Numerical propagation of partially coherent beams

Summary form only given. The numerical propagation of a partially coherent beam is a daunting task. Such a beam is characterized by the coherence properties between its field at any two points in a plane perpendicular to its direction of propagation. In general, the description of a partially coherent net beam with a two-dimensional transverse profile thus requires the use of a four-dimensional array of complex numbers, whose propagation is described by a quadruple integral. In order to reduce this considerable burden, numerical studies have considered partially coherent beams with a transverse profile that depends only on one coordinate or beams that are axially symmetric.