We report on the dual nature (capacitive and inductive) of the surface impedance of periodic graphene patches at low-terahertz frequencies. The transmission spectra of a graphene-dielectric stack shows that patterned graphene exhibits both the low-frequency (capacitive) passband of metal patch arrays and the higher-frequency (inductive) passband of metal aperture arrays in a single tunable configuration. The analysis is carried out using a transfer-matrix approach with two-sided impedance boundary conditions, and the results are verified using full-wave numerical simulations. In addition, the Bloch-wave analysis of the corresponding infinite periodic structure is presented in order to explain the passband and stopband characteristics of the finite graphene-dielectric stack.
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