial index-matching oils with well-defined refractive indices (details in Method). Both metasurfaces share the similar Q factor measured in the air to ensure the fair comparison (Figure S3). Their fabrication has been confirmed through the SEM images (Figure 2b). The fabrication process of the ε-qBIC metasurfaces can be found in Figure S1.

Figure 2:

Experimental characterization of the qBIC metasurfaces for refractive index sensing. (a) Schematic of the experimental setup for transmittance measurement for g-qBIC and ε-qBIC metasurfaces in an aqueous environment. (b) The SEM images for the g-qBIC metasurfaces, ε-qBIC metasurfaces, and BIC metasurfaces. (c) Measured transmittance spectra of g-qBIC metasurfaces immersed in commercial index-matching oils with refractive indices n _i = 1.30, 1.32, 1.34, 1.36, 1.38. The PMMA (n _cov = 1.49) serves as the cladding material. The corresponding resonance shifts are analyzed using a centroid method, shown on the right, where λ ₀ to λ ₄ denote the centroid wavelengths of the transmission dips, highlighting a clear monotonic wavelength shift as the RI increases. (d) Measured transmittance spectra of ε-qBIC metasurfaces under the same set of environmental refractive indices. In addition to the spectral shift, the modulation depth of the resonance also varies with n _i. The right panel presents changes in both centroid wavelength and normalized modulation depth.

The transmittance spectra of g-qBIC metasurfaces are shown in Figure 2c, measured across a series of index-matching oils (n _i = 1.30, 1.32, 1.34, 1.36, 1.38) with a refractive index step size of Δn = 0.02. As expected, the resonance wavelength exhibits a monotonic redshift with increasing environmental index, consistent with the behavior of conventional single-parameter high-Q RI sensing platforms, with a sensitivity of 118 nm/RIU. The centroid analysis provides the wavelength centroid of a resonance within a half-wavelength range, enabling a clearer tracking of its wavelength shift under different refractive indices (details of the centroid analysis are given in Figure S2). The centroid analysis on the right of Figure 2c confirms the linear trend, with a spectral shift of around 2 nm per RI step. Notably, the resonance modulation depth remains nearly constant, even at n _i = 1.49, indicating that the optical response is primarily governed by phase effects rather than radiative coupling changes.

In contrast, Figure 2d demonstrates the spectral response of ε-qBIC metasurfaces under the same set of environmental refractive indices. The resonance wavelength undergoes a redshift of approximately 2 nm with increasing n_i, similar to the g-qBIC case. Specifically, the sensitivity in terms of wavelength shift is 85 nm/RIU. It is slightly lower than that of the g-qBIC because the initial Q-factors of the two samples are not exactly the same, with the Q-factor of the ε-qBIC (Q = 124) being slightly smaller than that of the g-qBIC (Q = 131) (see supplementary information Figure S3). This results in a slightly lower sensitivity for the ε-qBIC. Nevertheless, it can be seen that the sensing capability in terms of wavelength shift remains on the same order of magnitude for both. In addition, the ε-qBIC provides an extra modulation of the resonance intensity, which can be further exploited in single-wavelength sensing to achieve improved sensing linearity. In Figure 2d, the modulation depth gradually decreases and eventually disappears at n _i = 1.49. This critical point corresponds to a fully permittivity symmetric configuration, where the system reverts to a BIC. The complete disappearance of the resonance provides a distinct optical signature, highlighting the strong potential sensing capability enabled by permittivity-induced asymmetry.

This variation in modulation depth reflects the dependence of the Q factor on the asymmetry factor α, as previously discussed in Figure 1c–e. The right panel of Figure 2d provides a quantitative analysis of both the resonance centroid and the modulation depth, clearly showing that ε-qBIC metasurfaces exhibit not only a resonance wavelength shift but also a change in resonance intensity.

After validation of the simulation results, the next step is to assess two common sensing readouts: the resonance wavelength shift and the transmittance change at a fixed wavelength. The analysis focuses on determining which signal provides a stronger and more robust response under background noise for the ε-qBIC metasurface.

2.3 Single-wavelength intensity modulation outperforms wavelength shift in signal robustness

To evaluate which of the two available signal channels in the ε-qBIC metasurface, resonance wavelength shift or intensity variation at a fixed wavelength, offers better performance in RI sensing, we conducted a set of high-resolution sensing experiments, implemented by narrowing the refractive index step, to extract the signal-to-noise ratio (SNR) under system noise conditions.

