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.
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...
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.
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...
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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...
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 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?
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?
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.
Hello!
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...
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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 +...
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...
Hi.
Is the superposition of two different monochromatic waves in a dispersive medium still a wave (i.e. a solution of a wave equation) if the phase velocity is not the same? Since the wave equation contains the phase velocity, the two individual waves are solutions of different wave equations...
Hello!
I still would like to thank those who participated to my previous thread about group velocity and dispersion. Now there is a (maybe) simpler question.
A sinusoidal, electro-magnetic plane wave in the vacuum propagates in a certain direction with the following wavenumber, which is supposed...
I have some qualitative questions about the relation between band structure, density of states, and Fermi energy (or Fermi level).
1) Say you have a given electronic band structure (energy as a function of k) obtained by any method. How do you relate this to the Fermi energy (or Fermi level) ...
I'm revising for a uni exam with past exam papers, and have gotten stuck on the details of dispersion. The two exam questions prompting this are a) What is the physical reason why the index of refraction for blue light is bigger than that of red light? and b) Explain how dispersion makes a...
In class I learn that we can get the dispersion relation for particles by using E=hbar*w and p=hbar*k. The calculated phase velocity is w/k = hbar*k/2m, while the group velocity is dw/dk=hbar*k/m. All these make sense to me, except one thing: I always thought that E=hbar*w=hf is only applicable...
I'm trying to get my head around what this means exactly. I've plotted the graph to help verse me with the functions that I've derived.
From the free electron model, the wavefunctions are treated as planewaves of the form
\psi_\mathbf{k}(\mathbf{r}) = e^{i\mathbf{k}\cdot\mathbf{r}}
Due to...
I know that in a vacuum, speed of light is constant. My question is more about the speed of light in a material like air. Dispersion of light in a prism tells us that the speed of light or the material index depends on the wavelength ( or frequency which is constant ) so I thought that air...