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.
In my lectures, we have derived the dispersion relation
$$ |\vec k|^2 = \frac {n^2 \omega^2}{c^2}$$
by substituting in a plane wave solution for the electromagnetic wave, into the wave equation derived from the Maxwell equations
$$\Delta\vec E= \mu_0\epsilon_0 \frac {\partial^2 \vec...
Hello,
for my PhD, I've been studying an influence of a gain medium on spectral linewidth of light inside a fiber cavity. I've encountered a formula in one paper to which I don't how to get to (see screenshot), it's the formula (A3).
On the left hand side there is electric flux density, the...
I first thought that the angle would have to be maximum when it is closest to the critical angle for total internal reflection. From my lectures the equation for the critical angle is ##\theta _1>\ sin ^{-1} \left( \frac {n_2} {n_1} \right),## so as ##n_2 = 1##, we have ##\theta _1=\sin...
I am not being able to understand what is the electronic dispersion exactly, I have came across it in few papers and I haven't find any resource that explained it clearly and simply.
I've came across 'the electronic dispersion is linear' and 'electronic dispersion is parabolic' and some graphs...
I know that red light has a lower index of refraction than blue light, but that’s not what I’m seeing. The blue light is where the red light should be.
I can’t afford to join CHEGG. Any chance that someone would help me out for free? I’d really appreciate it.
[Link to chegg removed by the Mentors]
I am getting confused by this question. Nevertheless, I tried answering this question.
When I see the word pulse, it brings to my mind a pulse traveling in a rope as shown in diagram below and I cannot relate dispersion to the rope medium in which pulse is travelling. What I do know is that...
Hi,
I was working on the problem below:
Question:
An optical fibre transmission system uses a step-index multimode optical fibre which has a core refractive index of 1.49 and a cladding refractive index of 1.48. The fibre is also subject to material dispersion which is a function of wavelength...
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i would like to know what is the physical significance of the dispersion relation , i know that it relates the energy and momentum vector and correspondingly the energy and momentum with each other , but what does this tell me about the system , and why should i care that the dispersion...
$$\tau _{01} = 10 \tau _{01}$$
If I calculate ##\frac{\tau_{p1}}{\tau_{p1}}## and set z=d=1cm I do not know how to continue from there as I can't solve the equation without knowledge of τ0 for D.
$$\frac{\tau_{p1}}{\tau_{p1}} = \frac{\tau_{02} \cdot 10}{\tau_{02}} \sqrt{\frac{1+\frac{d^2 \cdot 4...
since, in order to view the shape changes in our wave packet we are presented with the taylor expansion of the frequency
ω(k) = ω(k0) + (k − k0)dω/dk + 1/2*(k − k0)^2 (d^2ω/dk^2)
we are told that only the third term that is the
1/2*(k − k0)^2 (d^2ω/dk^2)
contributes to change in shape of the...
Summary:: Due tight-binding model I derived the energy spectrum of the particle, showing that it comprises three energy bands E+(k), E−(k) and E0(k)=0. Now, I have to find the dispersion laws. Why do I have a flat energy band? What is its physical significance?. Also, what happens to the...
Hi,
I am trying to find equation of motion and its solutions for a 2D infinite lumped mass spring system as depicted in figure. All the masses are identical, All the springs are identical, and even the horizontal and vertical periodicity is the same n=a.
I need to try find dispersive relation...
How do I get the wave dispersion for a 2D continuum unit cell subjected to a periodic boundary which is excited longitudinally? I'll be applying forces in ABAQUS with varying frequencies. I have come across Blochs theorem but I can't find any application of it in continuous systems. Every...
Consider water waves refraction in a ripple tank. What happen if we increased the ripple frequency. I mean the refraction angle would change or not? Also, propagation speed will change or not?
I had seen a photograph in PSSC Physics. According to that, the refraction angle was reducing if we...
After noting w=vk and differentiating with respect to k, and lots of simplifying, I get:
Vg = c/n +(2*pi*0.6)/(k*n)
This doesn't correspond to any numerical value though...
I am trying to learn about the dispersion of waves and used one of Walter Lewin's lectures (see below) as a source. I understand phase and group velocity and dispersion relations, but I don't understand when/what kinds of waves are prone to dispersion.
