Experimental generation of helical Mathieu–Gauss vector modes

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 paper we put forward a novel class of vector modes whose spatial degree of freedom is encoded in the helical Mathieu–Gauss beams of the elliptical cylindrical coordinates. We first introduce these modes theoretically and outline their geometric representation on the higher-order Poincaré sphere. Later on, we demonstrate their experimental generation using a polarisation-insensitive technique comprising the use of a digital micromirror device. Finally, we provide 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 desirable in various applications, such as optical trapping and optical communications.