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Updated: May 27, 2026

Measurement of Scattering Nonlinearities from a Single Plasmonic Nanoparticle

Measurement of Scattering Nonlinearities from a Single Plasmonic Nanoparticle

Published on: January 3, 2016

Boundary element method for surface nonlinear optics of nanoparticles.

Jouni Mäkitalo¹, Saku Suuriniemi, Martti Kauranen

¹Department of Physics, Optics Laboratory, Tampere University of Technology, P. O. Box 692, FI-33101 Tampere, Finland. jouni.makitalo@tut.fi

|November 24, 2011

Summary

We developed a boundary element method for surface second-harmonic generation in nanoparticles. This approach accurately models nonlinear optical phenomena in various nanoparticle shapes and materials.

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Area of Science:

Nanophotonics
Computational Electromagnetics
Materials Science

Background:

Surface second-harmonic generation (SHG) is a key nonlinear optical phenomenon.
Accurate modeling of SHG in nanoparticles is crucial for optical applications.
Existing methods may have limitations in handling arbitrary shapes and materials.

Purpose of the Study:

To present a frequency-domain boundary element formulation for surface SHG.
To enable accurate simulation of SHG from nanoparticles of arbitrary geometry and composition.
To provide a robust theoretical framework for studying nonlinear optical phenomena in nanostructures.

Main Methods:

Utilized the boundary element method (BEM) in the frequency domain.
Employed Rao-Wilton-Glisson (RWG) basis functions and Galerkin's testing for accuracy.
Validated the formulation against multipole expansion for spherical nanoparticles.

Main Results:

Achieved highly accurate solutions for both near-field and far-field SHG.
Demonstrated the method's applicability to non-centrosymmetric nanoparticles (e.g., L-shaped gold).
Illustrated the formation of surface nonlinear polarization and SHG radiation properties.

Conclusions:

The frequency-domain BEM offers a theoretically sound approach for modeling nanoparticle SHG.
The method accommodates experimentally measured or ab-initio material parameters.
This formulation advances the understanding and design of nanophotonic devices utilizing nonlinear effects.