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.

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.

Negative refractive index

Very nearly all materials encountered in optics, such as glass or water, have positive values for both permittivity $\backslash epsilon$ and permeability $\backslash mu$. However, many metals (such as silver and gold) have negative $\backslash epsilon$ at visible wavelengths. A material having either (but not both) $\backslash epsilon$ or $\backslash mu$ 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 $\backslash epsilon$ and $\backslash mu$, in practice the refractive index $N$ is often used. $N$ may be determined from $N=\backslash pm\backslash sqrt\{\backslash epsilon\backslash mu\}$. All known transparent materials possess positive values for $\backslash epsilon$ and $\backslash mu$. By convention the positive square root is used for $N$.

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

Metamaterials with negative $N$ have numerous startling properties:

• Snell's law ($N\_1\backslash sin\backslash theta\_1=N\_2\backslash sin\backslash theta\_2$) still applies, but rays 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".

Theoretical models

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.

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.

Development and applications

One common metamaterial is the Swiss roll.

The first Superlens (an optical lens that exceeds the diffraction limit, albeit only slightly) 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 ^*. But their lens didn't rely on negative refraction. Instead they just used a thin silver film to enhance the evanescent modes through surface plasmon coupling. This idea was first suggested by John Pendry in his seminal paper in PRL.

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 This application of metamaterials is currently being researched at Duke University [http://www.pratt.duke.edu/news/releases/index.php?story=276 .

External links

• Experimental Verification of a Negative Index of Refraction
• For a special issue featuring current research on the field of Metamaterials see the February 2005 issue of Journal of Optics A^*
• How To Make an Object Invisible^*

Electric and magnetic fields in matter

Metamaterial | Métamatériaux