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.

表面增强拉曼散射 (SERS) 的增强因子通常近似为局部电场增强强度的四次方。然而，该方法所使用的平面波近似的适用性仍然是SERS理论研究和与实验结果比较的主要问题。在这项工作中，我们同时计算了普通 SERS 结构中偶极子的平面波激发和发射增强因子下的局部入射场增强因子。对于孤立的粒子和二聚体，局部场增强因子与发射增强因子非常一致。然而，四次幂近似方法无法预测基板上结构的增强因子。结果表明，当 SERS 结构位于衬底上时，局部场方法低估了增强因子。使用珀塞尔效应并与发射增强进行比较。这表明 Purcell 因子与均匀介质中的粒子的发射增强匹配得很好，而 Purcell 因子高估了基板上粒子的发射增强。这些结果有助于 SERS 研究和增强因子计算。