Refraction and Diffraction of Waves in Electromagnetic (Photonic) Crystals Formed by Anisotropically Scattering Elements

摘要

Refraction and diffraction of waves in natural crystals and artificialcrystals formed by anisotropically scattering centers are considered. Adetailed study of the electromagnetic wave refraction in a two-dimensionalphotonic crystal formed by parallel threads is given by way of example. Theexpression is derived for the effective amplitude of wave scattering by athread (in a crystal) for the case when scattering by a single thread in avacuum is anisotropic. It is established that for a wave with orthogonalpolarization, unlike a wave with parallel polarization, the index of refractionin crystals built from metallic threads can be greater than unity, andVavilov-Chrernkov radiation becomes possible in them. The set of equationsdescribing the dynamical diffraction of waves in crystals is derived for thecase when scattering by a single center in a vacuum is anisotropic. Because amost general approach is applied to the description of the scattering process,the results thus obtained are valid for a wide range of cases without beingrestricted to either electromagnetic waves or crystals built from threads.