Analytical fields of an ultrashort, radially polarized laser with spatial chirp

We find the analytical electromagnetic fields, both paraxial and with non-paraxial corrections, of an ultrashort radially-polarized pulse-beam that has spatial chirp. This represents a powerful description of light that has a combination of both vector polarization and space-time structure, and results in a novel evolution of the fields. The non-paraxial corrections allow for the application of the field solutions to tightly-focused scenarios, whereby we can validate our solution via charged particle trajectories under the influence of such a pulse with high field strength