Electromagnetic contribution to surface-enhanced Raman scattering from rough metal surfaces: A transformation optics approach

The propagation of surface plasmons along rough metal surfaces is investigated with transformation optics. The roughness is modeled on a nanometer scale either by partly embedding a cylinder of metal into the surface (convex rough surface) or by excavating a cylindrical cavity from it (concave rough surface). These two structures can be treated analytically by means of conformal transformation. The interaction of surface plasmons with the singularities of these structures is shown to induce extreme field enhancements. These modes dominate the surface-enhanced Raman-scattering response and enhancement factors of the order of 107 are predicted. Interestingly, concave rough surfaces are shown to be the best candidates for surface-enhanced Raman scattering due to a stronger field enhancement and a lower sensitivity to the incident light polarization. Our analytical approach also points out the influence of the contact angle between the asperities and the metal surface on the bandwidth and the efficiency of the light-harvesting process.