Questions tagged [dispersion]

Dispersion refers to the frequency dependence of the properties of a wave.

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293 views

Understanding group velocity

Group velocity as a concept in Classical Waves confuse me. It's very easy to point out visually, like in this really helpful graphic here. Okay, it's the speed of the moving bulge, which, notably ...
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Numerical Solution of the Propagation-Dispersion equation

I have asked this question on Computational Science and also on Mathoverflow, but no satisfactory answers so far. I thought maybe the physics community could shed some insight on the issue. I am ...
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Using convolution to simulate acoustic dispersion in shallow water

Background I'm a marine biologist who's trying to wrap my head around shallow water propagation. I'm interested in how acoustic dispersion (as described by Pekeris' waveguide) alters how sounds ...
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1answer
283 views

Time delay of a laser pulse due to 2nd, 3rd and 4th order dispersions

I'll explain my problem : Given a Gaussian pulse with central wavelength 550 nm and a HMFW of 300 nm, and let's assume the pulse is transform-limited. I need to get the pulse through 1mm of quartz. ...
3
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0answers
397 views

How to calculate dispersion relation from a Finite Difference (FD) wave simulation

I have a python code that calculates the solution of the inhomogeneous acoustic wave equation for a 2D medium with any velocity and source configuration. It was implemented using Finite Differences ...
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22 views

Relation of dispersion for a plasma

Assuming the electric field : $\vec{E} = E_{0}\,e^{i(kz-\omega t)}\vec{e_{z}}$ and the complex relation by doing $\vec{rot}\,(\vec{rot}\times\vec{E})$ with $\vec{rot}\times \vec{E}= i \vec{k}\...
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306 views

Does an electron have a frequency (and hence an energy)?

The formulation is provocative, the question is similar to the question here. There I can follow the question, but not the answers, which for me imply that an electron in a momentum eigenstate does ...
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92 views

Perturbation theory with eigenvalue-dependent perturbation

Suppose I have an operator equation of the sort $$ [H_0 + H_1(\lambda)]\mathbf{v} = \lambda\mathbf{v}. $$ Here, $H_0$ defines unperturbed eigensolutions $\{\lambda_0, \mathbf{v}_0\}$, and $H_1(\...
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34 views

Does a MASER beam stay un-dispersed like that of a laser?

We know that a laser beam has a very low dispersion rate. Does the same apply for a MASER (Microwave Amplification by Stimulated Emission of Radiation) beam?
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3answers
966 views

What is the significance of dispersion relation i.e. frequency vs. wave vector relation?

There are lots of pages in my textbook dedicated to this sole relation and frequency vs. wave vector graph. I do not understand what are practical significance and uses of the relation and the graph. ...
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175 views

Rayleigh length determination for Laguerre-Gaussian Modes

Recently I have measured the Rayleigh length of a Gaussian electron beam probe in a scanning electron microscope, using the function: $$w(z) = w_0 \times \sqrt{1 + (z/z_r)^2}$$ Where $w$ is beam ...
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411 views

Third-order dispersion of glass

When working with short laser pulses, it is important to compensate the dispersion of a pulse passing through a material because it changes the pulse's shape. The effect of dispersion can be described ...
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2k views

How to calculate the dispersion relation for a wave equation with non-constant speed of wave propagation?

Specifically, it is a one-dimensional wave equation for waves on a string with a non-constant cross-section, i. e. $$S(x)=S_1+S_2 \cos{2x}; \qquad c(x)=\sqrt{F/\rho\, S(x)}.$$ Separating the variables ...
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What is the difference between Lehmann-Kallen and Dispersion relation?

I know that the Lehmann-Kallen (LK) form of an operator concerns just that, an operator. But the LK is very similar in form to dispersion relations found in analytic S-matrix theory.
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2answers
69 views

Finding dispersion relations

I was wondering if there is a general (theoretical, not experimental) method for finding the dispersion relation for waves in a medium, say given the equation governing purturbations in the medium? ...
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30 views

How does a pure and an impure spectrum look like in optics?

