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-Garnett effective-medium theory (EMT) to two-dimensional (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 microscopy. Because the anisotropic built-in boundary condition of 2D EMT is compatible with graphene's optical anisotropy, graphene can be modeled 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.
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