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