Plotting Laguerre Gaussian beam intensity in transverse and line profile via center?
Clash Royale CLAN TAG#URR8PPP
3
Hi can someone please help me with Laguerre Gaussian beam(looks like a doughnut or vortex)?
tikz-pgf
asked Feb 23 at 4:32
RD1153RD1153
754
add a comment |
3
Hi can someone please help me with Laguerre Gaussian beam(looks like a doughnut or vortex)?
tikz-pgf
asked Feb 23 at 4:32
RD1153RD1153
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
add a comment |
3
3
3
1
Hi can someone please help me with Laguerre Gaussian beam(looks like a doughnut or vortex)?
tikz-pgf
asked Feb 23 at 4:32
RD1153RD1153
754
Hi can someone please help me with Laguerre Gaussian beam(looks like a doughnut or vortex)?
tikz-pgf
tikz-pgf
asked Feb 23 at 4:32
RD1153RD1153
754
asked Feb 23 at 4:32
RD1153RD1153
754
edited Feb 23 at 4:46
RD1153
asked Feb 23 at 4:32
RD1153RD1153
754
asked Feb 23 at 4:32
RD1153RD1153
754
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
add a comment |
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
add a comment |
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
answered Feb 23 at 5:16
Symbol 1Symbol 1
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. SeePDF32000_2008.pdfAppendix 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 becausecos(20r+90)should becos^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
add a comment |
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1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
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
answered Feb 23 at 5:16
Symbol 1Symbol 1
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. SeePDF32000_2008.pdfAppendix 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 becausecos(20r+90)should becos^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
add a comment |
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
answered Feb 23 at 5:16
Symbol 1Symbol 1
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. SeePDF32000_2008.pdfAppendix 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 becausecos(20r+90)should becos^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
add a comment |
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
answered Feb 23 at 5:16
Symbol 1Symbol 1
25.7k241124
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
answered Feb 23 at 5:16
Symbol 1Symbol 1
25.7k241124
answered Feb 23 at 5:16
Symbol 1Symbol 1
25.7k241124
answered Feb 23 at 5:16
Symbol 1Symbol 1
25.7k241124
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. SeePDF32000_2008.pdfAppendix 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 becausecos(20r+90)should becos^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
add a comment |
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. SeePDF32000_2008.pdfAppendix 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 becausecos(20r+90)should becos^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
add a comment |
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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