In this paper, the frequency response of a detector antenna is investigated when a layer of dielectric is placed on it. For this purpose, the surface wave theory has been used to explain the propagation of the current pulses in the antenna electrodes. Examinations are also performed of the propagation spectra of two types of terahertz antennas, bow-tie and dipole (with LT-GaAs substrates), on which the dielectrics of gallium arsenide and silica are located. These antennas are simulated through the CST software (FDTD method). The simulations show that the presence of a surrounding dielectric on the surface of an antenna affects the velocity of the current pulse propagation on the electrodes. It is also shown that the change in the thickness and position of the surrounding dielectric have a negative effect on quality of detector antenna by shift its spectral response to lower frequencies.