Electromagnetic Pulse Propagation in Passive Media by the Lanczos Method
  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. 
Andrei G. Borisov and Sergei V. Shabanov