Intrinsic Limitations on the |E|4 Dependence of the Enhancement Factor for Surface-Enhanced Raman Scattering

Analysis of the bandwidth of the Clausius-Mosotti local field factor challenges the standard assumption that both incident and scattered fields are equally enhanced in surface-enhanced Raman scattering (SERS). The most common geometry for observation of SERS is on a nanoparticle or nanostructure where the localized surface plasmon resonance (LSPR) field enhancement arises from the electromagnetic environment produced by scattering off the conductor surface. Consequently, the electric field enhancement experienced by an adsorbate on the metal surface is a function of the magnitude of the transition dipole moment of the nanoparticle or nanostructure. Even in the treatment that considers the conducting nanostructure and molecule interactions as contributions to a collective scattering process, analytical expressions based on the Drude free-electron model reveal the importance of the bandwidth of the local field factor as a limitation on the SERS enhancement. These model calculations based on the Drude model are confirmed herein by explicit calculation using the dielectric functions for Au and Ag. The enhancement bandwidth depends on the ratio of the plasma frequency, omega(p) and the damping, Gamma, such that the greater the enhancement ratio, omega(p)/Gamma, the narrower the enhancement bandwidth. The relationship of the Raman shift to the enhancement bandwidth places severe constraints on the theoretical enhancement possible by the electromagnetic mechanism.