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Physical Review Letters

Observation of the Goos-Hänchen Shift with Neutrons

V.O. de Haan, Jeroen Plomp, Theo M. Rekveldt, Wicher H. Kraan, A.A. van Well, Robert M. Dalgliesh, Sean Langridge

Published Jan 8, 2010• 103 citations
Publisher

Abstract

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.

DOI
10.1103/physrevlett.104.010401

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On the Goos-Hänchen effect in neutron optics

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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.

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Goos–Hänchen effect in neutron optics and the reflection time of neutron waves

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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.

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Newton's idea spotted in neutrons

An optical effect first proposed in the 17th century by Isaac Newton has now been observed to affect matter as well, thus providing yet further affirmation of wave-particle duality. Newton predicted that a beam of light reflected at a glass–vacuum surface should undergo a minuscule lateral shift. He thought that wavefronts, having reached the vacuum, should “slide” a short distance along the interface before re-emerging and reflecting back into the glass. Given the tiny scale of this effect, however, it was not until 1947 that it was first observed experimentally by the physicists F Goos and H Hänchen.

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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.

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Goos-Hänchen shift for relativistic particles based on Dirac's equation

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The Goos-H\"anchen (GH) shift is a specifical optical phenomenon that describes a shift parallel to the reflected light inside the plane of incidence, when a finite-width light undergoes total internal reflection at the interface of medium. Although the GH shift in optics has been widely observed experimentally, its generalization remains uncovered completely in relativistic quantum mechanics for the spinor structure and the possible existence of Klein's paradox. Through approximation and angular spectrum analysis, we calculate the GH shift for Dirac fermions under relativistic conditions when they are incident obliquely on a three-dimensional infinite potential barrier. Furthermore, we find that the relativistic quantum GH shift will degenerate into the result based on Schr\"odinger equation under nonrelativistic limit, while the GH shift can be negative in Dirac's framework, which is different from the nonrelativistic case.

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Goos-Hänchen Shifts of Partially Coherent Light Fields

Li‐Gang Wang, Shi‐Yao Zhu, Muhammad Suhail Zubairy

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.

arXiv:1307.6256•Physical Review Letters•Nov 26, 2013•52 citations
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-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.
An optical effect first proposed in the 17th century by Isaac Newton has now been observed to affect matter as well, thus providing yet further affirmation of wave-particle duality. Newton predicted that a beam of light reflected at a glass–vacuum surface should undergo a minuscule lateral shift. He thought that wavefronts, having reached the vacuum, should “slide” a short distance along the interface before re-emerging and reflecting back into the glass. Given the tiny scale of this effect, however, it was not until 1947 that it was first observed experimentally by the physicists F Goos and H Hänchen.
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-H\"anchen (GH) shift is a specifical optical phenomenon that describes a shift parallel to the reflected light inside the plane of incidence, when a finite-width light undergoes total internal reflection at the interface of medium. Although the GH shift in optics has been widely observed experimentally, its generalization remains uncovered completely in relativistic quantum mechanics for the spinor structure and the possible existence of Klein's paradox. Through approximation and angular spectrum analysis, we calculate the GH shift for Dirac fermions under relativistic conditions when they are incident obliquely on a three-dimensional infinite potential barrier. Furthermore, we find that the relativistic quantum GH shift will degenerate into the result based on Schr\"odinger equation under nonrelativistic limit, while the GH shift can be negative in Dirac's framework, which is different from the nonrelativistic case.
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.