The degree of coherence function of a light beam could be used for optical encryption, robust optical imaging, and other purposes. However, recent works demonstrated that it has a puny self-reconstruction ability that gets worse as the obstacle is further away from the source. In this manuscript, we propose a method by which, with the help of only the introduction of a cross-phase structure in the degree of coherence function, the self-reconstruction ability of the degree of coherence function could be significantly enhanced. The performance of the method is independent of the location of the obstacle. The results, achieved in this manuscript, will shed new light on optical imaging, optical encryption, and optical communication in a complex environment.

Partially coherent pulses, especially those with non-Gaussian correlated functions, have rarely been explored in nonlinear media because of the demanding procedure of the widely used coherent-mode representation method. This study develops temporal analogues of the complex screen and phase screen methods, which were recently introduced for the spatial counterpart of a partially coherent beam. These methods were employed to study the beam propagation properties of partially coherent pulses, and the obtained results show that they both are highly precise, convenient, and powerful. We believe that these protocols can effectively provide useful insight into the behavior of many coherence-related phenomena in nonlinear media.