Gaussian-beam_intensity_surfaceplot.png

Summary

Description
English: Surface plot of the intensity profile of a Gaussian laser beam with beam waist . The height profile is proportional to the beam intensity, while the color is proportional to the electromagnetic field amplitude. The white lines represent the beam width, both at the FWHM and 1/e² intensity level.
Date
Source Own work
Author Geek3
PNG development
InfoField
This diagram was created with Mathematica .
Source code
InfoField

Mathematica code 

w0 = 2; zR = Pi*w0^2; rmax = 30; zmax = 100;
plot = Plot3D[
   Exp[-2 r^2/(w0^2 (1 + (z/zR)^2))]/(1 + (z/zR)^2),
   {r, -rmax, rmax}, {z, -zmax, zmax}, PlotRange -> {0, 1},
   PlotPoints -> 101, MaxRecursion -> 4, 
   Method -> {Refinement -> {ControlValue -> 0.01} },
   MeshFunctions -> {#1 &, #2 &, #3 &, Exp[-2 #1^2/(w0^2 (1 + (#2/zR)^2))] &}, 
   MeshStyle -> {Black, Black, Gray, White},
   Mesh -> {Range[-Floor[rmax, 10], Floor[rmax, 10], 10],
     Range[-Floor[zmax, 10], Floor[zmax, 10], 10], 
     Range[0.05, 0.95, 0.05], {1/2, 1/E^2} },
   ColorFunction -> Function[{r, z, i}, Lighter[ColorData["Rainbow"][Sqrt[i] ], 0.3] ],
   BoxRatios -> {rmax, zmax, 30},
   ViewPoint -> {1.2, -3, 0.7},
   AxesEdge -> { {-1, -1}, {1, -1}, {-1, -1} }, 
   AxesLabel -> {"r/\[Lambda]", "z/\[Lambda]", "I/\!\(\*SubscriptBox[\(I\), \(0\)]\)"},
   BaseStyle -> 13, 
   Epilog -> 
    Text["\!\(\*SubscriptBox[\(w\), \(0\)]\) = 2\[Lambda]", {-15, -3}, BaseStyle -> Gray] ]
Export["Gaussian-beam_intensity_surfaceplot.png", 
  ImageResize[Image[plot, ImageResolution -> 400], 2000, Resampling -> "Linear"] ];

Licensing

I, the copyright holder of this work, hereby publish it under the following license:
w:en:Creative Commons
attribution share alike
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You are free:
  • to share – to copy, distribute and transmit the work
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Under the following conditions:
  • attribution – You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
  • share alike – If you remix, transform, or build upon the material, you must distribute your contributions under the same or compatible license as the original.

Captions

Surface plot of a Gaussian beam profile

Items portrayed in this file

depicts

inception

15 January 2019