FDTD Modeling for Dispersive Media Using Matrix Exponential Method

This letter presents a finite-difference time-domain formulation to model electromagnetic wave propagation in dispersive media using matrix exponential method. The Maxwell's curl equations and the time domain relations between electric fields and auxiliary variables are formulated as a first order differential matrix system. The fundamental solution to such a system is derived in terms of matrix exponential and the update equations can be extracted conveniently from the solution. Numerical results show that this formulation yields higher accuracy compared to many other previous methods, without incurring additional auxiliary variable and complexity.