High accuracy models of sources in FDTD computations for subwavelength photonics design simulations
High accuracy models of sources in FDTD computations for subwavelength photonics design simulations
复制标题
DOI：
10.1117/12.2061838
复制
发表时间：
2014-09
期刊：
影响因子：
--
通讯作者：
J. B. Cole;Saswatee Banerjee
中科院分区：
文献类型：
--
作者：
J. B. Cole;Saswatee Banerjee
传统时域有限差分（FDTD）算法中使用的简单源模型会产生较大的误差。传统的二阶FDTD误差较大（阶数h**2/12，h=网格间距），而源模型引起的误差进一步增大了该误差。基于二阶有限差分叠加的非标准 (NS) FDTD 已被证明能够为无源波动方程和麦克斯韦方程 (h**6 / 24192) 提供比传统 FDTD 高得多的精度。由于自由空间中波动方程的格林函数是已知的，我们可以计算点源产生的场。将该解析解插入到 NS 有限差分 (FD) 模型中，并调整源模型的参数，使 FDTD 解与解析解相匹配。为了推导散射场源模型，我们使用总场和入射场的 NS-FD 模型来推导正确的源模型。我们发现产生散射场的源必须以不同于辐射到自由空间的源的方式进行建模。通过与解析解的比较，我们证明了源模型的高精度。这种方法显着提高了不准确性，特别是对于分散场，我们根据米氏理论验证了结果。计算时间和内存要求与传统 FDTD 大致相同。我们应用这些进展来解决亚波长结构中的传播问题。
The simple source model used in the conventional finite difference time domain (FDTD) algorithm gives rise to large errors. Conventional second-order FDTD has large errors (order h**2/ 12), h = grid spacing), and the errors due to the source model further increase this error. Nonstandard (NS) FDTD, based on a superposition of second-order finite differences, has been demonstrated to give much higher accuracy than conventional FDTD for the sourceless wave equation and Maxwell’s equations (h**6 / 24192). Since the Green’s function for the wave equation in free space is known, we can compute the field due to a point source. This analytical solution is inserted into the NS finite difference (FD) model and the parameters of the source model are adjusted so that the FDTD solution matches the analytical one. To derive the scattered field source model, we use the NS-FD model of the total field and of the incident field to deduce the correct source model. We find that sources that generate a scattered field must be modeled differently from ones radiate into free space. We demonstrate the high accuracy of our source models by comparing with analytical solutions. This approach yields a significant improvement inaccuracy, especially for the scattered field, where we verified the results against Mie theory. The computation time and memory requirements are about the same as for conventional FDTD. We apply these developments to solve propagation problems in subwavelength structures.