(* Content-type: application/mathematica *) (*** Wolfram Notebook File ***) (* http://www.wolfram.com/nb *) (* CreatedBy='Mathematica 6.0' *) (*CacheID: 234*) (* Internal cache information: NotebookFileLineBreakTest NotebookFileLineBreakTest NotebookDataPosition[ 145, 7] NotebookDataLength[ 50172, 1079] NotebookOptionsPosition[ 49916, 1066] NotebookOutlinePosition[ 50258, 1081] CellTagsIndexPosition[ 50215, 1078] WindowFrame->Normal ContainsDynamic->True *) (* Beginning of Notebook Content *) Notebook[{ Cell[BoxData[ TagBox[ StyleBox[ DynamicModuleBox[{$CellContext`labels$$ = { "\[Alpha]", "\[Epsilon]"}, $CellContext`loci$$ = { "\[Alpha]", "\[Epsilon]"}, $CellContext`plotEllipse$$ = True, $CellContext`plotPoincare$$ = True, $CellContext`S1$$ = -1.6081226496766366`*^-16, $CellContext`S2$$ = \ -1., $CellContext`S3$$ = 1.2246467991473532`*^-16, $CellContext`\[Alpha]$$ = -0.7853981633974484, \ $CellContext`\[Epsilon]$$ = 0., $CellContext`\[Phi]$$ = 3.141592653589793, $CellContext`\[Chi]$$ = 0.7853981633974484, Typeset`show$$ = True, Typeset`bookmarkList$$ = {}, Typeset`bookmarkMode$$ = "Menu", Typeset`animator$$, Typeset`animvar$$ = 1, Typeset`name$$ = "\"untitled\"", Typeset`specs$$ = {{{ Hold[$CellContext`\[Alpha]$$], 0., "\[Alpha]"}, Dynamic[$CellContext`MyManipulator[$CellContext`\[Alpha]$$, {(-Pi)/2., Pi/2.}, ({$CellContext`\[Chi]$$, $CellContext`\[Phi]$$} = \ $CellContext`AEToRP[{#, $CellContext`\[Epsilon]$$}]; {$CellContext`S1$$, \ $CellContext`S2$$, $CellContext`S3$$} = $CellContext`AEToS[{$CellContext`\ \[Alpha]$$ = #, $CellContext`\[Epsilon]$$}])& , Scale -> Pi]& ]}, {{ Hold[$CellContext`\[Epsilon]$$], 0.}, Dynamic[$CellContext`MyManipulator[$CellContext`\[Epsilon]$$, {(-Pi)/4., Pi/4.}, ({$CellContext`\[Chi]$$, $CellContext`\[Phi]$$} = \ $CellContext`AEToRP[{$CellContext`\[Alpha]$$, #}]; {$CellContext`S1$$, \ $CellContext`S2$$, $CellContext`S3$$} = $CellContext`AEToS[{$CellContext`\ \[Alpha]$$, $CellContext`\[Epsilon]$$ = #}])& , Scale -> Pi]& ]}, {{ Hold[$CellContext`\[Chi]$$], 0.}, Dynamic[$CellContext`MyManipulator[$CellContext`\[Chi]$$, { 0., Pi/2.}, ({$CellContext`\[Alpha]$$, $CellContext`\[Epsilon]$$} = \ $CellContext`RPToAE[{$CellContext`\[Chi]$$ = #, $CellContext`\[Phi]$$}]; \ {$CellContext`S1$$, $CellContext`S2$$, $CellContext`S3$$} = \ $CellContext`RPToS[{$CellContext`\[Chi]$$ = #, $CellContext`\[Phi]$$}])& , Scale -> Pi]& ]}, {{ Hold[$CellContext`\[Phi]$$], 0.}, Dynamic[$CellContext`MyManipulator[$CellContext`\[Phi]$$, {-Pi, 1. Pi}, ({$CellContext`\[Alpha]$$, $CellContext`\[Epsilon]$$} = \ $CellContext`RPToAE[{$CellContext`\[Chi]$$, $CellContext`\[Phi]$$ = #}]; \ {$CellContext`S1$$, $CellContext`S2$$, $CellContext`S3$$} = \ $CellContext`RPToS[{$CellContext`\[Chi]$$, $CellContext`\[Phi]$$ = #}])& , Scale -> Pi]& ]}, {{ Hold[$CellContext`S1$$], 1., "\!\(\*SubscriptBox[\n StyleBox[\"S\",\nFontSlant->\"Italic\"], \"1\"]\ \)"}, Dynamic[$CellContext`MyManipulator[$CellContext`S1$$, {-1., 1.}, {($CellContext`s2 = $CellContext`S2$$; $CellContext`s3 = \ $CellContext`S3$$)& , ({$CellContext`S2$$, $CellContext`S3$$} = \ $CellContext`NS[{#, $CellContext`s2, $CellContext`s3}]; \ {$CellContext`\[Alpha]$$, $CellContext`\[Epsilon]$$} = \ $CellContext`SToAE[{$CellContext`S1$$ = #, $CellContext`S2$$, \ $CellContext`S3$$}]; {$CellContext`\[Chi]$$, $CellContext`\[Phi]$$} = \ $CellContext`SToRP[{$CellContext`S1$$ = #, $CellContext`S2$$, \ $CellContext`S3$$}])& , Identity}]& ]}, {{ Hold[$CellContext`S2$$], 0., "\!\(\*SubscriptBox[\n StyleBox[\"S\",\nFontSlant->\"Italic\"], \"2\"]\ \)"}, Dynamic[$CellContext`MyManipulator[$CellContext`S2$$, {-1., 1.}, {($CellContext`s1 = $CellContext`S1$$; $CellContext`s3 = \ $CellContext`S3$$)& , ({$CellContext`S1$$, $CellContext`S3$$} = \ $CellContext`NS[{#, $CellContext`S1$$, $CellContext`S3$$}]; {$CellContext`\ \[Alpha]$$, $CellContext`\[Epsilon]$$} = \ $CellContext`SToAE[{$CellContext`S1$$, $CellContext`S2$$ = #, \ $CellContext`S3$$}]; {$CellContext`\[Chi]$$, $CellContext`\[Phi]$$} = \ $CellContext`SToRP[{$CellContext`S1$$, $CellContext`S2$$ = #, \ $CellContext`S3$$}])& , Identity}]& ]}, {{ Hold[$CellContext`S3$$], 0., "\!\(\*SubscriptBox[\n StyleBox[\"S\",\nFontSlant->\"Italic\"], \"3\"]\ \)"}, Dynamic[$CellContext`MyManipulator[$CellContext`S3$$, {-1., 1.