Strong Mode Coupling via Quasi-Bound States in the Continuum in Bianisotropic Metasurfaces

TL;DR

This work develops a temporal coupled-mode theory (TCMT) to describe omega-type (off-diagonal) bianisotropy in dielectric metasurfaces enabled by quasi-bound states in the continuum (q-BICs). By coupling two opposite-symmetry dipolar resonances through out-of-plane symmetry breaking, the model predicts and reveals Rabi-like anticrossing and strong mode hybridization, quantified via a coupling strength $g$ and a critical value $g_c=\sqrt{\gamma_p\gamma_m}$. The theory is validated against full-wave simulations and shows that the off-diagonal coupling $\hat{\alpha}_{xy}^{\rm em}$ scales with $g$, while the system can realize dual-band, directional absorption when losses are present. Embedding the metasurface inside a Fabry–Pérot background further enhances reflectivity, enabling large, reciprocal directional absorption differences ($>70\%$) across two spectral bands in a deeply subwavelength structure. Overall, the paper provides a compact, predictive framework for designing strongly coupled, bianisotropic metasurfaces and clarifies the physical mechanism behind mode hybridization in the optical regime.

Abstract

Electromagnetic mode coupling plays a key role in many resonant effects in nanophotonics. This coupling is also responsible for the appearance of bianisotropy, where electric and magnetic responses become interconnected through the interaction of their respective modes. In this work, we develop a simple and general temporal coupled-mode theory model to describe off-diagonal chiral bianisotropy. Using quasi-bound states in the continuum (q-BICs), we demonstrate how to control the hybridization of modes with opposite symmetries, resulting in Rabi-like splitting between the hybrid states in the regime of strong electromagnetic mode coupling. Beyond revealing the physical origin of the hybrid modes, our model predicts and explains the emergence of dual-band asymmetric reflection and absorption, and how to achieve maximum directional absorption difference. The theoretical predictions are verified by full-wave simulations, showing very good agreement with theory. Furthermore, very strong reciprocal bianisotropy is demonstrated with the use of q-BICs in a deeply subwavelength metasurface in the optical frequency range. Our results provide a clear physical picture of the interaction process between modes, offering a compact theoretical framework for understanding and designing bianisotropic dielectric metasurfaces not only in the traditional regime but also in the strong coupling regime.

Figures (4)

