Lanczos pseudospectral method for initial-value problems in electrodynamics and its applications to ionic crystal gratings

Maxwell's equations are cast in the form of the Schrödinger 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 propagation and scattering of broad-band electromagnetic pulses in dispersive and absorbptive 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, dielectric, and ionic crystal gratings with rectangular and cylindrical geometry. The effects of polaritonic excitations on transmission (reflection) properties of ionic crystal gratings in the infra-red range are investigated in detail. In particular, it is shown that, in addition to structural (geometric) resonances, resonant polaritonic excitations can drastically change light transmission.