What is Dispersion: Definition and 284 Discussions

In optics, dispersion is the phenomenon in which the phase velocity of a wave depends on its frequency.
Media having this common property may be termed dispersive media. Sometimes the term chromatic dispersion is used for specificity.
Although the term is used in the field of optics to describe light and other electromagnetic waves, dispersion in the same sense can apply to any sort of wave motion such as acoustic dispersion in the case of sound and seismic waves, in gravity waves (ocean waves), and for telecommunication signals along transmission lines (such as coaxial cable) or optical fiber. Physically, dispersion translates in a loss of kinetic energy through absorption.
In optics, one important and familiar consequence of dispersion is the change in the angle of refraction of different colors of light, as seen in the spectrum produced by a dispersive prism and in chromatic aberration of lenses. Design of compound achromatic lenses, in which chromatic aberration is largely cancelled, uses a quantification of a glass's dispersion given by its Abbe number V, where lower Abbe numbers correspond to greater dispersion over the visible spectrum. In some applications such as telecommunications, the absolute phase of a wave is often not important but only the propagation of wave packets or "pulses"; in that case one is interested only in variations of group velocity with frequency, so-called group-velocity dispersion.

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  1. P

    Wavepacket Dispersion and how this links to particle behaviour

    Hi, I'm trying to get my head round modelling particles in free space in quantum mechanics. I appreciate that we can "build" wavepackets by superposing many plane waves with different k-numbers (i.e. with different frequencies & momentums & energies I think). The greater the number of phase...
  2. A

    How to find a neutron dispersion curve

    A neutron is at rest inside a crystalline solid. Can a phonon come along and give up all of its energy to the neutron? Address the question with a graphical solution, i.e. overlay the dispersion curves for neutrons and phonons. For simplicity assume that the solid has a basis of a single atom...
  3. G

    Reading phonon dispersion curves

    I've got a question about interpreting these - mainly about how the horizontal axis works. See attached file - On the leftmost panel, it has a form of the wavevector q plotted from left to right, labeled as (000) on the left and (100) on the right. What does this mean? Does it mean that...
  4. S

    Applicability of Kramer Kronig relation in the context of normal dispersion

    In the context of complex refractive index, is it possible to apply the Kramer-Kronig relation in the region of normal dispersion ? What I want to do is the following. I can measure real part of complex refractive index of a material, n in the limited range of 200-1000 nm wavelength where...
  5. M

    Dispersion in for a free particle

    Hey, I am trying to calculate the dispersions \DeltaP and \DeltaX for a free particle with definite momentum \Phi(x) = Aexp(ikx) where A is a normalization constant. This i get \DeltaP = 0 \DeltaX = \infty What physical interpretation can I give to these results? Is is that the momentum is...
  6. L

    Why is there a spectrum on the back of a CD or DVD?

    Homework Statement When i see the back of a CD or DVD, there is a spectrum, in which the various colours are overlapping with each other(continuous spectrum) Homework Equations What is the reason for this phenomenon, diffraction or dispersion? The Attempt at a Solution Diffraction...
  7. N

    Electric charge build up and dispersion through mediums?

    If you sport some X-mas grade wool socks in the typical striding motion across a carpet floor... what causes that build up of charge to stay in the body and leave in such a (seemingly) similar fashion to lightning dispersing into the ground when it doesn't just "wind down"? My best guess has to...
  8. M

    Deviation and dispersion in a prism

    Hello,world [PLAIN]http://img718.imageshack.us/img718/1433/unledkzg.jpg Could you explain the reason for this?This would help me so much Thanks in advance
  9. M

    The Natural Dispersion of Black Holes

    Black holes are believed to be scattered throughout the universe. These ultra-dense bodies have a gravity field so dense that nothing, not even light can escape. If these bodies are able to consume everything that enters its event horizon than over the billions of years that the universe has...
  10. E

    Time dependent dispersion (Quantum Mechanics)

    Homework Statement The initial wave function \Psi (x,0) of a free particle is a normalized gaussian with unitary probability. Let \sigma = \Delta x be the initial variance (average of the square deviations) with respect to the position; determine the variance \sigma (t) in a moment later...
  11. A

    Trying to find dispersion relation

    Homework Statement \imath\frac{\partial u}{\partial t} + \frac{\partial^2 u}{\partial x^2}=0 \left(x,t\right) = \int^{\infty}_{-\infty}A\left(k\right)e^{\imath\left(kx-wt\right)}dk u\left(x,0\right)=\delta\left(x\right) Homework Equations Not sure how to get w(k) The...
  12. A

    How do I Find the Dispersion Relation for a PDE?

