Physics – Computational Physics
Scientific paper
2005-12-08
Physics
Computational Physics
Latex, 17 pages, 4 figures (separate png files); to appear in J. Comput. Phys
Scientific paper
10.1016/j.jcp.2005.12.011
Maxwell's equations for propagation of electromagnetic waves in dispersive and absorptive (passive) media are represented in the form of the Schr\"odinger equation $i\partial \Psi/\partial t = {H}\Psi$, where ${H}$ is a linear differential operator (Hamiltonian) acting on a multi-dimensional vector $\Psi$ 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 is much larger than that in finite differencing schemes, $\Delta t_F \gg \|H\|^{-1}$. 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, $\Delta t_C \sim \|H\|^{-1}$, is exceeded at least in 3000 times in the Faber propagation scheme.
Borisov Andrei G.
Shabanov Sergei V.
No associations
LandOfFree
Wave packet propagation by the Faber polynomial approximation in electrodynamics of passive media does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Wave packet propagation by the Faber polynomial approximation in electrodynamics of passive media, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Wave packet propagation by the Faber polynomial approximation in electrodynamics of passive media will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-443417