Generalized partially coherent beams with nonseparable phases.

A new, to the best of our knowledge, family of partially coherent beams incorporating a set of nonseparable phases is introduced. Due to the nonnegative definiteness of the cross-spectral density function, these phases cannot survive in the limit of full coherence, which distinguishes them from conventional phase terms. An example of a nonuniform model beam with a quartic nonseparable phase is presented. It is shown that the presence of such a phase in effect stretches the beam in a specific direction upon propagation. In particular, the interplay between the magnitude and phase of the source coherence state endows the beam with a wing-like structure. The fundamental concept developed here brings into evidence the countless nonseparable phases differing from twist, and can be exploited to generate customized partially coherent beams for applications in optics.