    \imath\frac{\partial u}{\partial t} + \frac{\partial^2 u}{\partial x^2}=0 \left(x,t\right) = \int^{\infty}_{-\infty}A\left(k\right)e^{\imath\left(kx-wt\right)}dk u\left(x,0\right)=\delta\left(x\right) This is what I am working with. I am supposed to find the dispersion relation. So far...
  13. C

    Dispersion relation and group velocity

    Hello there PF readers, The group velocity for example of electron waves is given by the derivative of the dispersion relation: \frac{dE}{dp}=v (this is for free electrons) ^{1}. Now the Heisenberg's uncertainty principle has two forms, one for position and momentum and the other for energy...
  14. Q

    Dispersion: frequency dependent wave speeds

    Assuming that light travels through an optically dense medium such as glass slower than in a vacuum: 1. What on the atomic level causes the different changes in speed for different wavelengths? 2. For a light wave incident at the normal (90 degress) of the entry boundary do the different...
  15. M

    Deriving the Phonon Dispersion Relation using Quantum-mechanical approach

    I'm doing a literature review on dispersion relations, and I've been told that if i can derive the phonon dispersion relation, it would help my review. So i was wondering if anybody could help me with the derivation either through Quantum-mechanical approach or Semi-classical treatment of...
  16. L

    Why aren't the <v^2> and <vr^2> curves different in my Hernquist model?

    Hello, I would appreciate very much some help on this problem. I have a Hernquist model (distribution function) and I am trying to generate equal mass initial conditions. The way I do it is this. I have the mass profile M(r) and I pick say 10^6 random numbers between 0 and 1=M(r->inf). Then I...
  17. T

    Dispersion Relations and Refractive INdex

    Homework Statement The conductivity of a plasma is defined as \sigma = i\frac{Ne^{2}}{m\omega} where N is the electron density. a) Prove the refractive index is: n = \sqrt{1- (\frac{\omega}{\omega_{p}})^{2}} with \omega_{p} = \sqrt{\frac{Ne^{2}}{m\epsilon_{0}}} b) Show the Attenuation...
  18. K

    Dispersion relation of amorphous materials

    Hi, I am trying to find dispersion relation of amorphous material (using data obtained by molecular dynamics simulation). As it is not periodic system one can not find it by standard method of diagonalizing the force constant matrix. I think one can do it by taking Fourier transform of...
  19. G

    Equations of Electron Dispersion in an E Field

    Homework Statement Given the dispersion equation of an electron in an electric field: Homework Equations a) calculate the velocity of the electron if k = π/a b) If the electric field E is applied in the -x direction, derive the time dependence of k for an electron initially at k...
  20. MalachiK

    Multipath dispersion in fibre optic cable

    Homework Statement I saw this question on this forum and the answer given At first I thought that it was obvious why reducing the width of the fibre would reduce the multipath dispersion. But having tried the problem with maths, I'm not so sure. Can anyone tell me where my maths...
  21. T

    Mass Dispersion of Observable Universe

    Does anyone know of any data regarding mass dispersion around Earth? That is to ask (more toward my interest), if the observable universe was broken into equal 3-D sections like "North to Northeast" "NE to E" "E to SE" and so on... would the mass of each section observed from Earth be equal...
  22. G

    Understanding London Dispersion Force: Theoretical Derivation Explained

    hi, lately i am concerned with Van der Waals forces and I often found in chemistry books the so-called London dispersion force, which says that the potential energy of the Van der Waals interaction is: U=-2/3 a1a2I1I2/(r^6*(I1+I2) but by now I could not find a theoretical derivation of...
  23. S

    Phonon Dispersion Interpretation

    Dear friends of physics forum I have calculated the phonon dispersion of an fcc phase using PHONON software. the fcc phase I am talking about is a metastable phase of Zr. Zr, as we all know exists in hcp and bcc phases. I wanted to calculate the heat capacity at constant volume using the...
  24. K

