Total reflection of a Gaussian beam from an inhomogeneous medium

Abstract

For the purpose of radio and optical propagation, it is of practical importance to study how the shape of a Gaussian beam is deformed by a total reflection from an inhomogeneous medium. A fundamental problem, where the two-dimensional Gaussian beam is obliquely incident on the boundary surface between a homogeneous half-space and an inhomogeneous half-space whose permittivity decreases linearly in one direction, is analyzed. The theoretical result obtained by means of a Fourier transform is valid for cases of a collimated beam and a slowly varying medium. The characteristics of the reflected beam after it has propagated through the inhomogeneous medium are discussed. It is found for the first time that the shape of the reflected beam has the same form as an original beam when incident anlge φ is equal to the critical angle defined by φc=cos−1[({1±[1−2b (Z0+L)]1/2}/2)1/2]. When φ is not equal to φc, the reflected beam is deformed compared with the original beam.