  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.
