Terahertz (THz) anisotropic absorption in graphene could be significantly modified upon applying a static magnetic field on its ultra-fast 2D Dirac electrons. In general, by deriving the generalized Fresnel coefficients for monolayer graphene under applied magnetic field, relatively high anisotropic absorption for the incoming linearly polarized light with specific scattering angles could be achieved. We also prove that the light absorption of monolayer graphene corresponds well to its surface optical conductivity in the presence of a static magnetic field. Moreover, the temperature-dependent conductivity of graphene makes it possible to show that a step by step absorption feature would emerge at very low temperatures. We believe that these properties may be considered to be used in novel graphene-based THz application.

Strong Goos-Hänchen (GH) effect at a prism-graphene interface in the quantum Hall effect (QHE) condition is reported. Based on the full quantum description of the temperature-dependent surface conductivity of graphene present in the unconventional quantum Hall regime, magnetically strong tunable QHE GH shifts emerge. Our approach is based on deriving the generalized Fresnel coefficients with antisymmetric conductivity tensor for the Kerr phase of the incident linearly polarized light. Moreover, it is demonstrated that at low temperatures, GH shifts map plateaus as the intensity of the magnetic field grows. This quantum modulation of the GH effect in graphene by an applied magnetostatic bias may open doors to new opportunities for optical devices and QHE sensing applications in 2D materials.