Effects of applied external fields on the nonlinear optical rectification, second, and third harmonic generation in a quantum well with exponentially confinement potential

In the present study, the nonlinear optical rectification (NOR), second harmonic generation (SHG), and third harmonic generation (THG) coefficients in GaAs/GaAlAs quantum well (QW) with exponentially confinement potential were theoretically analyzed for different applied static electric and magnetic fields as well as the non-resonant intense laser field (ILF). In addition, the effect of adjustable physical parameters ( $$\upeta $$ η and $$\upkappa $$ κ ) on the optical properties was also investigated. The subband energy levels and their corresponding envelope wave functions of an electron confined in a QW with exponentially confinement potential are calculated by diagonalization method within the framework of effective mass and single parabolic band approximations. The analytical expressions of the NOR, SHG, and THG are obtained using compact density matrix approach via iterative method. The numerical results show that the applied external fields and physical parameters have a great effect on the optical characteristics of the considered system. In particular, we have found the applied external fields have a significant effect on the position and magnitude of resonant peaks of NOR, SHG, and THG.