Effects of magnetic field and structural parameters on multi-photon absorption spectra in Morse quantum wells with electron-phonon interactions

We present a systematic theoretical study of the multi-photon nonlinear optical absorption properties of a $\text{GaAs/A}{\text{l}_{x}}\text{G}{\text{a}_{1-x}}\text{As}$ based quantum well (QW) structure with Morse confinement potential under the influence of a magnetic field. Based on the stationary states due to the electron confinement in Morse QWs and the Landau levels obtained by solving the Schrodinger equation in the effective mass approximation, we have developed calculations for the optical absorption power with MPA using second-order perturbation theory. Our model accounts for electron-phonon interactions and considers both optical and acoustic phonon mechanisms in the MPA process. Our findings show that the one-photon absorption (1PA) peaks are larger and appear to the right of the two-photon absorption (2PA) peaks, whereas 2PA peaks are larger and occur to the right of three-photon absorption (3PA) peaks. The resonance peak positions follow the magneto-phonon resonance condition and are temperature-independent. Increasing the magnetic field and aluminum concentration induces a blue shift in the absorption spectra, whereas increasing the QW width leads to a red shift. Variations in magnetic field, aluminum concentration, and QW width also affect the peak intensities and full-width at half maximum (FWHM), with increasing values of the former two enhancing the FWHM, while expanding the QW width reduces it. Thermal excitations increase peak intensity without shifting their positions. Our study highlights the significance of nonlinear absorption processes (2PA, 3PA) in understanding optical absorption, despite their smaller FWHM compared to linear absorption (1PA). Overall, the Morse QW model demonstrates promising magneto-optical properties, making it a strong candidate for future optoelectronic device applications.