▎ 摘　　要

We give a quantum formulation of the recently observed giant Faraday rotation (FR) in monolayer graphene (Crassee I., Nat. Phys., 7 (2011) 48) which incorporates graphene's anomalous Hall effect and the resonant interplay between Landau levels and Floquet sidebands in the limit of large Fermi energy. The same formalism is then used to discuss the Goos-Hanchen (GH) shift at the interface of two media of different permittivity, with graphene at their interface. This last feature introduces current into the electromagnetic boundary conditions. For the s-polarization case, the presence of the graphene-induced surface charge causes a much larger GH shift than without charge, and its usual monotonic behavior is altered. In the p-polarization case, surface charge and current may alter the conventional GH shift in opposite ways. We predict new phenomena such as minimum GH shift and a lateral broadening of the reflected beam, all of which should be observable with current experimental capabilities. Copyright (C) EPLA, 2011