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Weak Measurements on Optical Systems

Sayandip Dhara

Published Apr 1, 2016• 0 citations
OpenAlex

Abstract

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.

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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 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 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 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 basics of weak measurement and its various applications are discussed here. The optical analogue of weak measurement. which was predicted by E C G Sudarshan was also demonstrated with the experimental results. The optical activity of chiral molecules is also calculated with the help of weak measurement. We also 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 post selection schemes with appropriate linear polarization basis states for simultaneous weak measurements and amplification of both of these shifts.We also studied these GH and IF shifts for higher order beams (for example Vortex beams)and how its get coupled. Geometric Hall effect of light is also studied with the help of weak measurement and we get the expected nature according to the theory.
We describe how the notion of optical beam shifts (including the spatial and angular Goos-Hänchen shift and Imbert-Federov shift) can be understood as a classical analogue of a quantum measurement of the polarization state of a paraxial beam by its transverse amplitude distribution.Under this scheme, complex quantum weak values are interpreted as spatial and angular shifts of polarized scalar components of the reflected beam.This connection leads us to predict an extra spatial shift for beams with a radially-varying phase dependance.Contents 1. Introduction 2 2. Weak quantum measurement 4 3.The analogy between beam shifts and quantum measurement 5 4. The case of radial and azimuthally varying pointer phase 9 5. Discussion