Description of high-power laser radiation in the paraxial approximation

We consider the feasibility of an adequate description of a laser pulse of arbitrary shape within the framework of the paraxial approximation. In this approximation, using a parabolic equation and an expansion in the small parameter, expressions are obtained for the field of a sufficiently intense laser radiation given in the form of axially symmetric Hermite - Gaussian beams of arbitrary mode and arbitrary polarisation. It is shown that in the case of sufficiently short pulses, corrections to the transverse components of the laser field are the first-order rather than the second-order quantities in the expansion in the small parameter. The peculiarities of the description of higher-mode Hermite - Gaussian beams are outlined.