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

Jakob Rosenkrantz de Lasson; Jesper Mørk; Philip Trøst Kristensen

doi:10.1364/JOSAB.30.001996

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

Jakob Rosenkrantz de Lasson, Jesper Mørk, Philip Trøst Kristensen

Research output: Contribution to journal › Journal article › Research › peer-review

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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 quasi-normal 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.

Original language	English
Journal	Optical Society of America. Journal B: Optical Physics
Volume	30
Issue number	7
Pages (from-to)	1996-2007
ISSN	0740-3224
DOIs	https://doi.org/10.1364/JOSAB.30.001996
Publication status	Published - 2013

Bibliographical note

This paper was published in JOSA B and is made available as an electronic reprint with the permission of OSA. The paper can be found at the following URL on the OSA website: http://www.opticsinfobase.org/josab/abstract.cfm?uri=josab-30-7-1996. Systematic or multiple reproduction or distribution to multiple locations via electronic or other means is prohibited and is subject to penalties under law.

Keywords

Mathematical methods in physics
Surface plasmons
Multiple scattering
Computational electromagnetic methods

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10.1364/JOSAB.30.001996

Josab 30 7 1996Final published version, 0.98 MB

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title = "Three-dimensional integral equation approach to light scattering, extinction cross sections, local density of states, and quasi-normal 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{\textquoteright}s tensor, the projected local density of states, and the Purcell factor as well as the quasi-normal 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.",

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author = "{de Lasson}, {Jakob Rosenkrantz} and Jesper M{\o}rk and Kristensen, {Philip Tr{\o}st}",

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Three-dimensional integral equation approach to light scattering, extinction cross sections, local density of states, and quasi-normal modes. / de Lasson, Jakob Rosenkrantz; Mørk, Jesper ; Kristensen, Philip Trøst.
In: Optical Society of America. Journal B: Optical Physics, Vol. 30, No. 7, 2013, p. 1996-2007.

Research output: Contribution to journal › Journal article › Research › peer-review

TY - JOUR

T1 - Three-dimensional integral equation approach to light scattering, extinction cross sections, local density of states, and quasi-normal modes

AU - de Lasson, Jakob Rosenkrantz

AU - Mørk, Jesper

AU - Kristensen, Philip Trøst

N1 - This paper was published in JOSA B and is made available as an electronic reprint with the permission of OSA. The paper can be found at the following URL on the OSA website: http://www.opticsinfobase.org/josab/abstract.cfm?uri=josab-30-7-1996. Systematic or multiple reproduction or distribution to multiple locations via electronic or other means is prohibited and is subject to penalties under law.

PY - 2013

Y1 - 2013

N2 - 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 quasi-normal 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.

AB - 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 quasi-normal 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.

KW - Mathematical methods in physics

KW - Surface plasmons

KW - Multiple scattering

KW - Computational electromagnetic methods

U2 - 10.1364/JOSAB.30.001996

DO - 10.1364/JOSAB.30.001996

M3 - Journal article

SN - 0740-3224

VL - 30

SP - 1996

EP - 2007

JO - Optical Society of America. Journal B: Optical Physics

JF - Optical Society of America. Journal B: Optical Physics

IS - 7

ER -

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

Abstract

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Keywords

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