The scattering of a partially coherent plane-wave pulse on a Gaussian-correlated, quasi-homogeneous random medium is investigated. The analytical expressions for the temporal coherence length and the pulse duration of the scattered field are derived. We demonstrate that the scattering-induced changes in the temporal coherence length and the pulse duration may be used to determine the correlation function of the scattering potential of the medium.

A new class of partially coherent pulses of Schell type with cosine-Gaussian temporal degree of coherence is introduced. Such waves are termed the Cosine-Gaussian Schell-model (CGSM) pulses. The analytic expression for the temporal mutual coherence function of the CGSM pulse in dispersive media is derived and used to study the evolution of its intensity distribution and its temporal degree of coherence. Further, the numerical calculations are performed in order to show the dependence of the intensity profile and the temporal degree of coherence of the CGSM pulse on the incident pulse duration, the initial temporal coherence length, the order-parameter n and the dispersion of the medium. The most important feature of the novel pulsed wave is its ability to split into two pulses on passage in a dispersive medium at some critical propagation distance. Such critical distance and the subsequent evolution of the split pulses are shown to depend on the source parameters and on the properties of the medium in which the pulse travels.

We theoretically define a complete class of partially coherent vortex beams of any radial and azimuthal order and characterize the behavior of their phase singularities and orbital angular momentum. These beams are shown to exhibit a coherence vortex supplement to the van Cittert–Zernike theorem, in which the vortex structure of the random beam reconstitutes upon propagation. This full characterization of a class of partially coherent Laguerre-Gauss beams of any order may find application in free-space optical communication, among other uses.

On the basis of the extended Huygens–Fresnel principle, the analytic expression for the cross-spectral density function of the cosine-Gaussian-correlated Schell-model (CGSM) beams propagating in oceanic turbulence is derived and used to investigate the spectral density and spectral degree of coherence of CGSM beams. The dependence of the spectral density and spectral degree of coherence of CGSM beams on the oceanic turbulence parameters including temperature-salinity balance parameter ω , mean square temperature dissipation rate χ _T and energy dissipation rate per unit mass ϵ is stressed and illustrated numerically. It is shown that oceanic turbulence plays an important role in the evolution of spectral density and spectral degree of coherence of CGSM beams upon propagation.