For example, a simple wave in the form...
Homework Statement
ln the figure below you (b, which is taken from Jenö Sólyom Fundamentals of the physics of solids. Volume 2 chapter 19) see the Fermi sphere of radius k_F inside one section in two dimensions of the Brillouin zone of Na. Draw the dispersion relation E(k) from the I point in...
Hi.
We tried to make some quantitative measurements with a Pasco ripple tank system, a video camera and software for video analysis. We generated circular waves and tracked the propagation of a crest, from which the software computed the phase velocity:
We used 5 Hz, 10 Hz and 20 Hz...
Hi.
As far as I know, superpositions of waves are normally considered to be waves too, even in dispersive media. But how can they still be solutions of a wave equation of the form
$$\left(\frac{1}{c^2}\frac{\partial^2}{\partial t^2}-\Delta\right)u=0$$
if ##c## isn't the same for all of them...
In plasma physics we have what is known as plasma dispersion function. There are two approximation under which this function can be expanded: when the argument is less than 1, we can use power series expansion and when the argument is greater than 1 we can have asymptotic expression.
My...
Homework Statement
Do metal atoms, such as Ti and Na, have London-dispersion force?2. The attempt at a solution
In the textbook by Tro (6th ed), "Since all atoms and molecules have electrons, they all have dispersion forces." But metal atoms are held together by electrostatic forces. I think...
Need the dispersion equation for chain consisting of cell units ( LC unit scheme in attachments).
I know I need to make complex Kirchhoff equations and after get the dispersion equation but absolutely don't know how to do it. All examples that I find in web very poor including books, articles...
I am trying to verify the results of the hybrid polariton case with the following hamiltonian, but cannot seem to verify the results in various published papers. Can someone please explain what is wrong and how to get the a similar dispersion graph? I'm solving for the eigenenergies for the...
I'm in the process of learning special relativity (SR), and I'm a bit confused as to why the relativistic energy dispersion relation ##E^{2}=m^{2}c^{4}+p^{2}c^{2}## gives the energy for a free particle? I get that it is the sum of (relativistic) kinetic energy plus the rest mass term (a...
Hi,
I'm looking into how phonon dispersion changes with pressure analytically and need to know how the atomic spacing in copper changes with pressure in order to model the crystal. I can't find any helpful papers online :(
Any help would be appreciated
thanks
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Homework Statement
Homework EquationsThe Attempt at a Solution
## v = \frac { \omega } k ##
## \omega = \sqrt{ kg \tanh (k) } ##I have no idea to guess the graph.
I put g = 9.8 and tried to calculate ## \omega ## for different values of k.
## \omega (0 ) = 0,
\omega (30) =...
Homework Statement
Rays a and b are shown in the figure. Which corresponds to red and which to violet?
The answer in mastering physics says that ray a corresponds to red. Why is this? I've read that colors with higher frequencies will bend more than those of lower frequencies. From what i can...
Homework Statement
I know that for a dispersive wave packet, the group velocity equals the phase velocity, which is given by v=w/k. But how do I calculate the group velocity of a non-dispersive wave packet? I'm supposed to be giving an example with any functional form.
Homework Equations...
I've previously studied and used the k-epsilon turbulence model within Ansys to model water in a small stirred vessel. I am now interested in CFD models appropriate for modeling flue gas dispersion.
I'd like to know:
What additional considerations are required for modeling a gas as opposed to...
I am studying phase and group velocity in non-dispersive and dispersive media. My question is the following: Is there any reason why a dispersive medium simply cannot be modeled as a type of field?
Hello,
I may working through attached paper and really need help with deriving equation in appendix - A4 to give A10.
http://iopscience.iop.org/article/10.1088/0004-637X/744/2/182/pdf
Any help would be greatly appreciated.
thanks,
Sinéad
Dear all,
In a recent talk, I have heard that speed of gravitational waves is non-dispersive.
How is it proved "observationally" in LIGO detections that all the frequencies travel with the same speed, so one can say the speed is non-dispersive?
In the equation characterizing the mass transfer in laminar flow, the radial variation of velocity and concentration can be lumped into the axial dispersion term as below:
After reading the original paper about Taylor dispersion, I know how to derive this equation. But I am still not able to...
