Abstract
In studies of surface-enhanced Raman scattering (SERS), individual metal nanoparticle and particle assemblies introduce enhancement of electromagnetic fields. However, the contributions to enhancement due to the substrate supporting the particles are yet to be studied analytically. In this communication, we present an analytical method to investigate the effect of a substrate with realistic layers in SERS. The proposed method quantifies the effect of a substrate on the electric field on the nanoparticles surface in SERS experiments. By applying the proposed method, optimal constructions of a substrate can be obtained to maximize the surface electric field while a poorly constructed one can be avoided. The maximization can lead to a high Raman enhancement factor. The method is verified using numerical simulations.