File:Fractional OAM modes 3 to 4 svg.svg
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Captions
Captions
Amplitude and phase profiles of fractional OAM modes with topological charges between 3 and 4
Summary[edit]
| Description |
English: Numerical simulation of several fractional OAM modes, where helical phase profiles corresponding to the topological charges l = 3, 3.25, 3.5, 3.75, and 4 are imparted to a Gaussian beam and the beam is subsequently propagated using Fourier optics calculation. For l = 3, a single vortex of charge 3 is visible in the center and the beam corresponds to an integer OAM mode. For l = 3.25, the vortex splits into three vortices of charge 1. For l = 3.5, a series of additional vortices is visible along the positive x-axis in the phase profile, which is manifested as a half-line of intensity minimum in the amplitude profile. For l = 3.75, four vortices of charge 1 are visible, and finally for l = 4 these vortices merge into a single vortex with its topological charge equal to 4. Čeština: Numerická simulace několika zlomkových OAM módů, kde je Gaussovskému svazku po řadě dodán šroubovicovitý fázový profil odpovídající topologickým nábojům l = 3, 3,25, 3,5, 3,75 a 4 a svazek je posléze šířen prostorem s použitím výpočtu z Fourierovské optiky. Pro l = 3 je vidět uprostřed jediný optický vír s nábojem 3 a optický svazek odpovídá celočíselnému OAM módu. Pro l = 3,25 se tento vír štěpí na víry tři, každý s nábojem 1. Pro l = 3,5 je podél kladné x-ové poloosy ve fázovém profilu viditelná série dodatečných vírů, což se projevuje jako polopřímka minimální intenzity v profilu amplitudy. Pro l = 3,75 lze vidět čtyři víry s nábojem 1 a konečně pro l = 4 se tyto víry slévají do víru jediného o náboji 4. |
| Date | |
| Source | Own work |
| Author | JozumBjada |
Licensing[edit]
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
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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:: *)
(*charges34={3,3.25,3.5,3.75,4};*)
(*AbsoluteTiming[arrs34=plotMagnitudePhase/@charges34;]*)
(*{magn34,phas34}=Transpose[arrs34];*)
(* ::Input:: *)
(*colorBarMagn=colorbarFun["SunsetColors",{0,0.5,1},{0,35},{-350,350}];*)
(*colorBarPhas=colorbarFun[Hue,{Style[0,FontFamily->"Times"],\[Pi],Row[{Style[2,FontFamily->"Times"],"\[Pi]"}]},{0,35},{-350,350},Automatic];*)
(* ::Input:: *)
(*grid34=Grid[{Framed[Style["\[ScriptL] = "<>ToString[#],60,FontFamily->"Times"],Alignment->Center,ImageSize->{700,60},FrameStyle->Thick]&/@charges34,*)
(*Join[magn34,{colorBarMagn}],Join[phas34,{colorBarPhas}]}];*)
(* ::Section:: *)
(*Export*)
(* ::Input:: *)
(*SetDirectory[NotebookDirectory[]]*)
(* ::Input:: *)
(*Export["grid34.png",grid34,ImageResolution->200]*)
(* ::Input:: *)
(*Export["grid34.svg",grid34,ImageResolution->200]*)
File history
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| Date/Time | Thumbnail | Dimensions | User | Comment | |
|---|---|---|---|---|---|
| current | 19:11, 7 January 2022 | | 4,600 × 1,840 (4.06 MB) | JozumBjada (talk | contribs) | Cross-wiki upload from cs.wikipedia.org |
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