Quantization of Goos–Hänchen shift in monolayer graphene under partial and total internal reflection conditions

Abstract

We theoretically investigate the Goos-Hänchen (GH) shifts of a reflected light beam from the dielectric interface containing a monolayer graphene sheet in the presence of an external perpendicular magnetic field. Using Kubo formalism we derive the expressions for the magneto-optical (MO) conductivities. Based on the angular spectrum analysis, we calculate and demonstrate that quantized GH shifts on the surface of graphene monolayer can be tuned by varying the intensity of the applied magnetic field and the beam incidence angle. We show that the GH shifts are quantized due to the Landau level (LL) quantization of the magneto-optical conductivities. In the vicinity of Brewster's angle the GH shift exhibit extreme positive or negative peaks around the magneto-excitation photonic energies in the terahertz regime. We discuss the dependence of the GH shifts on the strength of the magnetic field, the incidence angle, chemical potential, and the impinging frequency of the Gaussian beam. We also discuss the GH shifts for partial reflection (PR) and total internal reflection (TIR) conditions. We find that in the total internal reflection geometry, we have giant angular and spatial GH shifts in the vicinity of the Brewster angle as well as near the critical angle. The MO-modulated GH shift in graphene–substrate system provides a new mechanism to realize photonic devices in the terahertz region.