Zhang Tiancheng, Peng Yan, Dai Zhou, Bao Huaguang, Xiao Zelong, Chen Xuewen, Ding Dazhi
Opt Express. 2023 Jan 2;31(1):344-354. doi: 10.1364/OE.478225.
In this paper, an efficient discontinuous Galerkin time-domain (DGTD) method is proposed to solve Maxwell's equations for nonlinear Kerr or Raman media. Based on our previous work, an arbitrary high-order derivatives DGTD method with a local time-stepping scheme is introduced for simulating dynamic optical responses in nonlinear dispersive media such that the nonlinear effects do not impose constraints on the stability conditions for linear subdomains. Therefore, the scheme enables the simulations in the nonlinear and linear media regions with independent time-stepping increments, which greatly improves the efficiency of the time-domain analysis. Moreover, by applying an iteration solution scheme, the proposed method preserves the intrinsic local features, which is favorable for the realization of highly parallelized algorithms. Numerical examples demonstrate the accuracy and the efficiency of our proposed method. We believe the proposed method provides an effective tool for numerical analysis of nonlinear optical phenomena.
本文提出了一种高效的时域间断伽辽金（DGTD）方法，用于求解非线性克尔或拉曼介质中的麦克斯韦方程组。基于我们之前的工作，引入了一种具有局部时间步长方案的任意高阶导数DGTD方法，用于模拟非线性色散介质中的动态光学响应，使得非线性效应不会对线性子域的稳定性条件施加限制。因此，该方案能够在非线性和线性介质区域中采用独立的时间步长增量进行模拟，这大大提高了时域分析的效率。此外，通过应用迭代求解方案，所提出的方法保留了固有的局部特征，这有利于实现高度并行化算法。数值算例证明了所提方法的准确性和效率。我们相信所提方法为非线性光学现象的数值分析提供了一种有效的工具。
