Optical Rectification and Second Harmonic Generation of Finite and Infinite Semi-Parabolic Quantum Wells

In this work, the optical rectification and the second harmonic generation of the infinite and finite semi-parabolic quantum wells are calculated. Optical properties are obtained using the compact density matrix approach and an iterative method. Numerical calculations are presented for typical GaAs/Al _x Ga_1−x As semi-parabolic quantum well. The Energy eigenvalues and eigenfunctions of these systems are calculated numerically. Results show that the energy eigenvalues and the matrix elements of the infinite and finite cases are different. Our calculations reveal that in contrast to the infinite case, the optical rectification and the second harmonic generation in the case of the finite well can only occur when the semi-parabolic confinement frequency is lower than a certain value. Our results indicate that the resonant peaks of the optical properties in the case of finite well occur at lower values of incident photon energy with respect to the infinite case. The calculations also show that the behavior of resonant peak values of these optical properties for the infinite and finite cases are nearly identical.