Optimized weak measurements of Goos–Hänchen and Imbert–Fedorov shifts in partial reflection

Abstract

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.

Geometric phase topology in weak measurement

“…The quarter wave plate-half wave plate-polarizer combination was also proposed and used for post-selecting the state beyond the ellipse orientation axis (equator) of the Poincaré sphere in the previously reported WM schemes [37][38][39][40][41]. However, the final component in all of the setup is the polarizer, which is a linear state projector that always post-selects the state on the ellipse orientation axis, and we consider the role of the wave plates as the unitary transformation of the weakly interacted state to another state on the Poincaré sphere.…”

Polarization beam splitting in a Glan-Taylor prism based on dual effects of both birefringence and Goos-Hanchen shift

“…Since F. Goos and H. Hanchen experimentally demonstrated GH shift through multiply-reflection [ 10 ], more and more researches have been carried out for the detection of sub-wavelength GH shift, numerous approaches based on multilayered and periodic structures [ 11 ], a single thin dielectric layer [ 12 ], surface plasmon resonance [ 13 ], Brewster angle [ 14 ] and graphene-coated surface [ 15 , 16 ] and Fano resonance [ 17 ], were proposed to enhance the displacement between reflecting point and incident point. In addition, the quantum weak measurement, which has unique advantage in the detection of tiny physical parameter through the weak value amplification, was introduced into the exploring of GH about the direct observation as well as indirect application study [ 18 , 19 , 20 , 21 ]. However, most of these investigations were conducted based on TIR.…”

Simultaneous weak measurement of angular and spatial Goos–Hänchen and Imbert-Fedorov shifts

“…This provides two-fold amplification, the spatial and angular shifts amplification, which are the real and imaginary parts of the weak value respectively due to nearly orthogonal states, and angular shift amplification additionally due to propagation to the far-field  ( ) Z Z R , where Z is propagation distance and Z R is Rayleigh range. Further, investigations have shown that with appropriate preselection and post-selection in a suitable polarization state, one can amplify, nullify or decouple the desired variant angular, spatial, or both, of GH and IF shifts [32][33][34].…”