Tunability of spin Hall effect of light with semiconductor metamaterial based on magneto-optical effects

In this paper, we have demonstrated a three-layer structure to explore the characteristics of spin Hall effect of light (SHEL). It is assumed that the structure is made of a semiconductor metamaterial which consists of GaAs\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathrm {GaAs}$$\end{document} and SiO2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathrm {SiO}_{2}$$\end{document} periodically and cladded with two different dielectrics, glass and TiO2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathrm {TiO}_{2}$$\end{document}. We investigated in detail how the spin Hall effect of reflected light at glass-semiconductor metamaterial is tuned after being exposed to an external magnetic field due to the magneto-optical effects. The Faraday and Voigt effects on the vertical and horizontal shifts of SHEL are calculated and discussed. The results show that magneto-optical effects have significantly enhanced or weakened the behavior of SHEL but the way of impact is different. This simple structure proposed in the paper can be used for yielding meaningful results for studying more complex systems related to SHEL.