Refraction and Diffraction of Waves in Electromagnetic (Photonic)   Crystals Formed by Anisotropically Scattering Elements
  Refraction and diffraction of waves in natural crystals and artificial crystals formed by anisotropically scattering centers are considered. A detailed study of the electromagnetic wave refraction in a two-dimensional photonic crystal formed by parallel threads is given by way of example. The expression is derived for the effective amplitude of wave scattering by a thread (in a crystal) for the case when scattering by a single thread in a vacuum is anisotropic. It is established that for a wave with orthogonal polarization, unlike a wave with parallel polarization, the index of refraction in crystals built from metallic threads can be greater than unity, and Vavilov-Chrernkov radiation becomes possible in them. The set of equations describing the dynamical diffraction of waves in crystals is derived for the case when scattering by a single center in a vacuum is anisotropic. Because a most general approach is applied to the description of the scattering process, the results thus obtained are valid for a wide range of cases without being restricted to either electromagnetic waves or crystals built from threads. 
V. G. Baryshevsky and E. A. Gurnevich
physics.optics physics.acc-ph