File:OAM superpositions.svg
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Original file (SVG file, nominally 1,279 × 890 pixels, file size: 297 KB)
Captions
Captions
Several superpositions of various orbital angular momentum modes
Summary
[edit]
| Description |
English: Superpositions of orbital angular momentum (OAM) modes of light. In the first and second row, the intensity and phase profiles of a beam cross section are shown, respectively. In the first column, an example of a "petal pattern" is shown, which is a uniform superposition of two modes with opposite values. In the second row, one can see that more than two OAM modes can be superposed and in the third row it is demonstrated that the coefficients are in general complex numbers and the structure of the resulting beam profiles may be quite complicated. Čeština: Superpozice módů orbitálního momentu hybnosti (OAM) světla. V prvním a druhém řádku jsou po řadě zobrazeny profily intenzity a fáze svazku. V prvním sloupci je vyobrazen příklad "okvětního vzoru", což je uniformní superpozice dvou módů s opačnými hodnotami. Ve druhém sloupci je ukázáno, že superpozici lze vytvořit i z více než dvou OAM módů, a ve třetím sloupci je demonstrováno, že koeficienty jsou obecně komplexní čísla a že profil výsledného svazku může mít velmi komplikovanou strukturu. |
| Date | |
| Source | Own work |
| Author | JozumBjada |
Licensing
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I, the copyright holder of this work, hereby publish it under the following license:
This file is licensed under the Creative Commons Attribution-Share Alike 4.0 International 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.
Source code
[edit]
This figure was created using Wolfram language 12.0.0 for Microsoft Windows (64-bit) (April 6, 2019). The source code follows.
(* ::Package:: *)
(* ::Section:: *)
(*OAM Superpositions*)
(* ::Subsection:: *)
(*Routines*)
(* ::Input::Initialization:: *)
beamLG[k_][\[Rho]_,\[Phi]_]:=Sqrt[2/(\[Pi] Abs[k]!)](Sqrt[2]\[Rho])^Abs[k]Exp[-\[Rho]^2]Exp[-I k \[Phi]]
(* ::Input::Initialization:: *)
colOpts={PlotRange->All,ImageSize->{Automatic,300},Exclusions->(#1<0&==0&),MaxRecursion->Automatic,PlotRangePadding->None,Frame->False};
(* ::Input::Initialization:: *)
plotSuperpositionMagn[coefsi_,modes_,plotPoints_:50,circ_:False]:=Module[{plotlim=3.5,fun,x,y,coefs=Normalize[coefsi]},
fun=Total@MapThread[#1 beamLG[#2][Sqrt[x^2+y^2],ArcTan[y,x]]&,{coefs,modes}];
DensityPlot[Evaluate[Abs[fun]^2],{x,-plotlim,plotlim},{y,-plotlim,plotlim},
PlotPoints->plotPoints,ColorFunction->"SunsetColors",RegionFunction->If[circ,(#1^2+#2^2<=plotlim^2&),True],Evaluate[Sequence@@colOpts]]
]
(* ::Input::Initialization:: *)
plotSuperpositionPhas[coefsi_,modes_,plotPoints_:50,circ_:False]:=Module[{plotlim=3.5,fun,x,y,coefs=Normalize[coefsi],\[Rho],\[Phi]},
fun=Total@MapThread[#1 beamLG[#2][\[Rho],\[Phi]]&,{coefs,modes}];
fun=Mod[Arg[fun],2\[Pi]]/(2\[Pi])/.{\[Rho]->Sqrt[x^2+y^2],\[Phi]->ArcTan[y,x]};
