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.

We introduce a new class of partially coherent sources of Schell type with cosine-Gaussian spectral degree of coherence and confirm that such sources are physically genuine. Further, we derive the expression for the cross-spectral density function of a beam generated by the novel source propagating in free space and analyze the evolution of the spectral density and the spectral degree of coherence. It is shown that at sufficiently large distances from the source the degree of coherence of the propagating beam assumes Gaussian shape while the spectral density takes on the dark-hollow profile.

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.

The propagating modes of a wide-sense stationary Schell-like source with arbitrary coherence state and a twist factor are determined. This suggests a convenient practical method for modeling novel classes of twisted partially coherent beam-like fields. The first example discusses the previously introduced twisted anisotropic Gaussian Schell-model source and verifies the feasibility of this method. As a second example, we introduce a new type of twisted partially coherent beam in which a radiated flat-top average intensity pattern remains invariant in shape (but not size) while it twists around the axis upon propagation.

A new mathematical model called "controllable dark-hollow beams" is introduced to describe hollow beams. The central dark size of this beam can be controlled easily by the beam order N and parameter epsilon. An analytical formula is derived for the propagation of a controllable dark-hollow beam through a paraxial optical system, and some numerical calculations are carried out. Some important propagation characteristics of this beam, such as the beam propagation factor and the kurtosis parameter, are studied in detail, and their variation rules versus the beam order N and parameter epsilon are presented and plotted.