Comparison of Goos–Hänchen shifts of the reflected beam from graphene on dielectrics and metals

The Goos–Hänchen shifts of the reflected beam from graphene-on-dielectric (or metal) in the optical wavelength are investigated by using the stationary-phase method. For the graphene-on-dielectric substrates, it is found that the pseudo-Brewster angle and Goos–Hänchen shift are influenced greatly by the introduced graphene sheets for TM polarization. By changing number of graphene sheets, the lateral shifts can be large positive or negative near the pseudo-Brewster angle. For TE polarization, the lateral shift is still small; however it can also be positive or negative by changing the number of graphene sheets. For the graphene-on-metal substrates, graphene sheets exert a great impact on the reflectance while has little effect on the lateral shifts of both polarizations. Finally, the role of the graphene sheets on the lateral shifts for the different visible wavelengths is discussed.