File:Focus of a Gaussian beam.gif

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Focus_of_a_Gaussian_beam.gif ‎(360 × 360 pixels, file size: 903 KB, MIME type: image/gif, looped, 21 frames)

Captions

Captions

Focus of a Gaussian beam

Summary

[edit]
Description
English: Ray optics predicts that when you focus light you concentrate all the energy in one point. But light is a wave and thus the focus will have a finite size. Shown: a focused Gaussian beam in the paraxial approximation (color is phase, brightness is intensity, and the white line shows the position dependent beam width).
Date
Source https://twitter.com/j_bertolotti/status/1202561190481858562
Author Jacopo Bertolotti
Permission
(Reusing this file)		 https://twitter.com/j_bertolotti/status/1030470604418428929


Mathematica 11.0 code

[edit]
 
\[Lambda] = 1;
\[Sigma] = 0.3 \[Lambda];
k0 = (2 \[Pi])/\[Lambda];
zR = \[Sigma]^2 k0;
w0 = Sqrt[(\[Lambda] zR)/\[Pi]];
w[z_] := w0 Sqrt[1 + z^2/zR^2];
R[z_] := (zR^2 + z^2)/z;

E2[x_, y_, z_] := w0/w[z] E^(I ArcTan[zR, z]) E^-((x^2 + y^2)/(w[z])^2) E^(I k0 (z + (x^2 + y^2)/(2 R[z])));
f = E2[x, 0, z];
psi = f;

p1 = Table[
   Show[
    RegionPlot[True, {z, -3, 3}, {x, -2, 2}, PlotPoints -> 200, ColorFunctionScaling -> False, ColorFunction -> Function[{z, x}, Hue[Arg[psi*E^(-I \[Phi])]/(2 Pi), 1, Abs[psi]^2]], Frame -> False]
    ,
    Plot[{w[z], -w[z]}, {z, -50, 50},  Background -> None, PlotStyle -> {White}]
    ]
   , {\[Phi], 0, 2 \[Pi], \[Pi]/10}];
ListAnimate[p1]

Licensing

[edit]
I, the copyright holder of this work, hereby publish it under the following license:
Creative Commons CC-Zero 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/TimeThumbnailDimensionsUserComment
current15:15, 6 December 2019Thumbnail for version as of 15:15, 6 December 2019360 × 360 (903 KB)Berto (talk | contribs)User created page with UploadWizard

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