File:Fractional OAM mode 3.5 phase svg.svg
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Captions
Captions
Phase profile of fractional OAM mode with topological charge 3.5
Summary[edit]
| Description |
English: Numerical simulation of a fractional OAM mode, where a helical phase profile corresponding to the topological charge 3.5 is imparted to a Gaussian beam and the beam is subsequently propagated using Fourier optics calculation. The resulting profile can be compared with Fig. 6 of the paper: J. B. GÖTTE , S. Franke-Arnold , R. Zambrini & Stephen M. Barnett (2007); Quantum formulation of fractional orbital angular momentum, Journal of Modern Optics, 54:12, 1723-1738, DOI: 10.1080/09500340601156827. There are three vortices of charge 1 in the central part, each highlighted with a circle, and a region around positive x-axis, where a series of vortices appears due to discontinuity resulting from a fractional charge. This region is enclosed in a rectangle. Čeština: Numerická simulace zlomkového OAM módu, kde je Gaussovskému svazku dodán šroubovicovitý fázový profil odpovídající topologickému náboji 3,5 a svazek je posléze šířen prostorem s použitím výpočtu z Fourierovské optiky. Výsledný profil lze srovnat s Obr. 6 článku: J. B. GÖTTE , S. Franke-Arnold , R. Zambrini & Stephen M. Barnett (2007); Quantum formulation of fractional orbital angular momentum, Journal of Modern Optics, 54:12, 1723-1738, DOI: 10.1080/09500340601156827. Ve střední části se nacházejí tři optické víry s nábojem 1, každý je vyznačen kroužkem, a oblast kolem kladné x-ové osy, kde se kvůli nespojitosti způsobené zlomkovým nábojem vyskytuje dlouhá řada vírů. Tato oblast je vyznačena obdélníkem. |
| Date | |
| Source | Own work |
| Author | JozumBjada |
Licensing[edit]
I, the copyright holder of this work, hereby publish it under the following license:
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Source code[edit]
The figure was created using Wolfram language 12.0.0 for Microsoft Windows (64-bit) (April 6, 2019). The source code follows.
(* ::Package:: *)
(* ::Section:: *)
(*Routines*)
(* ::Input::Initialization:: *)
colorbarFun[colorfun_,{low_,mid_,high_},{minx_:0,maxx_:35},{miny_:-350,maxy_:350},fontFamily_:"Times New Roman"]:=Module[{textoff=20,lineoff=50,fontSize=60,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]
]
(* ::Input::Initialization:: *)
fourierShift[arr_]:=Module[{nx,ny},
{nx,ny}=Dimensions[arr];
RotateRight[#,Floor[nx/2]]&/@RotateRight[arr,Floor[ny/2]]
]
(* ::Input::Initialization:: *)
plotMagnitudePhase[charge_,zoomnum_:50,sanmplingnum_:2^10]:=Module[{num=sanmplingnum,farr,nx,ny,zoom,magn,phas,transfun,ftmode,inmode,w0=.1,dist=900,len=2,dx,\[Lambda]=808*^-9,imgSize=700},
dx=len/num;
inmode=Table[If[x==0&&y==0,1.,N@Exp[I charge ArcTan[x,y]]Exp[-(x^2+y^2)/w0^2]],{x,-(len/2)+dx,len/2,dx},{y,-(len/2)+dx,len/2,dx}];
inmode=inmode/Norm[inmode,"Frobenius"];
transfun=Table[N@Exp[I \[Pi] dist \[Lambda] (kx^2+ky^2)],{kx,-(1/(2dx)),1/(2dx)-1/len,1/len},{ky,-(1/(2dx)),1/(2dx)-1/len,1/len}];
transfun=fourierShift[transfun];
ftmode=Fourier[fourierShift[inmode]];
farr=fourierShift[InverseFourier[transfun ftmode]];
{nx,ny}=Dimensions[farr];
zoom=farr[[Floor[nx/2-zoomnum];;Floor[nx/2+zoomnum],Floor[ny/2-zoomnum];;Floor[ny/2+zoomnum]]];
zoom=Reverse@Transpose@Reverse[zoom];
magn=Normalize[Abs[zoom]^2,Max];
magn=ListDensityPlot[magn,ImageSize->imgSize,PlotRange->All,ColorFunction->ColorData["SunsetColors"],Frame->False,PlotRangePadding->None];
phas=Arg[zoom];
phas=ListDensityPlot[phas,ImageSize->imgSize,PlotRange->All,ColorFunction->Hue,Frame->False,PlotRangePadding->None];
{magn,phas}
]
(* ::Section:: *)
(*Computation*)
(* ::Input:: *)
(*phas34=Last@plotMagnitudePhase[3.5];*)
(* ::Input:: *)
(*phaseRect34=Show[Legended[phas34,colorbarFun[Hue,{Style[0,FontFamily->"Times"],\[Pi],Row[{Style[2,FontFamily->"Times"],"\[Pi]"}]},{0,35},{-350,350},Automatic]],Graphics[{EdgeForm[{Black,Thickness[.005]}],Thickness[.005],Circle[#,ImageScaled[0.03]]&/@{{55.5,56},{48,56},{46.5,48}},Transparent,Rectangle[ImageScaled[{0.61,0.35}],ImageScaled[{1,0.55}]]},ImageSize->700]];*)
(* ::Section:: *)
(*Export*)
(* ::Input:: *)
(*SetDirectory[NotebookDirectory[]]*)
(* ::Input:: *)
(*Export["phaseRect34.svg",phaseRect34,ImageResolution->200]*)
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| Date/Time | Thumbnail | Dimensions | User | Comment | |
|---|---|---|---|---|---|
| current | 19:20, 7 January 2022 | | 1,055 × 878 (326 KB) | JozumBjada (talk | contribs) | Cross-wiki upload from cs.wikipedia.org |
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