Numerical methods for nanophotonics: standard problems and future challenges

Nanoscale photonic systems involve a broad variety of light-matter interaction regimes beyond the diffraction limit and have opened the path for a variety of application opportunities in sensing, solid-state lighting, light harvesting, and optical signal processing. The need for numerical modeling is central for the understanding, control, and design of plasmonic and photonic nanostructures. Recently, the increasing sophistication of nanophotonic systems and processes, ranging from simple plasmonic nanostructures to multiscale and complex photonic devices, has been calling for highly efficient numerical simulation tools. This article reviews the state of the art in numerical methods for nanophotonics and describes which method is the best suited for specific problems. The widespread approaches derived from classical electrodynamics such as finite differences in time domain, finite elements, surface integral, volume integral, and hybrid methods are reviewed and illustrated by application examples. Their potential for efficient simulation of nanophotonic systems, such as those involving light propagation, localization, scattering, or multiphysical systems is assessed. The numerical modeling of complex systems including nonlinearity, nonlocal and quantum effects as well [GRAPHICS] as new materials such as graphene is discussed in the perspective of actual and future challenges for computational nanophotonics.