DensityPlot[fun,{x,-plotlim,plotlim},{y,-plotlim,plotlim},
PlotPoints->plotPoints,ColorFunction->Hue,ColorFunctionScaling->False,RegionFunction->If[circ,(#1^2+#2^2<=plotlim^2&),True],Evaluate[Sequence@@colOpts]]
]
(* ::Input::Initialization:: *)
phaseLabel[ang_,pos_]:=Text[Style[ang,FontSize->35,FontFamily->"Times",Black],ImageScaled[pos]]
phaseGr[hue_,pol1_,pol2_,lab1_,lab2_]:=Graphics[{Hue[hue],Polygon[pol1],Hue[hue+1/2],Polygon[pol2],phaseLabel@@lab1,phaseLabel@@lab2},ImageSize->{Automatic,300},PlotRangePadding->None]
(* ::Input::Initialization:: *)
colorbarFun[colorfun_,{low_,mid_,high_},{minx_,maxx_},{miny_,maxy_},fontFamily_:"Times"]:=Module[{textoff=20,lineoff=50,fontSize=30,plot},
plot=DensityPlot[y+miny,{x,minx,maxx},{y,miny,maxy},ColorFunction->colorfun,Frame->False,PlotRangePadding->None];
plot=First@Cases[InputForm@plot,_GraphicsComplex,Infinity,1];
Graphics[{
Rectangle[{-2+minx,miny},{maxx+1,maxy}],
plot,
Line[{
{{-2+minx,miny},{lineoff+maxx,miny}},
{{-2+minx,maxy+1},{lineoff+maxx,maxy+1}},
{{-2+minx,0},{maxx+textoff/2,0}}
}],
Text[Style[low,FontFamily->fontFamily,FontSize->fontSize],{textoff+maxx,miny},{-1,-1}],
Text[Style[mid,FontFamily->fontFamily,FontSize->fontSize],{textoff+maxx,0},{-1,0}],
Text[Style[high,FontFamily->fontFamily,FontSize->fontSize],{textoff+maxx,maxy},{-1,1}]
},ImageSize->{Automatic,(maxy-miny)},PlotRangePadding->None]
]
(* ::Subsection:: *)
(*Generation of figure and export*)
(* ::Input:: *)
(*colorBarMagn=colorbarFun["SunsetColors",{0,0.5,1},{0,35},{-150,150}];*)
(*(*colorBarPhas=colorbarFun[Hue,{Style[0,FontFamily\[Rule]"Times"],\[Pi],Row[{Style[2,FontFamily\[Rule]"Times"],"\[Pi]"}]},{0,35},{-150,150},Automatic];*)*)
(*colorBarPhas=colorbarFun[Hue,{0,\[Pi],2\[Pi]},{0,35},{-150,150}];*)
(* ::Input:: *)
(*coefs={{1,1},{1,2,3},{1,-2I,3}};*)
(*modes={{5,-5},{1,2,3},{1,-2,-3}};*)
(*{magns,phases}=Transpose@MapThread[{plotSuperpositionMagn[#1,#2],plotSuperpositionPhas[#1,#2,70]}&,{coefs,modes}];*)
(* ::Input:: *)
(*kets={Row[{Ket[5],Ket[-5]},"\[ThinSpace]+\[ThinSpace]"],Row[{Ket[1],2 Ket[2],3 Ket[3]},"\[ThinSpace]+\[ThinSpace]"],Row[{Ket[1],"\[ThinSpace]-\[ThinSpace]",2 I Ket[-2],"\[ThinSpace]+\[ThinSpace]",3 Ket[-3]}]};*)
(*kets=Framed[Style[Row[{Ket["\[Psi]"]," \[Proportional] ",#}],25,FontFamily->"Times"],ImageSize->{300,100},Alignment->Center]&/@kets;*)
(* ::Input:: *)
(*grid=Grid[{Append[kets,""],Append[magns,colorBarMagn],Append[phases,colorBarPhas]}];*)
(* ::Input:: *)
(*SetDirectory[NotebookDirectory[]]*)
(* ::Input:: *)
(*Export["gridRand.png",grid,ImageResolution->200]*)
(*Export["gridRand.svg",grid,ImageResolution->200]*)
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| Date/Time | Thumbnail | Dimensions | User | Comment | |
|---|---|---|---|---|---|
| current | 20:12, 10 January 2022 | | 1,279 × 890 (297 KB) | JozumBjada (talk | contribs) | Cross-wiki upload from cs.wikipedia.org |
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