Hydrogenic impurity effect on the optical nonlinear absorption properties of spherical quantum dots with a parabolic potential

The linear, third-order and total optical absorption coefficients of a hydrogenic impurity in spherical quantum dots subjected to a parabolic potential are calculated by the compact density-matrix approach and the finite difference method. The effect of the potential parameter γp\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\gamma_{p}$\end{document} and the confining radius R on the optical absorption coefficients of the spherical quantum dots are investigated. The following conclusions are drawn: 1) The reduction of the size of the quantum dot can lead to a blue-shift of the absorption spectrum no matter whether there is an impurity or not; however, the intensity of the absorption spectrum slightly decreases as an impurity is introduced into the spherical quantum dot. 2) The saturation case of total optical absorption coefficients is observed more easily in the case of weak confinement than in the case of strong confinement; and there is a one-to-one correspondence relationship among the intensity of the absorption peak, the potential parameter γp\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\gamma_{p}$\end{document} and the saturation intensity Is, corresponding to the saturation case of the total optical absorption coefficients. 3) There is an approximate linear relationship between the value of Is and the value of γp\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$ \gamma_{p}$\end{document} as the value of γp\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$ \gamma_{p}$\end{document} is large.