Finite-Difference Time-Domain (FDTD) calculations are used to characterize the electric field in the vicinity of a sharp silver or gold cone with an apex diameter of 10 nm. The simulations are utilized to predict the intensity and the distribution of the locally enhanced electric field in tip-enhanced Raman spectroscopy (TERS). A side-by-side comparison of the enhanced electric field induced by a radially and a linearly polarized light in both gap-mode and conventional TERS setup is performed. For this purpose, a radially polarized source is introduced and integrated into the FDTD modeling. Additionally, the optical effect of a thin protective layer of alumina on the enhancement of the electric field is investigated.