BeschreibungGaussian beam with german description.svg
Gaussian beam with German description
English: This is a schematical drawing of a Gaussian beam with German description and fundamental dimensions. Usually, laser beams can be described as Gaussian beams.
Deutsch: Die Zeichnung stellt schematisch einen Gaußstrahl dar, angegeben sind grundlegende Abmessungen. Üblicherweise werden Laserstrahlen als Gaußstrahlen behandelt.
Software
Gnuplot, script is given below. Unfortunately, the script creates several items twice, so I had to remove them with Inkscape.
verbreitet werden – vervielfältigt, verbreitet und öffentlich zugänglich gemacht werden
neu zusammengestellt werden – abgewandelt und bearbeitet werden
Zu den folgenden Bedingungen:
Namensnennung – Du musst angemessene Urheber- und Rechteangaben machen, einen Link zur Lizenz beifügen und angeben, ob Änderungen vorgenommen wurden. Diese Angaben dürfen in jeder angemessenen Art und Weise gemacht werden, allerdings nicht so, dass der Eindruck entsteht, der Lizenzgeber unterstütze gerade dich oder deine Nutzung besonders.
# #############################################################
#
# This file was created by א and may
# only be used under the terms of the
# Creative-Commons-License CC-BY-SA-2.5
# with apropriate attribution.
#
# You MUST credit this: א (Aleph), http://commons.wikimedia.org
#
# #############################################################
# Gnuplot code as follows:
reset
set terminal svg enhanced size 1200 600 fsize 36 fname "Arial"
set output "gaussian_beam_german.svg"
set multiplot
# Variables used for gaussian beam
w0 = 2.0
z0 = 4.0
# Configure coordinate system
# set xzeroaxis linetype rgb "black"
# set yzeroaxis linetype rgb "black"
unset border
unset tics
set xtics axis mirror ("−z_0" -z0, "+z_0" z0) offset 0,0.75 scale 0.5
set xrange [-20:20]
set yrange [-12:10]
set label "z" at 18,-0.5
set label "r" at 0.5,8.5
# Arrows along the axes
set style arrow 2 filled size 1,10
set arrow arrowstyle 2 from -20,0 to 20,0
set arrow arrowstyle 2 from 0,-10 to 0,10
# Function for gaussian beam
w(z) = w0*sqrt(1+(z/z0)**2)
# Function for asymptotes
a(z) = w0/z0 * z
# Arrow for w0
set style arrow 1 heads filled size 0.5,10 front
set arrow arrowstyle 1 from 0,0 to 0,w0
set label "w_0" at 0.25,1.25
# Arrow for w(z)
z1 = 12
set arrow arrowstyle 1 from -z1,0 to -z1,w(z1)
set label "w(z)" at -z1+0.25,0.5*w(z1)
# Lines at the end of b
set style arrow 3 nohead lt rgb "grey"
set arrow arrowstyle 3 from z0,0 to z0,4
set arrow arrowstyle 3 from -z0,0 to -z0,4
# Arrow for b
set arrow arrowstyle 1 from -z0,w(z0)+1 to z0,w(z0)+1
set label "b" at -1,w(z0)+2.
# Arrow for w(z0)
set arrow arrowstyle 1 from -z0,0 to -z0,w(z0)
set label "√2·w_0" at -z0-4,0.5*w(z0)
k=2.5 #Variable needed for wavefronts
R(k) = k*(1+(z0/k)**2) # Radius of wavefronts
zM(k) = k - R(k) # Centre of wavefronts
# This is where the Wavefronts touch the border of the beam:
zQ(k) = zM(k)/(1.0 + (w0/z0)**2) + sqrt((zM(k)/(1.0+(w0/z0)**2))**2 - (w0**2+zM(k)**2-R(k)**2)/(1.0+(w0/z0)**2))
W(z) = z >= zQ(k) ? sqrt(R(k)**2-(z-zM(k))**2) : 1/0 # Wavefront ist plotted for k >= zQ only.
set dummy z
set key at 18.0,-10.0
# Plot wavefronts with many samples
set samples 100000
plot W(z) lt rgb "black" title "Wellenfronten", -W(z) lt rgb "black" notitle
k = k+2.5
plot W(z) lt rgb "black" notitle, -W(z) lt rgb "black" notitle
k = k+2.5
plot W(z) lt rgb "black" notitle, -W(z) lt rgb "black" notitle
k = k+2.5
plot W(z) lt rgb "black" notitle, -W(z) lt rgb "black" notitle
k = k+2.5
plot W(z) lt rgb "black" notitle, -W(z) lt rgb "black" notitle
k = k+2.5
plot W(z) lt rgb "black" notitle, -W(z) lt rgb "black" notitle
k = k+2.5
plot W(z) lt rgb "black" notitle, -W(z) lt rgb "black" notitle
set samples 1000
# Plot grey lines
plot w0 linetype rgb "grey" linewidth 1 notitle, -w0 linetype rgb "grey" linewidth 1 notitle, a(z) linetype rgb "grey" linewidth 1 notitle, -a(z) linetype rgb "grey" linewidth 1 notitle
# Plot borders of the beam
set key at 18.0,-12.0
plot w(z) lt rgb "red" linewidth 3 title "Begrenzung des Gaußstrahls", -w(z) linetype rgb "red" linewidth 3 notitle
# Angle Θ
set label "Θ" at -3.25,0.75
set polar
theta = atan(w0/z0)
set trange [-pi-theta:-pi+theta]
plot 2 lt rgb "black" notitle
# Undo everything
reset
Kurzbeschreibungen
Ergänze eine einzeilige Erklärung, was diese Datei darstellt.
{{Information |Description='''Gaussian beam with German description''' {{en|This is a schematical drawing of a Gaussian beam with German description and fundamental dimensions. Usually, laser beams can be described as Gaussian beams.}} {{de|Die Zeichnung
Diese Datei enthält weitere Informationen (beispielsweise Exif-Metadaten), die in der Regel von der Digitalkamera oder dem verwendeten Scanner stammen. Durch nachträgliche Bearbeitung der Originaldatei können einige Details verändert worden sein.