The Rytov theory for the propagation of Helmholtz-Gauss (HzG) beams in turbulent atmosphere is presented. We derive expressions for the first and second-order normalized Born approximations, the second-order moments, and the transverse intensity pattern of the HzG beams at any arbitrary propagation distance. The general formulation is applied to study the propagation of several special cases of the HzG beams, in particular, the Bessel-Gauss and Mathieu-Gauss beams and their pure nondiffracting counterparts, the Bessel and Mathieu beams. For numerical purposes, we assume the standard Kolmogorov distribution to model the power spectrum of the atmospheric fluctuations.
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Noriega-Manez et al. (2007) studied this question.
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