Dispersion
Created | Updated Jan 27, 2003
Dispersion is an optical effect where the refractive index of a material varies with the wavelength of light that passes through it. It is responsible for, amongst other things, rainbows, that really cool effect you get when light goes through a prism and major headaches for the fibre optic industry. It is a linear effect, which means that it is not affected by the intensity of light.
How does it work?
Imagine, if you will, a beam of white light interacting with a piece of glass. White light, as we all should know, is made up of all the different colours in the spectrum. When the light interacts with the glass atoms in the glass start to resonate in time with the frequency of the light that hits it. If the frequency of light is close to a frequency that the glass wants to absorb, the light interacts more strongly with the glass and hence travels slower.1,2 In glass, the higher frequency light (i.e. the blue end) interacts more strongly than the red end, and so the blue travels more slowly than the red, and in a prism is bent further.3
As a matter of fact, any light that is not truly monochromatic4 will experience dispersion.
Dispersion in real life
As well as the examples of rainbow and prism given above, dispersion can be found almost anywhere. Any material has a dispersion assosciated with it5 which can be described by Sellmeier's equations6. Since dispersion is a rather complicated effect, these act to simplify the relationships and make it possible for calculations to be done more quickly.
Dispersion is an important effect in laser physics and in optical fibre communications. In pulsed laser systems, to get a really short pulse there is a requirement that the laser be quite wide in frequency terms7. Pulsed lasers are used in fibre communication, and here the glass that the fibre is made from suffers dispersion. The amount of data that can be sent down a fibre depends on the duration of the pulse - the shorter the pulse, the more information can be sent down the fibre, as we can send more pulses per second. If, however, there is dispersion in the fibre, the pulses can spread out since one colour in the pulse travels slower than the rest. The effect may not be large, but when we're talking about 5000km of fibre, it can become significant. This type of dispersion (in pulses) is called group velocity dispersion, or GVD, and can really ruin your day if you work with fibres, especially when combined with self-phase modulation
Dispersion is also important in harmonic generation, frequency mixing and parametric processes when linked to birefringence. Here it is used in phasematching.
1This is not quite true, however the electromagnetic equations are rather complicated, and this will do to a first approximation.2The reason for the bending is known. It involves conservation of momentum, but the maths is a little nasty.3In fact, this too is not true, if you use near-infrared light. Above 1.5 microns, the bluer wavelengths can travel faster - this is called anomalous dispersion when it happens4Here it should be noted that even laser beams are not truly monochromatic, and some don't even come close.5Well, any transparent material - and you'd be surprised what can be transparent.6Sellmeier equations allow the dispersion to be modelled using four terms, imaginatively called A, B, C and D, as well as the wavelength of light used, in microns7Formally, there is an inverse relationship between pulse duration and bandwidth.
