In the fields of photonics, biosensing, and environmental monitoring, efficient plasmon-based light absorption and high-sensitivity sensing are essential. These technologies enable accurate detection and analysis of biological and chemical substances and have made great advances in medical diagnostics^[1,2], environmental protection^[3], and information technology^[4,5]. However, there are still challenges in achieving high Q resonances to strengthen light–matter interactions and boost sensing sensitivity. Traditional structures often face a trade-off between Q and absorption efficiency, restricting their performance and practical application. In recent years, bound states in the continuum (BICs) have attracted much attention because of their theoretically infinitely high Q-factor and unique optical localization ability^[6–9]. As a non-radiating mode in the radiation continuum, BIC can completely prevent energy leakage using structural symmetry. This can be applied to ultra-narrow line width lasers^[10], absorber designs^[11], and high-precision sensing^[12–14]. Nevertheless, the strict symmetry dependence of BIC makes it difficult to observe and apply directly. It is necessary to break the symmetry and transform it into a quasi-bound state in the continuum (Q-BIC) to achieve controlled light–matter interactions while preserving the high Q-factor^[15].

Due to surface plasmon resonance, metal nanostructures can significantly enhance the electromagnetic field, resulting in perfect absorption of high Q factors^[16–18]. In addition, the metasurface technology, with its subwavelength structure and flexible design capabilities, has shown great potential in light modulation. It provides an important opportunity to tailor the electromagnetic response and implement novel optical functions^[19–22]. Therefore, by combining metal nanostructures with metasurfaces, it is possible to introduce geometric asymmetry to modulate symmetry-protected BICs. This allows flexible tuning of the resonance characteristics of the Q-BIC for dual optimization of ultra-narrow band light absorption and high sensitivity sensing.

In this Letter, we designed and analyzed an E-shaped hole array metasurface, which has demonstrated efficient light absorption at specific wavelengths, achieving 98.9% absorption efficiency at 909 nm. The structure in the symmetry-protected BIC mode has a Q-factor two orders of magnitude higher than that under the symmetry-broken mode. We converted the symmetry-preserving bound state into a quasi-bound state by introducing an asymmetry factor (σ). Furthermore, by adjusting the incident angle, the Q-BIC generation is excited at 8°. For refractive index (RI) sensing, both the symmetry-protected BIC and the Q-BIC mode exhibit a sensitivity of 1000 nm/RIU (refractive index unit) in air. However, in organic solution, the figure of merit (FOM) value of the Q-BIC mode shows a slight increase compared to the symmetric structure. These results show that the structure performs excellently in optical absorption and refractive index sensing, making it suitable for high-precision biosensing, narrow-band filtering, and optoelectronic integration.

As shown in Fig. 1(b), the metasurface unit cell structure designed in this Letter consists of a periodic arrangement of an E-shaped metasurface embedded within the substrate. The array periods in the x-axis and y-axis directions are designated as px and py, respectively, as shown by the arrows. It is assumed that light (electromagnetic) waves are incident perpendicularly onto the metasurface, from the top to the bottom. The electric field (Ein), magnetic field (Hin), and wave vector (k) of the incident light are aligned along the x-axis, y-axis, and negative z-axis directions, respectively, as indicated by the three arrows located at the bottom left corner of Fig. 1(b). Periodic boundary conditions are applied along the x- and y-axis directions, and perfect matching layers (PMLs) are implemented along the z-axis direction to absorb the light waves escaping from the waveguide. In addition, we chose a regular mesh setting with a mesh precision of 3 to achieve a good balance between computational accuracy and efficiency. The mesh divisions are carefully sized to ensure that the electromagnetic field distribution in critical areas (e.g.,  near the E-hole) can be accurately captured. This ensures that the interference from the reflected waves within the computational domain is effectively reduced, thereby guaranteeing the accuracy of the simulation results.

