Calculations of the direct electromagnetic enhancement in surface enhanced Raman scattering on random self-affine fractal metal surfaces

We study the classical electromagnetic enhancement at the excitation wavelength related to surface enhanced Raman scattering (SERS) experimental configurations in the vicinity of random rough metal surfaces possessing self-affine scaling behavior. The scattered electromagnetic intensity is obtained by means of numerical calculations based on the rigorous integral equations formulation of the electromagnetic wave scattering, free from the limitations of electrostatic and/or dipolar approximations. From the enhancement of the scattered field intensity in the immediate vicinity of the surface, originated in the excitation of transversal-magnetic surface plasmon polaritons, the SERS electromagnetic mechanism on substrates of Ag, Au, and Cu is explored as a function of the surface fractal dimension, rms height, and excitation wavelength. It is found that fractality favors the occurrence of large electromagnetic enhancements, which in turn appear to be maximum at an optimum wavelength as a result of the compromise between roughness-induced light coupling into surface plasmons and absorptive losses. This optimum wavelength is shorter for Ag than for Au and Cu. Maximum local enhancements on the order of ${10}^3$ are encountered for the three metals being considered.