Computational modeling of femtosecond optical solitons from Maxwell's equations
Computational modeling of femtosecond optical solitons from Maxwell's equations
复制标题
DOI：
10.1109/3.159548
复制
发表时间：
1992-10
影响因子：
2.5
通讯作者：
P. Goorjian;A. Taflove;R. M. Joseph;S. Hagness
中科院分区：
文献类型：
--
作者：
P. Goorjian;A. Taflove;R. M. Joseph;S. Hagness
提出了一种全矢量非线性麦克斯韦方程组的直接时间积分算法。这种能力允许建模的线性和非线性的瞬时和色散效应在材料介质中的电极化。光学载体的建模被保留。基本的创新是注意到，它是可以处理的线性和非线性卷积积分，描述的色散，作为新的因变量。然后，通过在时域中对线性和非线性卷积积分进行微分，可以导出非线性二阶常微分方程的耦合系统。这些方程与麦克斯韦方程一起求解，确定了非线性色散介质中的电磁场。在考虑Kerr和拉曼相互作用的情况下，计算了飞秒电磁孤子的一维传输和碰撞过程. >
An algorithm is developed that permits the direct time integration of full-vector nonlinear Maxwell's equations. This capability permits the modeling of both linear and nonlinear instantaneous and dispersive effects in the electric polarization in material media. The modeling of the optical carrier is retained. The fundamental innovation is to notice that it is possible to treat the linear and nonlinear convolution integrals, which describe the dispersion, as new dependent variables. A coupled system of nonlinear second-order ordinary differential equations can then be derived for the linear and nonlinear convolution integrals, by differentiating them in the time domain. These equations, together with Maxwell's equations, are solved to determine the electromagnetic fields in nonlinear dispersive media. Results are presented of calculations in one dimension of the propagation and collision of femtosecond electromagnetic solitons that retain the optical carrier, taking into account the Kerr and Raman interactions. >