Numerical methods for nanophotonics: standard problems and future challenges

Abstract

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 as new materials such as graphene is discussed in the perspective of actual and future challenges for computational nanophotonics.

Template‐Directed Solidification of Eutectic Optical Materials

“…Phase-field simulations, coupled with well-established optical simulations, [223] can be critical in predicting the expected structures, and useful for designing templates to achieve microstructures specific to the desired optical applications. The developed phase-field model provides an efficient tool to investigate how a structure is influenced by a wide range of variables, including material properties and processing parameters.…”

Recent Advances in Resonant Waveguide Gratings

“…Integral methods have been reviewed in more detail for nanophotonics. [89] We describe below the method formulation for a periodic array of scatterers in a multilayer environment ( Figure 4c). Assuming that a single scatterer is composed of M subunits at position r i , the electric field in the unit cell of the periodic structure excited by an incident electric field E 0 is given by the following expression.…”

“…However, the computational effort scales rapidly with the size of the scatterers. Integral methods have been reviewed in more detail for nanophotonics …”

“…Hybrid and time domain methods based on FEs include the finite elements in time domain method (FETD) and the discontinuous Galerkin time domain method . In contrast to FDTD, the use of basis functions enables the accurate description of the geometry of micro‐ and nanostructures, which can be crucial when studying the influence of nanoscale variations of shapes on the electromagnetic response . The modes as well as their resonance frequencies, losses, and spatial extension can be directly calculated.…”

Near-Field Localization of Single Au Cubes: A Group Theory Description

“…The BEM method is related to the surface integral equation method. 43 For more details, see refs 18−20. The Au nanocubes are modeled on an infinite ITO layer whose refractive index is fixed at n ITO = 2.…”