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High Accuracy Algorithms for Computing Light Propagation in Dielectrics, Dispersive Matierials and Metamaterials

用于计算电介质、色散材料和超材料中光传播的高精度算法

基本信息

批准号：
17560029
负责人：
JAMES Cole B.
金额：
$ 2.44万
依托单位：
University of Tsukuba
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
2005
资助国家：
日本
起止时间：
2005 至 2007
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-17560029/
关键词：
Photonic crystal Maxwell's equation optical switch FDTD algorithm Mie scattering GNSFD calculation optical circuit optical memory 応用光学量子デバイス光工学フォトニック結晶メタマテリアル FDTD RCアルゴリズム

项目摘要

It is very difficult to compute the optical properties of structures (such as diffraction gratings) made out of metamaterials and dispersive materials. When the structure is neither symmetric nor infinitely periodic, there are no analytic solutions of Maxwell's equations, and it is necessary to use a numerical method. The finite difference time domain algorithm (FDTD) can handle arbitrary structures, but for dispersive materials recursive convolution (RC) must be added to the FDTD algorithm. This not only greatly increases the computational cost, but also the algorithm may become numerically unstable. For designing devices it is often sufficient to do a two-dimensional calculation.The high computational cost of two-dimensional calculations is also high, but in the TE mode (electric field, E, perpendicular to the incidence plane of an infinite plane wave) the electric and magnetic fields can be computed independently. Even when the electric permittivity varies with position, E is govern … More ed by the wave equation. We have developed a new RC-FDTD algorithm for the wave equation, which greatly reduces the computational cost of the TE mode. When RC is added to the FDTD algorithm, a physical model of the dispersion must be used, but unless the model parameters are carefully chosen the FDTD algorithm may become numerically unstable. We have carefully analyzed the stability of the FDTD algorithm, and have found the conditions that guarantee stability. We have done this for both the TE and TM mode (E perpendicular to the plane of incidence). In addition we have found out how to optimize the dispersion model parameters according to frequency to improve the accuracy of the calculation. Our new algorithm is more accurate than the usual one and is stable. We verified the accuracy of our new algorithm by computing the optical characteristics of large periodic structures 8 effectively infinite) and comparing with analytic solutions.We used our algorithm to study metallic gratings made of gold and silver in the infrared region. Less

计算由超材料和色散材料制成的结构（如衍射光栅）的光学特性是非常困难的。当结构既不是对称的，也不是无限周期的，没有解析解的麦克斯韦方程组，它是必要的，使用数值方法。时域有限差分算法（FDTD）可以处理任意结构，但对于色散材料，必须在FDTD算法中加入递归卷积（RC）。这不仅大大增加了计算成本，而且算法可能变得数值不稳定。对于设计器件来说，通常进行二维计算就足够了。二维计算的计算成本也很高，但在TE模式（电场，E，垂直于无限平面波的入射面）中，电场和磁场可以独立计算。即使当电容率随位置而变化时， ...更多信息艾德的波动方程。我们提出了一种新的RC-FDTD算法，大大降低了TE模式的计算量。当RC被添加到FDTD算法中时，必须使用色散的物理模型，但是除非仔细选择模型参数，否则FDTD算法在数值上可能变得不稳定。我们仔细分析了FDTD算法的稳定性，并找到了保证稳定性的条件。我们已经对TE和TM模式（E垂直于入射平面）进行了此操作。此外，我们还发现了如何根据频率优化色散模型参数，以提高计算的准确性。我们的新算法比通常的算法更准确，并且是稳定的。通过计算大周期结构的光学特性并与解析解进行比较，验证了新算法的准确性，并将其应用于金、银金属光栅的红外光谱研究。少