Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Journal of the Optical Society of America B

Weak measurement of the Goos–Hänchen shift of partially coherent light beams

Octávio J. S. Santana, Luı́s E. E. de Araujo

Published Jan 31, 2019• 6 citations
Publisher

Abstract

Optical beam shifts are very small and challenging phenomena to measure. Weak measurement techniques have been developed to amplify and more easily measure the shifts of spatially coherent beams. We here investigate theoretically a weak measurement technique for measuring the Goos–Hänchen shift of partially spatially coherent beams. We show that the amplification factor of the technique depends on the global coherence degree of the field and on the size of the Goos–Hänchen shift experienced by the beam. Large amplification factors can be obtained for low shifts, even for very incoherent beams. But, for higher beam shifts, such as those occurring near critical incidence, the amplification factors are modest to low for beams of low coherence.

DOI
10.1364/josab.36.000533

Related papers

Quantum weak measurement of Goos–Hänchen effect of light in total internal reflection using a Gaussian-mode laser beam

Akash Das, Manik Pradhan

Abstract We report a detailed experimental demonstration of the Goos–Hänchen (GH) shift of light in total internal reflection condition for a Gaussian mode laser beam of 633 nm passing through an air-glass interface. The quantum weak measurement (QWM) technique has been exploited as a weak value amplification scheme to observe the amplified optical GH shift. The amplification of the GH shift depends on the angular deviation from the exact orthogonal position required for weak measurement. We have subsequently investigated the profiles of the beam pattern and their horizontal and vertical shifts in detail. We also show that the beam shift values obtained experimentally agree well with the theoretical results for a specific choice of angle of deviation from the orthogonal condition of weak measurement. Our results clearly demonstrate the advantages of the QWM technique for amplifying and detecting tiny optical beam shift effects and may provide important applications in precision metrology.

Laser Physics Letters•May 11, 2020•10 citations

Probing Goos-Hänchen shifts in surface nonlinear optics by quantum weak measurements

Julien Bouchat, Julien Fagnart, Yves Caudano

The Goos-Hänchen shifts are tiny deviations, in the incidence plane, from the laws of geometrical optics, which are observed when applying these laws to the central axes of incident and reflected light beams. The axis of the reflected beam does not generally emanate from the surface at the incidence point of the impinging beam (spatial shift) and the angle of the axis of the reflected beam does not generally match exactly the incidence angle (angular shift). In this theoretical work, we show how to exploit pre- and post-selected weak measurements of the light polarization to probe the spatial and angular Goos-Hänchen shifts occurring for paraxial Gaussian beams emitted by a surface nonlinear optical process, such as second-harmonic (SHG) of sum-frequency generation (SFG). Pre- and post-selected weak measurements, which were initially developed to probe foundational issues in quantum mechanics, proved very useful to enhance the minute shifts in linear optics that were undetectable otherwise, through a process called weak-value amplification. We further reveal the usefulness of amplified weak measurements in the context of nonlinear optics.

International Conference on Transparent Optical Networks•Jul 14, 2024•0 citations

Weak measurement of the composite Goos–Hänchen shift in the critical region

Octávio J. S. Santana, Silvânia A. Carvalho, Stefano De Leo +1 more

By using a weak measurement technique, we investigated the interplay between the angular and the lateral Goos-Hänchen shift of a focused He-Ne laser beam for incidence near the critical angle. We verified that this interplay dramatically affects the composite Goos-Hänchen shift of the propagated beam. The experimental results confirm theoretical predictions that recently appeared in the literature.

arXiv:1608.07528•Optics Letters•Aug 11, 2016•61 citations

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

Negative and positive Goos-Hänchen shifts of partially coherent light fields

Ziauddin Ziauddin, You-Lin Chuang, Ray‐Kuang Lee

The negative and positive Goos-H\"anchen (GH) shifts in reflected light are revisited for a partial coherent light incident on a cavity. A three-level dilute gaseous atomic medium, which follows two-photon Raman transitions, is considered in a cavity. The anomalous (negative group index) and normal (positive group index) dispersions of the intracavity medium lead to negative and positive GH shifts, respectively. The effects of beam width, spatial coherence, and mode index of partial coherent light fields are studied on the negative and positive GH shifts. It is observed that the amplitude of negative and positive GH shifts are relatively large for a small range of beam width and for a small value of spatial coherence of partial coherent light beams. The amplitude of GH shifts becomes small for large beam width and spatial coherence of incident light. Further, the distortion in the reflected light field increases when the amplitude of the GH shifts increases and vice versa.

