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We present a self-consistent quantum optics approach to calculating thesurface enhanced Raman spectrum of molecules coupled to arbitrarily shapedplasmonic systems. Our treatment is intuitive to use and provides freshanalytical insight into the physics of the Raman scattering near metallicsurfaces and can be applied to a wide range of geometries including resonators,waveguides, as well as hybrid photonic-plasmonic systems. Our general theorydemonstrates that the detected Raman spectrum originates from an interplaybetween nonlinear light generation and propagation. Counter intuitively, at thenonlinear generation stage, we show that the Stokes (anti-Stokes) signal at themolecule location depends on the plasmonic enhancements, through the localdensity of photon states (LDOS), at the anti-Stokes (Stokes) frequency.However, when propagating from the vibrating molecule to the far field, theStokes (anti-Stokes) emission experiences a plasmonic enhancement at the Stokes(anti-Stokes) frequency, as expected. We identify the limits of the commonlyknown E^4 electric-field rule for Raman signal enhancement near plasmonicsurfaces at low pump powers, as well as a different E^8 rule at high pumppowers, and we clarify the role of the LDOS. Our theory uses a generalizedquantum master equation where the plasmonic system is treated as anenvironmental bath that is described through the photonic Green function of themedium. Therefore, any electrodynamics related physics, such as quenching andpropagation, are self-consistently included in the model. The presentedformalism is also capable of spatially describing the full Raman response in asimple analytical way, which is typically not possible using simpler coupledmode theories, even if one adopts a quantum picture.

Quantum Optics Model of Surface Enhanced Raman Spectroscopy for Arbitrarily Shaped Plasmonic Resonators