In this experiment, glycerol–water mixtures with refractive indices from 1.386 to 1.402 were prepared in increments of Δn = 0.004. These five RI values (n ₁ to n ₅) correspond to the spectra presented in Figure 3a. To highlight the relative changes between spectra, the transmission spectrum from the first measurement (n ₁) was taken as a reference. Its maximum and minimum values were normalized to 1 and 0, respectively, so that all subsequent spectra could be compared on the same scale. This normalization preserves the overall spectral shape while enabling the relative variations to be clearly observed. For each RI, the transmission spectrum was recorded, and two sensing parameters were extracted. The intensity variation signal ΔT _s is defined as the change in transmittance at a fixed probe wavelength, ΔT _s = T _i − T ₁, where T _i is the normalized transmittance for the i-th RI value. The resonance shift signal Δλ _s is defined as the change in resonance wavelength, where λ _i represent the resonance wavelength extracted from the i-th measurement.

Figure 3:

Comparative analysis of signal quality between wavelength shift and intensity variation in RI fine sensing. (a) Schematic representation of two types of signals used in RI fine sensing, along with normalized experimental spectra. The intensity variation ΔT _s refers to the transmittance difference at a fixed wavelength, while Δλ _s denotes the shift in resonance wavelength. Experiments were conducted in five refractive index environments (n ₁ to n ₅), ranging from 1.386 to 1.402, stepsize Δn = 0.004. (b) Illustration of system noise, showing small variations in transmittance (ΔT _n) and resonance position (Δλ _n) based on repeated measurements (m ₀ to m _i) under identical air conditions. Quantitative evaluation of noise levels was performed across five repeated measurements on the same ε-qBIC metasurface. (c–d) Signal-to-noise ratio (SNR) analysis for ΔT _s and Δλ _s based on the extracted signals in (a). Error bars represent the experimentally determined system noise. The signal ΔT _s exhibits a significantly higher SNR, indicating better robustness for sensing applications.

To evaluate the system noise, five repeated measurements in air were performed after each sensing step. Prior to each repetition, the sample was rinsed, dried and measured under identical conditions, simulating practical scenarios involving metasurface reuse and capturing typical instrumental and operational fluctuations. The corresponding variations in transmittance (ΔT _n) and resonance wavelength (Δλ _n) are presented in the right panel of Figure 3b, with a schematic illustration provided to the left. These repeated measurements were used to quantify the noise levels, which were then incorporated as error bars in the analysis of ΔT _s and Δλ _s. As shown in Figure 3c, the intensity variation signal exhibits consistently higher SNR values across the tested RI range, exceeding 15 dB. By contrast, the resonance shift signal Δλ _s, although above the noise threshold, displays greater fluctuations and a lower average SNR (Figure 3d).

These results indicate that, when accounting for measurement repetition and associated operational fluctuations, the intensity variation channel provides a more robust signal. In the following section, the advantages of using ΔT _s for RI sensing with ε-qBIC metasurfaces are examined in comparison with g-qBIC.

2.4 Higher linearity of ε-qBIC sensing data distribution under single wavelength detection

To further evaluate the sensing performance of ε-qBIC metasurfaces based on intensity variation signals, we conducted a direct comparison with g-qBIC under identical refractive index conditions (n ₁ to n ₅, ranging from 1.386 to 1.402 with a step size of Δn = 0.004). Figure 4a and b show the transmittance spectra and extracted intensity variation signals for ε-qBIC and g-qBIC, respectively.

Figure 4:

Comparison of sensing performance between ε-qBIC and g-qBIC metasurfaces under identical RI conditions. Refractive indices n ₁ to n ₅ range from 1.386 to 1.402, with a step size of Δn = 0.004. (a) Experimental transmittance spectra of the ε-qBIC metasurface under different RI environments, along with the extracted intensity variation signals. (b) Transmittance spectra and corresponding intensity variation signals for the g-qBIC metasurface under the same RI conditions. (c) Linear fitting of intensity variation signals at a single representative wavelength, comparing the responses of ε-qBIC and g-qBIC. (d) R ² values obtained from linear fitting across multiple wavelengths, used to evaluate the linearity of the intensity variation response. Higher R ² values indicate better linearity and lower fitting residuals. The ε-qBIC metasurface shows consistently higher R ² values across a broader wavelength range, indicating enhanced linearity.

