Evolution of Spatiotemporal Intensity of Partially Coherent Pulsed Beams with Spatial Cosine-Gaussian and Temporal Laguerre–Gaussian Correlations in Still, Pure Water

A new family of partially coherent pulsed beams with spatial cosine-Gaussian and temporal Laguerre–Gaussian correlations, named correlated Schell-model (SCTLGSM) beams, is introduced. An analytic propagation formula derived for the SCTLGSM beam through spatiotemporal ABCD optical system characterizing a continuous dispersive medium. As an example, evolution intensity in still, pure water column then investigated. It found that simultaneously exhibit self-splitting self-focusing phenomena, which can be attributed to special spatial/temporal coherence structures presence pulse chirper source plane. The physical interpretation obtained phenomena given. results this paper will interest underwater technologies, e.g., directed energy communications.