Green’s function of wave field in media with one-dimensional large-scale periodicity

Abstract

The Green's function of the wave field in a medium with a smooth one-dimensional periodicity is considered. The solution is constructed by the WKB method. It is shown that at large distances there is an analogy between the Green's function in a medium with one-dimensional periodicity and the Green's function in an anisotropic uniaxial medium. The periodic system is distinguished from an anisotropic medium by a discontinuity of the wave vector surface and a break of beam vector surface. The forbidden zone corresponds to capture of beams with small angles of incidence and formation of a wave guide channel. Within this wave guide channel the Green's function asymptotic differs from $1/r$ behavior. The fields outside and inside of the wave channel are described within the framework of a unique approach. A detailed analysis of the obtained results is carried out.