Exceptional points of resonant states on a periodic slab

A special kind of degeneracies known as the exceptional points (EPs), for resonant states on a dielectric periodic slab, are investigated. Due to their unique properties, EPs have found important applications in lasing, sensing, unidirectional operations, etc. In general, EPs may appear in non-Hermitian eigenvalue problems, including those related to PT-symmetric systems and those for open dielectric structures (due to the existence of radiation loss). In this paper, we study EPs on a simple periodic structure: a slab with a periodic array of gaps. Using an efficient numerical method, we calculate the EPs and study their dependence on geometric parameters. Analytic results are obtained for the limit as the periodic slab approaches a uniform one. Our work provides a simple platform for further studies concerning EPs on dielectric periodic structures, their unusual properties and applications.