Discontinuous Galerkin methods in nanophotonics

Abstract

This article reviews the state of the recently developed discontinuous Galerkin finite element method for the efficient numerical treatment of nanophotonic systems. This approach combines the accurate and flexible spatial discretisation of classical finite elements with efficient time stepping capabilities. We describe in detail the underlying principles of the discontinuous Galerkin technique and its application to the simulation of complex nanophotonic structures. In addition, formulations for both time- and frequency-domain solvers are provided and specific advantages and limitations of the technique are discussed. The potential of the discontinuous Galerkin approach is illustrated by modelling and simulating several experimentally relevant systems. This article reviews the state of the recently developed discontinuous Galerkin finite element method for the efficient numerical treatment of nanophotonic systems. This approach combines the accurate and flexible spatial discretisation of classical finite elements with efficient time stepping capabilities. The underlying principles of the discontinuous Galerkin technique and its application to the simulation of complex nanophotonic structures are described. The potential of the discontinuous Galerkin approach is illustrated by modelling and simulating several experimentally relevant systems. © 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.