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arXiv:1912.08632 · Journal of Modern Optics

Lateral shifts and angular deviations of Gaussian optical beams reflected by and transmitted through dielectric blocks: a tutorial review

Stefano De Leo, Gabriel G. Maia

Published Dec 1, 2019• 16 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1080/09500340.2019.1696995

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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.
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.
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.
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.
The interference between optical beams of different polarizations plays a fundamental role in reproducing the optical analog of the electron spin weak measurement. The extraordinary point in optical weak measurements is represented by the possibility to estimate with great accuracy the Goos-Haenchen (GH) shift by measuring the distance between the peak of the outgoing beams for two opposite rotation angles of the polarizers located before and after the dielectric block. Starting from the numerical calculation of the GH shift, which clearly shows a frequency crossover for incidence near to the critical angle, we present a detailed study of the interference between s and p polarized waves in the critical region. This allows to determine in which conditions it is possible to avoid axial deformations and reproduce the GH curves. In view of a possible experimental implementation, we give the expected weak measurement curves for Gaussian lasers of different beam waist sizes propagating through borosilicate (BK7) and fused silica dielectric blocks.