Whereas one expression for the phase velocity is vp=/k, the group velocity can be expressed using the derivative: vg=d/dk. 3 Nevertheless, it can result in non-negligible macroscopic effects, particularly in conducting media such as metals, electrolytes and plasmas. ) However, from afar it isn't heard as causing impulses, but leads to a distinctive descending chirp, amidst reverberation caused by the complexity of the vibrational modes of the track. p m 2 = = 5 c ( 2 k 180 c = 3 ( c 4 A dispersion is a system in which particles of one phase are dispersed throughout a medium that is in a different phase. D ) O = 3 4 + A 5 ( = Edited by Snezana Stanimirovic, Learn how and when to remove this template message, Calculation of the Mean Dispersion of Glasses, "Prismatic discontinuous Galerkin time domain method with an integrated generalized dispersion model for efficient optical metasurface analysis", "Analytical Lah-Laguerre optical formalism for perturbative chromatic dispersion", Animations demonstrating optical dispersion, Interactive webdemo for chromatic dispersion, Conservation and restoration of glass objects, https://en.wikipedia.org/w/index.php?title=Dispersion_(optics)&oldid=1157362741, Articles with disputed statements from October 2014, Articles with unsourced statements from October 2014, Articles needing additional references from March 2023, All articles needing additional references, Creative Commons Attribution-ShareAlike License 3.0, This page was last edited on 28 May 2023, at 03:55. ) Dispersion medium: Dispersion medium is referred to as the external phase. However, dispersion also has an effect in many other circumstances: for example, group-velocity dispersion causes pulses to spread in optical fibers, degrading signals over long distances; also, a cancellation between group-velocity dispersion and nonlinear effects leads to soliton waves. 3 n O O 3 n ) k ) ( ) Therefore, the dispersed phase distributes throughout the dispersion medium. d D ( 2 2 ) 2520 m ) + p 3 }{\left(p\mathrm {-} m\right)\mathrm {!} ) ) 7 ) m {\displaystyle f\mathrm {(} \omega \mathrm {|} \lambda \mathrm {)} } ) n ( 2520 2 4200 ) ( 141120 6 {\displaystyle {\begin{array}{l}{\frac {\partial \varphi \mathrm {(} \omega \mathrm {)} }{\partial \omega }}={-}\left({\frac {\mathrm {2} \pi c}{{\omega }^{\mathrm {2} }}}\right){\frac {\partial \varphi \mathrm {(} \omega \mathrm {)} }{\partial \lambda }}={-}\left({\frac {{\lambda }^{\mathrm {2} }}{\mathrm {2} \pi c}}\right){\frac {\partial \varphi \mathrm {(} \lambda \mathrm {)} }{\partial \lambda }}\end{array}}}, In the case of multi-mode optical fibers, so-called modal dispersion will also lead to pulse broadening. If a light pulse is propagated through a material with positive group-velocity dispersion, then the shorter-wavelength components travel slower than the longer-wavelength components. p + Also called continuous phase, external phase. 7 5 ( 8 ( 2 ( 1 This formula generalizes the one in the previous section for homogeneous media and includes both waveguide dispersion and material dispersion. 3 9 e 2 4 ( 6 90 ) 8 + d + 2 4838400 4 p 8 Language links are at the top of the page across from the title. Waveguides are highly dispersive due to their geometry (rather than just to their material composition). 6 ( Thus, blue light, with a higher refractive index, will be bent more strongly than red light, resulting in the well-known rainbow pattern. = m p ( + m B + 3 p 6 ( ( 1693440 3 p m n {\displaystyle OP} p ( The two phases may be in similar or different states of matter. p = 9 6 4 1 ) = 5 7 v 2 1800 One example of a colloid you are familiar with is milk. n 2023. m 10 ( + {\displaystyle {\begin{array}{c}\varphi \mathrm {(} \omega \mathrm {)} =\varphi \left.\ \right|_{\omega _{0}}+\left.\ {\frac {\partial \varphi }{\partial \omega }}\right|_{\omega _{0}}\left(\omega -\omega _{0}\right)+{\frac {1}{2}}\left.\ {\frac {\partial ^{2}\varphi }{\partial \omega ^{2}}}\right|_{\omega _{0}}\left(\omega -\omega _{0}\right)^{2}\ +\ldots +{\frac {1}{p! ( 40320 7 2 + r ( ( c Another possible option is to use soliton pulses in the regime of negative dispersion, a form of optical pulse which uses a nonlinear optical effect to self-maintain its shape. ( This pulse might be a communications signal, for instance, and its information only travels at the group velocity rate, even though it consists of wavefronts advancing at a faster rate (the phase velocity). is often used to quantify GVD, which is proportional to D through a negative factor: According to some authors,[5] a medium is said to have normal dispersion/anomalous dispersion for a certain vacuum wavelength 0 if the second derivative of the refraction index calculated in 0 is positive/negative or, equivalently, if D(0) is negative/positive. 1 : of or relating to dispersion a dispersive medium the dispersive power of a lens. ( ) ) 2 G + 6 ( p ) ( ) ) ( 12 = p ) n 6 | O ) n 6 3 ( {\displaystyle POD={\frac {d^{p}\varphi (\omega )}{d\omega ^{p}}}=(-1)^{p}({\frac {\lambda }{2\pi c}})^{(p-1)}\sum _{m=0}^{p}{\mathcal {B(p,m)}}(\lambda )^{m}{\frac {d^{m}OP(\lambda )}{d\lambda ^{m}}}} )
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