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Journal of Surface Investigation X-ray Synchrotron and Neutron Techniques

On Observation of the Goos–Hänchen Shift of a Neutron Beam

G. V. Kulin, Aleksandr I Frank, Владимир Алексеевич Бушуев, N. V. Rebrova, Yu. N. Khaydukov

Published Oct 1, 2020• 1 citation
Publisher

Abstract

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.

DOI
10.1134/s1027451020070277

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Physical Review A•Nov 18, 2020•22 citations
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.
The Goos-Hanchen effect, a longitudinal shift of a wave beam at total inner reflection, is a well-known optical phenomenon. It was discovered in 1947 and have been observed many times at reflection of micro- and ultrasonic waves since then. Here we present an elementary theory of the GH. effect to describe reflection of a massive particle and demonstrate how the shift is related to delay time at reflection. It is shown that giant positive or negative longitudinal shifts of the neutron beam may occur at neutron reflection from some specially manufactured planar system. The possibility of delay time measurement at neutron reflection and direct experimental observation of the GH shift are also discussed.
Abstract The Goos–Hänchen (GH) effect, a longitudinal shift of a wave beam at total internal reflection, is well known in optics and has been repeatedly observed for light, micro-, and ultrasonic waves. We consider the GH effect for a massive particle reflected from a material boundary. A close relation is shown to exist between the longitudinal shift and the time delay of reflection. In the case of a neutron reflected from a planar resonant system, a giant longitudinal shift of either positive or negative sign can occur, corresponding to a large reflection group delay time. This time can also be negative, which does not contradict the causality principle. Prospects of the experimental observation of the GH effect and group delay time for neutron reflection are reviewed.
The Goos-Hänchen effect is a spatial shift along an interface resulting from an interference effect that occurs for total internal reflection. This phenomenon was suggested by Sir Isaac Newton, but it was not until 1947 that the effect was experimentally observed by Goos and Hänchen. We provide the first direct, absolute, experimental determination of the Goos-Hänchen shift for a particle experiencing a potential well as required by quantum mechanics: namely, wave-particle duality. Here, the particle is a spin-polarized neutron reflecting from a film of magnetized material. We detect the effect through a subtle change in polarization of the neutron. Here, we demonstrate, through experiment and theory, that neutrons do exhibit the Goos-Hänchen effect and postulate that the associated time shift should also be observable.
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.
We propose a scheme to study the topic of manipulating the Goos-H\"anchen (GH) shift of the reflected beam in an optomechanical cavity (OMC). Our system consists of two mirrors where one is fixed and the other is movable and a two-level atom is trapped inside the OMC. The fixed mirror is partially reflecting, whereas the movable mirror is perfectly reflecting. We theoretically investigated the behavior of the GH shift in the reflected beam when a Gaussian beam is an incident on the OMC. We find that GH shifts can be greatly enhanced in positive or negative directions via manipulating the quantum parameters such as optomechanical strength gmc{g}_{\text{mc}}gmc​ and atom-cavity strength gac{g}_{\text{ac}}gac​ under the influence of beam width of a Gaussian beam. Besides, we study the GH shift in the case of the partially coherent light beam as an incident probe field. Giant negative GH shift is achieved for an incident partially coherent beam in the presence of gmc,gac{g}_{\text{mc}}, {g}_{\text{ac}}gmc​,gac​, a measure of global coherence and beam width of a partially coherent beam. The proposed model provides feasibility in practical experiments for studying the behavior of the GH shift.