We propose to understand surface-enhanced Raman scattering (SERS) as a higher-order Raman process that contains the plasmonic excitation. The SERS amplitudes are calculated with third- and fourth-order perturbation theory. Treating the plasmonic excitation as a quasiparticle, we derive analytic expressions for all coupling matrix elements. This leads to a general theory of plasmonic enhancement in SERS that can be applied to arbitrary plasmonic nanostructures. We obtain the plasmon eigenvectors of a gold nanosphere and a nanosphere dimer. They are used to calculate the enhancement of the Raman cross section of a molecule coupled to the dipole plasmon mode. The enhancement of the cross section is up to three orders of magnitude stronger than predicted by the theory of electromagnetic enhancement. The difference is most pronounced in vacuum and decreases with increasing dielectric constant of the embedding medium. The predictions from understanding SERS as a higher-order Raman process agree well with recent experiments; they highlight the dominance of plasmonic enhancement in SERS.

• Received 11 September 2015
• Revised 29 April 2016

DOI:https://doi.org/10.1103/PhysRevA.94.023813