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arXiv:1608.07528 · Optics Letters

Weak measurement of the composite Goos–Hänchen shift in the critical region

Octávio J. S. Santana, Silvânia A. Carvalho, Stefano De Leo, Luís E. E. de Araujo

Published Aug 11, 2016• 61 citations
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Abstract

By using a weak measurement technique, we investigated the interplay between the angular and the lateral Goos-Hänchen shift of a focused He-Ne laser beam for incidence near the critical angle. We verified that this interplay dramatically affects the composite Goos-Hänchen shift of the propagated beam. The experimental results confirm theoretical predictions that recently appeared in the literature.

DOI
10.1364/ol.41.003884

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By using a weak measurement technique, we investigated the interplay between the angular and the lateral Goos-Hänchen shift of a focused He-Ne laser beam for incidence near the critical angle. We verified that this interplay dramatically affects the composite Goos-Hänchen shift of the propagated beam. The experimental results confirm theoretical predictions that recently appeared in the literature.
For incidence in the critical region, the propagation of Gaussian lasers through dielectric blocks is characterized by the joint action of angular deviations and lateral displacements. This mixed effect, known as the composite Goos-H\"anchen shift, produces a lateral displacement that is dependent on the axial coordinate, recently confirmed by a weak measurement experiment. We discuss under which conditions this axial lateral displacement, which only exists for the composite Goos-H\"anchen shift, presents an oscillatory behavior. This oscillation phenomenon shows a peculiar behavior of light for critical incidence and, if experimentally tested, could stimulate further theoretical studies and lead to interesting optical applications.
Optical beam shifts are very small and challenging phenomena to measure. Weak measurement techniques have been developed to amplify and more easily measure the shifts of spatially coherent beams. We here investigate theoretically a weak measurement technique for measuring the Goos–Hänchen shift of partially spatially coherent beams. We show that the amplification factor of the technique depends on the global coherence degree of the field and on the size of the Goos–Hänchen shift experienced by the beam. Large amplification factors can be obtained for low shifts, even for very incoherent beams. But, for higher beam shifts, such as those occurring near critical incidence, the amplification factors are modest to low for beams of low coherence.
In this work, we summarize the current state of understanding of lateral displacement and angular deviations of an optical beam propagating through dielectric blocks. In part I, the analytical formulas, found for critical incidence, are compared with numerical calculations and, when possible, extended from Gaussian to more general angular distributions. Angular deviations are discussed both for the critical and for the Brewster incidence. The combined effect, known as the composite Goos–Hänchen shift, shows an interesting axial dependence and, under particular circumstances, the intriguing phenomenon of the light oscillation. In part II, the weak measurement technique is discussed in detail and compared with direct optical measurements.
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.
Abstract We analyze and compare the angular deviations for an optical beam reflected by and transmitted through a dielectric triangular prism. The analytic expressions derived for the angular deviations hold for arbitrary incidence angles. For incidence approaching the internal and external Brewster angles, the angular deviations transverse magnetic waves present the same behavior leading to the well‐known giant Goos‐Hänchen angular shift. For incidence near the critical angle a new region of large shift is seen both for transverse magnetic and transverse electric waves. While a direct measuring procedure is better in the vicinity of the Brewster region, a weak measurement breaks off the giant Goos‐Hänchen effect, preserving the amplification in the critical region. We discuss under which conditions it is possible to optimize the amplification and we also determine when a weak measurement is preferred to a direct measuring procedure.
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.