Theory of the Goos-Hänchen Displacement in Total Internal Reflection

Abstract

Since the Goos-Hänchen (GH) effect is the displacement of the totally reflected beam at a dielectric interface from the position prediction by geometrical reflection, the concept of GH displacement is applicable only when the reflected beam retains the shape of the geometrically reflected or incident beam. The necessary and sufficient condition has been advanced for the totally reflected beam to retain the shape of the incident beam. Numerical simulations have been performed to confirm this condition. It has been shown that the GH displacement results from the mechanism of beam reshaping due to the linear dependence of the reflection phase shift upon the parallel component of the wave vector, in the interval in which the angular spectral distribution function of the incident beam is appreciable.

Near-field optical trapping with an actively locked cavity

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“…Through decades' investigations by researchers (Artmann, 1948;Renard, 1964;Carniglia, 1976;McGuirk and Carniglia, 1977;Lai et al, 1986;Shi et al, 2007;Bliokh and Aiello, 2013), several approximated mathematical expressions have been derived for calculating the GHS by using the reflection coefficient, the energy flux vector, or the momentum. People found that albeit the GHS is typically a beam effect which appears for beams with finite cross-sections, the calculations of GHS can be achieved by computing plane waves' phase variations of the reflection coefficient.…”