theory

A double negative medium is composed of negative permeability and negative permitivity media. Negative permeability is obtained via resonant elements. Metal dielectric based resonators can have many different shapes such as split rings, spirals or cut wire pairs. Inductance and capacitance of these resonators can be found by using quasistatic circuit theory. From L and C the resonator quality factor and resonance frequency are calculated. Periodically arranged closely packed three-dimensional array of resonators can be modeled with Lorentz model. At a narrow frequency band the system can have negative or near-zero permeability. Similarly periodically arranged thin wires constitute a low-frequency plasmonic system that can be modeled with the Drude model. Up to plasma frequency the system has a negative permittivity. Composing these two media creates a negative index medium. As the wavelength of the light is much larger than the size of the negative index lattice period, the medium can be analyzed by using an effective medium theory. Consider a rectangle prism shaped metamaterial. Measured normal incidence complex transmission and reflection data can be used to extract the index and impedance of the medium as if it is homogeneous. The index and impedance directly give us permittivity and permeability.