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

The authors propose a non-Hermitian Hamiltonian to describe the resonances of photonic crystal slabs formed by coupled high-index contrast gratings. This model can potentially enable the discovery of novel photonic specie through the manipulation of bound states in the continuum and exceptional points. The authors then demonstrate experimentally, as proof-of-concept, the formation of a Dirac point at the merging of three bound states in the continuum.