Commun. Comput. Phys., 8 (2010), pp. 1224-1241.

Statistics for Surface Modes of Nanoparticles with Shape Fluctuations

Felix Ruting 1*, Hannes Uecker 2

1 Institut fur Physik, Carl von Ossietzky Universitat, Oldenburg D-26111, Germany.
2 Institut fur Mathematik, Carl von Ossietzky Universitat, Oldenburg D-26111, Germany.

Received 23 February 2010; Accepted (in revised version) 26 March 2010
Available online 25 June 2010


We develop a numerical method for approximating the surface modes of sphere-like nanoparticles in the quasi-static limit, based on an expansion of (the angular part of) the potentials into spherical harmonics. Comparisons of the results obtained in this manner with exact solutions and with a perturbation ansatz prove that the scheme is accurate if the shape deviations from a sphere are not too large. The method allows fast calculations for large numbers of particles, and thus to obtain statistics for nanoparticles with random shape fluctuations. As an application we present some statistics for the distribution of resonances, polariziabilities, and dipole axes for particles with random perturbations.

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PACS: 41.20.Cv, 73.20.Mf
Key words: Electrostatic (boundary-value problems), collective excitations (plasmons), shape fluctuations, numerical scheme, spherical harmonics, projection method.

*Corresponding author.
Email: (F. Ruting), (H. Uecker)

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