Modeling of extraordinary high-Q resonances in the scattering by periodically structured dielectric slab

An infinite dielectric wire grating in free space possesses 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-polarisation cases. Associated eigenproblems are solved for the real-valued lasing frequencies and the associated threshold values of material gain.