Equivalent-medium theory for metamaterials made by planar electronic materials

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Mapping a planar conductor with arbitrary electronic band structure (e.g., linear or parabolic) to a slab of bulk medium exhibiting the same optical responses, we formulated an equivalent-medium approach to study the optical properties of metamaterials (MTMs) made by patterning such a planar conductor, particularly for the graphene system. The theory was applied to study various graphene-based MTMs, with calculation results in one particular system (with no adjustable parameters) agreeing well with available experiments.