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In this thesis, the linear and the difference frequency polorizations were obtained by density matrix formalism of quantum mechanics. Based on Kane model to describe band-structure of zinc-blende semiconductors, GaAs and InP, we have calculated the refractive index and the second-order difference frequenncy susceptibility of these materials. It is shown that the second-order difference frequency susceptibility has absorptionlike behavior, In addition, respect to the incident photon energy, its distribution is similar to the optical rectification coefficient but shifted one half of the THz radiation frequency toward the lower energy. Not only the refractive index around the band gap transition can be calculated but also by including the empirical formula for that of nonresonant region match the experimental data quite well.
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