}, {($CellContext`s1 = $CellContext`S1$$; $CellContext`s2 = \ $CellContext`S2$$)& , ({$CellContext`S1$$, $CellContext`S2$$} = \ $CellContext`NS[{#, $CellContext`S1$$, $CellContext`S2$$}]; {$CellContext`\ \[Alpha]$$, $CellContext`\[Epsilon]$$} = \ $CellContext`SToAE[{$CellContext`S1$$, $CellContext`S2$$, $CellContext`S3$$ = \ #}]; {$CellContext`\[Chi]$$, $CellContext`\[Phi]$$} = \ $CellContext`SToRP[{$CellContext`S1$$, $CellContext`S2$$, $CellContext`S3$$ = \ #}])& , Identity}]& ]}, {{ Hold[$CellContext`plotEllipse$$], True, "Polarization ellipse:"}, { True, False}}, {{ Hold[$CellContext`plotPoincare$$], True, "Poincar\[EAcute] sphere:"}, { True, False}}, {{ Hold[$CellContext`labels$$], {"\[Alpha]", "\[Epsilon]"}, "Angles:"}, CheckboxBar[#, MapThread[# -> Style[#, #2]& , {{"\[Alpha]", "\[Epsilon]", "\[Chi]", "\[Phi]"}, Take[{ RGBColor[0.6, 0.24, 0.4428931686004542], RGBColor[0.6, 0.5470136627990908, 0.24], RGBColor[0.24, 0.6, 0.33692049419863584`], RGBColor[0.24, 0.35317267440181815`, 0.6], RGBColor[0.6, 0.24, 0.5632658430022721], RGBColor[0.6, 0.4266409883972719, 0.24], RGBColor[0.2634521802031821, 0.6, 0.24], RGBColor[0.24, 0.47354534880363613`, 0.6], RGBColor[0.5163614825959097, 0.24, 0.6], RGBColor[0.6, 0.3062683139954558, 0.24], RGBColor[0.3838248546049982, 0.6, 0.24], RGBColor[0.24, 0.5939180232054561, 0.6], RGBColor[0.3959888081940937, 0.24, 0.6], RGBColor[0.6, 0.24, 0.2941043604063603]}, Length[{"\[Alpha]", "\[Epsilon]", "\[Chi]", "\[Phi]"}]]}]]& }, {{ Hold[$CellContext`loci$$], {"\[Alpha]", "\[Epsilon]"}, "Loci:"}, CheckboxBar[#, MapThread[# -> Style[#, #2]& , {{"\[Alpha]", "\[Epsilon]", "\[Chi]", "\[Phi]"}, Take[{ RGBColor[0.6, 0.24, 0.4428931686004542], RGBColor[0.6, 0.5470136627990908, 0.24], RGBColor[0.24, 0.6, 0.33692049419863584`], RGBColor[0.24, 0.35317267440181815`, 0.6], RGBColor[0.6, 0.24, 0.5632658430022721], RGBColor[0.6, 0.4266409883972719, 0.24], RGBColor[0.2634521802031821, 0.6, 0.24], RGBColor[0.24, 0.47354534880363613`, 0.6], RGBColor[0.5163614825959097, 0.24, 0.6], RGBColor[0.6, 0.3062683139954558, 0.24], RGBColor[0.3838248546049982, 0.6, 0.24], RGBColor[0.24, 0.5939180232054561, 0.6], RGBColor[0.3959888081940937, 0.24, 0.6], RGBColor[0.6, 0.24, 0.2941043604063603]}, Length[{"\[Alpha]", "\[Epsilon]", "\[Chi]", "\[Phi]"}]]}]]& }}, Typeset`size$$ = {576., {153., 158.}}, Typeset`update$$ = 0, Typeset`initDone$$, Typeset`skipInitDone$$ = False, $CellContext`plotEllipse$52909$$ = False, $CellContext`plotPoincare$52910$$ = False}, DynamicBox[Manipulate`ManipulateBoxes[ 1, StandardForm, "Variables" :> {$CellContext`labels$$ = { "\[Alpha]", "\[Epsilon]"}, $CellContext`loci$$ = { "\[Alpha]", "\[Epsilon]"}, $CellContext`plotEllipse$$ = True, $CellContext`plotPoincare$$ = True, $CellContext`S1$$ = 1., $CellContext`S2$$ = 0., $CellContext`S3$$ = 0., $CellContext`\[Alpha]$$ = 0., $CellContext`\[Epsilon]$$ = 0., $CellContext`\[Phi]$$ = 0., $CellContext`\[Chi]$$ = 0.}, "ControllerVariables" :> { Hold[$CellContext`plotEllipse$$, $CellContext`plotEllipse$52909$$, False], Hold[$CellContext`plotPoincare$$, $CellContext`plotPoincare$52910$$, False]}, "OtherVariables" :> { Typeset`show$$, Typeset`bookmarkList$$, Typeset`bookmarkMode$$, Typeset`animator$$, Typeset`animvar$$, Typeset`name$$, Typeset`specs$$, Typeset`size$$, Typeset`update$$, Typeset`initDone$$, Typeset`skipInitDone$$}, "Body" :> Row[{{$CellContext`e1, $CellContext`e2, $CellContext`e3, \ $CellContext`e4} = { $CellContext`\[Alpha]\[Epsilon]F[$CellContext`\[Alpha]$$, \ $CellContext`\[Epsilon]$$, 0], $CellContext`\[Alpha]\[Epsilon]F[$CellContext`\[Alpha]$$, \ $CellContext`\[Epsilon]$$, Pi/2], $CellContext`\[Alpha]\[Epsilon]F[$CellContext`\[Alpha]$$, \ $CellContext`\[Epsilon]$$, Pi], $CellContext`\[Alpha]\[Epsilon]F[$CellContext`\[Alpha]$$, \ $CellContext`\[Epsilon]$$, 3 (Pi/2)]}; {$CellContext`co, $CellContext`si} = { Cos[$CellContext`\[Chi]$$], Sin[$CellContext`\[Chi]$$]}; Graphics[ If[$CellContext`plotEllipse$$, { Arrowheads[{-0.035, 0.035}], If[ MemberQ[$CellContext`labels$$, "\[Alpha]"], { Part[$CellContext`color, 2], $CellContext`Arc[{0, 0}, {0.6, 0.6}, { 0, $CellContext`\[Alpha]$$}, Label -> "\[Alpha]"]}, {}], If[ MemberQ[$CellContext`labels$$, "\[Epsilon]"], { Part[$CellContext`color, 3], $CellContext`Arc[{0, 0}, {0.6, 0.6}, {$CellContext`\[Alpha]$$, $CellContext`\[Alpha]$$ + \ $CellContext`\[Epsilon]$$}, Label -> "\[Epsilon]"], Arrow[{$CellContext`e3 + $CellContext`e2, $CellContext`e2}], Text[ "\!\(\*\nStyleBox[\"a\",\nFontSlant->\"Italic\"]\)", \ $CellContext`e3/2 + $CellContext`e2 + 0.08 Normalize[$CellContext`e2]], Arrow[{$CellContext`e3 + $CellContext`e2, $CellContext`e3}], Text[ "\!\(\*\nStyleBox[\"b\",\nFontSlant->\"Italic\"]\)", 0.08 Normalize[$CellContext`e3] + $CellContext`e3 + \ $CellContext`e2/2], $CellContext`dash, Line[{$CellContext`e1 + $CellContext`e2, $CellContext`e1 + \ $CellContext`e4, $CellContext`e3 + $CellContext`e4, $CellContext`e3 + \ $CellContext`e2, $CellContext`e1 + $CellContext`e2, {0, 0}}], Line[{$CellContext`e1 + $CellContext`e2, {0, 0}}]}, {}], If[ MemberQ[$CellContext`labels$$, Alternatives["\[Epsilon]", "\[Alpha]"]], { Part[$CellContext`color, 1], $CellContext`dash, Line[{$CellContext`e1, $CellContext`e3}], Line[{$CellContext`e2, $CellContext`e4}]}, {}], If[ MemberQ[$CellContext`labels$$, "\[Chi]"], { Part[$CellContext`color, 4], $CellContext`Arc[{0, 0}, {0.4, 0.4}, { 0, $CellContext`\[Chi]$$}, Label -> "\[Chi]"], Arrow[{{0, -Sin[$CellContext`\[Chi]$$]}, { Cos[$CellContext`\[Chi]$$], -Sin[$CellContext`\[Chi]$$]}}], Text[ "\!