Studies have shown that when the thickness of the silver film exceeds 50 nm, the light transmittance is almost zero^[23]. Based on this characteristic, the silver film substrate can effectively block the transmission of incident light, causing strong electromagnetic interactions between the incident light and the silver film surface as well as the E-shaped hole array structure above it, thereby achieving effective light absorption and dissipation. This physical mechanism lays an important foundation for the construction of high-performance perfect absorber structures with promising applications in optical absorption and sensing. Therefore, in this study, a silver film with a thickness of 200 nm was used as a coating material on the silicon layer.

In this Letter, we have numerically computed the reflection spectra and electromagnetic field distributions using COMSOL Multiphysics based on the finite element method. The air properties inside the cavity are implemented using the data obtained from the Peck and Reeder experiment in 1972^[24], with a dielectric constant of εd=1.0003. The complex refractive index of the silver is calculated using the Drude model^[25,26], ε(ω)=ε∞−ωp2ω(ω+iγ).(1)

In Eq. (1), ω represents the frequency of incident light, ε∞=3.7 corresponds to the relative permittivity of silver at infinite frequency, ωp=1.38×1016Hz is the plasma frequency of silver, and γ=2.73×1013Hz represents the free electron collision frequency.

Table 1 provides the structural parameters and numerical values of the E-type array metasurface. The metasurface proposed in this Letter can be experimentally fabricated using focused ion beam lithography^[26]. A machine from FEI Company, the Strata FIB (Focused Ion Beam) 201, can perform the milling of the proposed E-type array on the silver substrate.

In Fig. 2(a), we numerically simulated the normal-incidence absorption spectrum of the designed structure based on the array periods px and py, with the incident wave being a TM (transverse magnetic) wave. Distinct absorption peaks are clearly observed at wavelengths λ1=852nm, λ2=909nm, and λ3=929nm. Notably, the absorption efficiency at λ2 reaches 98.9%, indicating that the structure achieves near-perfect absorption of the incident light at this wavelength.

To better investigate the performance at different wavelengths, it is necessary to conduct an in-depth study of the resonance modes associated with the reflection dips. Based on the wavelengths corresponding to the three absorption peaks shown in Fig. 2(a), we plotted the corresponding electromagnetic field distributions. Surface plasmon resonance (SPR) typically induces localized electromagnetic field enhancement on metal surfaces, particularly at the edges and tips of nanostructures. Specifically, in Fig. 2(b), the magnetic field distribution reveals eight distinct bright spots around the E-shaped hole, indicating significant magnetic field enhancement. In Fig. 2(c), the magnetic field exhibits bright spots at the intersections of the three horizontal and vertical bars of the E-shaped hole, suggesting localized magnetic field enhancement at these specific locations. In Fig. 2(d)(i), the electric field distribution displays a symmetric pattern, with noticeable enhancement at the center and the four corners of the structure.

Furthermore, due to the presence of cavities in the structure, we further explored the resonance mode at the wavelength λ₂, which corresponds to perfect absorption, as shown in Fig. 2(d)(ii). The results reveal that the electric field enhancement is highly concentrated, and a standing wave pattern forms inside the cavity. This standing wave pattern is identified as a Fabry–Pérot cavity resonance mode, which, to some extent, explains the realization of perfect light absorption at this wavelength.

To elucidate the physical characteristics of the absorption peak, in Fig. 2(e), we present the current distributions at wavelength λ2 on the xy and yz planes, with the upper panel corresponding to z=100nm and the lower panel to x=400. It is evident that the uniform current is disrupted after passing through the two rectangular columns, primarily concentrating in the central region of the E-shaped hole and forming individual loops at the boundary areas. These current loops generate significant magnetic moments, which can interact with the magnetic field of the incident light. When the frequency of the incident light matches the resonance frequency of these magnetic moments, magnetic resonance will occur^[27]. Additionally, the yz plane reveals that the currents converge from both sides toward the center, a behavior that leads to the generation of plasmons. The free electrons in the plasmons exhibit strong absorption and scattering effects on the incident light, thereby significantly enhancing the light absorption efficiency.

