Unweaving a rainbow – Transparent materials and refractive indices

Materials World magazine
1 Feb 2008

It is axiomatic that nothing can move faster than light, but it is worth remembering that this is only true for propagations in vacuo. In all natural transparent materials the velocity of light is slower than it is in empty space. In water, light travels at only 75% of its speed in vacuo and, as a consequence, charged particles, such as electrons, can travel faster than light in water. This gives rise to the eerie blue glow in water-immersed nuclear reactors – the Cherenkov Effect (see Material Matters, Materials World, December 2007, p60).

Refractive index

The ratio of the speed of light in vacuo to that in a transparent material is known as the material's refractive index (R). If R>1, this is referred to as a positive refractive index, if R<1 the index is negative. For yellow light, R equals 1.0002 for air, 1.333 for water, 1.5717 for crown glass and 2.147 for diamond. In conformity to Snell's Law, R is also equal to the sine of the angle of incidence divided by the sine of the angle of refraction.

X-rays, like light, are a type of electromagnetic radiation, but they differ in one important aspect – they travel slightly faster in transparent materials than in vacuo, ie R<1. As often happens in the evolution of science and technology, the critical development is within the compass of material science. Some years ago, Professor John Pendry (admittedly a physicist), of Imperial College London, pointed out that if materials that are transparent to light, but with R<1, could be developed, then as the refracted ray would move away from, instead of towards, the normal, this could help create a perfect lens, or more fancifully, be woven into an invisibility cloak.

The possibility of transparent materials

Researchers have studied transparent materials that contain tiny metal precipitates which change the electromagnetic properties of the matrix. Such studies have produced materials with negative refractive indices (ie R<1), albeit for wavelengths of light outside the visible range.

These studies have a long way to go but this has not deterred Tsakmakidis, Boardman and Hess from publishing in Nature (15 November 2007, p397) a theoretical paper entitled ' "Trapped rainbow" storage of light in metamaterials'. They assume that further developments will produce a transparent material which has a negative refractive index for visible light, and have conducted a theoretical analysis of projecting light down a tapering duplex fibre consisting of a core of a material with a negative refractive index inside an outer sheath of a material with a positive refractive index. They imagine a ray of light travelling down the core of the fibre and bouncing back and forth from the boundary between core and cladding.

In such an arrangement an optical effect known as the Goos-Hänchen shift will narrow the width in which the light rays can bounce about. As the complex fibre is tapered, there will come a point beyond which the beam cannot progress – it will become immobilised and trapped. As the critical thickness for trapping is a function of the wavelength of the light, the different colours will not only be trapped, they will also be separated. All this is very speculative but it could become important. If light can be packaged and stored, a computer using photons instead of electrons may not be far behind.

Incidentally, 'Unweaving' in my title relates to Keats' intemporate attack on Newton for destroying with science the magic of a rainbow. What would the poet have thought of scientists not only unweaving a rainbow but then holding its component colours in the palm of their hands?


Further information:

'Trapped rainbow" storage of light in metamaterials', Nature, 15 November 2007