Three-dimensional integral equation approach to light scattering, extinction cross sections, local density of states and quasinormal modes

Abstract

We present a numerical formalism for solving the Lippmann-Schwinger equation for the electric field in three dimensions. The formalism may be applied to scatterers of different shapes and embedded in different background media, and we develop it in detail for the specific case of spherical scatterers in a homogeneous background medium. In addition, we show how several physically important quantities may readily be calculated with the formalism. These quantities include the extinction cross section, the total Green's tensor, the projected local density of states and the Purcell factor as well as the quasinormal modes of leaky resonators with the associated resonance frequencies and quality factors. We demonstrate the calculations for the well-known plasmonic dimer consisting of two silver nanoparticles and thus illustrate the versatility of the formalism for use in modeling of advanced nanophotonic devices.

14 pages, 10 figures. Accepted for JOSA B

References in corpus (4)

• On the use of Purcell factors for plasmon antennas
• Unusual resonances in nanoplasmonic structures due to nonlocal response
• Effective mode volumes and Purcell factors for leaky optical cavities
• Plasmon-mediated superradiance near metal nanostructures

Cited by in corpus (14)

• Light interaction with photonic and plasmonic resonances
• Modes and Mode Volumes of Leaky Optical Cavities and Plasmonic Nanoresonators
• Normalization of quasinormal modes in leaky optical cavities and plasmonic resonators
• Quasinormal mode solvers for resonators with dispersive materials
• Quasinormal mode approach to modelling light-emission and propagation in nanoplasmonics
• Nanophotonic chiral sensing: How does it actually work?
• How to calculate the pole expansion of the optical scattering matrix from the resonant states
• Design of an efficient single photon source from a metallic nanorod dimer: a quasinormal mode finite-difference time-domain approach
• Calculation, normalization and perturbation of quasinormal modes in coupled cavity-waveguide systems
• A roundtrip matrix method for calculating the leaky resonant modes of open nanophotonic structures
• The local density of optical states in the 3D band gap of a finite photonic crystal
• Resonance frequency and radiative Q-factor of plasmonic and dielectric modes of small objects
• Fourier finite element modeling of light emission in waveguides: 2.5-dimensional FEM approach
• A framework to compute resonances arising from multiple scattering