Bound states in the continuum of eigenmodes guided by a lamellar grating sandwiched between two dielectric media

Recently, the bound states in the continuum attracted a lot of interest due to potential applications in modern laser, quantum, and nanoscale technologies, including quantum computing and information processing. A few examples of such extremely long-lived bound states have been found and studied, mostly via numerical methods, in optoelectronics, condensed matter physics, and material science. Many efforts have been devoted to new design-optimization numerical schemes. Remarkably, the optimized structures look somewhat disordered and could possibly never have been guessed on the basis of the existing analytic results and intuition. Here, we apply a powerful analytic theory of mode coupling in optical gratings, that we proposed in Phys. Rev. A 100, 053854 (2019), to reveal the nature and properties of such bound states in photonic crystals. The results based on such an analytic, as opposed to purely numeric, approach could greatly facilitate finding and designing the optimal structures for bound states.