Comparison of the nonlinear optical properties of asymmetrical and symmetrical quantum wells

In this work, a detailed comparison of the nonlinear optical properties (NLOPs), including the absorption coefficients (ACs) and the refractive index changes (RICs) of symmetrical parabolic (SP) and asymmetrical semi-parabolic (ASP) quantum-wells (QWs) are investigated by utilizing the compact density matrix approach and iterative procedure. The wave functions of one electron, as well as its energy eigenvalue in the SPQW and the ASPQW, are also obtained by applying the effective mass approximation. Numerical calculations on GaAs/AlGaAs material reveal that the ACs and the RICs in both the SPQW and the ASPQW are affected strongly by the incident optical intensity (I) and the confining frequency ( $$\omega _0$$ ω 0 ), and depend sensitively on the relaxation time (T). Furthermore, if it is desired to obtain large ACs/RICs then a relatively weaker I and lower $$\omega _0$$ ω 0 should be chosen. However, the nonlinear (third-order) component influence is very important in the relatively large I case and cannot be neglected when examining the nonlinear optical features of both the SPQW and the ASPQW. More importantly, the total AC and the total RIC in the SPQW always are larger than those in the ASPQW. In addition, if we choose an optimized confining frequency for the SPQW, then we will get larger ACs/RICs. Graphical abstract