Giant the Goos-Hänchen shifts with high sensitivity by the interference of incoherent pump field

We investigate the Goos-Hänchen (GH) shifts of a laser for V-type three-level atoms with a fourth auxiliary level in a constant cavity structure. In the presence of interference mechanisms induced by spontaneous emission and incoherent pumping, the lateral shifts of the reflected and transmitted laser field switch from positive to negative just by the rates of direct and indirect incoherent pump fields. In the presence of quantum interference, the maximum lateral shifts of the reflected laser field appear. In this case, the sensitivity is 9.39×106λ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$9.39 \times 10^{6} \lambda$$\end{document}. Also, maximum lateral shifts of the reflected and transmitted laser field reach in zero field detuning.