Analytical non-Hermitian description of Photonic Crystals with arbitrary Lateral and Transverse symmetry

In this work we propose a general theoretical approach to the modelling of complex dispersion characteristics of leaky optical modes operating in photonic crystal slab composed of two high-index contrast gratings, beyond the protection of the light cone. Opening access of wave-guided resonances to free space continuum provides large amount of extra degrees of freedom for mode coupling engineering. Not only can the two gratings communicate via near field coupling, but they are also allowed to couple via the propagating radiated field. Our analytical model, based on a non-Hermitian Hamiltonian, including both coupling schemes, allows for a unified description of the wide family of optical modes which may be generated within uni-dimensional photonic crystal. Through a variety of illustrative examples, we show that our theoretical approach provide a simplified categorization of these modes, but it is also a powerful enabler for the discovery of novel photonic species. Finally, as 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 specie discussed in this work.