Abstarct: Recently there has been a great deal of interest in terahertz phenomena in elec tronic materials. This is mainly due to the rapid development of high-power, long wavelength, and tunable laser sources such as free electron lasers. In view of this rapid development of terahertz phenomena, a theoretical formalism describing strongly cou pled electron-photon systems becomes urgently required. The most useful quantity in understanding the transport and optical properties of an electronic system is the di electric function. In this thesis, we present a theoretical investigation of the electronic and dielectric properties of an electron gas strongly coupled to a THz radiation field. We first calculate the charge fluctuation of the quasi-one dimensional (Q1D) electron system using the time-dependent perturbation technique. The dielectric function can then be derived. We obtain elementary excitation spectrum of Q1D electron systems under THz radiation field within a parabolic confining potential. Then we study and obtain the plasmon modes using the random-phase approximation. The resultant di electric function shows that the plasma frequency of the system is strongly dependent on the intensity and frequency of the THz laser field.