Linear fitting of the intensity variation ΔT _s across the five RI values at each wavelength was performed. Figure 4c compares the fitted results for both metasurfaces at a selected representative wavelength. The slope of each fit corresponds to the sensitivity (ΔT _s / Δn), while the coefficient of determination R ² is used to evaluate the fitting quality. The R ² value is defined as R ² = 1 − S _res / S _tot, where S _res = Σ_i(y _i − ŷ _i)² is the residual sum of squares between the measured values y_i and the fitted values ŷ _i, and S _tot = Σ_i(y _i − ȳ)² is the total sum of squares with respect to the mean ȳ of all y_i. y_i is the corresponding sensing data ΔT _s. A higher R ² value for a fitting indicates better linearity and lower noise in the signal.

As shown in Figure 4c, both ε-qBIC and g-qBIC exhibit high sensitivity in the range of ∼5,000 % / RIU. While some recent studies using metallic sensing structures have demonstrated extremely high spectral resolution [42], the sensitivity values reported in recent works based on dielectric metasurfaces, particularly those employing single-wavelength transmittance variation readout, are typically around 2000 % / RIU [29], [43], [44].

For the g-qBIC, the maximum R ² observed across the wavelength range is 0.9617 at 727.5 nm. Since none of the wavelengths for g-qBIC reach R ² = 0.98 which is the commonly referenced benchmark [45], [46], [47], we selected the highest R ² point for comparison. In contrast, ε-qBIC achieves a competitive sensitivity (∼5,382 % / RIU) at a wavelength where R ² = 0.9813, exceeding the 0.98 threshold. This indicates that ε-qBIC not only offers excellent sensitivity but also delivers improved signal quality and linearity.

Moreover, simulations in Figure S4 suggest that the sensitivity of ε-qBIC can be further enhanced by adjusting the cladding index n_cov to closely match the refractive index of the sensing environment. In such high-Q regimes, even a small RI change can significantly alter the radiative loss channel to zero and restore the ε-qBIC resonance to a BIC, as the metasurface effectively exhibits symmetry both in geometry (identical rods) and in the surrounding dielectric environment. This leads to a sharp transition from a resonant to a non-resonant state and results in a unity intensity modulation at a fixed wavelength, representing an ideal condition for signal readout in RI sensing applications.

Beyond individual points, we further compared the R ² distribution across the wavelength range (Figure 4d). While g-qBIC fails to exceed threshold within the range, ε-qBIC consistently maintains R ² values above it. To quantify the effective linearity window, we applied a relaxed threshold of R ² = 0.96 and calculated the integrated area between the R ² curve and the threshold line. The ε-qBIC shows an area approximately 104 times larger than that of the g-qBIC, clearly demonstrating its much broader and more stable sensing window with reduced sensitivity to noise.

2.5 Environmentally permittivity restored symmetry-protected BIC

We demonstrate how a g-qBIC can be optically restored to a state that approaches a BIC with zero radiative losses by applying a compensating permittivity asymmetry. Specifically, the simulations start from a structure with the same periodicity, resonator height, and width as used in Figure 1. The initial configuration is a symmetric geometry with equal rod lengths (L ₁ = L ₂ = 320 nm), as shown on the right side of Figure 5a. In this case, the effective dipole moments (p ₁ and p ₂) cancel each other, resulting in a decoupled state with no resonance observable in the transmittance spectrum.

Figure 5:

Permittivity-controlled restoration of symmetry-protected BICs. (a) Conceptual illustration of transformation of g-qBIC into restored symmetry-protected BIC (RSP-BIC) via environmental permittivity control. Starting from a symmetric structure supporting a BIC (left), introducing a geometric perturbation (shorter L ₁) breaks the in-plane symmetry and produce a g-qBIC. By selectively covering the shorter resonator with a dielectric layer of refractive index n _cov, the permittivity asymmetry compensates the geometric imbalance, restoring the BIC (right) with radiative losses approaching to zero. The middle panel illustrates the corresponding electric dipole distributions, while the bottom panel shows the associated transmittance spectra during this process. Simulated transmittance spectra showing the evolution of a BIC under geometric perturbation (L ₁) and its recovery via covering the shorter rod (L ₁ = 209 nm) with growing height H of a dielectric layer (n _cov = 1.49). (b) Transforming of RSP-BIC into radiative qBIC due to immersing the metasurface into environment with n _env. In contrast, conventional BICs are optically inaccessible and remain completely isolated from the environment with n_env. (c) Calculated Q factor map as a function of rod length L ₁ and dielectric cover layer height H, demonstrating the condition for RSP-BIC characterized by a Q factor >10⁷. This indicates the compensation point where the permittivity asymmetry cancels the geometric perturbation.

