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Physical Review Letters

Photon Mass and New Experimental Results on Longitudinal Displacements of Laser Beams near Total Reflection

GORDON J. TROUP, Jim Francey, R. G. Turner, Andrew Z. Tirkel

Published Jun 5, 1972• 12 citations
Publisher

Abstract

The suggestion of de Broglie and Vigier that an "intermediate shift" might be expected to be obtained in the Goos-Hanchen effect, for plane polarized beams having components both parallel and perpendicular to the plane of incidence of the totally reflective surface, is shown to be untenable. Their quoted experimental results are adequately explained classically.

DOI
10.1103/physrevlett.28.1540

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Photon Mass and New Experimental Results on Longitudinal Displacements of Laser Beams near Total Reflection

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The suggestion of de Broglie and Vigier that an "intermediate shift" might be expected to be obtained in the Goos-Hanchen effect, for plane polarized beams having components both parallel and perpendicular to the plane of incidence of the totally reflective surface, is shown to be untenable. Their quoted experimental results are adequately explained classically.
In conventional optics for light waves, the pioneering work by Goos-Hänchen in 1947 on the lateral shift (or displacement) of a light beam along the surface of a dielectric boundary under the condition of total reflection has stimulated a large number of studies. The key physics behind the Goos-Hänchen shift is the nature of wave interference. From the perspective of wave optics, the incident beam of a finite transverse width can be viewed as composed of plane wave components, each of which has a slightly different transverse wavevector. Each wave component, after the total internal reflection, undergoes a different phase shift, and the superposition of all the reflected wave components gives rise to the lateral shift of the intensity peak in the reflected beam.
The Goos-Hänchen (GH) shift refers to a lateral displacement (from the path expected from geometrical optics) along an interface in totally internal reflection. This phenomenon results from a coherence effect. In order to bring to light the role of coherence, the reflection of partially coherent light fields was investigated within the framework of the theory of coherence. A formal expression for the GH shifts of partially coherent light fields is obtained in terms of Mercer's expansion. It is shown that both the spatial coherence and the beam width have an important effect on the GH shift, especially near the critical angles (such as totally reflection angle). These results are important to observe the GH shifts of the beams with imperfect coherence, like x-ray and matter-wave beams.
When a three-level atomic wavepacket is obliquely incident on a "medium slab" consisting of two far-detuned laser beams, there exists lateral shift between reflection and incident points at the surface of a "medium slab", analogous to optical Goos-Hänchen effect. We evaluate lateral shifts for reflected and transmitted waves via expansion of reflection and transmission coefficients, in contrast to the stationary phase method. Results show that lateral shifts can be either positive or negative dependent on the incident angle and the atomic internal state. Interestingly, a giant lateral shift of transmitted wave with high transmission probability is observed, which is helpful to observe such lateral shifts experimentally. Different from the two-level atomic wave case, we find that quantum interference between different atomic states plays crucial role on the transmission intensity and corresponding lateral shifts.
Abstract It is proposed to perform an experiment to observe the Goos–Hänchen shift during total reflection from a simple resonant system. The main features of the proposed experimental approach are the use of a resonant system that provides a significant increase in the longitudinal shift of the reflected beam, and the presence of an absorber that stops part of the reflected beam in case of its shift. The main goal of the experiment is to obtain quantitative data that allow the comparison with a theory based on the concept of the reflection time.