Scattering of the plane wave from a periodically perforated dielectric slab

An infinite grating of identical dielectric or metal cylinders or strips illuminated by a plane wave has high-quality optical resonances near the Rayleigh anomalies [1-16]. These resonances are present for any periodic 2-D structures and have striking properties as their Q-factors increase if the grating period becomes larger. Besides, in such a resonance the domain of high-intensity scattered field occupies a very wide domain along the grating. In this paper we investigate a configuration where we have a dielectric slab and an infinite grating of air holes inside it. This structure is closer to practical applications in nano and micro-optics and our study shows the presence of the grating resonances having complicated behaviour.