采用等效介电常数时域差分法分析二维介质型光子晶体色散特性

FDTD Analysis of Dispersion Characteristics of 2D Dielectric Photonic Crystal Described by Effective Permittivity in Grid

针对差分法中难以近似处理不同介质分界面处单元差分网格中沿x,y,z轴各方向等效介电常数值的问题,提出了将"电容串并联"的电路概念引入于各方向等效介电常数的近似计算中,并导出几种非匀质单元网格中等效介电常数的计算式.采用等效介电常数的时域有限差分法计算二维介质型光子晶体的色散特性可灵活地剖分网格,既能获得很高的计算精度,又可节省计算时间和计算内存.此等效介电常数公式也可用于其他电磁问题的差分法分析,以提高计算效率.

According to the analogy concept of series-parallel connection of the capacitance, the approximate formulae of effective permittivity along x,y,z direction for various inhomogeneous unit grids are deduced. Under the condition of numerical stability, these formulae are combined with the finite difference time domain (FDTD) scheme of arbitrary spatial grids to calculate the dispersion characteristics of 2D dielectric photonic crystal. This method can save several times computing time and memory compared with the conventional FDTD method. These effective permittivity formulae can also be employed in other electromagnetic problems to improve the computation efficiency.