Goos-Hanchen and Imbert-Fedorov shifts for Hermite-Gauss beams

We study the lateral Goos-Hanchen and the transverse Imbert-Fedorov shift produced during the reflection of Hermite-Gauss beams H(m0) or H(0m) at a plane interface. The vector angular spectrum method for a light beam in terms of a two-form angular spectrum consisting of the two orthogonal polarized components was used. We have carried out a detailed numerical calculation of these shifts at different angles of incidence, over the whole range of incidence without making the usual approximations. The shift variation as a function of refractive index and order of the Hermite-Gauss beam is studied. We also compare the shift variations with the orientation of the lobes of the Hermite-Gauss beam. We observed that the shifts are nearly equal for the two cases H(m0) (lobe oriented in the plane of incidence) and H(0m) (lobe oriented perpendicular to plane of incidence). These are the first quantitative estimates of the shifts for Hermite-Gauss beams as per our knowledge and are relevant for all cases of slab geometry.