Electrically tunable Goos-Hänchen shifts in weakly absorbing epsilon-near-zero slab

We theoretically calculated the Goos-Hanchen (G-H) shift of the beam that reflected from and transmitted through an epsilon-near-zero (ENZ) slab, which was covered by the different number of layers of graphene and also realized tunable G-H shifts with electrically controllable graphene in terahertz regime. It is shown that besides the impact of the thickness of the slab and the number of layers of graphene, Fermi energy (chemical potential),which can be electrically controlled through electrical modification of the charge density of graphene by gate voltage, also plays an important role in adjusting G-H shifts. In this work we achieved about 200 times the incident wavelength of the adjustment range which can be used in measuring the doping level of graphene due to the dependence of Fermi energy on G-H shifts. Furthermore, our results provide a richer control on G-H shifts in ENZ slab and also provide potential applications for ENZ metamaterials-based devices than semi-infinite structures.