File:OAM vs spin video.ogg
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OAM_vs_spin_video.ogg (file size: 1.61 MB, MIME type: application/ogg)
Summary
| Description |
English: The total angular momentum of light consists of two components (at least in the paraxial approximation). Both components act in a different way on a massive colloidal particle inserted into the beam of light, as shown in the animation. The spin component causes the particle to spin around its axis. It corresponds to the polarization of the beam and can take on only two values: with . A linear polarization can be seen as a superposition of the two and is represented by . In contrast, the other component, known as orbital angular momentum, causes the particle to rotate around the axis of the beam. It corresponds to the helical profile of the phase of the beam and can take on any value of the form , where is an integer. In the animation, only two values are shown.
Čeština: Celkový moment hybnosti světla sestává ze dvou složek (alespoň v paraxiální aproximaci). Obě složky působí odlišným způsobem na hmotné částečky vložené do svazku světla, jak je ukázáno v animaci. Spinová složka způsobí, že se částečka otáčí kolem své osy. Tato složka odpovídá polarizaci svazku a může nabývat pouze dvou hodnot: , kde . Lineární polarizaci lze chápat jako superpozici obou složek a představuje ji případ . Druhá složka, známá jako orbitální moment hybnosti, nutí částečku rotovat kolem osy svazku. Odpovídá jí šroubovicovitý profil fáze svazku a může nabývat jakékoliv hodnoty tvaru , kde je celé číslo. V animaci jsou ukázány pouze dvě hodnoty . |
| Date | |
| Source | Own work |
| Author | JozumBjada |
Source code
This animation was created using Wolfram language 13.0.1 for Microsoft Windows (64-bit) (January 28, 2022). The source code follows (formatted as a .wl package file).
(* ::Package:: *)
(* ::Title::Initialization:: *)
(*Spin vs. OAM*)
(* ::Subtitle::Initialization:: *)
(*Comparison of the action of spin and orbital angular momentum on massive particles*)
(* ::Section::Initialization:: *)
(*Preliminaries*)
(* ::Input::Initialization:: *)
fontSize=50;
fontFamily="CMU Serif";
(* ::Input::Initialization:: *)
omegaSpin=8;
omegaOAM=4;
(* ::Input::Initialization:: *)
num=30;
numStages=6;
\[CapitalDelta]t=1/(num numStages);
(* ::Input::Initialization:: *)
opts={Boxed->False,ViewPoint->{-1.551586529122855`,-2.4910493736907173`,1.6844145156343122`},ViewVertical->{-1,0,0},PlotRange->{{-3.7,3.6},{-3.5`,3.5`},{-4.8`,2.1`}}};
(* ::Section::Initialization:: *)
(*Intensity profiles 3D*)
(* ::Input::Initialization:: *)
Module[{l=2,w0=2,\[Lambda]=1,w0f,plot,zR,w,fun},
{w0f,zR}={0.05w0,(\[Pi] w0^2)/\[Lambda]};
w[z_]:=w0 Sqrt[1+(z/zR)^2];
fun[x_,y_,z_,l_,w0_]:=Module[{r=Sqrt[x^2+y^2]},Sqrt[2./(\[Pi] Abs[l]!)] w0/w[z] ((r Sqrt[2])/w[z])^Abs[l] Exp[-(r/w[z])^2]];
