Synthesis of transmission line models for metamaterial slabs at optical frequencies

We study the scattering parameters of typical transmission line resonant circuits and their corresponding nonlocal effective material parameters at optical frequencies using transmission line theory. We find that each circuit has specific features in terms of nonlocal permittivity and permeability and can be utilized to quantitatively synthesize transmission line circuit models for metamaterial slabs. As application examples, we construct circuit models for cut wires, cut-wire pairs, metallic meshes, and mesh pairs. Moreover, we calculate local material parameters in a simple way using fitted impedance parameters together with a transmission line homogenization procedure. Using transmission line (TL) models, we show how the material parameters can be optimized in actual metamaterials. The physical dependence of circuit parameters on structure geometries validates our TL model further.