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.

https://iopscience.iop.org/article/10.1088/0150-536X/8/2/001/pdf

General study of displacements at total reflection

On the possibility to observe the longitudinal Goos-Hänchen shift with cold neutrons

This work is the computation of the shift by reflexion, orthogonal to the incident plane (Imbert effect) of a transversally limited light beam. The incident wave satisfies Maxwell equations an is chosen so as the elementary plane waves into which it may be decomposed have a constant incident angle. Simple formulas of the shift have been obtained, which are in very close accordance with a computer calculation performed on the basis of a particular incident wave.

https://iopscience.iop.org/article/10.1088/0335-7368/5/1/301/pdf

Computation of the transverse shift by reflexion of a limited light beam

When a beam of light is totally reflected by a plane interface, a translation depending on its polarization occurs: one shift Lx is parallel to the incident plane π and the other Ly is perpendicular to π. Both the longitudinal Lx and the transverse shifts Ly are quantized, each having two eigenvalues which are the principal linear polarization states for Lx and the circularly polarized states for Ly. Thus the longitudinal and the transverse shifts should not be simultaneously observable. A very strong amplification of these shifts could be obtained by using a multilayered structure. Measurements have been done, giving 50 μm for Lx and 30 μm for Ly.

Displacement of a totally reflected light beam: filtering of he polarization states and amplification

Models for the Goos–Haenchen effect

This work is the computation of the shift, parallel to the incident plane, by total reflection, of a light beam (Goos and Hanchen effect). The incident wave is choosen so as to satisfy the Maxwell equations. It is expanded as a superposition of plane waves, part of which are inhomogeneous (or evanescent). The corresponding reflected plane waves are recomposed, which allows to obtain the energy flux of the reflected beam. The results are compared with those obtained by the approximate known formulas, and also with Goos and Hanchen's measurements.

http://iopscience.iop.org/article/10.1088/0335-7368/4/2/301/pdf

M Ricard

Papers

Computation of the Goos and Hänchen shift for a limited light beam