普适化坐标系下的FDTD算法及实现

Finite-difference time-domain method and implementing on general coordinate

时域有限差分(FDTD)算法在光子晶体理论研究中获得了较为广泛的应用,但它在处理一些非均匀、非正交问题时,计算耗时量大,计算效率低.研究了普适化坐标下的光子晶体理论研究方法,对常用的基于笛卡尔坐标系的FDTD算法作了扩展,并设计了一个可以计算一维到三维光子晶体的能带结构和态密度的软件.主要介绍了普适化坐标系下FDTD算法的程序实现,并简要描述了GCFE软件的设计思路.给出了利用该软件计算得到的立方和六角结构的光子晶体光纤的能带结构和光子态密度的结果,与其他研究者报道的结果相吻合.

Finite-Difference Time-Domain （FDTD） method is widely used in theoretical research about photonic crystal. However, it is very time consuming and inefficient. The theoretical method for photonic crystal based on general coordinate is studied , and a software is developed by the authors that can be used to calculate the photonic band structures and photonic states density for one dimensional to three dimensional photonic crystals. Implementing the FDTD method on general coordinate and the design idea of the GCFE software are described in detail. Moreover, the band structures and photonic states density for the photonic crystal fibers with cube and hexagonal structures are calculate by GCFE software, and numerical application results are also shown. The results are coincident with the results reported by other researchers.