Scaling phenomenon of graphene surface plasmon modes in grating-spacer-graphene hybrid systems

We investigate the excitations of graphene surface plasmon waves in grating-spacer-graphene hybrid systems. It is demonstrated that the resonant absorption rate is scaling invariant as the geometric parameters of the hybrid system are scaled, and this phenomenon is nearly unaffected by the dispersions of the optical parameters of graphene and the grating material. We present an analytical model to calculate the absorption rate and elucidate that the scaling invariant phenomenon originates from the scalabilities of the graphene surface plasmon modes. This study could benefit the development of graphene plasmonic devices at infrared and terahertz frequencies.