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.

Almost all of the beams under propagation are believed to suffer severe distortion when the source coherence deteriorates, due to the optical diffraction. This implies that low-coherence beams have poor self-healing ability, but were found to be robust against the turbulence, distortion, scattering, etc. In this letter, we first prove numerically that partially coherent Airy beams (PCABs), generated via Fourier processing, have better self-healing ability than that of conventional fully coherent Airy beams. Moreover, as the source coherence deteriorates and the propagation distance increases, the self-healing ability is found to increase. We believe that such PCABs may find Airy beam-related applications in adverse environments, such as particle trapping in biological tissues.