| abstract
| - [1][2]A comparison of refraction in a left-handed metamaterial to that in a normal materialMain articles: Negative index metamaterials and Negative refraction Almost all materials encountered in optics, such as glass or water, have positive values for both permittivity ε and permeability µ. However, metals such as silver and gold have negative permittivity at shorter wavelengths. A material such as a surface plasmon that has either (but not both) ε or µ negative is often opaque to electromagnetic radiation. However, anisotropic materials with only negative permittivity can produce negative refraction due to chirality. Although the optical properties of a transparent material are fully specified by the parametersεr and µr, refractive index n is often used in practice, which can be determined from . All known non-metamaterial transparent materials possess positive εr and µr. By convention the positive square root is used for n. However, some engineered metamaterials have εr < 0 and µr < 0. Because the product εrµr is positive, n is real. Under such circumstances, it is necessary to take the negative square root for n. [3]Video representing negative refraction of light at uniform planar interface. The foregoing considerations are simplistic for actual materials, which must have complex-valued εr and µr. The real parts of both εr and µr do not have to be negative for a passive material to display negative refraction. Metamaterials with negative n have numerous interesting properties:
* Snell's law (n1sinθ1 = n2sinθ2), but as n2 is negative, the rays will be refracted on the same side of the normal on entering the material.
* Cherenkov radiation points the other way.
* The time-averaged Poynting vector is antiparallel to phase velocity. However, for waves (energy) to propagate, a –µ must be paired with a –ε in order to satisfy the wave number dependence on the material parameters . For plane waves propagating in electromagnetic metamaterials, the electric field, magnetic field and wave vector follow a left-hand rule. This is a reversal of direction when compared to the behavior of conventional optical materials. Negative refractive index is an important characteristic in metamaterial design and fabrication. As reverse-refraction media, these occur when both permittivity ε andpermeability µ are negative. Furthermore, this condition occurs mathematically from the vector triplet E, H and k. In ordinary materials – solid, liquid, or gas; transparent or opaque; conductor or insulator – the conventional refractive indexdominates. This means that permittivity and permeability are both positive resulting in an ordinary index of refraction. However, metamaterials have the capability to exhibit a state where both permittivity and permeability are negative, resulting in an extraordinary,index of negative refraction.
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