Fast Analysis of Multi-Layered Anisotropic Electromagnetic Propagation Based on Z-Transform Finite-Difference Time-Domain Method with Scale-Compressed Technique

In this article, we present a novel method combining with the Z-transform finite-difference time-domain (Z-FDTD) algorithm and the scale-compressed technique (SCT) containing the wave vectors, abbreviated as SCT-Z-FDTD, to implement the multi-layered electromagnetic propagation in the computer and capture the reflection/refraction coefficients from the complex anisotropies for the short intervals. On first place, considering constitutive relationship between electromagnetic fields (E, H) and fluxes (D, B), Z-transform is employed to the anisotropic Maxwell’s curl equations for completing discrete-time form, and then the transverse wave vectors are exploited along a single direction to design the electromagnetic numerical differential process. After that, with the analysis corresponding flow chart, the plane waves are employed with different modes such as TEM, TE and TM to detect the specific propagation. To further verify lower memory and higher efficiency, we select various multi-layered examples with anisotropies for executing the proposed method. Compared with the popular commercial software COMSOL, those data from multi-layered computation are quite consistent with the approximate trend the 2^nd-order error convergence.