plot=DensityPlot3D[Abs[fun[x,y,z,l,w0]/fun[w0 Sqrt[l/2],0,0,l,w0]]^2,{x,-4,4},{y,-4,4},{z,0,5},OpacityFunction->Function[x,.07(1-Exp[-25 x^2])],ColorFunction->(Blend[{Purple,Orange},#]&),PlotPoints->70];
rastShaft=First@Cases[InputForm[plot],_Raster3D,Infinity,1];
plot=DensityPlot3D[Abs[fun[x,y,z,l,w0f]/fun[w0f Sqrt[l/2],0,0,l,w0f]]^2,{x,-4,4},{y,-4,4},{z,0,2},OpacityFunction->Function[x,.07(1-Exp[-25 x^2])],ColorFunction->(Blend[{Purple,Orange},#]&),PlotPoints->50];
rastFlange=First@Cases[InputForm[plot],_Raster3D,Infinity,1];
]
(* ::Section::Initialization:: *)
(*Components*)
(* ::Input::Initialization:: *)
{helixFun[2],helixFun[-2]}=Module[{aux},
aux=ParametricPlot3D[{u Cos[# 2\[Pi] t],u Sin[# 2\[Pi] t],t},{t,0,5},{u,1,3},PlotPoints->50,Mesh->None,Boxed->False,Axes->False];
First@Cases[InputForm[aux],_GraphicsComplex,Infinity,1]
]&/@{-1/2,+1/2};
(* ::Input::Initialization:: *)
hb=BoundaryDiscretizeRegion@RegionIntersection[Ball[{0,0,0},1],Cuboid[-1.1{1,1,1},1.1{1,1,0}]];
hb=First@Cases[InputForm[Show[hb]],_GraphicsComplex,Infinity,1];
hb=GraphicsComplex[hb[[1]],{EdgeForm[],hb[[2,2]]}];
ball=Scale[Rotate[{Green,hb,Red,Rotate[hb,\[Pi],{1,0,0}]}, \[Pi]/2,{0,1,0}],0.8];
(* ::Input::Initialization:: *)
arrow=Table[2{Cos[x],Sin[x],0},{x,0,2\[Pi] 0.95,0.1}];
AppendTo[arrow,With[{x=2\[Pi] 0.98},2.1{Cos[x],Sin[x],0}]];
{arrowSpinR,arrowSpinL}=
{Black,Arrowheads[0.05],Arrow[Tube[(RotationTransform[-\[Pi]/2,{0,0,1}]@*ScalingTransform[0.45{1,1,1}]@*TranslationTransform[{0,0,0.2}])[If[#,RotationTransform[-(\[Pi]/5),{0,0,1}]@RotationTransform[\[Pi],{1,0,0}][arrow],arrow]],0.04]]}&/@{True,False};
{arrowOAMR,arrowOAML}=
{Black,Arrowheads[0.05],Arrow[Tube[(RotationTransform[-\[Pi]/2,{0,0,1}]@*TranslationTransform[{0,0,0.1}])[If[#,RotationTransform[-(\[Pi]/5),{0,0,1}]@RotationTransform[\[Pi],{1,0,0}][arrow],arrow]],0.04]]}&/@{True,False};
(* ::Section::Initialization:: *)
(*Insets*)
(* ::Input::Initialization:: *)
label[text_,opts_:Plain]:=Style[text,opts,fontSize,FontFamily->fontFamily]
(* ::Input::Initialization:: *)
dashedLine={Lighting->"Neutral",Gray,Dashing[{.1,.04}],Thickness[0.005],Line[{{0,0,-6},{0,0,2}}]};
(* ::Input::Initialization:: *)
insetOAM[t_,l_]:=Graphics3D[{dashedLine,{Rotate[Translate[helixFun[l],{0,0,-5}],2\[Pi] Sign[l]omegaOAM t,{0,0,1}]}},Sequence@@opts]
(* ::Input::Initialization:: *)
vecplot=VectorPlot[{1,0},{x,-1,1},{y,-1,1},RegionFunction->(0.5<=#1^2+#2^2<=1.2&),VectorPoints->{8,8},VectorScale->Small,VectorStyle->Purple];
pos=Cases[InputForm[vecplot],Arrow[pts_]:>Append[ScalingTransform[2.5{1,1}][First[pts]],-2],Infinity];
arrowsFun[t_,0]:=Module[{len=Cos[2\[Pi] t]},If[Abs@len<0.5,Line[{#,#+{len,0,0}}]&/@pos,Arrow[{#,#+{len,0,0}}]&/@pos]];
arrowsFun[t_,\[Sigma]_]:=Arrow@Tube[{#,#+Append[AngleVector[2\[Pi] \[Sigma] t],0]}]&/@pos;
(* ::Input::Initialization:: *)
insetSpin[t_,\[Sigma]_]:=Graphics3D[{dashedLine,{Purple,arrowsFun[t,\[Sigma]]}},Sequence@@opts]
