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 focused RSABs, and to show, in particular, that only circular polarised RSABs maintain their self-accelerating character upon focusing. Moreover, we also calculate the linear and angular momentum for paraxial vector RSABs, and discuss both their global and local properties. (paper)