File:OAM superpositions.svg
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Summary
| 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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Source code
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 | Cross-wiki upload from cs.wikipedia.org |
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