Rigorous justification of the |E|4 enhancement factor in Surface Enhanced Raman Spectroscopy

We present and apply a general method to formally calculate Surface Enhanced Raman Scattering (SERS) enhancement factors, based on the optical reciprocity theorem. This approach emphasizes the fact that the widely used SERS enhancement factor proportional to the fourth power of the field (|E|4) is an approximation. It can moreover be used to define the range of validity of the |E|4 approximation and to provide a rigorous justification of a more general formula.