File:Collision Broadening.gif
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Collision_Broadening.gif (600 × 202 pixels, file size: 821 KB, MIME type: image/gif, looped, 56 frames, 5.6 s)
Captions
Captions
The spectrum of a monochromatic emitter with random phase jumps is not monochromatic.
Summary
[edit]
| Description |
English: A perfect sinusoidal is described (by definition) by a single frequency. But if you take a sinusoidal, and start adding random phase jumps, its spectrum will start broadening.
In Laser Physics, the emitters of a fluid gain medium will collide at random times, creating abrupt phase jumps, which will broaden the emission spectrum (collision broadening). |
| Date | |
| Source | https://twitter.com/j_bertolotti/status/1436285107350949896 |
| Author | Jacopo Bertolotti |
| Permission (Reusing this file) |
https://twitter.com/j_bertolotti/status/1030470604418428929 |
Mathematica 12.0 code
[edit]
k = 10; xmax = 100; segmentn = 10; segment = xmax/segmentn; njumps = segmentn*10;
jumpspos = Flatten@Transpose@Table[RandomReal[{(j - 1) segment, j*segment}, njumps/segmentn], {j, 1, segmentn}];
jumpsamp = RandomReal[{0, 2 \[Pi]}, njumps];
frames = Table[
signal = Table[Re[E^(I k x)*If[n == 0, 1, Product[E^(I UnitStep[x - jumpspos[[j]] ] jumpsamp[[j]]), {j, 1, n}] ] ], {x, 0, xmax, 0.01}];
dim = Dimensions[signal][[1]];
GraphicsRow[{
Plot[ Re[E^(I k x)*Product[E^(I UnitStep[x - jumpspos[[j]] ] jumpsamp[[j]]), {j, 1, n}] ], {x, 0, segment}, PlotStyle -> {Black, Thick}, Axes -> False],
ListPlot[(Abs[Fourier[signal]][[100 ;; 220]])^2, PlotRange -> {-50, 2500}, Joined -> True, PlotStyle -> {Black, Thick}, FrameTicks -> None, Axes -> False, Frame -> True, FrameLabel -> {{"Power spectrum", None}, {"\[Omega]", None}}, LabelStyle -> {Black, Bold}]
}]
, {n, 0, njumps, 2}];
ListAnimate[Join[Table[frames[[1]], 5], frames]]
Licensing
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I, the copyright holder of this work, hereby publish it under the following license:
 
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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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| Date/Time | Thumbnail | Dimensions | User | Comment | |
|---|---|---|---|---|---|
| current | 07:57, 13 September 2021 | | 600 × 202 (821 KB) | Berto (talk | contribs) | Uploaded own work with UploadWizard |
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