In optics, dispersion is a phenomenon that causes the separation of a wave into components with different frequencies, due to a dependence of the wave's speed on its frequency. There are generally two sources of dispersion: material dispersion, which comes from a frequency-dependent response of a material to waves; and waveguide dispersion, which comes because the solutions for waves confined laterally within a finite waveguide generally depend upon the frequency (i.e. on the relative size of the wave, the wavelength, and that of the waveguide). It is most often observed in light waves, though it may happen to any kind of wave that interacts with a medium or can be confined to a waveguide, such as sound waves.
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2 Group and phase velocity
3 Dispersion in gemmology
4 Related topics
In general, the refractive index is some function of the frequency ν of the light, thus n = n(ν), or alternately, with respect to the wave's wavelength n = n(λ). The wavelength dependency of a material's refractive index is usually quantified by an empirical formula, the Sellmeier equation.
The most commonly seen consequence of dispersion in optics is the separation of white light into a color spectrum by a prism. From Snell's law it can be seen that the angle of refraction of light in a prism depends on the refractive index of the prism material. Since that refractive index varies with wavelength, it follows that the angle that the light is refracted will also vary with wavelength, causing the angular separation of the colors.
For visible light, most transparent materials (e.g. glasses) have:
Group and phase velocityAnother consequence of dispersion manifests itself as a temporal effect. The formula above, v = c / n calculates the phase velocity of a wave; this is the velocity at which the phase of any one frequency component of the wave will propagate. This is not the same as the group velocity of the wave, which is the rate that changes in amplitude (known as the envelope of the wave) will progagate. The group velocity vg is given by:
The group velocity itself is usually a function of the wave's frequency. This results in group velocity dispersion (GVD), which causes a short pulse of light to spread in time as a result of different frequency components of the pulse travelling at different velocities. GVD is often quantified as the group delay dispersion parameter:
The result of GVD, whether negative or positive, is temporal spreading of the pulse. This makes dispersion management extremely important in optical communications systems based on optical fiber, since if dispersion is too high, a group of pulses representing a bit-stream will spread in time and merge together, rendering the bit-stream unintelligible. This limits the length of fiber that a signal can be sent down without regeneration. One possible answer to this problem is to send signals down the optical fibre with a wavelength of ~1.3 μm; this is a wavelength at which GVD is zero in silica glass, so pulses at this wavelength suffer minimal spreading from dispersion. Another possible option is to use soliton pulses, a form of optical pulse which uses a nonlinear optical effect to self-maintain its shape.
Dispersion control is also important in lasers that produce short pulses. The overall dispersion of the optical resonator is a major factor in determining the duration of the pulses emitted by the laser. A pair of prisms can be arranged to produce net negative dispersion, which can be used to balance the usually positive dispersion of the laser medium. Diffraction gratings can also be used to produce dispersive effects; these are often used in high-power laser amplifier systems.
Dispersion in gemmology
In the technical terminology of gemology, dispersion is the difference in the refractive index of a material at the B and G Fraunhofer wavelengths of 686.7 nm and 430.8 nm and is meant to express the degree to which a prism cut from the gemstone shows fire or color. Dispersion is a material property. Fire depends on the dispersion, the cut angles, the lighting environment, the refractive index, and the viewer.