Partially coherent beam propagation

We investigate the propagation of a partially coherent beam produce by a plane source. By utilizing Helmholtz equation, the intensity of the source in plane z=0, and plane z are obtained. Then by considering new theoretical prediction on cross-spectral density function of the field in the plane z=0, the root-means square (rms) beam radius, as a function of distance z are calculated. The effects of the size and coherence of the source on beam directionality will be then discussed. In the special case when the beam is the Gaussian Schell-Model type, our results reduces to well known expression.