tunable goos-hänchen shift of surface plasmon beam due to graphene in a metal-dielectric system

The tunneling of surface plasmon waves between two slabs of dielectric prisms superposed on the metal surface is studied. the prism with the incident surface plasmon wave is superposed by a stack of graphene sheets. the analytical theory is built to connect the fermi energy of graphene with the goos-hänchen shift of the transmitted surface plasmon waves. the obtained results be useful for developing integral switching devices on the basis of surface plasmon polaritons.