A Krylov‐subspace based solver for the linear and nonlinear Maxwell equations

Abstract

Abstract We describe an efficient Krylov‐subspace based operator‐exponential approach for solving the Maxwell equations. This solver exhibits excellent stability properties and high‐order time‐stepping capabilities that allow to address nonlinear wave propagation phenomena and/or coupled system dynamics. Furthermore, the usage of a non‐uniform spatial grid facilitates the realization of a high‐order spatial discretization in the presence of discontinuous material properties. This ideally complements the time‐stepping capabilities of our solver so that complex nano‐photonic problems may be treated with high accuracy and efficiency. We illustrate these features through an analysis of the prototypical problem of spontaneous emission from a collection of two‐level atoms that are embedded in finite Photonic Crystals and are exposed to dephasing as well as non‐radiative decay processes. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)