Spectral expansion method in problems of laser-beam propagation in the turbulent atmosphere

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Abstract
A mixed spectral expansion over elementary spherical and plane waves is suggested for use as an approximate solution of the stochastic wave equation describing propagation of optical waves in a turbulent medium. In this case, the complex amplitude of an elementary plane wave is calculated as a solution of a shortened equation, considering only the phase fluctuations of this wave. It is shown that such an approximate solution uniformly approximates statistical moments of the field (up to the fourth order, inclusive) under arbitrary conditions of wave propagation in a turbulent medium and conditions of wave diffraction on the transmitting aperture.