We describe a fourth-order accurate finite-difference time-domain scheme for solving dispersive Maxwell's equations with nonlinear multi-level carrier kinetics models. The scheme is based on an efficient single-step three time-level modified equation approach for Maxwell's equations in second-order form for the electric field coupled to ODEs for the polarization vectors and population densities of the atomic levels. The resulting scheme has a large CFL-one time-step. Curved interfaces between different materials are accurately treated with curvilinear grids and compatibility conditions. A novel hierarchical modified equation approach leads to an explicit scheme that does not require any nonlinear iterations. The hierarchical approach at interfaces leads to local updates at the interface with no coupling in the tangential directions. Complex geometry is treated with overset grids. Numerical stability is maintained using high-order upwind dissipation designed for Maxwell's equations in second-order form. The scheme is carefully verified for a number of two and three-dimensional problems. The resulting numerical model with generalized dispersion and arbitrary nonlinear multi-level system can be used for many plasmonic applications such as for ab initio time domain modeling of nonlinear engineered materials for nanolasing applications, where nano-patterned plasmonic dispersive arrays are used to enhance otherwise weak nonlinearity in the active media.
翻译:我们用非线性多级载体动动模型来描述一个第四阶级准确的有限差异时间- 边际办法, 用来用非线性多层载体动动模型解决分散式Maxwell的方程式。 这个办法基于一个高效的单步3个时间级修改方程办法, 用于电场的马克斯韦方程式, 第二阶形式为电极矢量和原子级人口密度的ODE, 并用于电极矢量和原子级人口密度的 ODE 。 由此产生的方案有一个大型的CFL- 1 时间步骤。 不同材料之间的曲线界面会以卷状线网格和兼容条件得到准确的处理。 新的等级调整方程法方法导致一个不要求非线性迭代。 界面的等级法方法导致在界面上进行本地更新,而不会在相近端方向上相交。 复杂的几度结构稳定使用高阶调调调调调调调调调调调调调调和调调调调调调调调, 以二维和三维度的媒体问题得到仔细的处理。 新的等级修改方位式方程式方法导致一个明确方案, 以不要求两个和三维的问题。 以不要求的平面型型型的内平面型的内内式的内式模型模型模型模式, 用于多种式的模型用于多级的多级的多级的多级的多级的内型号型号的内型号的模型, 用于多级的内型号的内型号的内型号的内型号内型号内型号内型号内型号内型号内型号内型号内型号内型号内型号内型号内型号内型号内型号内型号内型号内型号内型号内型号内型号内型号内型号内型号内型号内型号内型号内型号内型号内型号内型号内型号内型号内型号内型号内型号内型号内型号内型号内型内型内型内型内型内型内型内型内型号内型号内型号内型号内型号内型号内型号内型号内型号内型内型内型