The following text is from Concepts of Physics by Dr. H.C.Verma, from the chapter "Dispersion and Spectra", page 436, topic "Spectrum", sub topic "Pure and Impure Spectrum": [...] In an ideal ...
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24 views

What is a dispersive and reactive medium in mechanical waves?

Would it be possible to have some explanation about the dispersive and reactive medium in the field of mechanical waves. As far as I understand : Let $\omega$ be the excitation frequency and $\...
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0answers
47 views

Wave packet - phase vs group velocity

So, I've been revising QM recently and the concept of group vs phase velocity has me confused. Let's say we have a wave packet. As quoted in Griffiths, "...A wave packet is a superposition of ...
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2answers
219 views

Dispersion through Glass Slab

My questions related Dispersion through Glass Slab: Why does a parallel surface makes a difference? Why is that light do get disperse in a prism and a glass slab at surface one but at backs normal ...
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1answer
62 views

Physical significance of growth rate in plasma

Let us say that we have a dispersion relation curve and associated instability curve as shown below for a magnetised plasma, which have been formulated through kinetic theory. The frequencies and ...
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0answers
26 views

Why is the current in the nonrelativistic Dirac sea infinite?

Consider the model of a nonrelativistic noninteracting Dirac sea. I define the model as one with two infinite bands of single particle states: $$E_\pm (k) = \pm \biggr(\Delta + \frac{k^2}{2m}\biggr)$...
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51 views

If the velocity of light is different in different medium is it wavelength changes or frequency changes?

We know that the velocity of light is equal to the product of it's wavelength and frequency. And when light goes from vacuum to any other medium it's velocity changes depending the mediums refractive ...
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27 views

Theoretical constraints of relativity on dispersion relations

A wave has a dispersion relation $\omega=\omega(\vec{k})$. (The function has been made single valued usinng initial conditions.) A delta function in the origin at $t=0$ ( $\psi(\vec{x},0)=\delta(\vec{...
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60 views

What causes observed color differences in white LED's for near and far fields?

While running towards traffic early morning before sunrise I recently noticed that the new automobile LED (white) lights when viewed at a distance appear blueish, but when the light is viewed much ...
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337 views

Interpretation of antiferromagnetic magnons dispersion relation

The dispersion relation of magnons in a ferromagnetic 1d lattice is \begin{equation} \omega(k)=\omega_0\big[1-\cos(ka)\big] \end{equation} where $\omega_0$ is a constant and $a$ is the spacing ...
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57 views

Experimental data on the speed of heat

I know about the speed-of-information problem tied with the solution of the heat equation (diffusion equation) for the propagation of heat via conduction. Due to the quantum-statistical nature of ...
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1answer
96 views

Is there a way to explain a rainbow in an almost-QM-correct way to a 5 year old child?

My toddler asked me "how does rainbow happen", and I would like to give a pedagogical explanation of the relation of photon frequency, its color, and the way different frequencies are bent in a drop ...
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68 views

Light dispersion/diffraction model for optical measurement system

in a project of mine I have to model the dispersion effect (through a grating) of light in the context of a camera based measurement system. Imagine the following setup: Left to right: collimated ...
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0answers
108 views

$d$-dimensional Debye model: nonlinear dispersion

Given $\omega_k = c|k|^j$, where $j$ is some positive real number. I am attempting to compute the density of states $g(\omega) = \sum\limits_k \delta(\omega - \omega_k)$. Given one can write the sum ...
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49 views

How to obtain the dispersive refractive index of a sample in a Michelson interferometer from the interferogram?

In the Michelson interferometer setup shown below, first I obtain the interferogram of the source (without sample). Then I put in the sample. If the sample is not dispersive (its refractive index is ...
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145 views

entropy and dispersion

If I know the positions and the speeds of each particle in a box over the time, how can I compute the entropy ? (I`m making a simulation where I want to show that the disperion of the particles over ...
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496 views

Deriving Graphene energy dispersion in tight binding model

I'm trying to get into graphene, in detail, I try to derive the elec. energy dispersion. Sadly, I am not that familiar with condensed matter QM by now, so I got some basic questions and I hope to find ...
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0answers
121 views

What phenomenon is responsible for the evolution pattern of waves created by waterfalls?

