Theoretical investigation of nonlinear optical properties of Mathieu quantum well

In this study, for the first time, the effect of externally applied static electric, magnetic, and non-resonant THz intense laser fields on nonlinear optical properties such as the total optical absorption coefficients (TOACs) and relative refractive index changes (RRICs) in a GaAs/AlGaAs Mathieu quantum well are theoretically investigated in detail. Moreover, the influence of the adjustable physical parameters, linked to the potential shape of the structure, on the nonlinear optical properties of the system is also investigated. For this, firstly, the electronic subband energy levels of the Mathieu quantum well, and their envelope wave functions, are calculated using the diagonalization method within the framework of the effective mass and parabolic single-band approximations. Then, the outcome of the iterative solution of compact-density-matrix formalism is used to obtain the nonlinear optical properties of the structure. The obtained numerical results show that the increase in both the structure parameters and the value of the electric and magnetic field shifted the positions of the TOACs and RRICs peaks towards higher energies (blue-shift). On the other hand, the increase in the value of the intense laser field shifted the peak positions to lower energy levels (red-shift). The determination of the functional range for the optical properties of the Mathieu quantum well, using both the structure parameters and the external fields, is an important gain in terms of providing the initial parameters for experimental studies.