Study of high-order nonlinear propagation characteristics of partially coherent beams

This study develops a numerical simulation method and investigates the propagation characteristics of partially coherent beams in nonlinear media, specifically addressing the research gaps related to the accuracy of numerical methods and higher-order nonlinear effects. Key findings include the validated of a new simulation method against the split-step Fourier method with analytical formulas, demonstrating enhanced accuracy. Our findings reveal that, under the higher-order nonlinear effect conditions, the focusing ability of Gaussian-Schell model (GSM) beams under nonlinear conditions is opposite to that when only considering the third-order nonlinear refractive index coefficient (n₂). It is also shown that, at higher intensities, GSM beams exhibit a ring-like intensity distribution similar to Gaussian beams, significantly influenced by coherence levels. This distribution becomes more pronounced with higher-order nonlinear effects, highlighting the role of coherence in shaping beam intensity structures. Overall, this research introduces new methods and deeper insights into the behavior of partially coherent beams in nonlinear media, emphasizing the importance of coherence in controlling nonlinear optical phenomena.