Scattering T-matrix theory in wave-vector space for surface-enhanced Raman scattering in clusters of nanoscale spherical metal particles

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Abstract
Very large enhancements up to 14 orders of magnitude in the Raman cross section from a molecule adsorbed on a single cluster of a few nanoscale metal particles has been reported recently. The enhancement is believed mainly due to the enhanced electric field because of the excitation of the localized surface plasmon modes. We have developed a Green’s function theory using scattering matrix approach in the wave-vector space to solve the Maxwell equations for the enhanced field near a spherical metal particle cluster. The advantage of working in the wave-vector space is that one does not need to use complicated translational addition theorem required in the real space as used in earlier calculations. Therefore our theory can be easily extended to any shape or size of the cluster. We consider clusters of two, three, and four spherical particles forming a linear chain, triangle, and square and calculate their localized surface modes. These modes have much more localized field near the cluster compared to those of single metal sphere and are redshifted. We find the enhancement in the Raman cross section can reach up to 10 orders of magnitude due to the resonant excitation of these modes for silver particle clusters and is in a broad frequency range. We also find new results that chainlike clusters of three or more particles have very sharp resonant features that give a dramatic increase in the enhancement near the resonance. The results for gold particle clusters are also presented.