Extended theory of FDTD S- and P-eigenmodes in lossy media and its application to the analysis of coupled problems

FDTD solutions in lossy media are shown to comprise two orthogonal families of S- and P-eigenmodes. The S-modes are counterparts of physical waves, retaining their fundamental properties such as current continuity. Contrary to the lossless case, they are subject to bilateral dispersion, although the numerical anisotropy of the FDTD mesh is actually reduced. The P-modes do not propagate and decay exponentially in time. This makes Maxwell FDTD suitable for coupling with other physical solvers, which may change the electromagnetic media properties and boundaries in time. Any thus generated numerical changes are included in and dissipated by the P-modes.