Modeling Surface-Enhanced Spectroscopy With Perturbation Theory

Theoretical modeling of surface-enhanced Raman scattering (SERS) is of central importance for unraveling the interplay of underlying processes and a predictive design of SERS substrates. In this work we model the plasmonic enhancement mechanism of SERS with perturbation theory. We consider the excitation of plasmonic modes as an integral part of the Raman process and model SERS as higher-order Raman scattering. Additional resonances appear in the Raman cross section which correspond to the excitation of plasmons at the wavelengths of the incident and the Raman-scattered light. The analytic expression for the Raman cross section can be used to explain the outcome of resonance Raman measurements on SERS analytes as we demonstrate by comparison to experimental data. We also implement the theory to calculate the optical absorption cross section of plasmonic nanoparticles. From a comparison to experimental cross sections, we show that the coupling matrix elements need to be renormalized by a factor that accounts for the depolarization by the bound electrons and interband transitions in order to obtain the correct magnitude. With model calculations we demonstrate that interference of different scattering channels is key to understand the excitation energy dependence of the SERS enhancement for enhancement factors below 10³.