Lanczos Pseudospectral Propagation Method for Initial-Value Problems in Electrodynamics of Passive Media

Maxwell's equations for electrodynamics of dispersive and absorptive (passive) media are written in the form of the Schr\"odinger equation with a non-Hermitian Hamiltonian. The Lanczos time-propagation scheme is modified to include non-Hermitian Hamiltonians and used, in combination with the Fourier pseudospectral method, to solve the initial-value problem. The time-domain algorithm developed is shown to be unconditionally stable. Variable time steps and/or variable computational costs per time step with error control are possible. The algorithm is applied to study transmission and reflection properties of ionic crystal gratings with cylindric geometry in the infra-red range.