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International Conference on Transparent Optical Networks

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

Julien Bouchat, Julien Fagnart, Yves Caudano

Published Jul 14, 2024• 0 citations

Abstract

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.

DOI: 10.1109/icton62926.2024.10647424

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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 optical analogue of quantum weak measurements has shown considerable promise for the amplification and observation of tiny optical beam shifts, namely Goos-Hänchen (GH) and Imbert-Fedorov (IF) shifts. Here, we demonstrate simultaneous weak value amplification of both the angular GH and the IF shifts in partial reflection of a fundamental Gaussian beam at planar dielectric interfaces. We employ pre and postselection schemes with appropriate linear polarization basis states for simultaneous weak measurements and amplification of both of these shifts. The experimentally observed enhancement of the beam shifts and their dependence on the angle of incidence are analyzed/interpreted via theoretical treatment of weak measurements.

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.

An optical analog of the quantum weak measurement scheme proved to be very useful for the observation of optical beam shifts. Here we adapt the weak value amplification method to the observation of the angular Goos-Hänchen shift. We observe this effect in the case of external air-dielectric reflection, the more fundamental case in which it occurs. We show that weak measurements allow for a faithful amplification of the effect at any angle of incidence, even at Brewster's angle of incidence.

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.

The spatial and the angular variants of the Imbert-Federov (IF) beam shifts and the angular Goos-Hanchen (GH) shift contribute in a complex interrelated way to the resultant beam shift in partial reflection at planar dielectric interfaces. Here, we show that the two variants of the IF effects can be decoupled and separately observed by weak value amplification and subsequent conversion of spatial to angular nature of the beam shifts using appropriate pre and post-selection of polarization states. Such optimized weak measurement schemes also enable one to nullify one effect (either the GH or the IF) and exclusively observe the other. We experimentally demonstrate this and illustrate various other intriguing manifestations of optimized weak measurements in elliptical and / or linear polarization basis. We also present a Poincare sphere based analysis on conversion / retention of the angular or spatial nature of the shifts with pre and post-selection of states in weak measurement. In another separate experiment we set up a Mach-Zender interferometer with the weak measurement scheme for partial reflection in one hand of the interferometer to observe the effect of the geometric phase gradient at the time of weak measurement and interpret the effect as an effective rotation of the interference fringe pattern.