Planar, scalar, optical Schell-model, and quasi-homogeneous sources with correlations that are Fourier transforms of multi-Gaussian functions are introduced. It is demonstrated that far fields produced by these families of sources carry interesting characteristics, being flatlike with adjustable steepness of the edge. Beam conditions for such sources are also derived.

Two classes of scalar, stochastic sources are introduced, each capable of producing far fields with intensities forming rings. Although the Bessel–Gaussian and the Laguerre–Gaussian Schell-model sources are described by two different math models, the behavior of their degrees of coherence and, hence, the shapes of their far fields are qualitatively similar. The new beams are of importance for optical methods of particle manipulation.

In a recent publication [Opt. Lett. 37, 2970 (2012) [CrossRef] ], 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 class of random sources producing far fields with rectangular intensity profiles is introduced by modeling the source degree of coherence with the help of two one-dimensional multi-Gaussian distributions. By changing the rms correlation widths along the $x$ and $y$ directions and the number of terms in the summation of the multi-Gaussian functions, the shapes and the edge sharpness of the beams can be adjusted. The results based on the derived analytical expression for the far-zone spectral density are supplemented by the computer simulations.

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 α of the atmospheric power spectrum.

The behavior of scalar beams with nonuniform correlations in isotropic random media is investigated. An example illustrates the fact that the off-axis intensity maximum formed in the transverse cross section of a nonuniformly correlated beam on propagation in free space is suppressed when it passes at sufficiently large distances from its source through the isotropic turbulent atmosphere.