Spectral Methods and Domain Decomposition for Nanophotonic Applications
Spectral Methods and Domain Decomposition for Nanophotonic Applications
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DOI：
10.1109/jproc.2012.2218791
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发表时间：
2013-02
影响因子：
20.6
通讯作者：
M. Luo;Yun Lin;Q. Liu
中科院分区：
文献类型：
--
作者：
M. Luo;Yun Lin;Q. Liu
纳米光子应用通常涉及对计算资源有过度需求的大规模问题。我们开发了一个区域分解方法（DDM），以减少计算机内存和中央处理器（CPU）的时间需求相结合的谱元法（SEM）和谱积分法（SIM）的大规模有限周期结构。每个周期内的内部散射子域由SEM建模，而外部散射问题由SIM建模。相邻子域之间的相互作用是由频域版本的黎曼解。数值收敛的黎曼解是快速和弱依赖于系统的大小。两组例子展示了典型的纳米光子应用：第一个周期系统是基于光子晶体板的垂直耦合波导，它开辟了一种构建和模拟光路的方法。第二个周期系统是一个有限尺寸的超材料与有效的负折射率，其边缘效应进行了可视化和分析。
Nanophotonic applications often involve large-scale problems with excessive demand on computational resources. We develop a domain decomposition method (DDM) to reduce computer memory and central processing unit (CPU) time requirements by combining the spectral element method (SEM) and the spectral integral method (SIM) for large-scale finite periodic structures. The interior scattering subdomains within each period are modeled by the SEM while the exterior scattering problem is modeled by the SIM. The interactions between neighboring subdomains are modeled by the frequency-domain version of the Riemann solver. Numerical convergence of the Riemann solver is fast and weakly dependent on the size of the system. Two sets of examples demonstrate the typical nanophotonic applications: The first periodic system is a vertical coupling waveguide based on a photonic crystal slab which opens a way to construct and simulate optical circuits. The second periodic system is a finite-sized metamaterial with an effective negative refractive index, whose edge effects are visualized and analyzed.