  Maxwell's equations are cast in the form of the Schr\"{o}dinger equation.
  The Lanczos propagation method is used in combination with the fast Fourier
pseudospectral method to solve the initial value problem. As a result, a
time-domain, unconditionally stable, and highly efficient numerical algorithm
is obtained for the propagation and scattering of broad-band electromagnetic
pulses in dispersive and absorbing media. As compared to conventional
finite-difference time-domain methods, an important advantage of the proposed
algorithm is a dynamical control of accuracy: Variable time steps or variable
computational costs per time step with error control are possible. The method
is illustrated with numerical simulations of extraordinary transmission and
reflection in metal and dielectric gratings with rectangular and cylindrical
geometry.
