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arXiv:1511.03062

Selective observation of Goos-Hänchen and Imbert-Federov shifts in partial reflection via optimized weak measurements in linear and elliptical polarization basis

Goswami, S., Sajal Dhara, Mandira Pal, Arindam Nandi, Panigrahi, P. K., Nirmalya Ghosh

Published Nov 10, 2015• 1 citation
arXivHTMLPDF

Abstract

The spatial and the angular variants of the Goos-Hänchen (GH) and the Imbert-Federov (IF) beam shifts contribute in a complex interrelated way to the resultant beam shift in partial reflection at planar dielectric interfaces. Here, we show that the angular GH and the two variants of the IF effects can be decoupled, amplified and separately observed by weak value amplification and subsequent conversion of spatial$\leftrightarrow$angular nature of the beam shifts using appropriate pre and post selection of polarization states. We experimentally demonstrate such decoupling and illustrate various other intriguing manifestations of weak measurements by employing optimized pre and post selections (based on the eigen polarization states of the shifts) elliptical and / or linear polarization basis. The demonstrated ability to amplify, controllably decouple or combine the beam shifts via weak measurements may prove to be valuable for understanding the different physical contributions of the effects and for their applications in sensing and precision metrology

DOI
10.48550/arxiv.1511.03062

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The spatial and the angular variants of the Goos-Hänchen (GH) and the Imbert-Federov (IF) beam shifts contribute in a complex interrelated way to the resultant beam shift in partial reflection at planar dielectric interfaces. Here, we show that the angular GH and the two variants of the IF effects can be decoupled, amplified and separately observed by weak value amplification and subsequent conversion of spatial↔\leftrightarrow↔angular nature of the beam shifts using appropriate pre and post selection of polarization states. We experimentally demonstrate such decoupling and illustrate various other intriguing manifestations of weak measurements by employing optimized pre and post selections (based on the eigen polarization states of the shifts) elliptical and / or linear polarization basis. The demonstrated ability to amplify, controllably decouple or combine the beam shifts via weak measurements may prove to be valuable for understanding the different physical contributions of the effects and for their applications in sensing and precision metrology
The spatial and the angular variants of the Imbert-Federov (IF) beam shifts and the angular Goos-Hänchen (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 ↔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. The demonstrated ability to amplify, controllably decouple or combine the beam shifts via weak measurements may prove to be valuable for understanding the different physical contributions of the effects and for their applications in sensing and precision metrology.
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.
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 propose and demonstrate the weak measurement scheme to simultaneously measure the amplified angular and spatial contributions to the Goos–Hänchen (GH) and Imbert-Fedorov (IF) shifts, due to transmission through a glass plate. We have studied two cases of post-selection using a polarizer in the first case and a quarter-wave plate (QWP)–polarizer combination in the second case. The two cases are analyzed theoretically using Jones calculus of polarization formalism and the results are verified experimentally. In the first case of post-selection, the projection of the polarizer at ± Δ away from the crossed position amplifies the angular GH and IF shifts, while in the second case of post-selection, the projection of QWP at ± Δ and polarizer kept fixed measures the polarization ellipticity in the beam and thus amplifies the spatial shift along with the angular shift simultaneously, for Δ ≪ 1 .
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.
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.