Fig. 1. Diagram of simulating Kerr effect by split-step Fourier method

Fig. 2. Intensity distribution under low power density conditions. (a) Overall intensity after synthesis; (b) intensities of different Laguerre-Gaussian modes

Fig. 3. Intensity distribution under high power density conditions. (a) Overall intensity after synthesis; (b) intensity of different Laguerre-Gaussian modes

Fig. 4. Intensity distributions of partially coherent Laguerre-Gaussian beams with different coherent lengths at 0.65 m. (a) Two-dimensional intensity distribution; (b) ratio of peak intensity to center intensity

Fig. 5. Two-dimensional intensity distributions of partially coherent Laguerre-Gaussian beams with different coherent lengths at 0.65 m. (a) σ=1.0ω0; (b) σ=1.5ω0; (c) σ=2.0ω0

Fig. 6. Three-dimensional intensity distributions of partially coherent Laguerre-Gaussian beams with different topological charges at 0.65 m. (a) l=1; (b) l=3; (c) l=5