Fourier Invariant Singular Wavefields and Beam Shaping Problem

Hermite-Laguerre-Gaussian beams are paraxial structurally stable solutions of the parabolic equation. Some relations of these beams with fractional Fourier transform and the convolution transformation are investigated. The found formulae help to construct phase elements for the focusing of laser irradiance into the fields, whose intensity is shaped like a predetermined flat domain. Results of numerical simulation for some domains (a regular triangle, a square) are presented