Studies on the Second-Order Nonlinear Optical Properties of Parabolic and Semi-parabolic Quantum Wells with Applied Electric Fields

Within the framework of compact density matrix approach and iterative procedure, a detailed procedure for the calculation of the second-harmonic generation (SHG) susceptibility tensor is given in the electric-field-biased parabolic and semi-parabolic quantum wells (QWs). The simple analytical formula for the SHG susceptibility in the systems is also deduced. Numerical results on typical AlGaAs/GaAs materials show that, for the same effective width, the SHG susceptibility in semi-parabolic QW is larger than that in parabolic QW due to the self-asymmetry of the semi-parabolic QW, and the applied electric field can make the SHG susceptibilities in both systems enhance remarkably. Moreover, the SHG susceptibility is also related to the parabolic confinement frequency and the relaxation rate of the systems.