Vector Properties of Radially Self-Accelerating Beams

We present a complete and consistent theory of vector radially self-accelerating beams (RSABs). We use this theory as a model for describing the properties of focussed RSABs, and to show, in particular, that only circular polarised RSABs maintain their self-accelerating character upon focussing. Moreover, we also calculate the linear and angular momentum for paraxial vector RSABs, and discuss both their global and local properties.