Circuit Model in Design of THz Transparent Electrodes Based on Two-Dimensional Arrays of Metallic Square Holes

In this paper, we propose a circuit model for two-dimensional arrays of metallic square holes located on a homogeneous substrate, in order to propose a new scheme containing this type of metamaterials to obtain transparent electrodes with simultaneous terahertz transparency and low electrical resistance. The results of the introduced circuit model, which is a fully analytical model with explicit expressions, are in almost complete agreement with the full-wave simulations. Thanks to this analytical model, we can employ standard binomial matching transformer in order to minimize the reflected power from the structure at a desired frequency. Furthermore, taking advantage of this model, we design an optimized tri-layer structure by seeking for a high optical transmittance at the desired frequency and over a wide bandwidth. The obtained transparent electrode has a high power transmission (more than 85%) within a wide frequency range (48% of the central frequency) which is desirable in commonly used transparent electrodes. The square holes are perforated in thick metallic slabs which drastically reduce the electrical resistance of the structure.