A Fast Solution of the Dynamic Rate Equation for a High-Power Fiber Laser

In the study of dynamic behaviors, such as nonlinear effects, power evolution, and pulse evolution of light in fiber gain media, solving dynamic rate equations in fiber laser systems is involved, which is computationally intensive and directly affects overall computational efficiency. A modified difference scheme is proposed to solve fiber dynamic rate equations efficiently. The advantages of the improved scheme and its convergence rate are analyzed. By incorporating a correction coefficient into the finite difference, the approximations of spatial and temporal derivatives are improved, greatly enhancing the performance of the numerical method. The computational results of the proposed method are compared with those of the conventional upwind difference scheme, demonstrating that the improved method is more stable and requires fewer sampling points to maintain a certain level of precision, thereby saving significant computation time and computational resources. The power and spectral evolutions of the fiber laser oscillator under different pump conditions are simulated and compared with experimental data, validating the applicability and reliability of the rapid solving method.