In order to further investigate the unique performance of the E-shaped hole array metasurface, the C2 symmetry breaking is achieved by varying the parameter lm. For the convenience of research, the asymmetry factor σ is defined as σ=lm−lnln.(2)

Herein, the closer the absolute value of σ is to 0, the more symmetric the structure is. Conversely, the larger the absolute value of σ, the higher the degree of symmetry breaking.

Figure 3(a) presents the calculated reflection spectra for six different values of lm within the wavelength range of 900–950 nm, revealing two distinct phenomena with specific characteristics. Near 909 nm, where perfect light absorption is achieved, all values of lm produce a reflection dip. In addition, near 929 nm, the symmetric structure may exist degenerate or nearly degenerate optical modes, which manifest as a single reflection dip in the reflection spectrum. Upon breaking the C2 symmetry, these originally degenerate or nearly degenerate modes split into two distinct modes, each corresponding to a separate reflection peak. Consequently, the initial single reflection dip splits into two peaks induced by C2 symmetry breaking, referred to as the left peak (C2−BPl) and the right peak (C2−BPr).

In optical systems, the BIC has a theoretically infinite quality factor (Q-factor) due to its symmetry protection. However, when symmetry breaking is introduced into the system parameters, the originally strictly limited BIC mode degenerates into a Q-BIC and leaks energy into free space through the radiation channel^[28]. This physical process can be visualized by the dynamics of the Q-factor. In order to quantitatively characterize the mode evolution mechanism, we perform rigorous Q-factor calculations for the reflection valley at the 909 nm wavelength, and its numerical change effectively reveals the transition from ideal BIC to Q-BIC. The Q-factor’s calculation formula is given as follows^[29]: Qfactor=λ0FWHM,(3)where λ0 represents the resonant wavelength of the structure, and FWHM represents the full width at half-maximum. Figure 3(b) shows the variation of the Q-factor values under different asymmetry factors. When the structure maintains symmetry, i.e., the C2 symmetry remains unbroken, the Q-factor value is higher than that in the symmetry-broken state. However, once the C2 symmetry is broken, the Q-factor drops sharply, leading to the formation of Q-BIC modes. In addition, due to the presence of large losses in the silver medium, even in the case of symmetric protection, we are unable to perfectly reach its theoretical Q-factor value, which tends to infinity. In addition, by fitting the Q-factor, we find that there is a square relationship between it and the asymmetric factor, and the goodness of fit R2 can reach 99.79%.

Figure 3(c) depicts the electric field distributions of the structure under different values of σ (interior of cavity). By comparing with the symmetric structure, it is evident that the electric field intensity distribution is closely related to the asymmetry factor of the structure. Furthermore, the electric field distribution demonstrates a barrel effect, where the Fabry–Pérot cavity resonance intensity is constrained by the shorter cavity length (the smaller of lm and ln), thereby limiting the overall electric field distribution.

BICs can also be generated by varying the incident angle^[30]. As shown in Fig. 3(a), even after symmetry breaking, the parameter lm=350nm still maintains high optical absorption. Figure 4(a) presents the reflection spectra of the structure for incident angles θ ranging from 1° to 8°. As indicated by the red bullseye in the figure, at an incident angle of 5°, the structure exhibits near-perfect optical absorption at 900 nm, with an absorption coefficient as high as 98.3%. Additionally, Fig. 4(c) shows the variation of the reflection spectra of the coupled system with respect to the incident angle, where BICs are highlighted by the dashed circles. The Q-BIC corresponding to the circle in the lower left occurs at an incident angle of 8°, which satisfies a specific phase matching condition that allows the structure to support a quasi-bound state.

