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

TL;DR

This paper introduces a comprehensive numerical method for solving 3D light scattering problems, enabling calculation of key optical properties and resonances in complex nanostructures, demonstrated on silver nanoparticle dimers.

Contribution

The paper develops a versatile 3D integral equation formalism for light scattering, extending previous methods to compute various physical quantities and quasinormal modes in nanophotonics.

Findings

Successfully computes extinction cross sections and local density of states.

Accurately determines quasinormal modes and resonance properties.

Demonstrates applicability to plasmonic nanoparticle dimers.

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.