Questions tagged [dispersion]

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

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What's is the relation between band structure and dispersion relation?

I'm currently studying band structures, and I'm a little bit confused about how the band structure is related to the dispersion relation. Are they they same thing?
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Degree of dispersion of a simple slit spectroscope

To calculate the dynamic range of a spectroscope + CCD instrument, you first need to calculate the degree of dispersion $\frac{d\lambda}{pixel}$. I have some trouble understanding the model solution ...
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Why the fields of the quasi-TEM mode of microstrip line tend to concentrate in the dielectric as frequency goes higher?

A microstrip line is a waveguiding structure as shown below: Because of the inhomogeneity, the fundamental mode of propagation is a quasi-TEM mode, which means that the z components of the E and H ...
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Effective refractive index and refractive index [duplicate]

Is there any relation connecting between the effective refractive index $N$ and the refractive index $n$ in waveguide?
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Creating Different Colours From A Pulsed Monochromatic Light Source

I am currently learning about fibre optic communications, which I understand use pulsed laser sources to generate a "bitstream" to send through the fibre using some form of pulse width ...
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How to determine crystallographic directions from dispersion relation graph? [closed]

How does one determine the crystallographic directions in a phonon dispersion relation graph (e.g. see below)? I know it has something to do with the first Brillouin zone in reciprocal space (see ...
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Dispersive relation in quantum wave mechanics

Question 2. For nonrelativistic free particle $E=\frac{p^{2}}{2m}$ and using the de Broglie relations the corresponding dispersive relation becomes $$\omega(k)=\frac{\hbar k^{2}}{2m}$$ Then following ...
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What is the intuitution behind a wave with zero wavenumber?

I was recently solving a physics problem that gave you the electric field $$E(x, y, z, t) = E_{0}cos(k_{y}y + \psi_{y})sin(k_{x}x-{\omega}t)\hat{z}$$ and the question asked for a variety of things ...
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Why is String Stiffness Proportional to the Fourth Spatial Derivative of String Displacement?

I recently watched a lecture on dispersive medium. I understand that if you disregard the idea that a string is ideal, you must add a stiffness factor into the wave equation. From that you can derive ...
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Validity of hydrodynamic description

Spontaneous thermal fluctuations occur at microscopic level in liquids. It is said that hydrodynamic description is valid in the long wavelength and low frequency limit. So, to depict the thermal ...
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Why are red and blue light refracted differently if they travel at the same speed in the same medium?

When I look at Snell's law $\frac{\sin\theta_2}{\sin\theta_1} = \frac{v_2}{v_1} = \frac{n_1}{n_2}$ I don't see any reference to wavelength. If red and blue have the same speed in the same medium, why ...
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Speed of sound and diffusion in relativistic hydrodynamics

In the following the second part of the question Relativistic hydrodynamics is presented: Consider the hydrodynamic energy-momentum tensor in 3 + 1 dimensions in at space with the Minkowski metric $\...
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Dispersion law for a tight binding Hamiltonian and particle states at $t$$\rightarrow$$\infty$

A spinless fermion (possessing an electric charge) can move across the sites of the discrete (translationally-invariant) lattice. The structure features three kinds of sites: $α_n$, $β_n$, $γ_n$ with ...
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How do I calculate the group velocity of a waveguide?

I understand that the group velocity is computed by $d\omega/dk$. Given the relationship between the wavelength of a waveguide and its frequency: $$\lambda=\frac{c}{\sqrt{\nu^2-\nu^2_0}}$$ where $c$ ...
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Diffusion and dispersion relation

I'm looking at some dispersion relations for some complex systems and realised I actually don't have a clear understanding of what physics I can get from a dispersion relation from equations that ...
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Landau-Lifshitz Equation of Motion for Triangular Heisenberg Antiferromagnet

There is a paper (PhysRevB.95.014435) in which the dispersion relation for some Heisenberg model on the honeycomb lattice is derived from the Landau-Lifshitz equation: \begin{align} \frac{d S_i}{dt} = ...
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Wave explanation and derivation

Why must the term $kx-\omega t$ be constant? I mean from an intuitive point of view. I can mathematically prove it, however I don't seem to understand it very well.
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Theoretical question about waves and interference

Assume I’m given a standing wave function and I’m asked to find the phase velocity of the two waves that interfered and created the standing wave. Now, I have two questions: Is it possible to move ...
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Why is the speed of a quantum particle defined as coefficient of $t$ over coefficient of $x$?

