Analysis of High Order FDTD Methods For Maxwell’s Equations in Dispersive Media

The stability properties, and the phase error present in higher order (in space) staggered finite dif-ference schemes for Maxwell’s equations coupled with a Debye polarization model are analyzed. We present a novel expansion of the symbol of finite difference approximations, of arbitrary (even) order, of the first order spatial derivative operator. This representa-tion allows the derivation of a closed-form analytical stability condition for all (even) order schemes, in-cluding the limiting (infinite order) case. We further derive a concise formula for the numerical dispersion relation