Electromagnetic model and calculations of the surface-enhanced Raman-shifted emission from Langmuir-Blodgett films on metal nanostructures.

We present a theoretical study of the electromagnetic contribution to surface-enhanced Raman scattering (SERS) from a Langmuir-Blodgett film close to a metal surface. This macroscopic dipolar model fully accounts for the Raman-shifted emission so that meaningful SERS (electromagnetic) enhancement factors that do not depend only on the local electromagnetic field enhancement at the pump frequency are defined. For a plane metal surface, analytical SERS enhancement factors that are consistent for all pump beam polarization and molecular orientation are obtained. In order to investigate SERS on complex nanostructured metal surfaces, we introduce this model into the formally exact, Green's theorem surface integral equation formulation of the scattered electromagnetic field. This formulation is thus employed to calculate numerically the near-field and far-field emissions at the Raman-shifted frequency for very rough, random nanostructured surfaces, with emphasis on the impact of collective processes for varying pump frequency and Raman shift. Our results reveal that the widely used |E|4 approximation tends to overestimate average SERS enhancement factors.