Analytical solutions for the surface- and orientation-averaged SERS enhancement factor of small plasmonic particles

We derive analytical expressions for the surface- and orientation-averaged surface enhanced Raman scattering factor (SERS EF) for small plasmonic spheroids. These expressions are derived taking into account the Stokes shift and are shown to result in very different EFs to those in the |E|(4)-approximation for experimentally relevant parameters. The optical properties of spheroids are treated in terms of the common and improved electrostatic approximations (EA and IEA). The latter is newly introduced here and includes radiative damping, depolarization effects, and interactions with higher order multipoles, thus giving perfect agreement with exact T-matrix calculations of far-field cross sections and near-field SERS EFs over a much wider range of sizes. These accurate analytical expressions will be particularly relevant to SERS experiments in colloidal solutions where surface averaging (because of random molecular adsorption) and particle orientation averaging must both be taken into account. Comparison with recent experimental data and simulations for cigar-like particles show that the spheroid model tends to overestimate the SERS EF because of the higher curvature at the tips. Possible ways to generalize the analytic solution to other axially symmetrical particles are discussed.

Automated summary

Analytical expressions for the surface- and orientation-averaged surface enhanced Raman scattering factor for small plasmonic spheroids are derived in this study, showing significant differences from previous approximations. The introduction of an improved electrostatic approximation provides more accurate results and better agreement with T-matrix calculations. The overestimation of SERS EF for spheroids due to higher curvature at the tips is discussed, along with possible generalizations to other axially symmetrical particles.