I’m currently studying quantum mechanics from Introduction to Quantum Mechanics by Griffiths. In his free particle section, he says that the speed of a particle is the coefficient of $t$ over the ...
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Is the $E=E(k)$ dispersion relation periodic across Brillouin zones?

I am quite confused by the Brillouin zones. I know there is a dispersion relation $E=E(k)$ for the first Brillouin zone. But is this dispersion relation periodic across different Brillouin zones? ...
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Finding a constant in nonparabolic dispersion relation in conduction band

The dispersion relation for a semiconductor is $$\frac{\hbar^2 k^2}{2m^*}=\sqrt{\alpha E+E_g^2}-E_g$$ where $E$ is the energy from the conduction band edge, $E_g$ is the bandgap energy, $m^*$ is the ...
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Modal dispersion in optical fibers

I've got a couple of doubts regarding modal dispersion (with respect to optical fibers) What's the difference between intermodal and intramodal dispersion? How does intermodal dispersion affect ...
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What happens to the space group of a crystal when introducing a non-trivial basis?

I am trying to understand crystallography and the space groups of crystals, but I have one major question bugging me. The book I am using adresses different lattice symmetries and applications of ...
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Significance of Group velocity Equation

$$v_g\equiv\frac{\partial\omega}{\partial k}.$$ The above equation is for Group velocity of waves, so what is the Physical Interpretation of this Equation? As we know $k$ is wave number which shows ...
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Physical meaning of constant zero phonon dispersion relation

Consider a 2D lattice model like this Assuming the mass of atom and force constant is 1, we could easily calculate the dispersion relations of the system. As there are four atoms per unit cell, there ...
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Duffing equation

I have a differential equation: $$\ddot{\omega}+2k\dot{\omega}+2k^2{\omega}-2{\omega}^3=0$$ As I understand it's a Duffing equation, but I can't find the first integral. How can I do it? I didn't find ...
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Prism, Dispersion and Deviation

A very straightforward question- Is it possible to have no dispersion and no deviation for a combination of prisms? And by prisms, I mean, a triangular one, not a glass slab. If so, please provide the ...
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How to interpret band structure of $\rm Si$?

I found it very instructive to see how the $E$-$k$ relationship of a free particle can be roughly identified from the extended band structure of a solid: The following is the outcome of the one ...
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How does light, which is an electromagnetic wave, carry information?

We see an object when light from a source strikes the object and then reaches our eyes. How does light, which is an electromagnetic wave, gets encoded with the information about the object? Do the ...
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In what media the speed of light is slower than the speed of radio waves, if any?

In what media the speed of visible light is slower than the speed of radio waves, if any? Particles can be faster than visible light, but other electromagnetic waves?
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Colour patterns from the reflection of my window

The first picture is that of my window while the second is its reflection as seen from the floor. The pattern depends on the angle. That is when I move a little closer then look at the reflection the ...
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Dispersion in Rainbows

So I have tried searching for the working of a rainbow. I found many sources and the explanation was clear. I still have a problem though. Since dispersion happens due to different refractive indices ...
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Dispersion relation of a monoatomic chain

The dispersion relation for a 1D Monoatomic chain is given by $$\omega = 2*\sqrt\frac{C}{M} \sin\left(\frac{qa}{2}\right)$$ We say that strong dispersion occurs when $q$ approaches $\frac{\pi}{a}$. ...
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Dispersion relation in $\frac{d^2y}{dt^2}=c^2\frac{d^2y}{dx^2} + ac^2\frac{d^4y}{dx^4}$

