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












4















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



enter image description here






tikz-pgf







share|improve this question




















  • 1





    Like this tex.stackexchange.com/questions/333330/… ?

    – Symbol 1
    Feb 23 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.

    – RD1153
    Feb 23 at 4:51






  • 2





    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.

    – marmot
    Feb 23 at 5:02
















4















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



enter image description here






tikz-pgf







share|improve this question




















  • 1





    Like this tex.stackexchange.com/questions/333330/… ?

    – Symbol 1
    Feb 23 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.

    – RD1153
    Feb 23 at 4:51






  • 2





    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.

    – marmot
    Feb 23 at 5:02














4












4








4


2






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



enter image description here






tikz-pgf







share|improve this question
















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



enter image description here






tikz-pgf




tikz-pgf






share|improve this question















share|improve this question













share|improve this question




share|improve this question








edited Feb 23 at 4:46







RD1153

















asked Feb 23 at 4:32









RD1153RD1153

804




804








  • 1





    Like this tex.stackexchange.com/questions/333330/… ?

    – Symbol 1
    Feb 23 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.

    – RD1153
    Feb 23 at 4:51






  • 2





    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.

    – marmot
    Feb 23 at 5:02














  • 1





    Like this tex.stackexchange.com/questions/333330/… ?

    – Symbol 1
    Feb 23 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.

    – RD1153
    Feb 23 at 4:51






  • 2





    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.

    – marmot
    Feb 23 at 5:02








1




1





Like this tex.stackexchange.com/questions/333330/… ?

– Symbol 1
Feb 23 at 4:37





Like this tex.stackexchange.com/questions/333330/… ?

– Symbol 1
Feb 23 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.

– RD1153
Feb 23 at 4:51





The equation is very complex to plot. I am not sure if such functions are available on latex. It is called Laguerre polynomial.

– RD1153
Feb 23 at 4:51




2




2





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.

– marmot
Feb 23 at 5:02





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.

– marmot
Feb 23 at 5:02










1 Answer
1






active

oldest

votes


















16





+50









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



documentclass[tikz]{standalone}    

pgfdeclarefunctionalshading{Laguerre-Gaussian modes}{pgfpoint{-25bp}{-25bp}}{pgfpoint{25bp}{25bp}}{}{

                % 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}

    tikzpath[shading=Laguerre-Gaussian modes](-10,-10)rectangle(10,10);

end{document}







share|improve this answer



















  • 1





    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?

    – marmot
    Feb 23 at 5:19






  • 1





    @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.

    – Symbol 1
    Feb 23 at 5:25








  • 1





    You can tell that it is not from an automatic tool because cos(20r+90) should be cos^2(20r+90)

    – Symbol 1
    Feb 23 at 5:28






  • 1





    @marmot You can give +100 : start a bounty after 2 days.

    – Kpym
    Feb 23 at 9:21






  • 1





    @marmot you said "I would give +100 if I could". Come on! You have zillions of points to give ;)

    – Kpym
    Mar 24 at 21:05











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1 Answer
1






active

oldest

votes








1 Answer
1






active

oldest

votes









active

oldest

votes






active

oldest

votes









16





+50









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



documentclass[tikz]{standalone}    

pgfdeclarefunctionalshading{Laguerre-Gaussian modes}{pgfpoint{-25bp}{-25bp}}{pgfpoint{25bp}{25bp}}{}{

                % 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}

    tikzpath[shading=Laguerre-Gaussian modes](-10,-10)rectangle(10,10);

end{document}







share|improve this answer



















  • 1





    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?

    – marmot
    Feb 23 at 5:19






  • 1





    @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.

    – Symbol 1
    Feb 23 at 5:25








  • 1





    You can tell that it is not from an automatic tool because cos(20r+90) should be cos^2(20r+90)

    – Symbol 1
    Feb 23 at 5:28






  • 1





    @marmot You can give +100 : start a bounty after 2 days.