• Figure 1: Scattering properties of off-diagonal chiral bianisotropic particles and metasurfaces. (a) Scattering cross-section of a single cylindrical nanoparticle. (b) Scattering cross-section of a broken mirror symmetric particle. Different multipole contributions for different propagation directions. Geometrical parameters: $D=300$ nm, $h=250$ nm, and $n_{\rm d}=3.5$. (c) Absolute value of the normalized collective polarizabilities calculated for the symmetric metasurface. In the frequency range shown, the structure holds two q-BIC eigenmodes: a magnetic dipole and an electric dipole resonance. (d) A metasurface with broken out-of-plane symmetry, holding the new hybridized resonant modes. Omega type polarizability component, $|\hat{\alpha}_{xy}^{\rm em}|$, is different from zero. Nanodisks have diameters defined as $D_{\rm a}=D+\Delta/2$ and $D_{\rm b}=D-\Delta/2$. Geometrical parameters: $P=1000$ nm $D=600$ nm, $h=250$ nm, $\Delta=100$ nm, $n_{\rm d}=3.5$. The perturbation, i.e., the perforations on the top part of the nanodisks have dimensions $h_{\rm p}=20$ nm, $\sigma_{\rm p}=0.5$.
• Figure 2: Modelling of off-diagonal chiral bianisotropic metasurfaces with TCMT. (a) Schematic representation of the TCMT model. (b) Comparison between full-wave and TCMT calculations of the reflectance of the metasurface for different values of the normalized diameter $\sigma_{\rm p}=d_{\rm p}/D_{\rm i}$ when $P=1200$ nm, $D=530$ nm, $h=263$ nm, $\Delta=95$ nm, $h_{\rm p}=20$ nm, and $n=3.5$. For $\sigma_{\rm p}=0$ the system is close to Huygens' condition with $R$ close to zero at the resonant frequency. (c) Resonant frequency of the two hybridized modes for different values of the normalized diameter $\sigma_{\rm p}=d_{\rm p}/D_{\rm i}$. The values for the fitted parameters of the unperturbed structrure are also depicted, $\omega_{\rm p}$ and $\omega_{\rm m}$. (d) Values for the coupling strength, $g$, and the critical condition $g_{\rm c}=\sqrt{\gamma_{\rm p}\gamma_{\rm m}}$ in terms of the normalized diameter. (e) Real part of the collective electric, magnetic, and magnetoelectric polarizabilities as functions of the TCMT parameters, compared with the corresponding values obtained from FEM simulations.
• Figure 3: Scattering properties of resonance crossings in off-diagonal chiral type bianisotropic metasurfaces for different coupling scenarios. TCMT results have decay rates chosen as $\gamma_{\rm m}=3\gamma_{\rm p}$, with constant background process $r=0$, and the horizontal axis is normalized as $\Delta \omega=\omega_{\rm p}-\omega_{\rm m}$. (a) $\sigma_{\rm p}=0$ and $g=0$. No coupling between electric dipole resonance and magnetic dipole resonance, as $\sigma_{\rm h}$ is a symmetry. At $\Delta \omega=0$, a Huygens-like pair is created, achieving $R=0$ and transmittance $T=1$. (b) $g\simeq g_{\rm c}$ and $\sigma_{\rm p}=0.12$, at the crossing point, full reflection is achieved. (c) Strong coupling regime, $\sigma_{\rm p}=0.5$ and $g\simeq4g_{\rm c}$, at the same time $g>g_{\rm strong}$. At $\Delta \omega=0$, a clear anticrossing can be observed. The Rabi-like splitting can be controlled with the perturbation, as shown in Fig. 2. Geometrical parameters for the metasurface: $D=530$ nm, $\Delta=40$ nm, $h=263$ nm, $h_{\rm p}=20$ nm.
• Figure 4: Dual-band absorption in strongly coupled metasurfaces with off-diagonal chirality or omega-type bianisotropy. (a) Case in which $\omega_{\rm p}=\omega_{\rm m}=\omega_{0}$, $\gamma=\gamma_{\rm p}^{\rm r}=\gamma_{\rm p}^{\rm l}=\gamma_{\rm m}^{\rm r}=\gamma_{\rm m}^{\rm l}$, and $r=1$. The difference in absorption grows with the coupling strength for each branch of the hybrid modes. (b) Absorption difference evaluated at $\omega_{+}$ for $\omega_{\rm p}=\omega_{\rm m}=\omega_{0}$, $\gamma=\gamma_{\rm p}^{\rm r}=\gamma_{\rm p}^{\rm l}=\gamma_{\rm m}^{\rm r}=\gamma_{\rm m}^{\rm l}$ in terms of absolute value of the reflection coefficient for the background process and coupling strength. (c) Reflection from a Fabry-Pérot slab of dielectric of height $h=360$ nm and effective refractive index $n_{0}=(n_{\rm s}+n_{\rm d})/2=3.25$ . (d) Calculated absorption via FEM simulations for the metasurface embedded in a dielectric slab. Solid lines represent FEM results, while the TCMT fit is represented as dashed lines. Absorption FEM geometrical parameters: $n_{\rm s}=2.5$, $n_{d}=4$, $P=510$ nm, $\Delta=70$ nm, $h_{\rm p}=40$ nm, $\sigma_{\rm p}=0.5$, $h=360$ nm, $D=280$ nm, and $k_{\rm}=0.005$ as the imaginary part of the refractive index.