High-order aberrations of vortex constellations

TL;DR

This paper reports the first direct observation of topological aberration, where high-order optical vortices split into constellations upon reflection, supported by a new theoretical framework and experimental verification.

Contribution

It introduces a general theoretical framework for topological aberrations using symmetric polynomials and experimentally verifies vortex splitting for up to three vortices.

Findings

First direct observation of vortex constellation splitting upon reflection

Development of a theoretical model using elementary symmetric polynomials

Experimental verification with up to three vortices

Abstract

When reflected from an interface, a laser beam generally drifts and tilts away from the path predicted by ray optics, an intriguing consequence of its finite transverse extent. Such beam shifts manifest more dramatically for structured light fields, and in particular for optical vortices. Upon reflection, a field containing a high-order optical vortex is expected to experience not only geometrical shifts, but an additional splitting of its high-order vortex into a constellation of unit-charge vortices, a phenomenon known as topological aberration. In this article, we report on the first direct observation of the topological aberration effect, measured through the transformation of a vortex constellation upon reflection. We develop a general theoretical framework to study topological aberrations in terms of the elementary symmetric polynomials of the coordinates of a vortex constellation, a mathematical abstraction which we prove to be the physical quantity of interest. Using this approach, we are able to verify experimentally the aberration of constellations of up to three vortices reflected from a thin metallic film. Our work not only deepens the understanding of the reflection of naturally occurring structured light fields such as vortex constellations but also sets forth a potential method for studying the interaction of twisted light fields with matter.