Experimental generation of Helical Mathieu-Gauss vector modes

TL;DR

This paper introduces a new class of vector light modes called helical Mathieu-Gauss beams, demonstrating their theoretical foundation, experimental generation, and potential applications in optical trapping and communications.

Contribution

It presents the first theoretical and experimental realization of helical Mathieu-Gauss vector modes, expanding the diversity of spatial modes beyond cylindrical symmetry.

Findings

Successfully generated helical Mathieu-Gauss vector modes experimentally.

Provided both qualitative and quantitative characterizations of these modes.

Demonstrated potential applications in optical trapping and communications.

Abstract

Vector modes represent the most general state of light in which, the spatial and polarisation degrees of freedom are coupled in a non-separable way. Crucially, while polarisation is limited to a bi-dimensional space, the spatial degree of freedom can take any spatial profile. However, most generation and application techniques are mainly limited to spatial modes with polar cylindrical symmetry, such as Laguerre- and Bessel-Gauss modes. In this manuscript we put forward a novel class of vector modes with its spatial degree of freedom encoded in the set of helical Mathieu-Gauss beams of the elliptical cylindrical coordinates. We first introduce these modes theoretically and outline their geometric representation on the higher-order Poincar\'e sphere. Later on, we demonstrate their experimental generation using a polarisation-insensitive technique comprising the use of a digital micromirror device. Finally, we provide with a qualitative and a quantitative characterisation of the same using modern approaches based on quantum mechanics tools. It is worth mentioning that non-polar vector beams are highly desired in various applications, such as optical trapping and optical communications.