I have been fascinated lately by the pattern of the waves created by a waterfall in my town. Specifically, the pattern shows a gradual decrease in the density of the waves as they travel away from ...
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51 views

Is the composition of two plane waves also a plane wave?

I'm really interesting to know more about Plasma physics for waves , it comes in my mind to ask this question related to dispertion relation topic exactly plane waves , It is well known that the plane ...
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23 views

what is the different between dispersion and wave propagation?

can I talk about wave propagation as dispersion? and what is the relationship between them? I am asking that because when I was searching about the telegraph equation (that represents the current ...
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11 views

Index of refraction of a specific wavelength using Abbe number

I am stuck with a problem, maybe my understand of it is not correct. I would like to solve, given an Abbe number and some index of refraction at a known wavelength, the ior of any wavelength λ. From ...
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18 views

The effect of velocity on dispersion of light

It is stated that red light bends less than blue light as white light is dispersed through a glass prism. I understand that red light travels faster within the glass because of its higher wavelength, ...
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18 views

Dispersion: any software to work out the dispersed waveforms of EMW signals that propagate via interstellar medium for some distance?

I asked this question in the Astronomy site, but seems few people feel interested in, so I hope to have a try here in the Physics site...... Is there any software (toolbox, code, package, paid or ...
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1answer
82 views

What happens to frequency during dispersion?

I'm a bit confused about what happens to frequency during the dispersion of white light passing through a prism. I understand that when a light wave is travelling in one medium, velocity is constant ...
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24 views

Dispersion, surface acoustic wave devices

I am trying to understand dispersion, and to do it within the context of surface acoustic waves (SAWs). For surface acoustic wave devices the inter-digital transducers (IDTs) produce Rayleigh waves ...
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46 views

Klein-Gordon/Maxwell Equation: dissipative or dispersive?

In Aspects of Symmetry, Coleman says (p. 185) ''Most of the simple field theories with which we are familiar have the property that all of their non-singular solutions of finite total energy are ...
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41 views

Physical Interpretation of Energy-wavenumber Graphs

Consider an energy-wavenumber graph, typical in solid state physics, like the one below. I can follow the mathematics in the derivations with a KP model. But I don't understand the physical ...
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35 views

Dispersion relations in 2 atom and above

I am having a little trouble understanding this information of dispersion relations show below for a two atom basis. So it states that there should be in total 6 dispersion branches but there only 4. ...
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52 views

Group and phase velocity for a superposition of 2 monochromatic waves

A wave packet in one dimension with a dispersion relation $\omega$ is a function of the form: $$f(x,t):=\sum_{i=1}^n\lambda_i\exp[i(k_i x+\omega[k_i] t)]\hspace{1cm}\forall i\leq n\colon\lambda_i,k_i\...
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2answers
56 views

Time-of-flight spectroscopy and energy-time uncertainty

I am a bit confused about spectral and temporal filtering of light. I consider a single-photon source of a bandwidth of $1\,$nm at $1550$ nm. That means, that the wavelength of the emitted photons ...
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18 views

Number of allowed (phonon)wave vectors in a poliatomic-basis lattice?

Lets say that my crystal is of size $N=N_1N_2N_3$ , this is the typical textbook example and after that they say that the number of allowed wavevectors is N. But tbh I dont really know if they are ...
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1answer
72 views

How to find wavepacket time dependence from the $k$-wavefunction?

I am trying to code the time dependence of a gaussian wavepacket using the Fourier transform techniques. I began with constructing a wavepacket (real parts only at the moment) at $t=0$ by multiplying ...
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53 views

Dispersion of light

I've been taking digital signal processing course. It's pretty interesting for me. One thought came to my mind while I've been practicing numerical problem on Fourier transform. So my question is ...
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41 views

How does refractive index increase in anomalous dispersion?

Refractive index generally increases with decrease in wavelength but in anomalous dispersion it decreases with decrease in wavelength. What causes it to be like that?
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92 views

Spring constant and dispersion relation

In order to calculate the dispersion relation (i.e $w(k)$) for the electrons and protons, I used the following relations: $ E = ℏω$, $p = ℏk$, and I substituted them in this formula for energy: $E = ...