A Detailed Investigation in the Enhancement Factor of Surface-Enhanced Raman Scattering in Simulation

The enhancement factor of surface-enhanced Raman scattering (SERS) is usually approximated by the fourth power of local electric field-enhanced strength. However, the applicability of the plane wave approximation used in this method remains a major problem in the theoretical study of SERS and the comparison with experiment results. In this work, we simultaneously calculated the local incident field enhancement factor under plane wave excitation and emission enhancement factor of a dipole in common SERS structures. For isolated particles and dimers, the local field enhancement factors are in good agreement with the emission enhancement factors. Nevertheless, the fourth power approximation method fails to predict the enhancement factors for structures on the substrate. The results show that when the SERS structures locate on the substrate, the local field method under-estimates the enhancement factor. The Purcell effect was used and compared with the emission enhancement. It indicates that the Purcell factor matches the emission enhancement quite well for the particles in homogeneous medium, while the Purcell factor over-estimates the emission enhancement for the particles on the substrate. These results are helpful for the SERS studies and the enhancement factor calculations.