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arXiv:1205.2253 · Optics Express

Weak measurements of a large spin angular splitting of light beam on reflection at the Brewster angle

Xinxing Zhou, Hailu Luo, Shuangchun Wen

Published Jun 28, 2012• 31 citations
arXivHTMLPDF

Abstract

We reveal a large spin angular splitting of light beam on reflection at the Brewster angle both theoretically and experimentally. A simple weak measurements system manifesting itself for the built-in post-selection technique is proposed to explore this angular splitting. Remarkably, the directions of the spin accumulations can be switched by adjusting the initial handedness of polarization.

DOI
10.1364/oe.20.016003

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We reveal a large spin angular splitting of light beam on reflection at the Brewster angle both theoretically and experimentally. A simple weak measurements system manifesting itself for the built-in post-selection technique is proposed to explore this angular splitting. Remarkably, the directions of the spin accumulations can be switched by adjusting the initial handedness of polarization.
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Since its first introduction over twenty years ago, weak measurements have gradually became an useful metrology tool in the laboratory. Due to its desirable amplification effect, a small physical variable can be detected with weak measurements. Spin splitting of light, which stems from the interaction between the spin and orbital angular momentum in optical reflection or refraction at the interface of mediums, is always a weak effect. However, the spin splitting of light can be detected easily with weak measurements. Remarkably, the spin splitting of light is sensitive to the physical parameter variations of system. Using the spin splitting as a probe, the physical parameter can be accurately estimated with weak measurements. Here, we review some of our works on precision metrology with weak measurements using the spin splitting of light as a probe, such as estimation of the magneto-optical constant of a magnetic film, determination of the focused beam waist, and measurement of the polarization state of light.
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.
The magnitudes of beam shifts (Goos-Hänchen and Imbert-Fedorov, spatial and angular) are greatly enhanced when a reflected light beam is postselected by an analyzer, by analogy with superweak measurements in quantum theory. Particularly strong enhancements can be expected close to angles at which no light is transmitted for fixed initial and final polarizations. We derive a formula for the angular and spatial shifts at such angles (which includes the Brewster angle), and we show that their maximum size is limited by higher-order terms from the reflection coefficients occurring in the Artmann shift formula.
Geometric Spin Hall effect of light (SHEL) has attracted considerable attention because of the universality of this variant of the spin Hall shift and its independence on the light-matter interactions and materials properties. However, the magnitude of geometric SHEL is typically very small, in the sub-wavelength domain, making it difficult for direct experimental observation. Here, we have applied weak measurement schemes to amplify and faithfully observe the geometric SHEL. In our experiment, the input beam is pre-selected in linear polarization basis (p- or slinear polarization) and post selections are done at nearly orthogonal linear polarizations (small angle ϵ away from the exact orthogonal).This results in weak value amplification (~cotϵ) of the resulting shift of the beam centroid. Moreover, this process also leads to selective conversion of spatial to angular nature of geometric SHEL, which along with the weak value amplification leads to manifold amplification of the resulting SHEL, enabling its reliable experimental detection. A key feature of our weak measurement scheme is that both the weak perturbation (tiny geometric SHEL) and the post selection are done simultaneously by a single optical element, namely, a linear polarizer. The dependence of the weak value of the geometric SHEL on the pre and the post selection of polarization states in both linear and elliptical basis were also investigated in details. The specifics of the different weak measurement schemes, various intriguing experimental manifestations of the weak value amplified geometric SHEL, their analysis / interpretation via polarization operator based treatment of weak measurements is presented here.