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

## TL;DR

This paper develops simple, accurate coupled-wave models to predict bound states in the continuum in 1D guided-mode resonant gratings, providing closed-form formulas and analyzing two BIC formation mechanisms.

## Contribution

The paper introduces novel coupled-wave models that accurately predict BICs in 1D GMRGs and derive explicit conditions for their formation mechanisms.

## Key findings

- Models predict BIC locations with high accuracy
- Closed-form expressions for BICs in parameter space
- Validation against rigorous numerical simulations

## Abstract

We present simple yet extremely accurate coupled-wave models describing the formation of bound states in the continuum (BICs) in 1D-periodic guided-mode resonant gratings (GMRGs) 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 $\omega$-$k_x$ parameter space. We study two mechanisms of the BIC formation: coupling between two counter-propagating guided modes and coupling between a guided mode and a Fabry-P\'erot mode. The BIC conditions for the two 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 rigorous numerical simulations obtained using the Fourier modal method.