Coupled-wave formalism for bound states in the continuum in guided-mode resonant gratings

Abstract

We present simple yet extremely accurate coupled-wave models describing the formation of bound states in the continuum (BICs) in one-dimensional periodic guided-mode resonant gratings consisting of a slab waveguide layer with a binary grating attached to one or both of its interfaces. Using these models, we obtain simple closed-form expressions predicting the locations of the BICs and quasi-BICs in the $\ensuremath{\omega}\text{\ensuremath{-}}{k}_{x}$ parameter space. We study two mechanisms of the BIC formation: coupling between two counterpropagating guided modes and coupling between a guided mode and a Fabry-P\'erot mode. The BIC conditions corresponding to the considered mechanisms are formulated in terms of the scattering coefficients of the binary grating. The predictions of the presented models are in excellent agreement with the results of full-wave simulations obtained using the Fourier modal method.