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Modeling the Optical Response of Metallic Nanoparticles

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Optical Properties of Metallic Nanoparticles

Part of the book series: Springer Series in Materials Science ((SSMATERIALS,volume 232))

Abstract

A formal solution of rigorous scattering theory for nanoparticles is unfortunately only possible for restricted geometries. There exist analytical solutions for light scattering problems if we expand the electromagnetic potentials and fields to spherical harmonics and limit ourselves to spherical or spheroidal particle shapes. In reality, however, we want to work with arbitrary shaped nanostructures and take advantage of certain structure dependent qualities like the hot spots in the gap regions of bowtie antennas or the magnetic response of split-ring resonators. So in general a more sophisticated numerical method for solving Maxwell’s equations is essential and inevitable. Several different techniques are available and some of them will be discussed in the next sections.

Prediction is very difficult, especially if it’s about the future. Niels Bohr

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Notes

  1. 1.

    Consult [3] for a derivation and discussion of the theorem, also see [4].

  2. 2.

    When the light from our sun reaches earth, the electromagnetic waves get scattered, mostly elastically, by the molecules and suspensoids in our atmosphere which causes the diffuse sky radiation (the characteristic Fraunhofer lines provoked by spectral absorption also occur in a blue sky spectrum of course). Such atmospheric particles are usually much smaller than the light wavelength and thus are a typical example of Rayleigh scattering . Since the short-wavelength part of the radiation becomes more strongly scattered than the longer wavelengths, the bluish part dominates and yields the color of our sky .

  3. 3.

    Born 29th September 1868 in Rostock; † 13th February 1957 in Freiburg im Breisgau.

  4. 4.

    At this point usually a little pedantry sets in and we should not speak of it as a theory but rather call it Mie oder Mie-Gans solution, since it is just a result of Maxwell’s equations under certain circumstances. Nevertheless the name “Mie theory” has become established.

  5. 5.

    We follow the notation of Debye here, otherwise the first Riccati-Bessel function is usually denoted as \(S_{l}(\mbox{ $z$}) = \mbox{ $z$}j_{l}(\mbox{ $z$})\).

  6. 6.

    Examples of application cover the fields of elasticity, geomechanics, structural mechanics, electromagnetics, acoustics, hydraulics, biomechanics, and much more.

  7. 7.

    A short overview about the historical development of the BEM can be found in [29] for example.

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  1. Graz, Austria

    Andreas Trügler

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Trügler, A. (2016). Modeling the Optical Response of Metallic Nanoparticles. In: Optical Properties of Metallic Nanoparticles. Springer Series in Materials Science, vol 232. Springer, Cham. https://doi.org/10.1007/978-3-319-25074-8_4

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