\(\*SubsuperscriptBox[\"\[ScriptCapitalE]\", \n \ StyleBox[\"x\",\nFontSlant->\"Italic\"], \"0\"]\)", {$CellContext`co/ 2, -$CellContext`si - 0.1}], Arrow[{{$CellContext`co, 0}, {$CellContext`co, -$CellContext`si}}], Text[ "\!\(\*SubsuperscriptBox[\(\[ScriptCapitalE]\), \(y\), \ \(0\)]\)", {$CellContext`co + 0.1, (-$CellContext`si)/2}], $CellContext`dash, Line[{{$CellContext`co, $CellContext`si}, {-$CellContext`co, \ $CellContext`si}, {-$CellContext`co, -$CellContext`si}, {$CellContext`co, \ -$CellContext`si}, {$CellContext`co, $CellContext`si}, {0, 0}}]}, {}], { Arrowheads[ Table[{0.035, $CellContext`i}, {$CellContext`i, 0.025, 1 - 0.025, 0.05}]], ReplaceAll[ Part[ ParametricPlot[{{ Cos[$CellContext`t] $CellContext`co, Cos[$CellContext`t - $CellContext`\[Phi]$$] \ $CellContext`si}}, {$CellContext`t, 0, 2 Pi}], 1], Line -> Arrow]}}, {}], Frame -> True, FrameLabel -> { Style[ "\!\(\*SubscriptBox[\"\[ScriptCapitalE]\", \n StyleBox[\"x\",\n\ FontSlant->\"Italic\"]]\)", 12], Style["\!\(\*SubscriptBox[\(\[ScriptCapitalE]\), \(y\)]\)", 12]}, PlotRange -> {{-1, 1}, {-1, 1}}, Axes -> True, ImageSize -> 4 72], Graphics3D[{$CellContext`ax, If[$CellContext`plotPoincare$$, { If[ MemberQ[$CellContext`labels$$, "\[Alpha]"], { Graphics`Axes3D`ColorAll[ Part[$CellContext`color, 2]], Graphics`Axes3D`Circle3D[{0, 0, 0}, 0.5, { 0, 2 $CellContext`\[Alpha]$$}, Label -> "2\[Alpha]", Graphics`Axes3D`ArrowHeads -> 2]}, {}], If[ MemberQ[$CellContext`labels$$, "\[Epsilon]"], { Graphics`Axes3D`ColorAll[ Part[$CellContext`color, 3]], Graphics`Axes3D`RotateZ[2 $CellContext`\[Alpha]$$][ Graphics`Axes3D`RotateX[Pi/2][ Graphics`Axes3D`Circle3D[{0, 0, 0}, 0.5, { 0, 2 $CellContext`\[Epsilon]$$}, Label -> "2\[Epsilon]", Graphics`Axes3D`ArrowHeads -> 2]]]}, {}], If[ MemberQ[$CellContext`labels$$, Alternatives["\[Epsilon]", "\[Alpha]"]], { Part[$CellContext`color, 1], Line[{{$CellContext`S1$$, $CellContext`S2$$, \ $CellContext`S3$$}, {$CellContext`S1$$, $CellContext`S2$$, 0}}], Graphics`Axes3D`RotateZ[2 $CellContext`\[Alpha]$$][ Line[{{0, 0, 0}, {1, 0, 0}}]]}, {}], If[ MemberQ[$CellContext`labels$$, "\[Chi]"], { Graphics`Axes3D`ColorAll[ Part[$CellContext`color, 4]], Graphics`Axes3D`RotateX[$CellContext`\[Phi]$$][ Graphics`Axes3D`Circle3D[{0, 0, 0}, 0.5, { 0, 2 $CellContext`\[Chi]$$}, Label -> "2\[Chi]", Graphics`Axes3D`ArrowHeads -> 2]]}, {}], If[ MemberQ[$CellContext`labels$$, "\[Phi]"], { Graphics`Axes3D`ColorAll[ Part[$CellContext`color, 5]], Line[{{0, 0, 0}, Normalize[{0, $CellContext`S2$$, $CellContext`S3$$}]}], Line[{{$CellContext`S1$$, $CellContext`S2$$, \ $CellContext`S3$$}, {0, $CellContext`S2$$, $CellContext`S3$$}}], Graphics`Axes3D`RotateZ[Pi/2][ Graphics`Axes3D`RotateX[Pi/2][ Graphics`Axes3D`Circle3D[{0, 0, 0}, 0.5, { 0, $CellContext`\[Phi]$$}, Label -> "\[Phi]", Graphics`Axes3D`ArrowHeads -> 2]]]}, {}], If[ MemberQ[$CellContext`loci$$, "\[Alpha]"], { Part[$CellContext`color, 2], Graphics`Axes3D`RotateZ[2 $CellContext`\[Alpha]$$][ Graphics`Axes3D`RotateX[Pi/2][ Graphics`Axes3D`Circle3D[1]]]}, {}], If[ MemberQ[$CellContext`loci$$, "\[Epsilon]"], { Part[$CellContext`color, 3], Graphics`Axes3D`TranslateZ[ Sin[2 $CellContext`\[Epsilon]$$]][ Graphics`Axes3D`Circle3D[ Cos[2 $CellContext`\[Epsilon]$$]]]}, {}], If[ MemberQ[$CellContext`loci$$, "\[Chi]"], { Part[$CellContext`color, 4], Graphics`Axes3D`TranslateX[ Cos[2 $CellContext`\[Chi]$$]][ Graphics`Axes3D`RotateY[Pi/2][ Graphics`Axes3D`Circle3D[ Sin[2 $CellContext`\[Chi]$$]]]]}, {}], If[ MemberQ[$CellContext`loci$$, "\[Phi]"], { Part[$CellContext`color, 5], Graphics`Axes3D`RotateX[$CellContext`\[Phi]$$][ Graphics`Axes3D`Circle3D[{0, 0, 0}, 1, {0, Pi}]]}, {}], Graphics`Axes3D`RotateZ[2 $CellContext`\[Alpha]$$][ Graphics`Axes3D`RotateY[(-2) \ $CellContext`\[Epsilon]$$][$CellContext`arr3d]], { Opacity[0.06], Specularity[White, 5], Blue, Sphere[]}}, {}]}, Boxed -> False, ViewPoint -> 10 {1, 1.2, 0.9}, ViewVertical -> {0, 0, 1}, PlotRange -> 1.3, PlotRegion -> $CellContext`Crop[{{0.21, 0.78}, {0.25, 0.81}}], ImageSize -> 4 72, Lighting -> {{"Point", White, {1, 2, 5}}}]}], "Specifications" :> {{{$CellContext`\[Alpha]$$, 0., "\[Alpha]"}, Dynamic[$CellContext`MyManipulator[$CellContext`\[Alpha]$$, {(-Pi)/ 2., Pi/2.}, ({$CellContext`\[Chi]$$, $CellContext`\[Phi]$$} = \ $CellContext`AEToRP[{#, $CellContext`\[Epsilon]$$}]; {$CellContext`S1$$, \ $CellContext`S2$$, $CellContext`S3$$} = $CellContext`AEToS[{$CellContext`\ \[Alpha]$$ = #, $CellContext`\[Epsilon]$$}])& , Scale -> Pi]& ]}, {{$CellContext`\[Epsilon]$$, 0.}, Dynamic[$CellContext`MyManipulator[$CellContext`\[Epsilon]$$, {(-Pi)/ 4., Pi/4.}, ({$CellContext`\[Chi]$$, $CellContext`\[Phi]$$} = \ $CellContext`AEToRP[{$CellContext`\[Alpha]$$, #}]; {$CellContext`S1$$, \ $CellContext`S2$$, $CellContext`S3$$} = $CellContext`AEToS[{$CellContext`\ \[Alpha]$$, $CellContext`\[Epsilon]$$ = #}])& , Scale -> Pi]& ]}, {{$CellContext`\[Chi]$$, 0.}, Dynamic[$CellContext`MyManipulator[$CellContext`\[Chi]$$, { 0., Pi/2.