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westwolf

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[交流] 负折射率亚稳态材料(zt)

An introduction to negative refraction...

Refraction and Snell's Law
　　One of the most fundamental of optical effects is refraction, or the bending of light as it crosses the interface between two materials. The phenomenon of refraction is well-known to most of us: for example, an object under water viewed by an observer in air always appears closer to the surface than it actually is. Refraction is the basic principle behind lenses and other optical elements that focus, steer, guide or otherwise manipulate light. Highly sophisticated and complex optical devices are developed by carefully shaping materials so that light is refracted in desired ways (think of a camera lens or a microscope objective).

　　The underlying principle of refraction can be easily understood and applies to all electromagnetic waves--not just visible light. Every material, including air, has an index-of-refraction (or refractive index). When an electromagnetic wave traverses the interface from a material with refractive index n1 to another material with refractive index n2, the change in its trajectory can be determined from the ratio of refractive indices n2/n1 by the use of Snell's Law.
http://www.ee.duke.edu/~drsmith/content/snell_law.gif
To apply Snell's Law, consider an interface between two materials and an imaginary line that runs perpendicular to the interface (the surface normal). The angles in Snell's law are measured away from the surface normal. If the refractive indices of the two materials are not equal, the angle of the transmitted beam will differ from the angle of the incident beam. The beam is then bent at the interface.

A common way to determine the refractive index of a material is to form a prism out of the material, shine a beam of light through it and observe the deflection of the beam on the other side. Light enters the prism through one of the interfaces at direct incidence, striking the opposite interface at an oblique angle. The figure below shows what happens to the beam when the material has the same index as the surrounding medium, or has an index that is greater than the surrounding medium but either positive or negative.

Veselago and negative index

All transparent or translucent materials that we know of possess positive refractive index--a refractive index that is greater than zero. However, is there any fundamental reason that there should not be materials with negative refractive index? This question was asked by Victor Veselago, a Russian physicist. In 1968, Veselago published a theoretical analysis of the electromagnetic properties of materials with negative permittivity and negative permeability. The electric permittivity and the magnetic permeability are commonly used material parameters that describe how materials polarize in the presence of electric and magnetic fields. Maxwell's equations relate the permittivity and the permeability to the refractive index as follows:

The sign of the index is usually taken as positive. However, Veselago showed that if a medium has both negative permittivity and negative permeability, this convention must be reversed: we must choose the negative sign of the square root!

This reversal of the refractive index can seem confusing. As an example, it is often said that the velocity of a wave in a material is given by c/n, where c is the speed of light in vacuum. The implication of a negative index, then,is that the wave travels backwards, as indicated in the animation below. An electromagnetic wave can be depicted as a sinusoidally varying function that travels to the right or to the left as a function of time. In the top animation in the figure below, a wave is incident on a positive index material (the reflected wave has been ignored). The greater index of the second medium implies that the wavelength decreases (by a factor of 1/n); however, to maintain the same phase at the interface as a function of time, the speed of the wave must also be reduced, again by a factor of 1/n.

When the refractive index is negative, the speed of the wave--given by c/n--is negative and the wave travels backwards toward the source as in the bottom animation in the figure below. Yet, we would reasonably expect that since energy is incident on the material from the left, the energy in the the material should likewise travel to the right, away from the interface. This seeming paradox is resolved, as Veselago showed, by realizing there are more ways to define the velocity of a wave. The definition c/n is well known as the phase velocity and determines the rate at which the peaks (or zeros) of a wave pass a given point in time. But this is not most relevant definition of a wave's velocity: we can also define the group, energy, signal and front velocities, and these generally differ from the phase velocity.

When the refractive index of a material does not vary with the wavelength of light that travels through it, then all of the velocity definitions above are the same and we can intuitively use the index as a measure of the wave's velocity. However, when a material is dispersive--has an index that varies with wavelength--then the various definitions of velocity no longer agree and we can no longer determine the actual velocity of the wave, or at least the rate at which energy is transported, from the value of the refractive index alone. So, even though the positive and negative index materials in the figure above seem to display drastically different behaviors, a calculation of the group or the energy velocity reveals that energy is actually flowing to the right in both cases. Thus, as Veselago showed, the phase and energy velocities are opposite in a negative index material.

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westwolf

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亚稳态材料（Metamaterial）（From Wikipedia, the free encyclopedia）

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.

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 [1]. 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 [2]. This application of metamaterials is currently being researched at Duke University [3] .

External links

* Experimental Verification of a Negative Index of Refraction (see: http://physics.ucsd.edu/lhmedia/)
* For a special issue featuring current research on the field of Metamaterials see the April 2006 issue of Journal of Optics A[4]
* How To Make an Object Invisible[5]
[1] http://www.eurekalert.org/pub_releases/2005-04/uoc--nso041805.php
[2] http://www.cnn.com/2006/TECH/05/ ... cloak.ap/index.html
[3] http://www.pratt.duke.edu/news/releases/index.php?story=276
[4] http://www.iop.org/EJ/toc/1464-4258/8/4
[5] http://physicsweb.org/articles/news/10/5/16/1