Metamaterial - Theoretical Models

Theoretical Models

Left-handed materials were first described theoretically by Victor Veselago in 1967.

John Pendry was the first to theorize a practical way to make a left-handed metamaterial. Left-handed in this context means a material in which the right-hand rule is not followed, allowing an electromagnetic wave to convey energy (have a group velocity) in the lode against its phase velocity. Pendry's initial idea was that metallic wires aligned along the direction of propagation could provide a metamaterial with negative permittivity (ε < 0). Note however that natural materials (such as ferroelectrics) were already known to exist with negative permittivity; the challenge was to construct a material which also showed negative permeability (µ < 0). In 1999 Pendry demonstrated that a split ring (C shape) with its axis placed along the direction of wave propagation could provide a negative permeability. In the same paper, he showed that a periodic array of wires and ring could give rise to a negative refractive index. A related negative-permeability particle, which was also proposed by Pendry, is the Swiss roll.

The analogy is as follows: All materials are made of atoms, which are dipoles. These dipoles modify the light velocity by a factor n (the refractive index). The ring and wire units play the role of atomic dipoles: the wire acts as a ferroelectric atom, while the ring acts as an inductor L and the open section as a capacitor C. The ring as a whole therefore acts as an LC circuit. When the electromagnetic field passes through the ring, an induced current is created and the generated field is perpendicular to the magnetic field of the light. The magnetic resonance results in a negative permeability; the index is negative as well. (The lens is not truly flat, since the capacitance of the structure imposes a slope for the electric induction.)

In peer reviewed journal articles (see References), there are several (mathematical) material models which describe frequency response in DNGs. One of these is the Lorentz model. This describes electron motion in terms of a driven-damped, harmonic oscillator. When the acceleration component of the Lorentz mathematical model is small compared to the other components of the equation, then the Debye model is applied. When the restoring force component is negligible, and the coupling coefficient is generally the plasma frequency, then the Drude model is applied. There are other component distinctions that call for the use of one of these models, depending on its polarity, or purpose.