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

In this work, we develop a novel computational method, referred to as SCT-$Z$-FDTD, which integrates the $Z$-transform finite-difference time-domain algorithm with a scale-compressed technique incorporating wave vectors. The proposed approach facilitates accurate modeling of electromagnetic wave propagation through multilayered anisotropic media, enabling precise evaluation of reflection and refraction coefficients over short time 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 transverse electromagnetic, transverse electric, and transverse magnetic to detect the specific propagation. To further verify lower memory and higher efficiency, we select various multilayered examples with anisotropies for executing the proposed method. Compared with the popular commercial software COMSOL, those data from multilayered computation are quite consistent with the approximate trend the 2nd-order error convergence.