  We show that radiation from complex and inherently random but correlated wave
sources can be modelled efficiently by using an approach based on the Wigner
distribution function. Our method exploits the connection between correlation
functions and theWigner function and admits in its simplest approximation a
direct representation in terms of the evolution of ray densities in phase
space. We show that next leading order corrections to the ray-tracing
approximation lead to Airy-function type phase space propagators. By exploiting
the exact Wigner function propagator, inherently wave-like effects such as
evanescent decay or radiation from more heterogeneous sources as well as
diffraction and reflections can be included and analysed. We discuss in
particular the role of evanescent waves in the near-field of non-paraxial
sources and give explicit expressions for the growth rate of the correlation
length as function of the distance from the source. Furthermore, results for
the reflection of partially coherent sources from flat mirrors are given. We
focus here on electromagnetic sources at microwave frequencies and modelling
efforts in the context of electromagnetic compatibility.
