Analytical solutions for the surface‐ and orientation‐averaged SERS enhancement factor of small plasmonic particles. (26th August 2020) - Khlebtsov, Nikolai G.; Le Ru, Eric C.
Abstract: 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. Abstract : Analytical expressions for the surface‐ and orientation‐averaged SERS enhancement factor are derived for small spheroids using an improved electrostatic approximations (IEA), which includes radiative damping, depolarization effects, and interactions with higher order multipoles. Perfect agreement with exact T‐matrix calculations is observed over a wide range of sizes and aspect ratios.