File:OAM vs spin animation.gif
OAM_vs_spin_animation.gif (403 × 309 pixels, file size: 5.69 MB, MIME type: image/gif, looped, 150 frames, 33 s)
Captions
Captions
Summary
[edit]DescriptionOAM vs spin animation.gif |
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: 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: |
Date | |
Source | Own work |
Author | JozumBjada |
Licensing
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- You are free:
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- to remix – to adapt the work
- Under the following conditions:
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Source code
[edit]This animation was created using Wolfram language 12.0.0 for Microsoft Windows (64-bit) (April 6, 2019). The source code follows (formatted as a .wl package file).
(* ::Package:: *)
(* ::Title:: *)
(*Spin vs. OAM*)
(* ::Subtitle:: *)
(*Comparison of the action of spin and orbital angular momentum on massive particles*)
(* ::Section:: *)
(*Preliminaries*)
(* ::Input:: *)
(*fontSize=50;*)
(*fontFamily="CMU Serif";*)
(* ::Input:: *)
(*omegaSpin=8;*)
(*omegaOAM=4;*)
(* ::Input:: *)
(*num=30;*)
(*numStages=6;*)
(*\[CapitalDelta]t=1/(num numStages);*)
(* ::Input:: *)
(*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:: *)
(*Intensity profiles 3D*)
(* ::Input:: *)
(*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:: *)
(*Components*)
(* ::Input:: *)
(*{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:: *)
(*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:: *)
(*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:: *)
(*Insets*)
(* ::Input:: *)
(*label[text_,opts_:Plain]:=Style[text,opts,fontSize,FontFamily->fontFamily]*)
(* ::Input:: *)
(*dashedLine={Lighting->"Neutral",Gray,Dashing[{.1,.04}],Thickness[0.005],Line[{{0,0,-6},{0,0,2}}]};*)
(* ::Input:: *)
(*insetOAM[t_,l_]:=Graphics3D[{dashedLine,{Rotate[Translate[helixFun[l],{0,0,-5}],2\[Pi] Sign[l]omegaOAM t,{0,0,1}]}},Sequence@@opts]*)
(* ::Input:: *)
(*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:: *)
(*insetSpin[t_,\[Sigma]_]:=Graphics3D[{dashedLine,{Purple,arrowsFun[t,\[Sigma]]}},Sequence@@opts]*)
(* ::Input:: *)
(*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:: *)
(*Scene*)
(* ::Input:: *)
(*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:: *)
(*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:: *)
(*Rasterization and export*)
(* ::Input:: *)
(*SetDirectory[NotebookDirectory[]]*)
(* ::Input:: *)
(*seq=Module[{tglob=0},Flatten[Table[animationStages[\[CapitalDelta]t tglob++,t,s],{s,1,numStages},{t,N@Subdivide[num-1]}],1]];*)
(* ::Input:: *)
(*AbsoluteTiming[frames=Rasterize[#,RasterSize->600]&/@seq;]*)
(* ::Input:: *)
(*Export["anim.gif",frames,AnimationRepetitions->Infinity,"DisplayDurations"->0.22]*)
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Date/Time | Thumbnail | Dimensions | User | Comment | |
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current | 09:32, 17 February 2022 | ![]() | 403 × 309 (5.69 MB) | JozumBjada (talk | contribs) | Cross-wiki upload from cs.wikipedia.org |
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