Numerical Study on Normalized Split-step Fourier Method and Fourth-order Runge-Kutta Method in Laser Pulses Generation by Use of Photonic Crystal Fibers

In this work, we study the generation of ultrashort femtosecond laser pulses in photonic crystal fibers through the widely used symmetric split-step Fourier method (S-SSFM). The results are compared with the method of fourth-order Runge-Kutta method (RK4) as the most recognized and powerful method in the analysis of the evolution of ultrashort femtosecond laser pulses. The results show that although S-SSFM is a widely used method, its accuracy decreases for the selected relatively large step sizes of  in comparison with RK4. In contrast, the accuracy of the mentioned methods becomes closer to each other by selecting relatively small step sizes of .