Summary edit

Licensing edit

This file is licensed under the Creative Commons Attribution-Share Alike 2.5 Generic license. You are free: to share – to copy, distribute and transmit the work to remix – to adapt the work 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. https://creativecommons.org/licenses/by-sa/2.5CC BY-SA 2.5 Creative Commons Attribution-Share Alike 2.5 truetrue

If you use this image, you have to credit this: Image by א (Aleph), http://commons.wikimedia.org

Wenn Sie dieses Bild verwenden, müssen Sie folgendes angeben: Bild von א (Aleph), http://commons.wikimedia.org

Gnuplot Script edit

# #############################################################
#
# 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