Electromagnetic Theory Calculations for Spheroids: An Accurate Study of the Particle Size Dependence of SERS and Hyper-Raman Enhancements

Abstract

The electromagnetic contribution to the enhancements in Raman and hyper-Raman scattering from molecules adsorbed onto Ag, Cu and Au spheroids is studied, with an emphasis on the variation of the enhancements with spheroid size and shape. These calculations differ from several earlier spheroid model studies in that the effects of surface scattering on the particle dielectric constants, and of radiation damping and dynamic depolarization are included in the electrodynamic description. For particles between 1 and 100 nm in size, we show that our results reduce to the exact numerical results of Barber, Chang and Massoudi for the specific shapes which they studied. Our applications to Kaman enhancements on Ay, Cu and Au show that the optimum particle size is not strongly dependent on particle shape, with the optimum semi-major axis being 20–30 nm for Ag, 60–80 nm for Cu and 60–80 nm for Au, Optimum Raman enhancements for a/b = 0.5 are 10⁴ for Ag. Hyper-Raman scattering shows significant enhancements for particle shapes where either the input or scattered photons have plasmon resonances, with the relative magnitudes of these resonant enhancements dependent on particle size.

Alfred P. Sloan Fellow and Camille and Henry Dreyfus Teacher-Scholar.