  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.
