Extraordinary high-Q resonances in the scattering by a dielectric slab containing a grating of circular cylinders

Abstract

An infinite dielectric wire grating in free space is known to possess very high-Q resonances at the frequencies close to the Rayleigh anomalies. Still a practical implementation of such a resonator may require its embedding in a dielectric slab. In this paper, it is shown that this can bring additional improvement of the Q-factors. A dielectric slab with a symmetrically embedded dielectric-wire grating is investigated under the normal incidence of plane waves. Accurate numerical solutions are derived for the E- and H-polarization cases. Associated eigenvalue problems are solved for the realvalued lasing frequencies and the threshold values of material gain.