Bound states in the continuum in symmetric and asymmetric photonic crystal slabs

We develop a semianalytical model to describe bound states in the continuum (BICs) in photonic crystal slabs. We model leaky modes supported by photonic crystal slabs as a transverse Fabry-Perot resonance composed of a few propagative Bloch waves bouncing back and forth vertically inside the slab. This multimode Fabry-Perot model accurately predicts the existence of BICs and their positions in the parameter space. We show that, regardless of the slab thickness, BICs cannot exist below a cutoff frequency, which is related to the existence of the second-order Bloch wave in the photonic crystal. Thanks to the semianalyticity of the model, we investigate the dynamics of BICs with the slab thickness in symmetric and asymmetric photonic crystal slabs. We evidence that, as the horizontal mirror symmetry is broken, the symmetry-protected BICs that exist in symmetric structures at the $\mathrm{\ensuremath{\Gamma}}$ point of the dispersion diagram become resonance-trapped BICs, but only for specific values of the slab thickness.