}, ({$CellContext`\[Alpha]$$, $CellContext`\[Epsilon]$$} = \ $CellContext`RPToAE[{$CellContext`\[Chi]$$ = #, $CellContext`\[Phi]$$}]; \ {$CellContext`S1$$, $CellContext`S2$$, $CellContext`S3$$} = \ $CellContext`RPToS[{$CellContext`\[Chi]$$ = #, $CellContext`\[Phi]$$}])& , Scale -> Pi]& ]}, {{$CellContext`\[Phi]$$, 0.}, Dynamic[$CellContext`MyManipulator[$CellContext`\[Phi]$$, {-Pi, 1. Pi}, ({$CellContext`\[Alpha]$$, $CellContext`\[Epsilon]$$} = \ $CellContext`RPToAE[{$CellContext`\[Chi]$$, $CellContext`\[Phi]$$ = #}]; \ {$CellContext`S1$$, $CellContext`S2$$, $CellContext`S3$$} = \ $CellContext`RPToS[{$CellContext`\[Chi]$$, $CellContext`\[Phi]$$ = #}])& , Scale -> Pi]& ]}, {{$CellContext`S1$$, 1., "\!\(\*SubscriptBox[\n StyleBox[\"S\",\nFontSlant->\"Italic\"], \"1\ \"]\)"}, Dynamic[$CellContext`MyManipulator[$CellContext`S1$$, {-1., 1.}, {($CellContext`s2 = $CellContext`S2$$; $CellContext`s3 = \ $CellContext`S3$$)& , ({$CellContext`S2$$, $CellContext`S3$$} = \ $CellContext`NS[{#, $CellContext`s2, $CellContext`s3}]; \ {$CellContext`\[Alpha]$$, $CellContext`\[Epsilon]$$} = \ $CellContext`SToAE[{$CellContext`S1$$ = #, $CellContext`S2$$, \ $CellContext`S3$$}]; {$CellContext`\[Chi]$$, $CellContext`\[Phi]$$} = \ $CellContext`SToRP[{$CellContext`S1$$ = #, $CellContext`S2$$, \ $CellContext`S3$$}])& , Identity}]& ]}, {{$CellContext`S2$$, 0., "\!\(\*SubscriptBox[\n StyleBox[\"S\",\nFontSlant->\"Italic\"], \"2\ \"]\)"}, Dynamic[$CellContext`MyManipulator[$CellContext`S2$$, {-1., 1.}, {($CellContext`s1 = $CellContext`S1$$; $CellContext`s3 = \ $CellContext`S3$$)& , ({$CellContext`S1$$, $CellContext`S3$$} = \ $CellContext`NS[{#, $CellContext`S1$$, $CellContext`S3$$}]; {$CellContext`\ \[Alpha]$$, $CellContext`\[Epsilon]$$} = \ $CellContext`SToAE[{$CellContext`S1$$, $CellContext`S2$$ = #, \ $CellContext`S3$$}]; {$CellContext`\[Chi]$$, $CellContext`\[Phi]$$} = \ $CellContext`SToRP[{$CellContext`S1$$, $CellContext`S2$$ = #, \ $CellContext`S3$$}])& , Identity}]& ]}, {{$CellContext`S3$$, 0., "\!\(\*SubscriptBox[\n StyleBox[\"S\",\nFontSlant->\"Italic\"], \"3\ \"]\)"}, Dynamic[$CellContext`MyManipulator[$CellContext`S3$$, {-1., 1.}, {($CellContext`s1 = $CellContext`S1$$; $CellContext`s2 = \ $CellContext`S2$$)& , ({$CellContext`S1$$, $CellContext`S2$$} = \ $CellContext`NS[{#, $CellContext`S1$$, $CellContext`S2$$}]; {$CellContext`\ \[Alpha]$$, $CellContext`\[Epsilon]$$} = \ $CellContext`SToAE[{$CellContext`S1$$, $CellContext`S2$$, $CellContext`S3$$ = \ #}]; {$CellContext`\[Chi]$$, $CellContext`\[Phi]$$} = \ $CellContext`SToRP[{$CellContext`S1$$, $CellContext`S2$$, $CellContext`S3$$ = \ #}])& , Identity}]& ]}, {{$CellContext`plotEllipse$$, True, "Polarization ellipse:"}, { True, False}}, {{$CellContext`plotPoincare$$, True, "Poincar\[EAcute] sphere:"}, { True, False}}, {{$CellContext`labels$$, {"\[Alpha]", "\[Epsilon]"}, "Angles:"}, CheckboxBar[#, MapThread[# -> Style[#, #2]& , {{"\[Alpha]", "\[Epsilon]", "\[Chi]", "\[Phi]"}, Take[{ RGBColor[0.6, 0.24, 0.4428931686004542], RGBColor[0.6, 0.5470136627990908, 0.24], RGBColor[0.24, 0.6, 0.33692049419863584`], RGBColor[0.24, 0.35317267440181815`, 0.6], RGBColor[0.6, 0.24, 0.5632658430022721], RGBColor[0.6, 0.4266409883972719, 0.24], RGBColor[0.2634521802031821, 0.6, 0.24], RGBColor[0.24, 0.47354534880363613`, 0.6], RGBColor[0.5163614825959097, 0.24, 0.6], RGBColor[0.6, 0.3062683139954558, 0.24], RGBColor[0.3838248546049982, 0.6, 0.24], RGBColor[0.24, 0.5939180232054561, 0.6], RGBColor[0.3959888081940937, 0.24, 0.6], RGBColor[0.6, 0.24, 0.2941043604063603]}, Length[{"\[Alpha]", "\[Epsilon]", "\[Chi]", "\[Phi]"}]]}]]& }, {{$CellContext`loci$$, { "\[Alpha]", "\[Epsilon]"}, "Loci:"}, CheckboxBar[#, MapThread[# -> Style[#, #2]& , {{"\[Alpha]", "\[Epsilon]", "\[Chi]", "\[Phi]"}, Take[{ RGBColor[0.6, 0.24, 0.4428931686004542], RGBColor[0.6, 0.5470136627990908, 0.24], RGBColor[0.24, 0.6, 0.33692049419863584`], RGBColor[0.24, 0.35317267440181815`, 0.6], RGBColor[0.6, 0.24, 0.5632658430022721], RGBColor[0.6, 0.4266409883972719, 0.24], RGBColor[0.2634521802031821, 0.6, 0.24], RGBColor[0.24, 0.47354534880363613`, 0.6], RGBColor[0.5163614825959097, 0.24, 0.6], RGBColor[0.6, 0.3062683139954558, 0.24], RGBColor[0.3838248546049982, 0.6, 0.24], RGBColor[0.24, 0.5939180232054561, 0.6], RGBColor[0.3959888081940937, 0.24, 0.6], RGBColor[0.6, 0.24, 0.2941043604063603]}, Length[{"\[Alpha]", "\[Epsilon]", "\[Chi]", "\[Phi]"}]]}]]& }}, "Options" :> {ControlPlacement -> Top}, "DefaultOptions" :> {}], ImageSizeCache->{620., {318., 323.}}, SingleEvaluation->True], Deinitialization:>None, DynamicModuleValues:>{}, Initialization:>({$CellContext`e1 = {1., 0.}, $CellContext`e2 = {0., 0.}, $CellContext`e3 = {-1., 0.}, $CellContext`e4 = {0., 0.