Short pulse laser beam beyond paraxial approximation.

Nonparaxial perturbative equations are derived from the scalar wave equation by taking into account spatiotemporal couplings. General solutions are obtained in Fourier space and further transformed back in direct space. They depend on parameters that can be used to match various boundary conditions and the perturbative expansion of any nonparaxial exact solutions. This parametrization is used to study the sensitivity of direct electron acceleration off an ultrashort tightly focused laser pulse to nonparaxial corrections of radially polarized electromagnetic fields.