Coexistence of polariton bound states in the continuum and 2D radiative excitons
Bound states in the continuum (BICs) enable optical modes with ideally infinite radiative lifetimes despite lying within the radiation continuum. Radiation-matter interaction in periodically patterned planar waveguides embedding two-dimensional (2D) optically active excitations can be described quantum mechanically by diagonalizing a non-Hermitian operator, known as the Hopfield matrix, which can be generalized to incorporate independent photonic and excitonic losses into the polaritonic states. However, since 2D excitons undergo intrinsic wavevector-dependent radiative decay within the light cone, whether the Hopfield formalism can consistently account for this process while preserving polariton BICs has remained an open question. Here we show that a non-Hermitian Hopfield formalism incorporating excitonic radiative losses correctly captures the existence of genuine $k=0$ polariton BICs with diverging radiative lifetimes. The theory provides a unified microscopic framework for radiative excitons and polariton BICs, and an efficient predictive tool for designing photonic-crystal platforms coupled to quantum wells, transition-metal dichalcogenides, and other 2D excitonic materials.