Quantum theory of enhanced Raman scattering by molecules on metals: Surface-plasmon mechanism for plane metal surface

Abstract

The enhancement ratio of Raman scattering for adsorbed versus isolated molecules has been calculated quantum mechanically using coupled eigenstates obtained in the preceding paper. There, the surface-plasmon states for a plane surface were coupled with molecular dipole eigenstates by Fano's method; the resulting eigenstates with, or without, consideration of spatial dispersion were discussed. An enhancement ratio ${10}^6$ can be obtained in this theory only at an effective resonant frequency ${\omega }_L^m$: The ratio is sharply peaked about ${\omega }_L^m$. The location of ${\omega }_L^m$ and the maximum ratio obtainable depend sensitively upon the dielectric function used to describe the metal. The experimentally observed ratio by pyridine on silver cannot be obtained using realistic parameter values for the spatially dispersive dielectric function $\epsilon (\omega , \overrightarrow{\mathrm{k}})$ of silver and the parameters for pyridine. This mechanism, invoking surface plasmons for a plane surface, is most likely responsible for only a small fraction of the total observed enhancement, contrary to what could be anticipated from classical image-field theory.