Metamaterial

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 features with size comparable or smaller than to 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 optical structures.

J. B. Pendry was the first to imagine 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. So the whole ring can be considered 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. There is a magnetic resonance so the permeability is negative, and the index is negative too.

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

However, some engineered metamaterials have $\epsilon <0$ and $\mu <0$; because the product $\epsilon \mu$ 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 are transparent to light.

Metamaterials with negative $N$ have numerous startling properties:

• Snell's law ($N_{1}\sin \theta _{1}=N_{2}\sin \theta _{2}$) still applies, but rays are refracted away from 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)

One common metamaterial is the Swiss roll.

Such metamaterials follow a "left-hand rule".

Development and applications

The first Superlens (an optical lens employing negative refraction 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 [1]

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 [2].

External links

• Experimental Verification of a Negative Index of Refraction
• For a special issue featuring current research on the field of Metamaterials see the April 2006 issue of Journal of Optics A[3]
• How To Make an Object Invisible[4]