  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.
