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Dipole Re-Radiation Effects in Surface Enhanced Raman Scattering

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The Mie Theory

Part of the book series: Springer Series in Optical Sciences ((SSOS,volume 169))

Abstract

In this chapter we use extensions of Mie theory to study electromagnetic enhancement factors associated with surface enhanced Raman scattering (SERS) from molecules adsorbed onto metal sphere array structures, comparing results from the more rigorous dipole re-radiation (DR) expression for Raman enhancement with the commonly used plane-wave (PW) enhancement formula. The DR and PW calculations are based on the T-matrix method for determining optical scattering from multiple spheres. In the PW expression, the enhancement is considered to be equal to the product of the squares of the local electric fields, \(|\mathbf{E}_\mathrm{ loc}(\omega )|^2|\mathbf{E}_\mathrm{ loc}(\omega ^{\prime })|^2\) or \(|\mathbf{E}_\mathrm{ loc}(\omega )|^4\) for zero Stokes shift, obtained from plane wave Mie scattering. In the DR calculation, the induced dipole in a molecule that is located at the surface of one of the particles serves as a dipole source at the Stokes-shifted frequency that scatters from the particles to define an overall enhancement factor. The SERS enhancement factors are determined for chains of 100 nm diameter Ag spheres and for chains of 100 nm Ag sphere dimers for various sphere and dimer separations and for various chain lengths, with the dimer gap fixed at 6.25 nm. We compare the PW and DR results for two different detector locations, a backscattering configuration normal to the axis of the chain, and a \(135^\circ \) scattering direction that includes the plane of the chain axis, in order to highlight far-field phase interference effects that are incorporated in the DR result but not PW. We find that the DR and PW results have negligible differences for the backscattering geometry, but far-field effects play a significant role in the overall enhancement factor for the non-backscattered location. This demonstrates the importance of including DR effects in the interpretation of SERS experiments.

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Acknowledgments

This research was supported by grant DE-SC0004752 funded by the US Department of Energy, Office of Science and Office of Basic Energy Sciences.

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Authors and Affiliations

  1. Department of Chemistry, Northwestern University, 2145 Sheridan Road, Evanston, IL, 60208-311, USA

    Logan K. Ausman & George C. Schatz

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  1. Logan K. Ausman
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  2. George C. Schatz
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Correspondence to George C. Schatz .

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Editors and Affiliations

  1. Halle-Wittenberg, Fakultät für Naturwissenschaften II, Martin-Luther-Universität, Von-Seckendorff-Platz 1, Halle/Saale, 06120, Germany

    Wolfram Hergert

  2. Stiftung Institut für Werkstofftechnik, Badgasteiner Str. 3, Bremen, 28359, Germany

    Thomas Wriedt

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Ausman, L.K., Schatz, G.C. (2012). Dipole Re-Radiation Effects in Surface Enhanced Raman Scattering. In: Hergert, W., Wriedt, T. (eds) The Mie Theory. Springer Series in Optical Sciences, vol 169. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-28738-1_5

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  • DOI: https://doi.org/10.1007/978-3-642-28738-1_5

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