  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.
