Numerical representation of tightly focused ultra-short laser pulses

Abstract

A scheme for numerical representation for the fields of tightly focused laser pulses is presented going beyond the paraxial framework that gives accurate values up to near single-cycle pulses. The laser field is defined by a solution of the paraxial Helmholtz equation and a temporal pulse profile in light-cone coordinates, the fourth- and second-order corrections are provided for short pulses and vector beams, and the absolute error of these terms is presented. The method can give an accurate field description for any transverse electromagnetic mode, and it is suited for providing initial fields for existing solvers for Maxwell’s equations, such as in the particle-in-cell codes.