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

The name of the pictureThe name of the pictureThe name of the pictureClash Royale CLAN TAG#URR8PPP












3















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






  • 1





    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















3















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






  • 1





    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













3












3








3


1






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

754




754







  • 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






  • 1





    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






  • 1





    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




1




1





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


















12














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



documentclass[tikz]standalone 
pgfdeclarefunctionalshadingLaguerre-Gaussian modespgfpoint-25bp-25bppgfpoint25bp25bp
 % 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

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







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











  • @Kpym I let you do it, you had the idea first. ;-)

    – marmot
    Feb 23 at 12:29










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1 Answer
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active

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1 Answer
1






active

oldest

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active

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active

oldest

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12














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



documentclass[tikz]standalone 
pgfdeclarefunctionalshadingLaguerre-Gaussian modespgfpoint-25bp-25bppgfpoint25bp25bp
 % 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

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







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











  • @Kpym I let you do it, you had the idea first. ;-)

    – marmot
    Feb 23 at 12:29















12














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



documentclass[tikz]standalone 
pgfdeclarefunctionalshadingLaguerre-Gaussian modespgfpoint-25bp-25bppgfpoint25bp25bp
 % 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

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







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











  • @Kpym I let you do it, you had the idea first. ;-)

    – marmot
    Feb 23 at 12:29













12












12








12







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



documentclass[tikz]standalone 
pgfdeclarefunctionalshadingLaguerre-Gaussian modespgfpoint-25bp-25bppgfpoint25bp25bp
 % 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

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







share|improve this answer













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



documentclass[tikz]standalone 
pgfdeclarefunctionalshadingLaguerre-Gaussian modespgfpoint-25bp-25bppgfpoint25bp25bp
 % 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

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








share|improve this answer












share|improve this answer



share|improve this answer










answered Feb 23 at 5:16









Symbol 1Symbol 1

25.7k241124




25.7k241124







  • 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











  • @Kpym I let you do it, you had the idea first. ;-)

    – marmot
    Feb 23 at 12:29












  • 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











  • @Kpym I let you do it, you had the idea first. ;-)

    – marmot
    Feb 23 at 12:29







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













@Kpym I let you do it, you had the idea first. ;-)

– marmot
Feb 23 at 12:29





@Kpym I let you do it, you had the idea first. ;-)

– marmot
Feb 23 at 12:29

















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