}, $CellContext`\[Alpha]\[Epsilon]F[ Pattern[$CellContext`\[Alpha], Blank[]], Pattern[$CellContext`\[Epsilon], Blank[]], Pattern[$CellContext`t, Blank[]]] = {(Cos[$CellContext`t] Cos[$CellContext`\[Alpha]]) Cos[$CellContext`\[Epsilon]] - (Sin[$CellContext`t] Sin[$CellContext`\[Alpha]]) Sin[$CellContext`\[Epsilon]], (Cos[$CellContext`t] Cos[$CellContext`\[Epsilon]]) Sin[$CellContext`\[Alpha]] + (Cos[$CellContext`\[Alpha]] Sin[$CellContext`t]) Sin[$CellContext`\[Epsilon]]}, $CellContext`co = 1., $CellContext`si = 0., $CellContext`color = { RGBColor[0.24720000000000017`, 0.24, 0.6], RGBColor[0.6, 0.24, 0.4428931686004542], RGBColor[0.6, 0.5470136627990908, 0.24], RGBColor[0.24, 0.6, 0.33692049419863584`], RGBColor[0.24, 0.35317267440181815`, 0.6], RGBColor[0.6, 0.24, 0.5632658430022721], RGBColor[0.6, 0.4266409883972719, 0.24], RGBColor[0.2634521802031821, 0.6, 0.24], RGBColor[0.24, 0.47354534880363613`, 0.6], RGBColor[0.5163614825959097, 0.24, 0.6], RGBColor[0.6, 0.3062683139954558, 0.24], RGBColor[0.3838248546049982, 0.6, 0.24], RGBColor[0.24, 0.5939180232054561, 0.6], RGBColor[0.3959888081940937, 0.24, 0.6], RGBColor[0.6, 0.24, 0.2941043604063603]}, $CellContext`Arc[{ Pattern[$CellContext`x, Blank[]], Pattern[$CellContext`y, Blank[]]}, { Pattern[$CellContext`r1, Blank[]], Pattern[$CellContext`r2, Blank[]]}, { Pattern[$CellContext`\[Theta]1, Blank[]], Pattern[$CellContext`\[Theta]2, Blank[]]}, OptionsPattern[]] := Module[{$CellContext`pos = OptionValue[Graphics`Axes3D`LabelPosition]}, If[$CellContext`\[Theta]1 == $CellContext`\[Theta]2, {}, { Apply[Arrow, Part[ Cases[ Flatten[ Part[ ParametricPlot[{$CellContext`x + $CellContext`r1 Cos[$CellContext`\[Theta]], $CellContext`y + \ $CellContext`r2 Sin[$CellContext`\[Theta]]}, {$CellContext`\[Theta], \ $CellContext`\[Theta]1, $CellContext`\[Theta]2}], 1]], Line[ Blank[]]], 1]], If[OptionValue[Label] =!= None, Rotate[ Text[ OptionValue[Label], { Mean[{$CellContext`r1, $CellContext`r2}] Part[$CellContext`pos, 2], 0}], Part[$CellContext`pos, 1] ($CellContext`\[Theta]2 - $CellContext`\[Theta]1) + Mean[{$CellContext`\[Theta]1, $CellContext`\[Theta]2}], {0, 0}], {}]}]], Options[$CellContext`Arc] = { Label -> None, Graphics`Axes3D`LabelPosition -> {0, 1.1}, LabelStyle -> {}}, TagSet[Graphics`Axes3D`LabelPosition, MessageName[Graphics`Axes3D`LabelPosition, "usage"], ""], $CellContext`dash = Dashing[{0.02, 0.02}], $CellContext`ax = { GrayLevel[0], Specularity[0], EdgeForm[ GrayLevel[0]], Glow[ GrayLevel[0]], { Translate[ Rotate[{ Translate[{ Translate[{ Line[{{0, 0, -1.25}, {0, 0, 1.25}}]}, {0, 0, -0.05}], Rotate[ Translate[ Polygon[{{-0.03, 0, -0.010000000000000002`}, {0, 0, 0.1}, { 0.03, 0, -0.010000000000000002`}, {0, 0, 0}, {-0.03, 0, -0.010000000000000002`}}], {0, 0, 1.2}], 0, {0, 0, 1}], {}, Rotate[ Style[ Text[ "\!\(\*SubscriptBox[\n StyleBox[\"S\",\n\ FontSlant->\"Italic\"], \"1\"]\)", {0.13, 0, 1.1700000000000002`}], {12}], Pi/ 4, {0, 0, 1}]}, {0, 0, 1.3}]}, {{0, 0, 1}, { 1., 0, 0}}], {-1.3, 0, 0}], Translate[ Rotate[{ Translate[{ Translate[{ Line[{{0, 0, -1.25}, {0, 0, 1.25}}]}, {0, 0, -0.05}], Rotate[ Translate[ Polygon[{{-0.03, 0, -0.010000000000000002`}, {0, 0, 0.1}, { 0.03, 0, -0.010000000000000002`}, {0, 0, 0}, {-0.03, 0, -0.010000000000000002`}}], {0, 0, 1.2}], Pi/ 2, {0, 0, 1}], {}, Rotate[ Style[ Text[ "\!\(\*SubscriptBox[\n StyleBox[\"S\",\n\ FontSlant->\"Italic\"], \"2\"]\)", {0.1, 0, 1.1700000000000002`}], {12}], Pi/ 4, {0, 0, 1}]}, {0, 0, 1.3}]}, {{0, 0, 1}, {0, 1., 0}}], { 0, -1.3, 0}], Translate[ Rotate[{ Translate[{ Translate[{ Line[{{0, 0, -1.25}, {0, 0, 1.25}}]}, {0, 0, -0.05}], Rotate[ Translate[ Polygon[{{-0.03, 0, -0.010000000000000002`}, {0, 0, 0.1}, { 0.03, 0, -0.010000000000000002`}, {0, 0, 0}, {-0.03, 0, -0.010000000000000002`}}], {0, 0, 1.2}], 0, {0, 0, 1}], {}, Rotate[ Style[ Text[ "\!\(\*SubscriptBox[\n StyleBox[\"S\",\n\ FontSlant->\"Italic\"], \"3\"]\)", {0.13, 0, 1.1700000000000002`}], {12}], (3 Pi)/4, {0, 0, 1}]}, {0, 0, 1.3}]}, {{0, 0, 1}, { 0, 0, 1.}}], {0, 0, -1.3}]}}, Graphics`Axes3D`ColorAll[ Pattern[$CellContext`col, Blank[]]] := Sequence[Black, Specularity[0], EdgeForm[$CellContext`col], Glow[$CellContext`col]], TagSet[Graphics`Axes3D`ColorAll, MessageName[Graphics`Axes3D`ColorAll, "usage"], ""], Graphics`Axes3D`Circle3D[ Pattern[Private`r, Blank[]], Pattern[Private`opts, BlankNullSequence[Rule]]] := Graphics`Axes3D`Circle3D[{0, 0, 0}, Private`r, {0, 2 Pi}, Private`opts], Graphics`Axes3D`Circle3D[ Pattern[Private`p, { Pattern[Private`x, Blank[]], Pattern[Private`y, Blank[]], Pattern[Private`z, Blank[]]}], Pattern[Private`r, Blank[]], Pattern[Private`opts, BlankNullSequence[Rule]]] := Graphics`Axes3D`Circle3D[ Private`p, Private`r, {0, 2 Pi}, Private`opts], Graphics`Axes3D`Circle3D[ Pattern[Private`p, { Pattern[Private`x, Blank[]], Pattern[Private`y, Blank[]], Pattern[Private`z, Blank[]]}], Pattern[Private`r, Blank[]], { Pattern[Private`t1, Blank[]], Pattern[Private`t2, Blank[]]}, Pattern[Private`opts, OptionsPattern[]]] := Module[{Private`lp = OptionValue[Graphics`Axes3D`LabelPosition], Private`w, Private`hw, Private`hl, Private`t1a, Private`t2a, Private`rs = OptionValue[Graphics`Axes3D`RenderStyle], Private`ppopts, Private`ah = OptionValue[Graphics`Axes3D`ArrowHeads], Private`head, Private`end}, {Private`w, Private`hw, Private`hl} = ReplaceAll[ ReplaceAll[If[OptionValue[Scale] === Automatic, Private`r, OptionValue[Scale]] { Graphics`Axes3D`Width, Graphics`Axes3D`HeadWidth, Graphics`Axes3D`HeadLength}, {Private`opts}], Options[Graphics`Axes3D`Circle3D]]; If[ Or[Private`t1 == Private`t2, Private`r == 0], {}, If[Abs[Private`t1 - Private`t2] >= Private`hl/Private`r, Private`t1a = Min[Private`t1, Private`t2] + If[Private`ah >= 2, Private`hl/Private`r, 0]; Private`t2a = Max[Private`t1, Private`t2] - If[ Private`ah >= 1, Private`hl/Private`r, 0]; Null, Private`ah = 0; {Private`t1a, Private`t2a} = Sort[{Private`t1, Private`t2}]]; Private`ppopts = FilterRules[ Join[{Private`opts}, Options[Graphics`Axes3D`Circle3D]], Options[ParametricPlot3D]]; Private`head = Switch[Private`rs, Full, Graphics`Axes3D`FatHead, Flat, Graphics`Axes3D`FlatHead][Private`hw, Private`hl]; Private`end = Switch[Private`rs, Full, Graphics`Axes3D`Disk3D[{0, 0, 0}, Private`w], Flat, {}]; Translate[{ Switch[Private`rs, Full, Part[ ParametricPlot3D[{(Private`r + Private`w Cos[Private`v]) Cos[Private`u], (Private`r + Private`w Cos[Private`v]) Sin[Private`u], Private`w Sin[Private`v]}, { Private`u, Private`t1a, Private`t2a}, {Private`v, 0, 2 Pi}, Mesh -> False, Evaluate[ Apply[Sequence, Private`ppopts]]], 1], Flat, Part[ ParametricPlot3D[Private`r { Cos[Private`t], Sin[Private`t], 0}, {Private`t, Private`t1a, Private`t2a}, Evaluate[Private`ppopts]], 1, 1, -1, -1]], Graphics`Axes3D`RotateZ[Private`t1a][ Graphics`Axes3D`TranslateX[Private`r][ Graphics`Axes3D`RotateX[Pi/2][ If[Private`ah >= 2, Private`head, Private`end]]]], Graphics`Axes3D`RotateZ[Private`t2a][ Graphics`Axes3D`TranslateX[Private`r][ Graphics`Axes3D`RotateX[Pi/2][ If[Private`ah >= 1, Graphics`Axes3D`RotateX[Pi][Private`head], Private`end]]]], If[OptionValue[Label] =!= None, Graphics`Axes3D`RotateZ[(Private`t1 + Private`t2)/ 2 + (Part[Private`lp, 1] (Private`t2 - Private`t1))/2][ Text[ OptionValue[Label], { Private`r Part[Private`lp, 2], 0, Private`r Part[Private`lp, 3]}]], {}]}, Private`p]]], Options[Graphics`Axes3D`Circle3D] := { Label -> None, Graphics`Axes3D`LabelPosition -> {0, 1.2, 0}, LabelStyle -> {}, Graphics`Axes3D`RenderStyle -> Flat, Graphics`Axes3D`Width -> 0.015, Graphics`Axes3D`ArrowHeads -> 0, Graphics`Axes3D`HeadWidth -> 0.03, Graphics`Axes3D`Width -> 0.01, Graphics`Axes3D`HeadLength -> 0.1, Scale -> Automatic, PlotPoints -> Automatic}, TagSet[Graphics`Axes3D`Circle3D, MessageName[Graphics`Axes3D`Circle3D, "usage"], ""], TagSet[Graphics`Axes3D`RenderStyle, MessageName[Graphics`Axes3D`RenderStyle, "usage"], ""], TagSet[Graphics`Axes3D`ArrowHeads, MessageName[Graphics`Axes3D`ArrowHeads, "usage"], ""], TagSet[Graphics`Axes3D`Width, MessageName[Graphics`Axes3D`Width, "usage"], ""], TagSet[Graphics`Axes3D`HeadWidth, MessageName[Graphics`Axes3D`HeadWidth, "usage"], ""], TagSet[Graphics`Axes3D`HeadLength, MessageName[Graphics`Axes3D`HeadLength, "usage"], ""], Graphics`Axes3D`FatHead[ Pattern[Private`width, Blank[]], Pattern[Private`length, Blank[]], Pattern[Private`opts, BlankNullSequence[Rule]]] := Graphics`Axes3D`TranslateZ[(-0.1) Private`length][{ Graphics`Axes3D`Cone[ Private`width, 0.1 Private`length, Graphics`Axes3D`Opening -> Down, Private`opts], Graphics`Axes3D`Cone[ Private`width, 1.1 Private`length, Graphics`Axes3D`Opening -> Down, Private`opts]}], Graphics`Axes3D`FatHead[ Pattern[Private`length, Blank[]], Pattern[Private`width, Blank[]], Pattern[Private`inset, Blank[]], Pattern[Private`opts, BlankNullSequence[Rule]]] := Graphics`Axes3D`TranslateZ[-Private`inset - Private`length][{ Graphics`Axes3D`Cone[ Private`width, Private`inset, Graphics`Axes3D`Opening -> Down, Private`opts], Graphics`Axes3D`Cone[ Private`width, Private`inset + Private`length, Graphics`Axes3D`Opening -> Down, Private`opts]}], TagSet[Graphics`Axes3D`FatHead, MessageName[Graphics`Axes3D`FatHead, "usage"], ""], Graphics`Axes3D`TranslateZ[ Pattern[Private`x, Blank[]]][ Pattern[Private`g, Blank[]]] := Translate[Private`g, {0, 0, Private`x}], TagSet[Graphics`Axes3D`TranslateZ, MessageName[Graphics`Axes3D`TranslateZ, "usage"], ""], Graphics`Axes3D`Cone[ Pattern[Private`r, Blank[]], Pattern[Private`h, Blank[]], Pattern[Private`opts, OptionsPattern[]]] := Module[{Private`rp3dopts = FilterRules[ Join[{Private`opts}, Options[Graphics`Axes3D`Cone]], Options[RevolutionPlot3D]], Private`pp}, If[OptionValue[Graphics`Axes3D`RenderStyle] === Full, If[OptionValue[Graphics`Axes3D`Opening] === Down, Part[ RevolutionPlot3D[ Private`h (1 - Private`t/Private`r), {Private`t, 0, Private`r}, Mesh -> False, Evaluate[ Apply[Sequence, Private`rp3dopts]]], 1], Part[ RevolutionPlot3D[ Private`h (Private`t/Private`r), {Private`t, 0, Private`r}, Mesh -> False, Evaluate[ Apply[Sequence, Private`rp3dopts]]], 1]], Private`pp = ReplaceAll[ OptionValue[PlotPoints], Automatic -> 10]; If[OptionValue[Graphics`Axes3D`Opening] === Down, { Graphics`Axes3D`Circle3D[{0, 0, 0}, Private`r], Table[ Line[{{0, 0, Private`h}, { Private`r Sin[Private`t], Private`r Cos[Private`t], 0}}], { Private`t, 0, 2 Pi - (2 Pi)/Private`pp, (2 Pi)/Private`pp}]}, { Graphics`Axes3D`Circle3D[{0, 0, Private`h}, Private`r], Table[ Line[{{0, 0, 0}, { Private`r Sin[Private`t], Private`r Cos[Private`t], Private`h}}], { Private`t, 0, 2 Pi - (2 Pi)/Private`pp, (2 Pi)/Private`pp}]}]]], Options[Graphics`Axes3D`Cone] = { Graphics`Axes3D`Opening -> Down, PlotPoints -> Automatic, Graphics`Axes3D`RenderStyle -> Full}, TagSet[Graphics`Axes3D`Cone, MessageName[Graphics`Axes3D`Cone, "usage"], ""], TagSet[Graphics`Axes3D`Opening, MessageName[Graphics`Axes3D`Opening, "usage"], ""], Graphics`Axes3D`FlatHead[ Pattern[Private`width, Blank[]], Pattern[Private`length, Blank[]], Pattern[Private`opts, BlankNullSequence[Rule]]] := Polygon[{{-Private`width, 0, (-0.1) Private`length}, { 0, 0, Private`length}, {Private`width, 0, (-0.1) Private`length}, { 0, 0, 0}, {-Private`width, 0, (-0.1) Private`length}}], Graphics`Axes3D`FlatHead[ Pattern[Private`length, Blank[]], Pattern[Private`width, Blank[]], Pattern[Private`inset, Blank[]], Pattern[Private`opts, BlankNullSequence[Rule]]] := Graphics`Axes3D`TranslateZ[-Private`length][ Polygon[{{-Private`width, 0, -Private`inset}, { 0, 0, Private`length}, {Private`width, 0, -Private`inset}, {0, 0, 0}, {-Private`width, 0, -Private`inset}}]], TagSet[Graphics`Axes3D`FlatHead, MessageName[Graphics`Axes3D`FlatHead, "usage"], ""], Graphics`Axes3D`Disk3D[{ Pattern[Private`x, Blank[]], Pattern[Private`y, Blank[]], Pattern[Private`z, Blank[]]}, Pattern[Private`r, Blank[]]] := Translate[ Part[ RevolutionPlot3D[0, {Private`t, 0, Private`r}, Mesh -> False], 1], { Private`x, Private`y, Private`z}], TagSet[Graphics`Axes3D`Disk3D, MessageName[Graphics`Axes3D`Disk3D, "usage"], ""], Graphics`Axes3D`RotateZ[ Pattern[Private`theta, Blank[]]][ Pattern[Private`g, Blank[]]] := Rotate[Private`g, Private`theta, {0, 0, 1}], TagSet[Graphics`Axes3D`RotateZ, MessageName[Graphics`Axes3D`RotateZ, "usage"], ""], Graphics`Axes3D`TranslateX[ Pattern[Private`x, Blank[]]][ Pattern[Private`g, Blank[]]] := Translate[Private`g, {Private`x, 0, 0}], TagSet[Graphics`Axes3D`TranslateX, MessageName[Graphics`Axes3D`TranslateX, "usage"], ""], Graphics`Axes3D`RotateX[ Pattern[Private`theta, Blank[]]][ Pattern[Private`g, Blank[]]] := Rotate[Private`g, Private`theta, {1, 0, 0}], TagSet[Graphics`Axes3D`RotateX, MessageName[Graphics`Axes3D`RotateX, "usage"], ""], Graphics`Axes3D`RotateY[ Pattern[Private`theta, Blank[]]][ Pattern[Private`g, Blank[]]] := Rotate[Private`g, Private`theta, {0, 1, 0}], TagSet[Graphics`Axes3D`RotateY, MessageName[Graphics`Axes3D`RotateY, "usage"], ""], $CellContext`arr3d = { GrayLevel[0], Specularity[0], EdgeForm[ RGBColor[0.24720000000000017`, 0.24, 0.6]], Glow[ RGBColor[0.24720000000000017`, 0.24, 0.6]], Thickness[0.007], Rotate[{ Translate[{ Translate[{ Line[{{0, 0, -0.425}, {0, 0, 0.425}}]}, { 0, 0, -0.07500000000000001}], Rotate[ Translate[ Polygon[{{-0.045, 0, -0.015000000000000003`}, { 0, 0, 0.15000000000000002`}, { 0.045, 0, -0.015000000000000003`}, {0, 0, 0}, {-0.045, 0, -0.015000000000000003`}}], {0, 0, 0.35}], 0, {0, 0, 1}], {}, {}}, {0, 0, 1/2}]}, Pi/2, {0, 1, 0}]}, $CellContext`Crop[{{ Pattern[$CellContext`xmin, Blank[]], Pattern[$CellContext`xmax, Blank[]]}, { Pattern[$CellContext`ymin, Blank[]], Pattern[$CellContext`ymax, Blank[]]}}] := {{0, 1} + {-$CellContext`xmin, 1 - $CellContext`xmax}/($CellContext`xmax - $CellContext`xmin), { 0, 1} + {-$CellContext`ymin, 1 - $CellContext`ymax}/($CellContext`ymax - $CellContext`ymin)}, Attributes[$CellContext`MyManipulator] = { HoldAll}, $CellContext`MyManipulator[ Pattern[$CellContext`var, Blank[]], Pattern[$CellContext`range, Blank[]], Pattern[$CellContext`func, Blank[]], Scale -> Pattern[$CellContext`scale, Blank[]]] := Row[{ Manipulator[ Dynamic[$CellContext`var, $CellContext`func], $CellContext`range], \ $CellContext`PaddedInputField[ Dynamic[$CellContext`var], $CellContext`scale]}, Spacer[5]], $CellContext`MyManipulator[ Pattern[$CellContext`var, Blank[]], Pattern[$CellContext`range, Blank[]], Pattern[$CellContext`func, Blank[]]] := Row[{ Manipulator[ Dynamic[$CellContext`var, $CellContext`func], $CellContext`range], \ $CellContext`PaddedInputField[ Dynamic[$CellContext`var]]}, Spacer[5]], $CellContext`PaddedInputField[ Pattern[$CellContext`x, Blank[]]] := InputField[ Dynamic[ DisplayForm[ StyleBox[ ToString[ $CellContext`MyNumberForm[$CellContext`x]]]], ($CellContext`x = \ #)& ], FieldSize -> 5], $CellContext`PaddedInputField[ Pattern[$CellContext`x, Blank[]], Pattern[$CellContext`p, Blank[]]] := InputField[ Dynamic[ DisplayForm[ RowBox[{ ToString[ $CellContext`MyNumberForm[$CellContext`x/$CellContext`p]], TraditionalForm[$CellContext`p]}]], ($CellContext`x = #)& ], FieldSize -> 5], $CellContext`MyNumberForm[ Pattern[$CellContext`x, Blank[]]] := NumberForm[ N[$CellContext`x, 2], {2, 2}, NumberSigns -> {"-", " "}, ExponentFunction -> (Null& )], $CellContext`AEToRP[ Pattern[$CellContext`st, Blank[]]] := $CellContext`ReparameterizeField[$CellContext`st, \ $CellContext`AngleEllipticity -> $CellContext`RatioPhase], \ $CellContext`ReparameterizeField[{ Pattern[$CellContext`S1, Blank[]], Pattern[$CellContext`S2, Blank[]], Pattern[$CellContext`S3, Blank[]]}, $CellContext`Stokes -> $CellContext`RatioPhase] := { ArcCos[Sqrt[1 + $CellContext`S1]/Sqrt[2]], If[$CellContext`S2 == $CellContext`S3 == 0., Pi/4, ArcTan[$CellContext`S2, $CellContext`S3]]}, \ $CellContext`ReparameterizeField[{ Pattern[$CellContext`\[Chi], Blank[]], Pattern[$CellContext`\[Phi], Blank[]]}, $CellContext`RatioPhase -> $CellContext`Stokes] := { Cos[2 $CellContext`\[Chi]], Cos[$CellContext`\[Phi]] Sin[2 $CellContext`\[Chi]], Sin[$CellContext`\[Phi]] Sin[2 $CellContext`\[Chi]]}, $CellContext`ReparameterizeField[{ Pattern[$CellContext`\[Alpha], Blank[]], Pattern[$CellContext`\[Epsilon], Blank[]]}, $CellContext`AngleEllipticity -> $CellContext`Stokes] := \ {Cos[2 $CellContext`\[Alpha]] Cos[2 $CellContext`\[Epsilon]], Cos[2 $CellContext`\[Epsilon]] Sin[2 $CellContext`\[Alpha]], Sin[2 $CellContext`\[Epsilon]]}, $CellContext`ReparameterizeField[{ Pattern[$CellContext`S1, Blank[]], Pattern[$CellContext`S2, Blank[]], Pattern[$CellContext`S3, Blank[]]}, $CellContext`Stokes -> $CellContext`AngleEllipticity] := \ { If[$CellContext`S1 == $CellContext`S2 == 0., 0, (Sign[$CellContext`S2] + KroneckerDelta[$CellContext`S2]) ArcSin[ Sqrt[ 1/2 - $CellContext`S1/(2 Sqrt[$CellContext`S1^2 + $CellContext`S2^2])]]], ( Sign[$CellContext`S3] + KroneckerDelta[$CellContext`S3]) ArcCos[ Sqrt[ 1/2 + (1/2) Sqrt[$CellContext`S1^2 + $CellContext`S2^2]]]}, \ $CellContext`ReparameterizeField[{ Pattern[$CellContext`\[Chi], Blank[]], Pattern[$CellContext`\[Phi], Blank[]]}, $CellContext`RatioPhase -> \ $CellContext`AngleEllipticity] := $CellContext`ReparameterizeField[ $CellContext`ReparameterizeField[{$CellContext`\[Chi], $CellContext`\ \[Phi]}, $CellContext`RatioPhase -> $CellContext`Stokes], $CellContext`Stokes -> \ $CellContext`AngleEllipticity], $CellContext`ReparameterizeField[{ Pattern[$CellContext`\[Alpha], Blank[]], Pattern[$CellContext`\[Epsilon], Blank[]]}, $CellContext`AngleEllipticity -> \ $CellContext`RatioPhase] := $CellContext`ReparameterizeField[ $CellContext`ReparameterizeField[{$CellContext`\[Alpha], \ $CellContext`\[Epsilon]}, $CellContext`AngleEllipticity -> \ $CellContext`Stokes], $CellContext`Stokes -> $CellContext`RatioPhase], \ $CellContext`AEToS[ Pattern[$CellContext`st, Blank[]]] := $CellContext`ReparameterizeField[$CellContext`st, \ $CellContext`AngleEllipticity -> $CellContext`Stokes], $CellContext`RPToAE[ Pattern[$CellContext`st, Blank[]]] := $CellContext`ReparameterizeField[$CellContext`st, \ $CellContext`RatioPhase -> $CellContext`AngleEllipticity], $CellContext`RPToS[ Pattern[$CellContext`st, Blank[]]] := $CellContext`ReparameterizeField[$CellContext`st, \ $CellContext`RatioPhase -> $CellContext`Stokes], $CellContext`s2 = -1., \ $CellContext`s3 = 0., $CellContext`NS = $CellContext`NormalizeStokes, \ $CellContext`NormalizeStokes[{ Pattern[$CellContext`s1, Blank[]], Pattern[$CellContext`s2, Blank[]], Pattern[$CellContext`s3, Blank[]]}] := Module[{$CellContext`a}, Which[ And[Abs[$CellContext`s2] < 0.01, Abs[$CellContext`s3] < 0.01], { Sqrt[1 - $CellContext`s1^2]/Sqrt[2], Sqrt[1 - $CellContext`s1^2]/ Sqrt[2]}, Abs[$CellContext`s1] == 1., {0., 0.}, True, $CellContext`a = Sqrt[(1 - $CellContext`s1^2)/($CellContext`s2^2 + \ $CellContext`s3^2)]; {$CellContext`s2 $CellContext`a, $CellContext`s3 \ $CellContext`a}]], $CellContext`s1 = -1., $CellContext`SToAE[ Pattern[$CellContext`st, Blank[]]] := $CellContext`ReparameterizeField[$CellContext`st, \ $CellContext`Stokes -> $CellContext`AngleEllipticity], $CellContext`SToRP[ Pattern[$CellContext`st, Blank[]]] := $CellContext`ReparameterizeField[$CellContext`st, \ $CellContext`Stokes -> $CellContext`RatioPhase]}; Typeset`initDone$$ = True), SynchronousInitialization->True, UnsavedVariables:>{Typeset`initDone$$}, UntrackedVariables:>{Typeset`size$$}], "Manipulate", Deployed->True, StripOnInput->False], Manipulate`InterpretManipulate[1]]], "Input"] }, WindowSize->{1367, 759}, WindowMargins->{{51, Automatic}, {Automatic, 64}}, FrontEndVersion->"6.0 for Microsoft Windows (32-bit) (June 19, 2007)", StyleDefinitions->"Default.nb" ] (* End of Notebook Content *) (* Internal cache information *) (*CellTagsOutline CellTagsIndex->{} *) (*CellTagsIndex CellTagsIndex->{} *) (*NotebookFileOutline Notebook[{ Cell[568, 21, 49344, 1043, 658, "Input"] } ] *) (* End of internal cache information *)