Hi all,
Recently I am reading some online material about Tully-Fisher relation and Faber-Jackson relation
which is describing the dynamical constrain on the mass of spiral/elliptical galaxies.
In spiral galaxy, TF relation suggest Luminsoty ≈ (some const) (Vmax)^4
while in elliptical galaxy...
The Nonlinear Schrodinger Equation (NSE) is presented as:
$$i\frac{∂A}{∂z} = \frac{1}{2}β_2\frac{∂^2A}{∂t^2}-\gamma|A^2|A$$
The steady state solution
$$A(z)$$
Can be derived as an Ansatz given by:
$$ A(z) = \rho(z)e^{i\phi(z)}$$
By substituting and solving the ODE, the steady state...
Homework Statement
Im stuck on a old exam in plasma physics. It is about how to determine dispersion relations for high frequency waves in cold plasma's. I'm not sure how they do in the solution manual.
Homework Equations
B = B_0z^
E = E_0exp(i(kx-wt))z^
The Attempt at a Solution
The...
I'm trying to build a fanless computer case for a small electronic device. I'm trying to figure out what type of heat-sink material I should use. I have a solid copper rod about 3cm in length with a radius of .05cm.
I've determined and calculated the density, specific heat, thermal...
i'm trying to understand the solution to this problem:
http://physweb.bgu.ac.il/COURSES/StatMechCohen/ExercisesPool/EXERCISES/ex_2065_sol_Y13.pdf
(link to the problem and the solution of it)
All my questions come from the partition function:
1) From where the term (2*pi)^d comes from?, I...
Hi!
Dealing about wave propagation in a medium and dispersion, wavenumber k can be considered as a function of \omega (as done in Optics) or vice-versa (as maybe done more often in Quantum Mechanics). In the first case,
k (\omega) \simeq k(\omega_0) + (\omega - \omega_0) \displaystyle \left...
As the Figure shown, a white light beam is dispersed by the prism. The refracted beams will have different directions. My question is, will their reverse extension lines intersect into one point, or not? If it will, where is the point? And the proof? Thanks a lot.
Let’s suppose we have an electron with a Gaussian eigenstate, as the time runs, the wave spreads in space without changing its energy, however, the induced EM field caused by the particle decreases its energy. I assert this from the classical electromagnetism result in which the more...
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Starting from a gaussian waveform propagating in a dispersive medium, is it possible to obtain an expression for the waveform at a generic time t, when the dispersion is not negligible?
I know that a generic gaussian pulse (considered as an envelope of a carrier at frequency k_c) can be...
I wonder about this. The explanation that I keep finding is that "dipoles" occur "randomly" when "electrons move" to different sides of the atom. Yet I find this difficult to reconcile with what I understand about quantum mechanics -- so I must be missing something, on either side or both.
In...
It seemed to have been asked before, but I am still a bit confused.
How is the velocity dispersion formed? Doesn't the evidence of dark matter tells us that the orbital speed is uniform in a galaxy?
Is there a direction of dispersion? (e. g velocity gets larger to the core)
And why does...
Hi all!
Can anyone confirm (or point me to literature) that the dispersion relation for the attractive Kronig-Penney potential is correctly given on Wikipedia (https://en.wikipedia.org/wiki/Particle_in_a_one-dimensional_lattice):
$$cos(ka) = cos(\beta b)cos(\alpha (a-b))-\frac{\alpha ^2 +...
Homework Statement
One diffraction grating has 9600 lines uniformly spaced over a width of 3cm, it is illuminated by light from a mercury vapour discharge.
The other has 5000 lines/cm and is a 3.5cm grating, this one is used in the second order to resolve spectral lines close to 587.8002 nm...
Hamiltonian of tight binding model in second quantization is given as H = -t \sum_{<i,j>} a_i^{\dagger} a_j
After changing basis it is H = \sum_{\vec{k}} E_{\vec{k}} a_{\vec{k}}^{\dagger} a_{\vec{k}}
where E_{\vec{k}} = -t \sum_{\vec{b}} e^{i \vec{k} \cdot \vec{b}}
where \vec{b} is a nearest...