Time-Domain Simulations of the Nonlinear Maxwell Equations Using Operator-Exponential Methods
Time-Domain Simulations of the Nonlinear Maxwell Equations Using Operator-Exponential Methods
复制标题
使用算子指数方法对非线性麦克斯韦方程进行时域模拟
DOI：
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复制
发表时间：
2009
影响因子：
5.7
通讯作者：
K. Busch
中科院分区：
文献类型：
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作者：
Martin Pototschnig;J. Niegemann;L. Tkeshelashvili;K. Busch
本文提出了一种基于Krylov子空间的算子指数方法，用于一般非线性极化的麦克斯韦方程的时域模拟。这包括（经典的）chi（2）-或chi（3）-非线性和/或非线性耦合系统动力学。作为一个例子，我们比较我们的方法的性能与某些众所周知的方法的情况下，脉冲自陡峭的材料与负克尔非线性。对于该系统，我们还开发了适当的分析参考解决方案。此外，我们还证明，我们的方法可以处理与电磁场耦合的各种物理系统（经典和/或量子）的复杂非线性动力学。
In this paper, we propose a Krylov-subspace-based operator-exponential method for time-domain simulations of the Maxwell equations with general nonlinear polarizations. This includes (classical) chi(2)- or chi(3)- nonlinearities and/or nonlinear coupled system dynamics. As an illustration, we compare the performance of our approach to certain well-known methods for the case of pulse self-steepening in a material with negative Kerr-nonlinearity. For this system, we also develop an appropriate analytical reference solution. In addition, we demonstrate that our approach allows to treat the complex nonlinear dynamics of various physical systems (classical and/or quantum) coupled to electromagnetic fields.