Simulation of the nonlinear Kerr and Raman effect with a parallel local time-stepping DGTD solver

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. (c) 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement

Automated summary

In this paper, an efficient discontinuous Galerkin time-domain (DGTD) method is proposed for solving Maxwell's equations in nonlinear Kerr or Raman media. The method incorporates a high-order derivatives DGTD method with a local time-stepping scheme, allowing for independent time-stepping increments in the nonlinear and linear media regions. This greatly improves the efficiency of time-domain analysis. The proposed method preserves local features and offers an effective tool for numerical analysis of nonlinear optical phenomena.