等离子体散射FDTD分析的移位算子方法

Shift operator method applied for dispersive medium in FDTD analysis

色散介质的介电系数是频率的函数,使本构关系在时域成为卷积关系,这就给应用FDTD方法计算色散介质中波的散射和传播带来困难。文中把色散介质的相对个电系数写成以jω为自变量的有理分式函数,用/t代替jω,过渡到时域,再引入离散时域移位算子代替时间微分算子来处理有理分式函数形式的介电系数,进而导出FDTD中电位移矢量D和电场强度E之间的关系。所得结果与Z变换理论的梯形近似结果一致,但与Z变换理论相比较,移位算子方法推导简单,概念简明。文中用移位算子结合FDTD方法分别计算一维等离子体平板的反射系数和二维等离子体柱的远场散射。所得结果与用Z变换理论结合FDTD方法计算的结果相符合。

The analysis of electromagnetic scattering and propagation for dispersive media is complicated in time domain, because its dielectric property is frequency-dependent. The complex permittivity of general dispersive media may be described by rational polynomial fraction in jω. By introducing z, defined as a shift operator, the relation between D and ?is derived in time domain. This shift operator method is then applied to the dispersive medium case. The recursive relation for D and E a-vailable for FDTD computation is obtained. The derived formulation is of the same form as trapezoidal approximation used in Z transform. However the proposed concept is concise and easily understandable. The FDTD and the relation between D and E are applied t0 calculate scattering for electromagnetic wave incident on perfectly conducting cylinder coated with plasma. The computed result is in good a-greement with the one obtained by using Z-transform technique.