A periodic FMM for Maxwell's equations in 3D and its applications to problems related to photonic crystals
A periodic FMM for Maxwell's equations in 3D and its applications to problems related to photonic crystals
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DOI：
10.1016/j.jcp.2008.01.029
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发表时间：
2008-04
期刊：
影响因子：
--
通讯作者：
Y. Otani;N. Nishimura
中科院分区：
文献类型：
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作者：
Y. Otani;N. Nishimura
本文提出了一种求解三维麦克斯韦方程组周期边值问题的快速多极子方法。考虑到周期性的影响的帮助下，周期性矩局部扩张（M2L）的转换公式，其中包括晶格总和。我们验证所提出的方法通过比较得到的数值结果与多层介质板模型的解析解。然后，我们将所提出的方法应用于周期性二维阵列的介质球的散射问题，并比较所获得的能量透射率与以前的研究。我们也考虑散射问题的木堆晶体，在那里我们找到一个通带相关的本地化模式。通过这些数值试验，我们得出结论，所提出的方法是有效的和准确的。
This paper presents an FMM (Fast Multipole Method) for periodic boundary value problems for Maxwell’s equations in 3D. The effect of periodicity is taken into account with the help of the periodised moment to local expansion (M2L) transformation formula, which includes lattice sums. We verify the proposed method by comparing the obtained numerical results with analytic solutions for models of the multi-layered dielectric slab. We then apply the proposed method to scattering problems for periodic two-dimensional arrays of dielectric spheres and compare the obtained energy transmittances with those from the previous studies. We also consider scattering problems for woodpile crystals, where we find a passband related to a localised mode. Through these numerical tests we conclude that the proposed method is efficient and accurate.