Metamaterial

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In electromagnetism (covering areas like optics and photonics), a meta material (or metamaterial) is an object that gains its (electromagnetic) material properties from its structure rather than inheriting them directly from the materials it is composed of. This term is particularly used when the resulting material has properties not found in naturally-formed substances. Metamaterials are promising for a diversity of optical/microwave applications, such as new types of beam steerers, modulators, band-pass filters, superlenses, microwave couplers, and antenna radomes.

In order for its structure to affect electromagnetic waves, a metamaterial must have structural features at least as small as the wavelength of the electromagnetic radiation it interacts with. In order for the metamaterial to behave as a homogeneous material accurately described by an effective refractive index, the feature sizes must be much smaller than the wavelength. For visible light, this is on the order of one micrometre; for microwave radiation, this is on the order of one decimetre. An example of a visible light metamaterial is opal, which is composed of tiny cristobalite (metastable silica) spheres. Microwave frequency metamaterials are almost always artificial, constructed as arrays of current-conducting elements (such as loops of wire) that have suitable inductive and capacitive characteristics. Photonic crystals is a general term for periodic and quasi-periodic structures designed to affect electromagnetic waves.

1 Negative refractive index
2 Theoretical models
3 Development and applications
4 References
5 External links

[edit] Negative refractive index

$A comparison of refraction in a left-handed metamaterial to that in a normal material$

Very nearly all materials encountered in optics, such as glass or water, have positive values for both permittivity <math>\epsilon</math> and permeability <math>\mu</math>. However, many metals (such as silver and gold) have negative <math>\epsilon</math> at visible wavelengths. A material having either (but not both) <math>\epsilon</math> or <math>\mu</math> negative is opaque to electromagnetic radiation (see surface plasmon for more details).

Although the optical properties of a transparent material are fully specified by the parameters <math>\epsilon</math> and <math>\mu</math>, in practice the refractive index <math>N</math> is often used. <math>N</math> may be determined from <math>N=\pm\sqrt{\epsilon\mu}</math>. All known transparent materials possess positive values for <math>\epsilon</math> and <math>\mu</math>. By convention the positive square root is used for <math>N</math>.

However, some engineered metamaterials have <math>\epsilon<0</math> and <math>\mu<0</math>; because the product <math>\epsilon\mu</math> is positive, <math>N</math> is real. Under such circumstances, it is necessary to take the negative square root for <math>N</math>. Physicist Victor Veselago proved that such substances can transmit light.

Metamaterials with negative <math>N</math> have numerous startling properties:

Snell's law (<math> N_1\sin\theta_1=N_2\sin\theta_2</math>) still applies, but as <math>N_2</math> is negative, the rays will be refract on the same side of the normal on entering the material.
The Doppler shift is reversed (that is, a light source moving toward an observer appears to reduce its frequency)
Cherenkov radiation points the other way
The group velocity is antiparallel to phase velocity (as opposed to parallel for normal isotropic materials)
Higher frequencies have longer, not shorter, wavelengths in such a material

Such metamaterials follow a left-hand rule. For an illustration in non-technical language of one of the bizarre properties of materials with negative <math>N</math>, consider the following: a person submerged in a swimming pool filled with a hypothetical liquid with negative <math>N</math> would appear underneath where the viewer was standing.

[edit] Theoretical models

Left-handed (LH) materials were first introduced theoretically in Veselago (1968). V.G. Veselago, "The electrodynamics of substances with simultaneously negative values of ε and μ", Sov. Phys. Uspekhi, 1968, 10(4), 509-514 (doi 10.1070/PU1968v010n04ABEH003699).

J. B. Pendry was the first to theorize a practical way to make a left-handed metamaterial (LHM). 'Left-handed' in this context means a material in which the 'right-hand rule' is not obeyed, allowing an electromagnetic wave to convey energy (have a group velocity) in the opposite direction to its phase velocity. Pendry's initial idea was that metallic wires aligned along propagation direction 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 that also showed negative permeability (µ<0). In 1999, Pendry demonstrated that an open ring ('C' shape) with axis along the propagation direction 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 that was also proposed by Professor Pendry is the Swiss roll.

The analogy is as follows: Natural 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 a 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.

[edit] Development and applications

The unique properties of metamaterials were verified by full-wave analysis in Caloz et al. (2001). <ref>C. Caloz, C.-C. Chang, and T. Itoh, "Full-wave verification of the fundamental properties of left-handed materials in waveguide configurations," J. Appl. Phys. 2001, 90(11).</ref> However, the LH structures devised up to 2002 were impractical for microwave applications, because they had a too narrow bandwidth and were quite lossy. Eleftheriades et al. (2002), and Caloz et al. (2002) provided a method to realize left-handed metamaterials using artificial lumped-element loaded transmission lines in microstrip technology.<ref>G.V. Eleftheriades, A.K. Iyer and P.C. Kremer, “Planar negative refractive index media using periodically L-C loaded transmission lines,” IEEE Trans. on Microwave Theory and Techniques, vol. 50, no. 12, pp. 2702-2712, 2002</ref><ref>C. Caloz and T. Itoh, "Application of the transmission line theory of left-handed (LH) materials to the realization of a microstrip 'LH line'," IEEE Antennas and Propagation Society International Symposium, 2002, 2, 412-415 (doi 10.1109/APS.2002.1016111).</ref>

The first superlens with a negative refractive index provided resolution three times better than the diffraction limit and was demonstrated at microwave frequencies at the University of Toronto by A. Grbic and G.V. Eleftheriades<ref>A. Grbic and G.V. Eleftheriades, “Overcoming the diffraction limit with a planar left-handed transmission-line lens,” Physical Review Letters, vol. 92, no. 11, pp. 117403 , March 19, 2004</ref>. Subsequently, the first optical superlens (an optical lens that exceeds the diffraction limit) was created and demonstrated in 2005 by Xiang Zhang et al. of UC Berkeley, as reported that year in the April 22 issue of the journal Science.<ref>http://www.eurekalert.org/pub_releases/2005-04/uoc--nso041805.php</ref> But their lens didn't rely on negative refraction. Instead, they used a thin silver film to enhance the evanescent modes through surface plasmon coupling. This idea was first suggested by John Pendry, Sir Proffesor at Imperial College London, in Physical Review Letters.

Metamaterials have been proposed as a mechanism for building a cloaking device. These mechanisms typically involve surrounding the object to be cloaked with a shell that affects the passage of light near it.<ref>http://www.cnn.com/2006/TECH/05/25/invisibility.cloak.ap/index.html</ref> Duke University is currently researching this use of metamaterials and has managed to use metamaterials to cloak an object (in the microwave spectrum) using special concentric rings; the microwaves were barely affected by the presence of the cloaked object.<ref>http://www.pratt.duke.edu/news/releases/index.php?story=276</ref>