The nonlinear optical absorption in $$\hbox {Al}_{{x}}\hbox {Ga}_{1-x}$$As/GaAs double-graded quantum wells: magnetic field effect and the position-dependent effective mass effect

In this study, the intersubband optical absorption coefficients (OACs) in double-graded quantum wells (QWs) with constant effective mass and position-dependent effective mass (PDEM) are investigated for different applied magnetic field, respectively. The energy levels and the envelope wave functions of an electron confined in finite potential double-graded QWs are calculated by finite difference method. The analytical expressions of the linear, third-order nonlinear and total OACs are obtained using compact density matrix approach. The numerical results show that the applied magnetic field, structure parameters and PDEM have a great effect on the optical characteristics of these structures. In particular, we have found the PDEM have a significant effect on the magnitude position of resonant peaks of OACs.