Next, by decreasing the length of L ₁, we break the in-plane symmetry, resulting in a nonzero net dipole moment. This leads to a radiative qBIC mode that becomes observable as a resonance peak in the spectrum.

We then fix the short rod length (L ₁ = 209 nm) and gradually add a PMMA cladding layer (n = 1.49) over that rod, increasing the coverage height H from 0 to 110 nm. This dielectric coating selectively enhances the local permittivity around the short rod, increasing its effective dipole moment p ₁. As p ₁ approaches p ₂ in magnitude in the given antiparallel configuration, the effective total dipole moment of the system approaches zero again, restoring the destructive interference condition. As a result, the system transitions to a new restored symmetry-protected BIC (RSP-BIC), and the resonance disappears in the spectrum, as shown in the bottom panel of Figure 5a.

To quantify this transition, we extracted the Q-factors from the spectra across a range of L ₁ and H values. Figure 5c shows the Q-factor map, clearly indicating the region where a RSP-BIC emerges. At this RSP-BIC condition, the Q factor exceeds 10⁷, substantially higher than surrounding regions, confirming that a permittivity-induced compensation can effectively reestablish the BIC condition from a geometrically asymmetric structure.

Crucially, unlike conventional BICs, which are isolated from the external environment and remain stable under permittivity perturbations, the RSP-BIC is environmentally accessible. Small changes in the surrounding refractive index can significantly perturb this balance, driving a transition from the RSP-BIC back to a qBIC. This approach, which leverages the environmental RI to reversibly tune the system between RSP-BIC and qBIC, offers a novel mechanism that has not been addressed in prior studies and may open new directions in metasurface-based sensing. Possible applications are discussed in the supplementary information, Note 1.

4.1 Optical characterizations

Transmittance spectra were measured using a white-light transmission microscope (Witec Alpha Series 300). The samples were illuminated with linearly polarized white light, and the transmitted signal was collected using a 20× immersion objective with a numerical aperture of 0.5. The collected light was coupled into a multimode fiber and directed to a grating-based spectrometer equipped with a silicon CCD detector. All measurements were normalized to its corresponding signal from a bare fused silica substrate. For the initial sensing experiments in Figure 2, commercial refractive index liquids from Cargille Labs (Series: AAA) were used, with refractive indices ranging from n = 1.30 to 1.39 in steps of 0.01. To further evaluate the sensing performance in Figures 3 and 4, additional refractive index liquids were prepared by mixing water and glycerol to obtain a finer range of indices between n = 1.386 and 1.414, with an increment of Δn = 0.004.

4.2 Numerical simulations

Simulations were performed using CST Studio Suite, a commercial finite-element-based solver. The model was configured in the frequency domain with periodic boundary conditions and employed adaptive mesh refinement to ensure convergence. The dielectric functions of TiO₂ and PMMA used in the simulations were obtained from spectroscopic ellipsometry measurements and subsequently imported into CST. For sensing simulations, the background refractive index was varied to simulate changes in the surrounding environment.

4.3 Nano fabrications

Fused silica substrates were first cleaned in an ultrasonic acetone bath, then rinsed with isopropanol (IPA) and treated with oxygen plasma to remove any remaining contaminants. A 110 nm TiO₂ layer was then deposited by sputtering a titanium target in an oxygen-containing plasma (Angstrom Engineering). A layer of PMMA 950k A4 resist was spin-coated and baked at 180 °C for 3 min. To avoid charging during electron beam lithography (EBL), a conductive polymer (E-Spacer 300Z) was spin-coated on top of the PMMA. In the initial patterning step, a 30 nm gold markers system was defined on the TiO₂ film for alignment in the following processes. Using these markers, the second patterning step positioned two-rod nanostructure metasurfaces. After exposure, the sample was developed for 135 s in a 3:1 IPA–MIBK solution. A 50 nm chromium layer was then deposited by e-beam evaporation to serve as a hard mask, and lift-off took place in Microposit Remover 1,165 at 80 °C overnight. The structures were transferred into the TiO₂ layer by reactive ion etching (RIE) in a PlasmaPro 100 ICP-RIE (Oxford Instruments), and the chromium mask was then removed in a wet Cr etchant. In the final patterning step, another PMMA layer was spin-coated and patterned onto the fabricated BIC metasurfaces using the same marker system. The patterned regions were cleaned using the same development protocol.