On the importance of incorporating dipole reradiation in the modeling of surface enhanced Raman scattering from spheres

Surface enhanced Raman scattering (SERS) enhancement factors G for nanoparticles consisting of a single Ag sphere or a dimer of Ag nanospheres are calculated using a T-matrix method that rigorously incorporates dipole reradiation (DR) effects. A comparison with the commonly used plane wave (PW) approximation, |Eloc(ω)|2|Eloc(ω′)|2, which for zero Stokes shift is |Eloc(ω)|4, is made so as to determine the error associated with using the PW enhancement factor instead of DR in modeling SERS intensities. Calculations for the single sphere are performed for various molecule locations, detector locations, and sphere sizes, while the dimer calculations consider the effects of molecule and detector locations for 50 nm diameter spheres with a 2 nm gap. In both the single sphere and dimer calculations, excellent agreement (<0.3%) is found between the PW approximation and DR calculations when the molecule is located along the incident field polarization direction and with the detector along an axis that is orthogonal both to the polarization and wave vector directions. The errors for other molecule locations, different detector locations, and larger sphere sizes can be considerably larger. A qualitative description of the nature of the errors is developed based on interferences between radiation emitted by the sphere and by the molecule and on quadrupole excitation in the metal spheres. An average over molecule and detector locations for both the single sphere and dimer results leads to DR enhancement factors that differ by factors of 2–3 (sometimes higher, sometimes lower) from the PW results. This indicates that for quantitative field enhancement factor calculations, the more rigorous DR result is important.