提出三种求解多模光纤非线性传输方程的误差估计准则—max, sum, ave准则, 将多模误差向量转换为误差标量, 基于对称分步傅里叶的局部误差法实现多模传输自适应步长统一变化.通过仿真高斯脉冲在渐变折射率多模光纤中的传输, 验证了定变步长方法在不同准则下局部误差与全局误差的性能.实验结果表明三种准则的变步长算法都具有收敛性, 且利用sum准则计算局部误差控制步长变化, 在相同计算量的情况下能得到更高的数值精度, 相同全局误差的情况下计算量相对更少, 对进一步提高多模非线性传输方程的计算效率有参考意义.

Three error estimation criteria for solving nonlinear transmission equation of multimode fiber— max, sum and ave criterion are proposed. The multimode error vector is converted to the error scalar, and the adaptive step size uniform change of multi-mode is realized based on the local error method of symmetric split-step Fourier. By simulating the transmission of Gaussian pulse in the graded-index multimode fiber, the performance of local error and global error of the fixed-step and variable-step method in different criteria are verified. The experimental results show that all the variable step size algorithms of the three criteria are convergent, besides, using the sum criterion calculate local error to control step size change can obtain higher numerical precision under the same calculation amount, and in the case of the same global error, the calculation amount is relatively less. The study is of significance for further improving the computational efficiency of multimode nonlinear transmission equations.