Starting with Maxwell's equations the authors try to make a comprehensive study of phenomena observed when a beam is totally reflected from a boundary surface, a system of thin films or from a more complex system such as Goos-Hanchen or Imbert prisms. The aim is to obtain a maximum of results from analytical considerations leading to formulae which make it possible to anticipate the essential results without recourse to a computer. After having formulated the problem in terms of electromagnetic fields, a global study of the beam shift is proposed taking into account only the displacement of the center of gravity of the beam impact. Such a study, valid for a very general case, does not make evident the separation of the of the polarization states. This is done with the help of a local study which gives the two orthogonal polarisations for which a flat incident beam suffers a translation.
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Hugonin et al. (1977) studied this question.