Analytical propagation of supergaussian-like beams in the far-field

The analytical propagation of coherent supergaussian (SG)-like beams was calculated after F. Gori [Optics Comm. 107 (1994) 335] by introducing a linear superposition of Laguerre-Gauss functions called ''flattened gaussian beam''. Here we propose a new family of SG-like beams, written as the convolution of a gaussian with a rectangle function; then, the well known convolution theorem allows a straightforward and simple analytical calculation of the beam profile in the focal plane of an arbitrary focusing system, In addition, this method tan be successfully applied to more complex cases, as the SG-like beams commonly emitted by hard-edged unstable resonators (beam energy distribution with a hole).