Generalized Elliptical Vector modes

Abstract: The strong coupling between the spatial and polarisation degrees of freedom (DoF) in vector modes enables a diverse array of exotic, inhomogeneous polarisation distributions through a non-separable superposition, which are conventionally generated in circular-cylindrical symmetry. Here, we theoretically and experimentally demonstrate a generalized class of vector modes specified in elliptical spatial coordinates and elliptical polarisation. This generalisation gives rise to an even larger set of vector beams with more intricate polarisation distributions. Crucially, controlling the beam parameters allows engineering of vector beams with predefined polarisation trajectories on the Poincar\'e sphere. This capability offers potential applications, for example in optical communications, where precise polarisation control can significantly enhance data transmission and security.