In this paper, the far field and near field optical responses of a gold nanoparticle are studied and simulated numerically. The electromagnetic field was excited by an electric dipole located near one end of the nanorod, which is used to model the emission of a quantum dot. Another excitation method was also simulated in which an incident plane wave is used. The excitation of dark plasmon modes of the gold nanorod is presented. The Poynting equation was solved numerically to study the influence of the gold nanorod on the dipole radiative power. In addition, the extinction cross section of the gold nanoparticle illuminated by the incident plane wave was calculated to estimate the amount of the scattered and absorbed light.