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In a recent publication [Opt. Lett.37, 2970 (2012)10.1364/OL.37.002970], a novel class of planar stochastic sources, generating far fields with flat intensity profiles, was introduced. In this paper we examine the behavior of the spectral density and the state of coherence of beamlike fields generated by such sources on propagation in free space and linear isotropic random media. In particular, we find that at sufficiently large distances from the source, the medium destroys the flat intensity profile, even if it remains such for intermediate distances from the source.

A recently introduced class of scalar multi-Gaussian Schell-model (MGSM) beams is extended to the electromagnetic domain. The realizability conditions and the beam conditions for the parameters of the new source are established. The behavior of the polarization properties of the beam on propagation in free space and in first-order imaging systems is investigated. The formation of the uniform polarization state in the central part of the transverse beam cross-section is explored in detail.

We present a detailed investigation, qualitative and quantitative, on how the atmospheric turbulence with a non-Kolmogorov power spectrum affects the major statistics of stochastic electromagnetic beams, such as the spectral composition and the states of coherence and polarization. We suggest a detailed survey on how these properties evolve on propagation of beams generated by electromagnetic Gaussian Schell-model sources, depending on the fractal constant alpha of the atmospheric power spectrum.

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The review covers publications concerned with propagation of laser beams through turbulent media described by the Kolmogorov theory and generalizations thereof to describe signal transmission in optical communications and detection systems. In this case, the turbulent medium is interpreted as an optical channel with random parameters. Various optical signals considered include partially coherent beams, non-uniformly polarized vector beams, as well as specifically configured spatial laser beams. Special attention is given to vortex laser beams. The latter are shown to have a number of remarkable properties that give them an advantage over conventional Gaussian beams.

The dependence of spectral shifts and switches in optical stochastic beams propagating through nonclassic turbulent medium on the slope of the power spectrum of fluctuations in the refractive index is revealed.

Optical beams radiated by a recently introduced class of Rectangular Multi-Gaussian Schell-Model (RMGSM) source are examined on propagation in free space and in atmospheric turbulence, with both classic and non-classic power spectra of the refractive-index fluctuations. The expression for the cross-spectral density function of such beams has been derived and used for the analysis of their spectral density (average intensity). The RMGSM beams are shown to preserve the square/rectangular shape of the transverse intensity distribution and the maximum intensity level in the flat part for relatively large distances from the source on propagation in classic turbulence. This makes the novel beams attractive for free-space optical communications and surface processing in the presence of the atmosphere.