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Here, we report on the transmissivity of electromagnetic waves through a stack of monolayer graphene sheets separated by dielectric slabs at low-terahertz frequencies. It is observed that the multilayer structure possesses band-gap properties and supports a series of bandpass and band-stop regions, similar to the cases of stacked metallic meshes separated by dielectric slabs at microwave/THz frequencies and a metal-dielectric stack at optical frequencies. The transmission resonances in the bandpass region are identified as coupled Fabry-Pérot resonances associated with the individual cavities of dielectric slabs loaded with graphene sheets. It is also noticed that these resonances lie within a certain characteristic frequency band, independent of the number of layers in the graphene-dielectric stack. The study is carried out using a simple analytical transfer-matrix approach or, equivalently, a circuit-theory model, resulting in the exact solution for the multiple dielectric/graphene sheet surface-conductivity model. Also, an independent verification of the observed phenomena is obtained with commercial numerical simulations.

This paper presents a simple analytical circuit-like model to study the transmission of electromagnetic waves through stacked two-dimensional (2-D) conducting meshes. When possible the application of this methodology is very convenient since it provides a straightforward rationale to understand the physical mechanisms behind measured and computed transmission spectra of complex geometries. Also, the disposal of closed-form expressions for the circuit parameters makes the computation effort required by this approach almost negligible. The model is tested by proper comparison with previously obtained numerical and experimental results. The experimental results are explained in terms of the behavior of a finite number of strongly coupled Fabry-Pérot resonators. The number of transmission peaks within a transmission band is equal to the number of resonators. The approximate resonance frequencies of the first and last transmission peaks are obtained from the analysis of an infinite structure of periodically stacked resonators, along with the analytical expressions for the lower and upper limits of the pass-band based on the circuit model.

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.

An analytical model is presented for the analysis of multilayer wire media loaded with 2-D arrays of thin material terminations, characterized in general by a complex surface conductivity. This includes the cases of resistive, thin metal, or graphene patches and impedance ground planes. The model is based on the nonlocal homogenization of the wire media with additional boundary conditions (ABCs) at the connection of thin (resistive) material. Based on charge conservation, new ABCs are derived for the interface of two uniaxial wire mediums with thin imperfect conductors at the junction. To illustrate the application of the analytical model and to validate the new ABCs, we characterize the reflection properties of multilayer absorbing structures. It is shown that in such configurations the presence of vias results in the enhancement of the absorption bandwidth and an improvement in the absorptivity performance for increasing angles of an obliquely incident TM-polarized plane wave. The results obtained using the analytical model are validated against full-wave numerical simulations.