Analytical non-Hermitian description of photonic crystals with arbitrary lateral and transverse symmetry

We propose a general theoretical approach to the modeling of complex dispersion characteristics of leaky optical modes operating in photonic crystal slabs composed of two coupled high-index contrast gratings. Our analytical model, based on a non-Hermitian Hamiltonian, allows for a unified description of the wide family of optical modes which may be generated within unidimensional photonic crystals. Our theory stands for a variety of illustrative examples relating to the manipulation of bound states in the continuum and exceptional points and can be used as a powerful enabler for the discovery of novel photonic species. Finally, as a proof of concept, we demonstrate experimentally the formation of a Dirac point at the merging of three bound states in the continuum that is the most achieved photonic species discussed in this work.