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arXiv physics/0504060physics.opticsphysics.comp-ph
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三维光子晶体和光子晶体波导的FEM模型

FEM Modelling of 3D Photonic Crystals and Photonic Crystal Waveguides

S. Burger, R. Klose, A. Schaedle, F. Schmidt, L. Zschiedrich

摘要:

我们提出了一个有限元模拟工具,用于计算三维纳米光学器件中的光场。这允许在标准个人计算机上解决具有挑战性的问题。我们提出了解决本征值问题,如布洛赫型本征值在光子晶体和光子晶体波导,散射问题,如通过有限光子晶体的传输。离散化是基于非结构化的四面体网格与自适应网格细化控制和误差估计器引导。我们使用高阶向量元素(Nederlands,edge elements)作为反函数。为了快速收敛解,我们使用适用于矢量麦克斯韦方程组的高级多重网格算法。

英文摘要:

We present a finite-element simulation tool for calculating light fields in 3D nano-optical devices. This allows to solve challenging problems on a standard personal computer. We present solutions to eigenvalue problems, like Bloch-type eigenvalues in photonic crystals and photonic crystal waveguides, and to scattering problems, like the transmission through finite photonic crystals. The discretization is based on unstructured tetrahedral grids with an adaptive grid refinement controlled and steered by an error-estimator. As ansatz functions we use higher order, vectorial elements (Nedelec, edge elements). For a fast convergence of the solution we make use of advanced multi-grid algorithms adapted for the vectorial Maxwell's equations.

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