Studies aimed at understanding the nonlinear optical properties of GaAs/AlGaAs semiparabolic quantum well under applied electric have focused on optical rectification and second harmonic generation. These studies have taken two complimentary approaches: (1) the compact-density-matrix approach and iterative method have been used to obtain the expressions of optical rectification and second harmonic generation. (2) the finite difference techniques has been used to obtain the energy eigenvalues and their corresponding oeigenfunctions of the semiparabolic quantum well under applied electric field. The energy eigenvalues, the shape of the confined potential, optical rectification and second harmonic generation are modulated by the confined potential frequencies, and electric field. So the results of a number of numerical experiments indicate that the nonlinear optical rectification and second harmonic generation strongly depends on the confined potential frequencies, and applied electric field. This gives a new degree of freedom in various device applications based on the intersubband transitions of electrons.
