Wave packet propagation by the Faber polynomial approximation in electrodynamics of passive media

JOURNAL OF COMPUTATIONAL PHYSICS

卷:216

Article

Borisov, Andrei G. ; Shabanov, Sergei V.

关键词: Maxwell's equation;    time-domain algorithms;    Fabers polynomial approximation;    global propagation methods;    photonics;    gratings;   

DOI  :  10.1016/j.jcp.2005.12.011

来源: Elsevier

【 摘 要 】

Maxwell's equations for propagation of electromagnetic waves in dispersive and absorptive (passive) media are represented in the form of the Schrodinger equation i partial derivative psi/partial derivative t = H psi, where His a linear differential operator (Hamiltonian) acting on a multidimensional vector T composed of the electromagnetic fields and auxiliary matter fields describing the medium response. In this representation, the initial value problem is solved by applying the fundamental solution exp(-itH) to the initial field configuration. The Faber polynomial approximation of the fundamental solution is used to develop a numerical algorithm for propagation of broad band wave packets in passive media. The action of the Hamiltonian on the wave function psi is approximated by the Fourier grid pseudospectral method. The algorithm is global in time, meaning that the entire propagation can be carried out in just a few time steps. A typical time step Delta t(F) is much larger than that in finite differencing schemes, Delta t(F) >> parallel to H parallel to(-1). The accuracy and stability of the algorithm is analyzed. The Faber propagation method is compared with the Lanczos-Arnoldi propagation method with an example of scattering of broad band laser pulses on a periodic grating made of a dielectric whose dispersive properties are described by the Rocard-Powels-Debye model. The Faber algorithm is shown to be more efficient. The Courant limit for time stepping, Delta t(C) similar to parallel to H parallel to(-1), is exceeded at least in 3000 times in the Faber propagation scheme. (c) 2006 Elsevier Inc. All rights reserved.

【 授权许可】

Free