A Wave-Equation-Based Spatial Finite-Difference Method for Electromagnetic Time-Domain Modeling

The conventional finite-difference time-domain method applies discretization to both space and time, leading to the discrete solutions in both space and time. In this letter, we propose a wave-equation-based spatial finite-difference method that discretizes a solution domain in space but not in time. It is based on the spatial eigen decompositions of the field solutions without approximations to temporal derivatives in Maxwell's equations. The solutions of the proposed method are derived analytically, and the field solutions at any time can then be found quickly. The effectiveness and accuracy of this proposed method are numerically validated with examples.