Efficient Finite-Difference Time-Domain Method for Solving Electromagnetic Scattering in Layered Anisotropies

In this article, we propose an efficient numerical method for layered models based on the conventional finite difference time-domain (FDTD) method. The three-dimensional (3-D) layered model is compressed into one-dimensional (1-D) calculation, which improves the problem of large space memory and long running time for 3-D modeling while ensuring the accuracy and feasibility of the algorithm. On the one hand, by employing the transformation relationship between the transverse wave vector and the field in space, the expanded Maxwell's rotation equations are simplified, so that the equation system only retains the spatial transformation in the propagation direction. This processing allows for the calculation of the propagation characteristics of layered media without requiring more computational resources. On the other hand, to ensure the universality of the algorithm, a fully tensor anisotropic medium is selected for detecting the propagation data. At the same time, we design the layered structure and conduct the consistent 3-D modeling in the simulation software COMSOL. The results showed that our proposed efficient numerical algorithm greatly reduced the loss of computing resources while ensuring accuracy.