File:Dispersion pulse.gif
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Dispersion_pulse.gif (576 × 189 pixels, file size: 1.5 MB, MIME type: image/gif, looped, 61 frames)
Captions
Captions
Diagram of how different velocities of the Fourier components distort and stretch a pulse.
Summary
[edit]| Description |
English: Any pulse can be thought as the superposition of sinusoidals
If all sinusoidals travel at the same speed, the pulse will propagate without changing shape. But if different frequencies travel at different speeds, the pulse will be distorted (dispersion). |
| Date | |
| Source | https://twitter.com/j_bertolotti/status/1189524047538855936 |
| Author | Jacopo Bertolotti |
| Permission (Reusing this file) |
https://twitter.com/j_bertolotti/status/1030470604418428929 |
Mathematica 11.0 code
[edit]g1 = Sum[(E^(I k x) E^(-(k - k0)^2/(2 \[Sigma]^2)) E^(-I (c k) t)) /. {\[Sigma] -> 1, k0 -> 4, c -> 1}, {k, 0, 10, 0.05}];
g2 = Sum[(E^(I k x) E^(-(k - k0)^2/(2 \[Sigma]^2)) E^(-I (Sqrt[2 c^2 k^2 + \[Omega]p^2 - Sqrt[4 c^4 k^4 + \[Omega]p^4]]/Sqrt[2]) t)) /. {\[Sigma] -> 1, k0 -> 4, c -> 1, \[Omega]p -> 5}, {k, 0, 10, 0.05}];
p1 = Table[
GraphicsRow[{Plot[
Evaluate@Join[{Re[g1]/25}, Evaluate@Table[Re[(E^(I k x) E^(-(k - k0)^2/(2 \[Sigma]^2)) E^(-I (c k) t) - k) /. {\[Sigma] -> 1, k0 -> 4, c -> 1}], {k, 2, 6, 1}] ], {x, -3, 40},
PlotStyle -> {Black, Purple, Orange, Cyan}, Axes -> False, PlotRange -> {-6.5, 2.1}, PlotLabel -> "Non dispersive", LabelStyle -> {Black, Bold}]
,
Plot[
Evaluate@Join[{Re[g2]/25}, Evaluate@Table[Re[(E^(I k x) E^(-(k - k0)^2/(2 \[Sigma]^2)) E^(-I (Sqrt[2 c^2 k^2 + \[Omega]p^2 - Sqrt[4 c^4 k^4 + \[Omega]p^4]]/Sqrt[2]) t) - k) /. {\[Sigma] -> 1, k0 -> 4, c -> 1, \[Omega]p -> 5}], {k, 2, 6, 1}] ], {x, -3, 40}, PlotStyle -> {Black, Purple, Orange, Cyan}, Axes -> False, PlotRange -> {-6.5, 2.1}, PlotLabel -> "Dispersive", LabelStyle -> {Black, Bold}]}, ImageSize -> Large]
, {t, 0, 30, 0.5}];
ListAnimate[p1]
Licensing
[edit]I, the copyright holder of this work, hereby publish it under the following license:
 
|
This file is made available under the Creative Commons CC0 1.0 Universal Public Domain Dedication. |
| The person who associated a work with this deed has dedicated the work to the public domain by waiving all of their rights to the work worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law. You can copy, modify, distribute and perform the work, even for commercial purposes, all without asking permission.
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File history
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| Date/Time | Thumbnail | Dimensions | User | Comment | |
|---|---|---|---|---|---|
| current | 10:07, 31 October 2019 | 576 × 189 (1.5 MB) | Berto (talk | contribs) | User created page with UploadWizard |
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