Robustness of Bound States in the Continuum in Bilayer Structures against Symmetry Breaking

TL;DR

This work examines the robustness of bound states in the continuum (BICs) in a bilayer periodic array of dielectric rods, distinguishing symmetry-protected (SP) BICs and Fabry-Pérot (FP) BICs under perturbations. Using a TE-polarized, infinite-array model and coupled-mode theory, it analyzes material losses, interlayer spacing, and lateral layer displacement, linking these to distinct Q-factor contributions and resonance conditions. Key findings include that FP-BICs become quasi-FP-BICs under losses via second-order radiative leakage, SP-BICs remain radiative-free when symmetry is preserved, FP-BICs' Q grows with interlayer distance, and both BIC types show exponentially reduced sensitivity to C$_2$-breaking with larger L; oblique incidence can also generate additional FP-BICs. The results offer design principles for robust BIC-based photonic devices tolerant to fabrication imperfections, environmental changes, and material losses.

Abstract

We investigate the robustness of bound states in the continuum (BICs) in a bilayer dielectric rod array against geometric and material perturbations. Our analysis focuses on both symmetry-protected and Fabry-Pérot BICs, examining their transformation into quasi-BICs under three structural modifications: (i) in-plane displacement of one layer, which breaks the C$_2$ symmetry of the system; (ii) introduction of material losses that break time-reversal symmetry; and (iii) variation in the interlayer distance, which preserves structural symmetry. In particular, we demonstrate that material losses inevitably induce radiation in Fabry-Pérot BICs via second-order perturbation processes, converting them into quasi-BICs, while symmetry-protected BICs remain non-radiative. We further show that, despite the inherent instability of BICs under symmetry-breaking effects, their resilience can be significantly enhanced through proper design. Both Fabry-Pérot and symmetry-protected BICs exhibit exponentially weak sensitivity to C$_2$-breaking perturbations as the interlayer distance increases. Finally, we show that additional FP-BICs emerge under oblique incidence, originating from the interference of two high-Q quasi-BICs near the symmetry-protected ones. Our findings pave the way for the development of BIC-based photonic devices with improved robustness against fabrication imperfections, environmental variations, and material losses.

Figures (9)

• Figure 1: (a) Classification of BICs in bilayer structure. (b) Schematic view of the considered resonator and the parameters affecting the $Q$ factor.
• Figure 2: Bound states in the continuum in the bilayer structure of infinite dielectric rods. (a) Schematic view of the photonic structure. (b) Distribution of the $E_\mathrm{z}$ electric field of the Fabry-Pérot and symmetry-protected BICs at the $\Gamma$-point. (c) Dependence of $Q$ factors of different BICs on the distance between the layers of dielectric rods $L$.
• Figure 3: Comparison of numerically simulated (markers) and analytical (solid lines) transmission spectra of a single-layer structure for different losses: $\tan\delta=0$ (black), $\tan\delta=10^{-4}$ (red), $\tan\delta=10^{-3}$ (blue), $\tan\delta=10^{-2}$ (cyan), and $\tan\delta=10^{-1}$ (green). Inset shows single-layer structure and the propagation direction of the incident field.
• Figure 4: Dependence of $Q$ factors of different qBICs on loss tangent $\tan\delta$: (a) numerical results for the interlayer distances defined by the Fabry-Pérot quantization condition: $L = 4.69$ cm for symmetry-protected qBICs and $B_{1u}$ FP-qBIC; $L = 6.2$ cm for $B_{3g}$ FP-qBIC; (b) analytical and numerically simulated loss contributions to the $Q$ factor of the $B_{1u}$ FP-qBIC, including asymptotics given by Eqs. \ref{['eq:Q_rad_a']}, \ref{['eq:Q_abs_a']}, and \ref{['eq:Q_rad_L']}, for interlayer distance detuned from the Fabry-Pérot resonance condition.
• Figure 5: Dependence of $Q$ factors of different qBICs on the interlayer distance $L$ of dielectric rods with fixed losses $\tan\delta=0.01$ and $Q_\text{abs}^{\gamma_a}$ asymptotics given by Eq. \ref{['eq:Q_abs_a']}.