    Calculating Phonon Dispersion from 2D Hamiltonian

    Hello, I am constructing a 2d atomistic mass spring Hamiltonian with nearest neighbor bonds (harmonic potential) in an attempt of calculating the phonon dispersion. I solve the eigenvalue system and calculated the eigenvalues or phonon energy levels (y-values of dispersion). I am fine up to...
  25. L

    Calculate the line of sight velocity dispersion of the cluster in km/sec

    Please Help :) "Calcium H and K lines have rest frame wavelengths of 3968.5 A (angstrom). Spectroscopy of 5 stars in a cluster revealed that the Ca H line was detected at 3970.1 A 3966.3 A 3967.5 A 3971.0 A 3968.2 A in each of these five stars. Calculate the line of sight velocity dispersion of...
  26. N

    How should I understand the dispersion in fiber optics?

    Homework Statement What is the physical definition of this graph and the unit of dispersion? I know it is picosec/(km times nm), but I am not sure for what it refers to. Homework Equations The Attempt at a Solution I asked my mates for the meaning and I typed them on the right of...
  27. B

    Confused about dispersion (optics)

    Hi I'm trying to get a better understanding of dispersion in light. Specifically, the relationship between refractive index and wavelength, and why the refractive index increases for decreasing wavelengths. However, I've been confused by all the various information I've come across...
  28. D

    Waveguide Dispersion: Investigating Properties & Complications

    Greeting. I am currently investigating the dispersion properties of waveguides. The dispersion of an optical fiber is usually mostly contributed to by the material dispersion. Ignoring any dopant, this is just dependent on the refractive index of silica. It is easy to take the Sellmeier...
  29. M

    Exploring Anomalous Dispersion for Resonant Cavities

    In anomalously dispersive media, the change in phase velocity with wavelength is negative; that is dv/dλ < 0. I wanted to ask: (a) whether you could fit a wide range of frequencies into a resonant cavity by taking advantage of anomalous dispersion (b) whether a material like this exists...
  30. C

    Optics fibre dispersion, pulse propagation

    Homework Statement A pulse train of Gaussian shaped pulses travels in a single mode fibre. The separation (T) of the pulse centres is five times the temporal width (\Delta \tau) of an individual pulse i.e. T=5*\Delta \tau. The dispersion of the material is D=200ps/nm/km. L=0.1km, n plastic =...
  31. S

    Why is standard deviation the preferred method for measuring dispersion?

    I’m wondering why standard deviation is used as the main method of measuring dispersion, when i would consider that more ergonomic (user friendly) measurements are possible. An example of such would be, the sum of |x-mean|/ n . I would think that the mean plus and minus this value would...
  32. Dimani4

    Is Group Velocity Dispersion Infinite for Light in Air?

    Hey ppl, I have a question for you. For the case of light propagation in the air the the group-velocity dispersion parameter D is infinity because the derivative of the group velocity should be a zero (group velocity is constant ; w=ck and Vgroup=dw/dk). Who can explain me this? dispersion...
  33. N

    Superconducting d-wave dispersion

    Hi In litterature, I have noticed some authors write the dispersion for the d-wave gap as Δ(k)=Δ[cos(kx)-cos(ky)]/2, and some write it as Δ(k)=2Δ[cos(kx)-cos(ky)]. Where does this difference come from?
  34. S

    Sketching Dispersion Relations for Protons, Free Electrons & Solid Electrons

    Really struggling with this question guys, any help/advice will be greatly appreciated. Thanks in advance! Homework Statement Sketch dispersion relations for, (i) a proton (ii) a free electron (iii) an electron, in a crystalline solid. Comment on the similarities between (ii) and...
  35. F

    Refractive index and dispersion (name & usage of eq and conceptual questions)

    Sry for a proper wall of text, and it´s probably pretty "chatty" too, as I reason about things back and forth... Plz do feel free to comment on the reasoning since I post it to learn how to think about these things... I believe that I have sometime learned that one can relate refractive index...
  36. I

    Langmuir waves dispersion relation

    I was just looking at an expression (a dispersion relation, omega^2 = ...) similar to that of warm electron's in a plasma http://en.wikipedia.org/wiki/Plasma_oscillation expect with an extra imaginary term, which I think comes out from the full derivation of the dispersion relation for warm...
  37. J