So I was reading through some lectures notes and I found this: The equation of motion of a non-ideal string is $\frac{d^2y}{dt^2}=c^2\frac{d^2y}{dx^2} + ac^2\frac{d^4y}{dx^4}$ and we are asked to ...
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Is propagation speed depending of wavelength? (QM)

In case of a single free particle, no potential field, the wave function is: $$ \Psi = A e^{i(kx-\omega t)}. $$ As it must fulfill the Schrödinger equation $$ - \frac{\hbar^2}{2m} \nabla^2 \ \psi(\...
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Group velocity in solid state physics force equation

When reading about electron holes here https://en.wikipedia.org/wiki/Effective_mass_(solid-state_physics), the group velocity is introduced as the reciprocal space gradient of the dispersion relation. ...
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Why can’t we use energy momentum relation given as $E=pc^2/v$?

Why don’t we use energy momentum relation as $E=pc^2/v$ instead of $E^2=(pc)^2+(mc^{2})^2$ in general & for getting relativistic version of quantum mechanics in particular?
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Does absorption in the cladding material change the real value of the propagation constant of a waveguide?

Imagine two scenarios: two cladding materials with the same real refractive index, but one has absorption while the other does not. Now, these materials act as the top cladding of a waveguide (for ...
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What is the physical description and $E$-$k$ plots for Dirac Semimetal, Weyl Semimetal, and Magnetic Weyl Semimetal?

I've been trying to get a physical understanding of these three concepts, and any help would be appreciated. So far this is what I understand: Dirac semi-metals have relativistic quasi-particles (...
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Why does the $E$ vs $k$ curve disrupt at Bragg planes?

Interaction between 'nearly free' or 'bound' electrons is what leads to bands. I understand this but why specifically at Brillouin zone boundaries?
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Ampere's Circuital law in non-linear and dispersive medium

For a linear and non-dispersive medium $\vec{B} = \mu \vec{H}$. So amperes circuital law in integral form (without Maxwell's correction term) can be written in two ways $\oint_C \vec{B}\cdot\vec{dl} =...
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Can matter waves of bound systems experience dispersion? If so, how would it manifest itself experimentally?

Electromagnetic waves experience dispersion and these result in a "chirp" in frequency after traversing some distance. This chirp can be heard when waves from a lightning strike in one ...
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Massless particles in the Lagrangian formalism of special relativity

In the Lagrangian picture of special relativity we usually define the action $S = -m \int d\tau$. This is clearly 0 for massless particles, so it says absolutely nothing about their motion. Despite ...
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Why do we only see VIBGYOR colours from dispersion?

I read all the suggested duplicates and they seem to be addressing the relation between primary colours and VIBGYOR. But my straightforward question is when so many colours with different wavelengths ...
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Why does higher frequency sound dampen faster in air?

I know as a general fact that higher frequency sound dampens quicker in air so when music is heard from a distance only the bass part is audible.But I don't know what the physical reasoning behind ...
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Confusion on the indice of refraction: is it dependent on the frequency or not? [duplicate]

I saw in my course than when light hit a medium, it makes some dipole oscillating with the same frequency as the one of the light $\omega$. By a classical mechanics reasoning, one can show that the ...
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2D Fourier Transform of a general function satisfying the wave equation

A function $f(x,t)$ which satisfies the wave equation can be expressed generally as a function of a single argument $f(x-ct)$, where $c=\frac{\omega}{k}$. This is because you can express this function ...
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Cutoff wave-number in wave-guides

When defining the dispersion relation in a waveguide we have an equation that also includes a cutoff wave-number. This cutoff wave number depends on the geometry of the waveguide. $$ k_z = \sqrt{\...
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What is physical interpretation of the band structure diagrams ($k$ vs $E$)?

I am confused that what is the actual meaning of lines given in the band structure diagram. For example, the $k$ vs $E$ relation for a simple 1D periodic lattice is $E(k) = -2\cos(k)$ What is ...
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What is dispersion measure (DM)?

I’m an undergraduate physics student working on a project, part of which involves studying “dispersion measure” (as used in study of pulsars, etc). I think I understand it, but I’m not sure. What is ...

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