The Centroid Shifts of Light Beams Reflected from Multi-Layers and the Effects of Angular Momentum Manifestations

TL;DR

This paper investigates how Laguerre-Gaussian beams' centroid shifts upon reflection from multi-layered dielectrics, highlighting the effects of angular momentum, especially vortex beams, and providing a unified analysis of these phenomena.

Contribution

It introduces a combined perturbation and computational method to quantify centroid shifts in layered dielectrics, extending analysis to vortex beams with intrinsic orbital angular momentum.

Findings

Centroid shifts can reach microns for vortex beams with significant reflection.

Angular momentum influences lateral shifts, especially under total internal reflection.

Layer thickness affects the magnitude of centroid shifts, with thinner layers enhancing shifts.

Abstract

Laguerre-Gaussian (LG) beams reflected from a multi-layered dielectric experience a shift in their centroid that is different than that from a single interface. This has been previously investigated for linearly polarized beams and, to a much lesser extent, beams with spin angular momentum. Here a combination of perturbation and computational analyses is used to provide a unified quantification of these shifts in layered dielectrics with two parallel interfaces. The approach is then extended to consider the qualitatively new behavior that results when the light is endowed with an intrinsic orbital angular momentum--i.e. vortex beams. Destructive interference causes singular lateral shifts in the centroid of the reflected vortex beam for which spin alone produces only a mild modulation. In the case of total internal reflection, both spin and intrinsic orbital angular momentum contribute to an enhancement of these lateral shifts as the interlayer thickness is decreased. This is just the opposite of the trend associated with longitudinal shifts. Two geometries are considered: air/glass/air and glass/air/glass multi-layers. A commonly available glass is used to show that vortex beams can result in centroid shifts on the order of microns for beams with a significant reflection coefficient.