    Dispersion of soluble matter in tube

    Hi I am reading and trying to comprehend the article "Dispersion of soluble matter in solvent flowing slowly through a tube", Sir Geoffrey Taylor, Proceedings of the Royal Society of London, 1953. I am particularly interested in cases A2 and B2, where a concentrated solution is injected...
  38. D

    Phonon dispersion relation : meaning of mode crossings

    Hello all, What does it mean when two phonon branches get crossed in phonon dispersion relation ? Also, in certain high symmetry direction, one can find only one transverse branch and other direction two separate branches, what do these response mean? (Ref. Solid state physics by...
  39. M

    From phonon dispersion to density of state

    I have searched this topic in our forums. no answer about that. I have obtained the phonon dispersion curve by applied a numerical simulation. However, how can I obtain the phonon density of state from such a curve? generally speaking, g(q)dq = g(w)dw, here q is the wave-vector; w is...
  40. C

    Difference between Material dispersion and waveguide dispersion?

    Can someone please explain the difference between Material dispersion and waveguide dispersion?
  41. Simfish

    Central velocity dispersion vs rotation cuves for estimating galactic mass

    Okay, so, say, you're trying to measure the mass of the very center of the Andromeda galaxy (within 1 arcsecond of the center). You have a central velocity dispersion of 250 km/s and a rotation curve of 100 km/s (1 arcsecond away from the center). Now, from the virial equilibrium equation, M(r)...
  42. P

    Is it Taylor Dispersion or Something Similar in Drug Injection?

    I'm having a wording issue in a paper I'm writing. Specifically, I'm trying to decide between arguing something is "diffusion" vs. "dispersion". Can anyone point me to a reference that clearly demarcates between these? In specific, I'm referring to the diffusion/dispersion of an injected drug...
  43. X

    Group velocity and Dispersion Relation

    Hi there So I was looking into group velocity and related matters and found myself quite confused. So now I have a few questions which I feel I need to understand (primarily the first one). Any help with these would be awesome and I would be very grateful... 1) Why is the group...
  44. T

    Electron dispersion in a conductor

    I'm curious why electrons will travel near the perimeter of a large wire as opposed to using the whole cross section. I understand that electrons flowing through the wire repel each other and thus want to be as far apart as possible. Yes, but from this electrons should not just occupy the...
  45. N

    Optics: Anomalous Dispersion & Absorption Explained

    Hi I am reading about dispersion and index of refraction, and I have encountered the term "anomalous dispersion". This is where dn/dω<0, and where the absorption is strongest because of damping. Now, I can't seem to connect those two dots (and my book does not explain it nor Wiki): Why does...
  46. N

    Understanding Dispersion Relations in Fluid Dynamics

    I am having trouble understanding a basic problem in fluids that came up during an exam I took last quarter. Namely, we are given a dispersion relation and asked to quantify how a one dimensional surface disturbance propagates in space. (The disturbance is initially an approximate delta function...
  47. S

    Understanding Wave Dispersion & Group Velocity: Help Needed!

    *for a group of waves, the energy is transmitted with the group velocity. what does that mean? *what is meant, as in actually meant, by dispersion of a wave in a medium? whatever i looked up says phase velocity depends on frequency for a dispersive medium and vice versa. Why? * wave...
  48. D

    References for non-vacuum dispersion relations

    Hi guys, I'm looking for some references where dispersion relations, say for photons, are explicitely written out in a generic medium. In other words, the dispersion relation for particles not propagating in the vacuum is a different one than the standard vacuum one E^2 = p^2 + m^2 and I'm...
  49. K

    Can anyone explain dispersion to me in simple words?

    Can anyone explain "dispersion" to me in simple words? Can anyone explain "dispersion" to me in simple words? like,, when waves escape from a small gap why would they s[read out in circles? thnx for help!
  50. H

    Chromatic Dispersion, and Variability of Refractive Index on Wavelength

    Hi I'm trying to sort this concept out in my head and have reached a stumbling block! 1. ok so light travels through medium a and transmits through medium b and refracts. The angle or refraction is given by snell's law, and quantified by the refractive index of materials a and b. 2. But I...
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