# Plotting Laguerre Gaussian beam intensity in transverse and line profile via center?

Hi can someone please help me with Laguerre Gaussian beam(looks like a doughnut or vortex)?

• Like this tex.stackexchange.com/questions/333330/… ? Commented Feb 23, 2019 at 4:37
• The equation is very complex to plot. I am not sure if such functions are available on latex. It is called Laguerre polynomial. Commented Feb 23, 2019 at 4:51
• Here are additional possibilities. No, Laguerre polynomials are not too complex to be plotted, but this is a LaTeX site, so if you provide equations and an example, people will be happy to help you, but they are less eager to dig out from the internet and guess what you might want.
– user121799
Commented Feb 23, 2019 at 5:02

Here is an attempt to draw the most complicated one I saw on google image.

\documentclass[tikz]{standalone}
% x y
2 copy      % x y x y
exch atan   % x y theta
4 mul       % x y 4theta
cos         % x y cos(4theta)
dup mul     % x y cos^2(4theta)
3 1 roll    % cos^2(4theta) x y
dup mul exch dup mul
add sqrt    % cos^2(4theta) r
20 mul      % cos^2(4theta) 20r
90 add      % cos^2(4theta) 20r+90
cos dup mul % cos^2(4theta) cos(20r+90)
mul         % cos^2(4theta)*cos(20r+90)
sqrt
}
\begin{document}
\end{document}


• I would give +100 if I could. Do you know the postscript syntax, or do you use a tool to convert human readable instructions into this language?
– user121799
Commented Feb 23, 2019 at 5:19
• @marmot The shading accepts a very restricted subset of postscript. See PDF32000_2008.pdf Appendix B. I have some muscle memory inherited from the last time I answered the Hermite-Gaussian question. Commented Feb 23, 2019 at 5:25
• You can tell that it is not from an automatic tool because cos(20r+90) should be cos^2(20r+90) Commented Feb 23, 2019 at 5:28
• @marmot You can give +100 : start a bounty after 2 days.
– Kpym
Commented Feb 23, 2019 at 9:21
• @marmot you said "I would give +100 if I could". Come on! You have zillions of points to give ;)
– Kpym
Commented Mar 24, 2019 at 21:05