Classically-entangled Ince-Gaussian modes

Complex vector light modes, classically-entangled in their spatial and polarisation degrees of freedom (DoF), havebecome ubiquitous in a vast diversity of research fields. Crucially, while polarisation is limited to a bi-dimensionalspace, the spatial mode is unbounded, it can be specified by any of the sets of solutions the wave equation can supportin the different coordinate systems. Here we report on a class of vector beams with elliptical symmetry where thespatial DoF is encoded in the Ince-Gaussian modes of the cylindrical elliptical coordinates. We outline their geometricrepresentation on the Higher-Order Poincar\'e Sphere, demonstrate their experimental generation and analyse the qualityof the generated modes via Stokes polarimetry. We anticipate that such vector modes will be of great relevance inapplications, such as, optical manipulations, laser material processing and optical communications amongst others.