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Journal of Optics

Weak measurement of the Goos–Hänchen shift for a Hermite–Gaussian laser beam

Soumen Mandal, Akash Das, Manik Pradhan

Published Feb 23, 2024• 8 citations
Publisher

Abstract

Abstract We report on an experimental investigation of the Goos–Hänchen (GH) optical beam shift in the vicinity of the critical angle of incidence at an air–glass interface using a weak value amplification (WVA) technique for two mutually orthogonal first order Hermite–Gaussian (HG) modes (HG10 and HG01) of a light beam at 633 nm generated by a phase-only reflective spatial light modulator. We have developed a mathematical approach to visualize the beam shaping due to the WVA scheme of beam shifts for the HG modes. The study reveals the angle of incidence dependency of the GH shift in the total internal reflection condition. For both modes, a detailed study of the horizontal and transverse beam shift values with varied post-selection angles is also reported. In addition, a comparison of the beam shift values for both of the selected modes with the fundamental mode (HG00) has been demonstrated. We found a significant enhancement (about two to three times) in the beam shifts for the first order HG10 and HG01 modes compared to the fundamental mode (HG00). Our results clearly demonstrate the advantages of the HG modes of the light beam-exploiting WVA technique and thus may contribute significantly to this field and open up important applications in photonic manipulation and future technologies.

DOI
10.1088/2040-8986/ad2ca6

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Abstract We report on an experimental investigation of the Goos–Hänchen (GH) optical beam shift in the vicinity of the critical angle of incidence at an air–glass interface using a weak value amplification (WVA) technique for two mutually orthogonal first order Hermite–Gaussian (HG) modes (HG10 and HG01) of a light beam at 633 nm generated by a phase-only reflective spatial light modulator. We have developed a mathematical approach to visualize the beam shaping due to the WVA scheme of beam shifts for the HG modes. The study reveals the angle of incidence dependency of the GH shift in the total internal reflection condition. For both modes, a detailed study of the horizontal and transverse beam shift values with varied post-selection angles is also reported. In addition, a comparison of the beam shift values for both of the selected modes with the fundamental mode (HG00) has been demonstrated. We found a significant enhancement (about two to three times) in the beam shifts for the first order HG10 and HG01 modes compared to the fundamental mode (HG00). Our results clearly demonstrate the advantages of the HG modes of the light beam-exploiting WVA technique and thus may contribute significantly to this field and open up important applications in photonic manipulation and future technologies.
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.
We report what we believe is the first experimental evidence of a polarization-controlled Goos–Hänchen (GH) shift for a fundamental Gaussian beam (633 nm) of arbitrary polarization in the vicinity of the critical angle of incidence at the glass–air interface employing a quantum weak measurement technique. Characteristics of the GH shift with different polarization angles and angles of incidence are demonstrated. The experimental findings are in good agreement with the theoretical predictions. This study establishes the critical role of the polarization states of incident light to obtain maximum amplification of a spatial GH shift. We expect that our results may open a pathway toward highly tunable GH shifts that can boost new applications in the modern optical device industry.
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.
We report the direct experimental evidence of the Goos–Hänchen (GH) shift in monolayer molybdenum disulphide ( M o S 2 ) for a Gaussian beam via the quantum weak measurement scheme. We demonstrate the dependence of the GH shift in monolayer M o S 2 on the angle of incidence including the critical angle in the total internal reflection condition. We have also compared the results to the GH shift for single-layer graphene and plane glass–air interface. Our results may open up important applications of M o S 2 in optical devices and sensor industry.
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.
During the past two decades there has been increased interest in the optical excitation of surface plasmon resonance (SPR) at a metal-dielectric interface. This is due in large part to its potential applications in such areas as medical diagnostics and pharmaceutical research. Also occurring during this time has been a growing recognition by the quantum physics community that weak value amplification (WVA) can serve as a valuable metrological research resource. Recently WVA has been used to amplify very small optical Goos-Hänchen (GH) shifts in glass and it has also been shown that SPR can greatly enhance optical GH shifts at the metal/air interface in Kretschmann-Raether (KR) devices. This paper demonstrates experimentally the WVA of an off-resonance GH shift in a KR device and explains why WVA of sufficiently SPR enhanced optical GH shifts cannot be achieved.