Surface-enhanced nonlinear-optical processes in molecules in a two-oscillator electromagnetic model

A two-oscillator electromagnetic model is used to find the effect of a solid or a metal substrate of dielectric function $\epsilon \left(\omega \right)$ on several nonlinear optical processes in a molecule adsorbed on the surface. In particular, the case of the second-order optical mixing, the stimulated Raman scattering, the third-order polarizability for the four-wave mixing, and the case of two-photon absorption in the molecule have been considered explicitly in the approximation in which the ionic oscillator frequency is assumed to be small compared with both the electronic oscillator frequency and the optical frequencies involved. The two-oscillator model considered here, with a trilinear coupling potential function, is the same as the one recently used by us to investigate the spontaneous Raman process. From our analysis it is quite clear that the enhancement, if any, in each of the processes involves (1) the enhancement of each of the incident optical fields ${\overrightarrow{\mathrm{E}}}^{\mathrm{in}}$ to ${\overrightarrow{\mathrm{E}}}^{\mathrm{}\left(0\right)\mathrm{}}$ at the molecular site, (2) the renormalization of the effective nonlinear polarizabilities at short molecular distances from the surface, and (3) the change of the outgoing radiation propagator (Green's function) from the free-space ${\mathit{G}}_0$ to $\mathit{G}$, due to the presence of the surface. For a metal surface of a given shape, each of these factors may contain possible surface-plasmon-polariton resonances at various frequencies involved.