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

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.

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