To simulate nondiffraction-limited laser beams numerically, one needs to understand their nature better. For a phase aberration the correlation length of which is much less than the width of the beam, one can show that the far-field irradiance distribution can be written as the sum of two beams. One beam is the attenuated diffraction-limited beam; the other is a much wider beam the exact shape of which is closely related to the power spectrum of the phase fluctuations. Computer simulations of random phase aberrations are shown to agree well with the analytic predictions. Attempts at simulation of nondiffraction-limited beams for nonlinear wave propagation problems are discussed.
C. B. Hogge, R. R. Butts, and M. Burlakoff, "Characteristics of Phase-Aberrated Nondiffraction-Limited Laser Beams," Appl. Opt. 13, 1065-1070 (1974)