An analytical model of the response of a free electron gas within a nano-antenna interacting with an electromagnetic wave with normal incidence was developed. By examining the longitudinal oscillations of the plasma in the nano-antenna, a relationship was obtained for the wavelengths generated by the plasmons in the nano-antenna. The nearfield amplitudes are expressed in an analytical way. Finally, the amplitudes of the scattered fields at a given distance from the nano-antenna are compared. It was shown how the intensity of the dispersed Electromagnetic Field decays as a function of the excitation modes and we see that these can be functions in the visible regime, a property sought in these devices for energy applications.