A Uniform Asymptotic Solution for Reflection and Beam Shift of a Gaussian Beam at a Plane Dielectric Interface

Abstract

The problem of a Gaussian beam that is incident on a plane dielectric interface from a denser dielectric medium to a rarer one and is reflected at the interface has been important research subjects studied by many researchers. In this paper, we have obtained a novel uniform asymptotic solution for reflection and beam shift of the Gaussian beam that is incident on the interface from the denser medium. The uniform asymptotic solution consists of the geometrically reflected beam, the lateral beam if any, and the newly derived transition beam which plays an important role in the transition region near the critical angle of the total reflection. We have confirmed the validity of the uniform asymptotic solution by comparing with the reference solution obtained numerically from the integral representation. We have shown that, in addition to the Goos-Hanchen shift and the angular shift, the Gaussian beam is shifted to either direction by the interference of the geometrically reflected beam and the lateral beam near the critical angle of the total reflection.