Editing Optics (section)

====Dispersion and scattering====
{{Main|Dispersion (optics)|Scattering}}

[[File:Light dispersion conceptual waves.gif|thumb|right|Conceptual animation of light dispersion through a prism. High frequency (blue) light is deflected the most, and low frequency (red) the least.]]

Refractive processes take place in the physical optics limit, where the wavelength of light is similar to other distances, as a kind of scattering. The simplest type of scattering is [[Thomson scattering]] which occurs when electromagnetic waves are deflected by single particles. In the limit of Thomson scattering, in which the wavelike nature of light is evident, light is dispersed independent of the frequency, in contrast to [[Compton scattering]] which is frequency-dependent and strictly a [[quantum mechanical]] process, involving the nature of light as particles. In a statistical sense, elastic scattering of light by numerous particles much smaller than the wavelength of the light is a process known as [[Rayleigh scattering]] while the similar process for scattering by particles that are similar or larger in wavelength is known as [[Mie scattering]] with the [[Tyndall effect]] being a commonly observed result. A small proportion of light scattering from atoms or molecules may undergo [[Raman scattering]], wherein the frequency changes due to excitation of the atoms and molecules. [[Brillouin scattering]] occurs when the frequency of light changes due to local changes with time and movements of a dense material.<ref>{{cite book|author1=C.F. Bohren  |author2=D.R. Huffman |name-list-style=amp |title=Absorption and Scattering of Light by Small Particles|publisher=Wiley|year=1983|isbn=978-0-471-29340-8}}</ref>

Dispersion occurs when different frequencies of light have different [[phase velocity|phase velocities]], due either to material properties (''material dispersion'') or to the geometry of an [[optical waveguide]] (''waveguide dispersion''). The most familiar form of dispersion is a decrease in index of refraction with increasing wavelength, which is seen in most transparent materials. This is called "normal dispersion". It occurs in all [[dielectric|dielectric materials]], in wavelength ranges where the material does not absorb light.<ref name=J286>{{cite book|author=J.D. Jackson|title=Classical Electrodynamics|edition=2nd|publisher=Wiley|year=1975|isbn=978-0-471-43132-9|page=[https://archive.org/details/classicalelectro00jack_0/page/286 286]|url=https://archive.org/details/classicalelectro00jack_0/page/286}}</ref> In wavelength ranges where a medium has significant absorption, the index of refraction can increase with wavelength. This is called "anomalous dispersion".<ref name=J286/>

The separation of colours by a prism is an example of normal dispersion. At the surfaces of the prism, Snell's law predicts that light incident at an angle {{mvar|θ}} to the normal will be refracted at an angle {{math|arcsin(sin (''θ'') / ''n'')}}. Thus, blue light, with its higher refractive index, is bent more strongly than red light, resulting in the well-known [[rainbow]] pattern.{{sfnp|Young|Freedman|2020|p=1116}}

[[File:Wave group.gif|frame|Dispersion: two sinusoids propagating at different speeds make a moving interference pattern. The red dot moves with the [[phase velocity]], and the green dots propagate with the [[group velocity]]. In this case, the phase velocity is twice the group velocity. The red dot overtakes two green dots, when moving from the left to the right of the figure. In effect, the individual waves (which travel with the phase velocity) escape from the wave packet (which travels with the group velocity).]]

Material dispersion is often characterised by the [[Abbe number]], which gives a simple measure of dispersion based on the index of refraction at three specific wavelengths. Waveguide dispersion is dependent on the [[propagation constant]].{{sfnp|Hecht|2017|pp=202–204}} Both kinds of dispersion cause changes in the group characteristics of the wave, the features of the wave packet that change with the same frequency as the amplitude of the electromagnetic wave. "Group velocity dispersion" manifests as a spreading-out of the signal "envelope" of the radiation and can be quantified with a group dispersion delay parameter:

<math display="block">D = \frac{1}{v_\mathrm{g}^2} \frac{dv_\mathrm{g}}{d\lambda}</math>

where {{math|''v''{{sub|g}}}} is the group velocity.<ref name=optnet>{{cite book |author1=R. Ramaswami |author2=K.N. Sivarajan |title=Optical Networks: A Practical Perspective |url=https://books.google.com/books?id=WpByp4Ip0z8C |isbn=978-0-12-374092-2 |publisher=Academic Press |location=London |year=1998 |url-status=live |archive-url=https://web.archive.org/web/20151027164628/https://books.google.com/books?id=WpByp4Ip0z8C&printsec=frontcover |archive-date=2015-10-27 }}</ref> For a uniform medium, the group velocity is

<math display="block">v_\mathrm{g} = c \left( n - \lambda \frac{dn}{d\lambda} \right)^{-1}</math>

where {{mvar|n}} is the index of refraction and {{mvar|c}} is the speed of light in a vacuum.<ref>Brillouin, Léon. ''Wave Propagation and Group Velocity''. Academic Press Inc., New York (1960)</ref> This gives a simpler form for the dispersion delay parameter:

<math display="block">D = - \frac{\lambda}{c} \, \frac{d^2 n}{d \lambda^2}.</math>

If {{mvar|D}} is less than zero, the medium is said to have ''positive dispersion'' or normal dispersion. If {{mvar|D}} is greater than zero, the medium has ''negative dispersion''. If a light pulse is propagated through a normally dispersive medium, the result is the higher frequency components slow down more than the lower frequency components. The pulse therefore becomes ''positively [[chirp]]ed'', or ''up-chirped'', increasing in frequency with time. This causes the spectrum coming out of a prism to appear with red light the least refracted and blue/violet light the most refracted. Conversely, if a pulse travels through an anomalously (negatively) dispersive medium, high-frequency components travel faster than the lower ones, and the pulse becomes ''negatively chirped'', or ''down-chirped'', decreasing in frequency with time.<ref>{{cite book|author1=M. Born  |author2=E. Wolf |name-list-style=amp |author-link = Max Born|title=Principle of Optics|publisher=Cambridge University Press|year=1999|location=Cambridge|pages=14–24|isbn=978-0-521-64222-4}}</ref>

The result of group velocity dispersion, whether negative or positive, is ultimately temporal spreading of the pulse. This makes dispersion management extremely important in optical communications systems based on [[optical fibre]]s, since if dispersion is too high, a group of pulses representing information will each spread in time and merge, making it impossible to extract the signal.<ref name=optnet />