Reflection and refraction of a gaussian beam at a planar dielectric interface

The problem of e.m. gaussian beam interaction with a planar interface separating two lossless dielectric media, for regular incidence, is considered. Employing a modal plane wave expansion and the continuity of the fields across the boundary, the reflected and refracted beams are obtained. Use is made of the Fresnel approximation and a Taylor series expansion of both the reflectance and transmittance, for both polarization cases. Particular emphasis is given to the shift of both the reflected and refracted beams, the change in width of the transmitted beam, and the behaviour at polarizing incidence.