    – Kpym
    Feb 23 at 9:21






  • 1





    @marmot you said "I would give +100 if I could". Come on! You have zillions of points to give ;)

    – Kpym
    Mar 24 at 21:05
















16





+50









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



documentclass[tikz]{standalone}    

pgfdeclarefunctionalshading{Laguerre-Gaussian modes}{pgfpoint{-25bp}{-25bp}}{pgfpoint{25bp}{25bp}}{}{

                % 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}

    tikzpath[shading=Laguerre-Gaussian modes](-10,-10)rectangle(10,10);

end{document}







share|improve this answer



















  • 1





    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?

    – marmot
    Feb 23 at 5:19






  • 1





    @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.

    – Symbol 1
    Feb 23 at 5:25








  • 1





    You can tell that it is not from an automatic tool because cos(20r+90) should be cos^2(20r+90)

    – Symbol 1
    Feb 23 at 5:28






  • 1





    @marmot You can give +100 : start a bounty after 2 days.

    – Kpym
    Feb 23 at 9:21






  • 1





    @marmot you said "I would give +100 if I could". Come on! You have zillions of points to give ;)

    – Kpym
    Mar 24 at 21:05














16





+50







16





+50



16




+50





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



documentclass[tikz]{standalone}    

pgfdeclarefunctionalshading{Laguerre-Gaussian modes}{pgfpoint{-25bp}{-25bp}}{pgfpoint{25bp}{25bp}}{}{

                % 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}

    tikzpath[shading=Laguerre-Gaussian modes](-10,-10)rectangle(10,10);

end{document}







share|improve this answer













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



documentclass[tikz]{standalone}    

pgfdeclarefunctionalshading{Laguerre-Gaussian modes}{pgfpoint{-25bp}{-25bp}}{pgfpoint{25bp}{25bp}}{}{

                % 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}

    tikzpath[shading=Laguerre-Gaussian modes](-10,-10)rectangle(10,10);

end{document}








share|improve this answer












share|improve this answer



share|improve this answer










answered Feb 23 at 5:16









Symbol 1Symbol 1

25.9k241125




25.9k241125








  • 1





    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?

    – marmot
    Feb 23 at 5:19






  • 1





    @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.

    – Symbol 1
    Feb 23 at 5:25








  • 1





    You can tell that it is not from an automatic tool because cos(20r+90) should be cos^2(20r+90)

    – Symbol 1
    Feb 23 at 5:28






  • 1





    @marmot You can give +100 : start a bounty after 2 days.

    – Kpym
    Feb 23 at 9:21






  • 1





    @marmot you said "I would give +100 if I could". Come on! You have zillions of points to give ;)

    – Kpym
    Mar 24 at 21:05














  • 1





    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?

    – marmot
    Feb 23 at 5:19






  • 1





    @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.

    – Symbol 1
    Feb 23 at 5:25








  • 1





    You can tell that it is not from an automatic tool because cos(20r+90) should be cos^2(20r+90)

    – Symbol 1
    Feb 23 at 5:28






  • 1





    @marmot You can give +100 : start a bounty after 2 days.

    – Kpym
    Feb 23 at 9:21






  • 1





    @marmot you said "I would give +100 if I could". Come on! You have zillions of points to give ;)

    – Kpym
    Mar 24 at 21:05








1




1





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?

– marmot
Feb 23 at 5:19





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?

– marmot
Feb 23 at 5:19




1




1





@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.

– Symbol 1
Feb 23 at 5:25







@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.

– Symbol 1
Feb 23 at 5:25






1




1





You can tell that it is not from an automatic tool because cos(20r+90) should be cos^2(20r+90)

– Symbol 1
Feb 23 at 5:28





You can tell that it is not from an automatic tool because cos(20r+90) should be cos^2(20r+90)

– Symbol 1
Feb 23 at 5:28




1




1





@marmot You can give +100 : start a bounty after 2 days.

– Kpym
Feb 23 at 9:21





@marmot You can give +100 : start a bounty after 2 days.

– Kpym
Feb 23 at 9:21




1




1





@marmot you said "I would give +100 if I could". Come on! You have zillions of points to give ;)

– Kpym
Mar 24 at 21:05





@marmot you said "I would give +100 if I could". Come on! You have zillions of points to give ;)

– Kpym
Mar 24 at 21:05


















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