(* ::Input::Initialization:: *)
With[{pt={0.15,0.1},tots={-3,-2,-1,1,2,3},\[CapitalDelta]=.4,num=6},
buttons=Table[{EdgeForm[{Purple,Thickness[0.005]}],Blend[{White,Purple},.5],Rectangle[-pt+{\[CapitalDelta] idx,0},pt+{\[CapitalDelta] idx,0},RoundingRadius->.05],Text[Style[tots[[idx]],Bold,Black,fontSize,FontFamily->fontFamily],{\[CapitalDelta] idx,0}]},{idx,num}];
]
insetCount[l_,\[Sigma]_]:=Module[{count=l+\[Sigma],buttons=buttons,active},
If[count<0,count+=4,count+=3];
buttons=MapAt[ReplaceAll[col_?ColorQ:>Blend[{White,col},0.3]],buttons,Transpose[{Drop[Range[Length[buttons]],{count}]}]];
Prepend[buttons,Text[label["\[ScriptL]\[ThinSpace]+\[ThinSpace]\[Sigma]:"],{0,0}]]
]
(* ::Section::Initialization:: *)
(*Scene*)
(* ::Input::Initialization:: *)
scene[t_,tloc_,l_,\[Sigma]_]:=Graphics[{
Inset[Graphics3D[{
Translate[rastShaft,{0,0,-5}],
Translate[rastFlange,{0,0,-1.5}],
Rotate[Translate[helixFun[l],{0,0,-5}],Sign[l]2\[Pi] omegaOAM t,{0,0,1}],
Switch[l,2,arrowOAML,-2,arrowOAMR],
Translate[{
Rotate[ball,If[\[Sigma]!=0,2\[Pi] \[Sigma] omegaSpin t,2\[Pi] (-1)omegaSpin (\[CapitalDelta]t num)If[l>0,4,1]],{0,0,1}],
Switch[\[Sigma],0,{},1,arrowSpinL,-1,arrowSpinR]
},2{Cos[Sign[l]2\[Pi] omegaOAM t],Sin[Sign[l]2\[Pi] omegaOAM t],0}]
},Sequence@@opts]
,{-0.3,0.0},ImageScaled[{1,1}/2],2.7]
,
Inset[insetOAM[t,l],{1.1,0.3},ImageScaled[{1,1}/2],1.1],
Inset[insetSpin[tloc,\[Sigma]],{1.1,-0.55},ImageScaled[{1,1}/2],1.1],
Translate[insetCount[l,\[Sigma]],{-1.25,-1.15}],
Text[
TextGrid[{
{label["OAM",Bold],label[":",Bold],label["\[ScriptL]"],label["= "<>ToString[l]]},
{label["spin",Bold],label[":",Bold],label["\[Sigma]"],label["= "<>ToString[\[Sigma]]]}
},Alignment->{{Right,Center,Right,Left},Center},Spacings->{{0.1,0.1,0.5},25}],
{0.5,0.9},{-1,1}]
},PlotRange->{1.5{-1,1},{-1.3,1}},ImageSize->1000]
(* ::Input::Initialization:: *)
animationStages[tglob_,t_,stage_]:=Module[{l,\[Sigma]},
{l,\[Sigma]}=Switch[stage-1,0,{-2,-1},1,{-2,0},2,{-2,1},3,{2,-1},4,{2,0},5|6,{2,1}];
scene[tglob,t,l,\[Sigma]]
]
(* ::Section::Initialization:: *)
(*Rasterization and export*)
(* ::Input::Initialization:: *)
SetDirectory[NotebookDirectory[]]
(* ::Input::Initialization:: *)
seq=Module[{tglob=0},Flatten[Table[animationStages[\[CapitalDelta]t tglob++,t,s],{s,1,numStages},{t,N@Subdivide[num-1]}],1]];
(* ::Input::Initialization:: *)
AbsoluteTiming[frames=Rasterize[#,RasterSize->600]&/@seq;]
(* ::Input::Initialization:: *)
Export["oam_vs_spin_video.ogv", Video@AnimatedImage[frames, FrameRate -> 6]]
Licensing
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.
File history
Click on a date/time to view the file as it appeared at that time.
| Date/Time | Dimensions | User | Comment | |
|---|---|---|---|---|
| current | 14:15, 19 August 2022 | (1.61 MB) | wikimediacommons>JozumBjada | Uploaded own work with UploadWizard |
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