分析周期结构的Crank-Nicolson FDTD方法

常规FDTD方法的最大时间步长受最小离散网格的限制,需要满足CFL(courant-friedrich-levy)稳定性条件。一维Crank-Nicolson FDTD方法采用隐式差分格式,突破了稳定性条件的限制,是求解PBG(photonicband-gap)这类周期性结构目标的有效方法之一。讨论了一维Crank-Nicolson FDTD方法中总场边界的设置,引入总场边界后便于提取周期性结构的反射系数。应用该方法分析了一种周期性结构的反射特性,与用传播矩阵方法所得结果一致。算例也表明了当时间步长取为常规FDTD时间步长100倍时,该算法仍然是无条件稳定的。

Study on the periodic structures with the Crank-Nicolson FDTD method

As the conventional finite-difference time-domain (FDTD) method is based on explicit finite-difference algorithm, the courant-friedrich-levy (CFL) condition must be satisfied when this method is used. Therefore the maximum time-step size is limited by the minimum cell size in computational domain. Based on the implicit finite-difference algorithm, one-dimensional Crank-Nicolson FDTD method free from the CFL condition restraint is discussed. The Crank-Nicolson FDTD is of high efficiency to deal with the periodic structures such as PBG structures. In order to obtain the reflection coefficient of materials, the connection boundary is introduced into this method. The reflection coefficient for a periodic structure computed by this method is in good agreement with the result calculated by the propagating matrix method. Numerical simulation shows that the time-step size can be set 100 times as large as that of the conventional FDTD method, while the C-N FDTD algorithm is still unconditionally stable.