Returning to Fig. 4(a), at an incident angle of 8°, the reflection coefficient is relatively low, indicating that under Q-BIC conditions, most of the incident light is transmitted rather than reflected. This low reflectivity is a distinctive feature of Q-BIC, as it enables light to be localized within the structure without coupling to external radiation modes. When the incident angle is slightly below 8°, such as at 7°, the reflection coefficient suddenly increases, exhibiting a sharp Fano resonance^[31]. This sharp resonance arises from a slight deviation from the Q-BIC condition, which may be caused by minor variations in the incident angle or structural parameters. Notably, as shown in Fig. 4(b), the symmetric structure does not exhibit the characteristic of generating Q-BIC based on the incidence angle induction. This shows that in the structure designed in this Letter, Q-BIC can only be generated by angle change after breaking the symmetry, while the symmetric structure is unable to realize BIC by angle change alone. Although it has been mentioned in the literature that BICs can be generated at arbitrary incident angles when two or more BICs with different mechanisms are merged, our study shows that the cavity in the structure introduces a cavity-membrane resonance in some cases, which destroys the original BIC properties. This cavity-membrane resonance changes the electromagnetic field distribution and resonance modes, which in turn affect the conditions for BIC formation.

To investigate the potential sensing applications of the structure designed in this Letter, we conduct a refractive index sensing performance analysis for both the symmetry-protected BIC mode and the Q-BIC mode mentioned earlier. When the refractive index of the surrounding medium undergoes slight changes, the reflection peak exhibits a significant shift, indicating a high sensitivity to refractive index variations. Traditionally, two key parameters are widely used to evaluate sensing performance: sensitivity (S) and FOM. S and FOM can be defined as S=ΔλΔn,FOM=SFWHM(4)

Here, Δλ represents the spectral shift of the reflection peak, and Δn denotes the change in the refractive index.

Figures 5(a) and 5(b) show the sensitivity variations of the two modes in air, with a refractive index step size of 0.0001. Figure 5(c) shows that both modes achieve a sensitivity of 1000 nm/RIU. The FOM value for the symmetric structure is 2710, while the FOM value for the BIC mode is significantly lower at 699. Further investigations are conducted on the sensitivity variations of the structure in organic solutions, as shown in Fig. 5(d), simulating the refractive index change of the organic solution from 1.35 to 1.45 with a step size of 0.01. The sensitivity of the symmetry-protected BIC mode is 930 nm/RIU, while the Q-BIC mode exhibits a slightly lower sensitivity of 900 nm/RIU. However, the FOM value (463.9) of the Q-BIC mode is significantly higher than that of the symmetry-protected BIC mode (172.2). Overall, the values of both performance parameters are highly competitive, and a comparison with other studies is provided in Table 2.

In conclusion, we have designed an E-shaped hole array metasurface by combining the BIC and Q-BIC mechanisms and successfully achieved a bifunctional collection of near-perfect absorption and high-sensitivity refractive index sensing. Numerical simulations demonstrated 98.9% light absorption at 909 nm under symmetric conditions. By varying the asymmetry factor, we observe that the Q-factor shows a significant decreasing trend, which indicates that the structure gradually changes from the BIC mode to the Q-BIC mode. Further analysis reveals that there is a quadratic relationship between the Q-factor and the asymmetry factor with a goodness-of-fit of 99.79%, thus confirming the strong correlation between the two. Breaking the C2 symmetry resulted in a double split peak at 929 nm, and the Q-BIC mode was excited at an incident angle of 8°. Notably, 98.3% absorption at 900 nm was achieved at a 5° incident angle. For sensing applications, both symmetry-protected BIC and Q-BIC modes showed 1000 nm/RIU sensitivity in air, while the Q-BIC mode outperformed in organic solutions with a superior FOM (463.9). Compared with the existing studies, the refractive index sensitivity and FOM obtained from the structure proposed in this Letter are superior. These results highlight the structure’s dual functionality and exceptional performance in ultra-narrowband photonics, offering promising potential for biosensing, optoelectronic integration, and precision optical filtering technologies.