Modeling of plasmonic nanostructures: Green's function integral equation methods

Abstract

AbstractThree Green's function integral equation methods are considered for modeling of plasmonic nanostructures, namely the Green's tensor volume integral equation method (VIEM), the Green's tensor area integral equation method (AIEM), and the Green's function surface integral equation method (SIEM). Modeling of plasmonic nanostructures is challenging because of the large contrast between the involved materials, namely metals and dielectrics, sharp corners and edges with associated electric field singularities, and possibly plasmonic resonances. It was found that a standard discretization scheme based on cubic volume elements (VIEM) for a cylindrical gold scatterer or square area elements (AIEM) for a silver cylinder did not work, which is related to the stair‐cased description of the curved surfaces. In the case of the VIEM an alternative approach is studied based on ring volume elements and softening of sharp edges by using a gradual transition of the dielectric constant rather than having sharp interfaces. In the case of the AIEM special surface matching area elements are shown to drastically improve convergence. In the SIEM it is demonstrated that rounding of corners can be crucial for obtaining convergence in the case of a plasmonic resonance. The three methods are exemplified for a range of plasmonic nanostructures, namely the surface plasmon polariton bandgap structure with a bent waveguide channel, the long‐range surface plasmon polariton grating, and a metal nano‐strip resonator for short‐range surface plasmon polaritons. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)