Discontinuous Galerkin methods in nanophotonics

• Published in: Laser & photonics reviews Vol. 5; no. 6; pp. 773 - 809
• Main Authors: Busch, K., König, M., Niegemann, J.
• Format: Journal Article
• Language: English
• Published: Berlin WILEY-VCH Verlag 01-11-2011; WILEY‐VCH Verlag; Wiley-VCH
• Subjects: Applied classical electromagnetism; Computer simulation; discontinuous Galerkin methods; Electromagnetic wave propagation, radiowave propagation; Electromagnetism; electron and ion optics; Exact sciences and technology; Finite element method; frequency-domain simulations; Fundamental areas of phenomenology (including applications); Galerkin methods; light-matter interaction; Mathematical analysis; Maxwell's equations; Micro- and nanooptical devices; Nanocomposites; Nanomaterials; Nanophotonics; Nanostructure; Optics; Physics; plasmonics; Solvers; time-domain simulations; frequency-domain simulations; Theoretical study; Maxwell's equations; Radiation matter interactions; Nanostructures; Maxwell equations; time-domain simulations; Galerkin-Petrov method; Finite element method; Nanophotonics; discontinuous galerkin methods; light-matter interaction; Plasmonics
• ISSN: 1863-8880; 1863-8899; 1863-8899
• DOI: 10.1002/lpor.201000045

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.