Graphene Induced Large Shift of Surface Plasmon Resonances of Gold Films: Effective Medium Theory for Atomically Thin Materials

Despite successful modeling of graphene as a 0.34-nm thick optical film synthesized by exfoliation or chemical vapor deposition (CVD), graphene induced shift of surface plasmon resonance (SPR) of gold films has remained controversial. Here we report the resolution of this controversy by developing a clean CVD graphene transfer method and extending Maxwell-Garnet effective medium theory (EMT) to 2D materials. A SPR shift of 0.24 is obtained and it agrees well with 2D EMT in which wrinkled graphene is treated as a 3-nm graphene/air layered composite, in agreement with the average roughness measured by atomic force microscope. Because the anisotropic built-in boundary condition of 2D EMT is compatible with graphene's optical anisotropy, graphene can be modelled as a film thicker than 0.34-nm without changing its optical property; however, its actual roughness, i.e., effective thickness will significantly alter its response to strong out-of-plane fields, leading to a larger SPR shift.