The reflection of a Maxwell-Gaussian beam by a planar surface

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The reflection of a three-dimensional vectorial Maxwell-Gaussian beam by a planar surface is studied. The surface is characterized by its complex reflection coefficients rₛ() and rₚ() for TE and TM electromagnetic plane waves of wavevector, respectively. The field impinging upon the reflecting surface is modeled as a quasi-monochromatic fundamental Gaussian beam suitably modified in order to satisfy Maxwell equations (Maxwell-Gaussian beam). Analytical expressions, correct up to the second order in a perturbation expansion, are given for the reflected electric and magnetic field, respectively. We found that first order terms in the perturbation expansion account for a longitudinal shift (Goos-Hänchen effect) of the whole reflected beam, while second order terms modifies the transverse shape of the beam which is, at this order, no longer cylindrically symmetric.