Scale-Compressed Technique in Finite-Difference Time-Domain Method for Multi-Layered Anisotropic Media

In this article, to breakthrough the constraint from conventional finite-difference time-domain (FDTD) method, we firstly propose a scale-compressed technique (SCT) working for the FDTD method, been called SCT-FDTD for short, to reduce three-dimensional (3-D) into one-dimensional (1-D) processes and capture the propagation coefficients. Combining with Maxwell's curl equations, the transverse wave vectors (<italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k_x</i>, <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k_y</i>) can be defined as the fixed values, which let the curl operator become the curl matrix with only <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">z</i>-directional derivative. The obvious advantage demonstrated by above is that it does not require excessive computational processes to obtain high-dimensional numerical results with reasonable accuracy. By comparing with commercial software COMSOL by the TE/TM illumination in multi-layered biaxial anisotropy, those results from SCT-FDTD method are entirely consistent. More importantly, the SCT-FDTD possesses less CPU time and lower computational resources for COMSOL.