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Metamaterials, as you know, show EpsR<0 or 0<=EpsR<1. This properties is inherited from the structure geometry rather than electrical properties. For example, consider an hypothetic material with negative refractive index. From transmission Snell's law, at the interface between an incident media and a metamaterial, the wave refraction is inverted and lies on the same side of the normal entering the material. Moreover, phase fronts and power flux move along opposite directions. Some applications: cloacking devices, superlenses, agile antennas.
I worked on materials with a positive but less than 1 refraction index, so called metamaterial grids. These structures have the characteristic of an almost 0 refraction angle. In a few words, given any antenna, 2 or 3 metallic grids are placed at a proper distance over the antenna itself. The gratings behave as a kind of array of convergent microlenses. Distance from antenna and grid periodicity must be correctly chosen not to significantly affect the antenna input impedance and to obtain the desired gain. The wave incident on grids from antenna is refracted with a near-zero angle (refraction index close to zero), so the two grids act like a metamaterial. As consequence, beam-width reduces, with a great improvement of antenna gain in broadside direction.
The metamaterial used in wireless power transmission would likely be made of hundreds to thousands depending on the application of individual thin conducting loops arranged into an array. Each piece is made from the same copper-on-fiberglass substrate used in printed circuit boards, with excess copper etched away.
Actually it is well known what is a metamaterial, and how is it used? Well I can say that primarily its modifies the actual performance of a conventional device, for example adding the concept of a metamaterial in a directional couplers enhanced its directivity, also with metamaterial you can reduce the size of a circuit like in a power divider.
Mostly with a metamaterial you improve the performance of a microwave circuit and miniaturization. So you can make better and cheaper microwave devices.
Also, if you are interested in the under workings of Metamaterials, I would recommend investigating periodic structures and dispersion properties - these are critical to understanding how we actually build the structures.
I would start with David Smith's Split Ring Resonator (SRR). It was basically the first mu negative periodic structure developed, and is still used today. There is also another class of metamaterials called Transmission Line Metamaterials (TLM) - see the work of George Eleftheriades.
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