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K.S.Yee提出的FDTD方法,在差分的过程中,引进了时间、空间的半个步长,需要对格点按半整数进行标记,而矩阵元都是按整数编号,使计算中对矩阵元编号很不方便。本文分析了FDTD差分方法的实质,全部用整数步长和整数格点的中心差分法,得到与K.S.Yee提出的FDTD方法相同的计算效果;在中心介质区对H_z=H_(zx)+H_(zy)进行分离,用PML层中的统一公式,而令公式中σ_x=σ_y=0,σ_x~*=σ_y~*=0,自然得到中心介质区的公式,使中心介质区与PML层的公式在形式上统一起来。本文还计算了高斯型点信号源电磁波在二维均匀介质、在2×2和5×5空气洞阵列介质中的传播,发现在介质中,信号幅值下降,在空气洞中,电磁场的幅值明显上升,说明介质背景中的空气洞有增强电磁波的功能。
KSYee proposed FDTD method, in the process of differentiation, the introduction of the time and space of a half step, the need to mark half-integer lattice points, and matrix elements are integer numbers, the calculation of the matrix element number Very inconvenient. In this paper, we analyze the essence of the FDTD difference method, and use the center difference method of integer steps and integer lattices to obtain the same computational effect as the FDTD method proposed by KSYee. In the central media region, the H_z = H_ (zx) + H_ zy), using the uniform formula in the PML layer, and making the formula σ_x = σ_y = 0 and σ_x ~ * = σ_y ~ * = 0 in the formula, the formula of the central dielectric region is naturally obtained, so that the formula of the central dielectric region and the PML layer Unite in form. In this paper, we also calculate the propagation of Gaussian point source electromagnetic wave in 2 × 2 and 5 × 5 air-hole array medium in two-dimensional homogeneous medium. It is found that the amplitude of the signal decreases in medium, and in the air hole, The value is significantly higher, indicating that the air hole in the media background has the function of enhancing the electromagnetic wave.