Asymptotic approximations of lasing eigenvalues of an infinite grating of circular quantum wires in the free space

Abstract

One of fundamental problems of electro-magnetics is the scattering of a plane wave from a grating of infinite circular dielectric cylinders (wires). Lord Rayleigh was apparently one of the first researchers who formulated it in the XIX century. We consider the associated lasing eigenvalue problem and focus our attention on the asymptotic approximations of the eigenvalues for large values of the ratio of the grating period to the wire radius. Classification of the modes located near the Rayleigh anomalies is given.