Physical Review A•Jan 5, 2015•38 citations

Observing angular deviations in light beam reflection via weak measurements

Gaurav Jayaswal, Giampaolo Mistura, Michele Merano

We report the first observation of the angular Goos-Hänchen shift for a Gaussian light beam via weak value amplification. Weak measurements faithfully amplify the effect at any angle of incidence, even at Brewster.

Frontiers in Optics•Jan 1, 2014•6 citations
Optical beam shifts are very small and challenging phenomena to measure. Weak measurement techniques have been developed to amplify and more easily measure the shifts of spatially coherent beams. We here investigate theoretically a weak measurement technique for measuring the Goos–Hänchen shift of partially spatially coherent beams. We show that the amplification factor of the technique depends on the global coherence degree of the field and on the size of the Goos–Hänchen shift experienced by the beam. Large amplification factors can be obtained for low shifts, even for very incoherent beams. But, for higher beam shifts, such as those occurring near critical incidence, the amplification factors are modest to low for beams of low coherence.
Abstract We report a detailed experimental demonstration of the Goos–Hänchen (GH) shift of light in total internal reflection condition for a Gaussian mode laser beam of 633 nm passing through an air-glass interface. The quantum weak measurement (QWM) technique has been exploited as a weak value amplification scheme to observe the amplified optical GH shift. The amplification of the GH shift depends on the angular deviation from the exact orthogonal position required for weak measurement. We have subsequently investigated the profiles of the beam pattern and their horizontal and vertical shifts in detail. We also show that the beam shift values obtained experimentally agree well with the theoretical results for a specific choice of angle of deviation from the orthogonal condition of weak measurement. Our results clearly demonstrate the advantages of the QWM technique for amplifying and detecting tiny optical beam shift effects and may provide important applications in precision metrology.
The Goos-Hänchen shifts are tiny deviations, in the incidence plane, from the laws of geometrical optics, which are observed when applying these laws to the central axes of incident and reflected light beams. The axis of the reflected beam does not generally emanate from the surface at the incidence point of the impinging beam (spatial shift) and the angle of the axis of the reflected beam does not generally match exactly the incidence angle (angular shift). In this theoretical work, we show how to exploit pre- and post-selected weak measurements of the light polarization to probe the spatial and angular Goos-Hänchen shifts occurring for paraxial Gaussian beams emitted by a surface nonlinear optical process, such as second-harmonic (SHG) of sum-frequency generation (SFG). Pre- and post-selected weak measurements, which were initially developed to probe foundational issues in quantum mechanics, proved very useful to enhance the minute shifts in linear optics that were undetectable otherwise, through a process called weak-value amplification. We further reveal the usefulness of amplified weak measurements in the context of nonlinear optics.
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.
The negative and positive Goos-H\"anchen (GH) shifts in reflected light are revisited for a partial coherent light incident on a cavity. A three-level dilute gaseous atomic medium, which follows two-photon Raman transitions, is considered in a cavity. The anomalous (negative group index) and normal (positive group index) dispersions of the intracavity medium lead to negative and positive GH shifts, respectively. The effects of beam width, spatial coherence, and mode index of partial coherent light fields are studied on the negative and positive GH shifts. It is observed that the amplitude of negative and positive GH shifts are relatively large for a small range of beam width and for a small value of spatial coherence of partial coherent light beams. The amplitude of GH shifts becomes small for large beam width and spatial coherence of incident light. Further, the distortion in the reflected light field increases when the amplitude of the GH shifts increases and vice versa.