Polarization

David McIntyre
9 March 2017

Initialization

SetOptions[Plot,BaseStyle->{FontFamily->"Arial",FontSize->12},PlotStyle->{{Black,AbsoluteThickness[1.5]}},AxesStyle->{{Black,AbsoluteThickness[0.5]},{Black,AbsoluteThickness[0.5]}},TicksStyle->{{Black,AbsoluteThickness[0.5]},{Black,AbsoluteThickness[0.5]}}];

SetOptions[ParametricPlot,BaseStyle->{FontFamily->"Arial",FontSize->16},PlotStyle->{{Black,AbsoluteThickness[1.5]}},AxesStyle->{{Black,AbsoluteThickness[0.5]},{Black,AbsoluteThickness[0.5]}},TicksStyle->{{Black,AbsoluteThickness[0.5]},{Black,AbsoluteThickness[0.5]}}];

SetOptions[ParametricPlot3D,BaseStyle->{FontFamily->"Arial",FontSize->16},PlotStyle->{{Black,AbsoluteThickness[1.5]}}];

Off[General::spell]

Off[General::spell1]

imgsz=600;

ctrl-9 to start inline formula and ctrl-0 to end. ctrl-_ to begin subscript, ctrl-space to end. esc-alpha-esc to enter Greek letters.  Spell checker for symbol names turned off since many have similar names.

Polarization

Ex[t_]:=Sin[2*π*t]
Ey[t_]:=Sin[2*π*t-π/4]

t=0;
Graphics[{AbsoluteThickness[4],Red,Arrowheads[0.1],Arrow[{{0,0},{Ex[t],Ey[t]}}]}]

z=1/16;
ParametricPlot[{Ex[t],Ey[t]},{t,0,1},AxesLabel->{"(Subscript[E, x])","(Subscript[E, y])"},Epilog->{AbsoluteThickness[4],Red,Arrowheads[0.1],Arrow[{{0,0},{Ex[z],Ey[z]}}]}]

Ex[t_]:=Sin[2*π*t]
Ey[t_]:=Sin[2*π*t-δ]
δ=π/4;
ParametricPlot[{Ex[t],Ey[t]},{t,0,1},AxesLabel->{"(Subscript[E, x])","(Subscript[E, y])"},ImageSize->600,Epilog->{Arrowheads[0.1],
 (* t=0 arrow *) AbsoluteThickness[4],Arrow[{{0,0},{Ex[0],Ey[0]}}],
 (* t=T/4 arrow *)Dashing[Large], Arrow[{{0,0},{Ex[0.25],Ey[0.25]}}]}]

Ex[t_]:=Sin[2*π*t]
Ey[t_]:=Sin[2*π*t-δ]
δ=π/4;
ParametricPlot[{Ex[t],Ey[t]},{t,0,1},AxesLabel->{"(Subscript[E, x])","(Subscript[E, y])"},ImageSize->600,Epilog->{Arrowheads[0.1],
 (* t min arrow *) AbsoluteThickness[4],Arrow[{{0,0},{Ex[δ/(4*π)],Ey[δ/(4*π)]}}],
 (* t max arrow *)Dashing[Large], Arrow[{{0,0},{Ex[(δ+π)/(4*π)],Ey[(δ+π)/(4*π)]}}]}]

Ex[t_]:=Cos[2*π*t]
Ey[t_]:=Cos[2*π*t+δ]
δ=π/2;
ParametricPlot[{Ex[t],Ey[t]},{t,0,1},AxesLabel->{"(Subscript[E, x])","(Subscript[E, y])"},ImageSize->600,Epilog->{Arrowheads[0.1],
 (* t=0 arrow *) AbsoluteThickness[4],Arrow[{{0,0},{Ex[0],Ey[0]}}],
 (* t=T/4 arrow *)Dashing[Large], Arrow[{{0,0},{Ex[0.25],Ey[0.25]}}]}]

Manipulate[ParametricPlot[{Ex[t],Ey[t]},{t,0,1},Epilog->{AbsoluteThickness[4],Red,Arrowheads[0.1],Arrow[{{0,0},{Ex[z],Ey[z]}}]}],{z,0,1}]

E3y[x_,t_]:=Cos[x-2*π*t]
E3z[x_,t_]:=Cos[x-2*π*t-π/2]

ParametricPlot3D[{x,E3y[x,0],E3z[x,0]},{x,0,10}]

ParametricPlot3D[{{x,0,E3z[x,0]},{x,E3y[x,0],0}},{x,0,10},BoxRatios->{2,1,1}]

ParametricPlot3D[Evaluate[{x,0,E3z[x,0]}*v+{x,0,0}*(1-v)],{x,0,10},{v,0,1},Mesh->None,PlotStyle->Opacity[0.2],BoxRatios->{2,1,1}]

Show[ParametricPlot3D[{{x,0,E3z[x,0]},{x,E3y[x,0],0}},{x,0,10},BoxRatios->{2,1,1},PlotStyle->{{Red,AbsoluteThickness[2]},{Blue,AbsoluteThickness[2]}},ImageSize->600],
Graphics3D[{Black,Line[{{0,0,0},{10,0,0}}],Arrowheads[0.015],AbsoluteThickness[1],
Red,Table[Arrow[{{i,0,0},{i,0,E3z[i,0]}}],{i,0,10,0.4}],
Blue,Table[Arrow[{{i,0,0},{i,E3y[i,0],0}}],{i,0,10,0.4}]}],ParametricPlot3D[Evaluate[{x,0,E3z[x,0]}*v+{x,0,0}*(1-v)],{x,0,10},{v,0,1},Mesh->None,PlotStyle->{Red,Opacity[0.2]},BoxRatios->{2,1,1}],
ParametricPlot3D[Evaluate[{x,E3y[x,0],0}*v+{x,0,0}*(1-v)],{x,0,10},{v,0,1},Mesh->None,PlotStyle->{Blue,Opacity[0.2]},BoxRatios->{2,1,1}]]

xlength=15;
Show[ParametricPlot3D[{{x,0,E3z[x,0]},{x,E3y[x,0],0},{x,E3y[x,0],E3z[x,0]}},{x,0,xlength},BoxRatios->{2,1,1},PlotStyle->{{Red,AbsoluteThickness[0.5]},{Blue,AbsoluteThickness[0.5]},{Black,AbsoluteThickness[4]}},ImageSize->600],
Graphics3D[{Black,Line[{{0,0,0},{xlength,0,0}}],Arrowheads[0.006],AbsoluteThickness[0.5],
Red,Table[Arrow[{{i,0,0},{i,0,E3z[i,0]}}],{i,0,xlength,0.4}],
Blue,Table[Arrow[{{i,0,0},{i,E3y[i,0],0}}],{i,0,xlength,0.4}],
Black,Arrowheads[0.012],AbsoluteThickness[1],Table[Arrow[{{i,0,0},{i,E3y[i,0],E3z[i,0]}}],{i,0,xlength,0.4}]}],ParametricPlot3D[Evaluate[{x,0,E3z[x,0]}*v+{x,0,0}*(1-v)],{x,0,xlength},{v,0,1},Mesh->None,PlotStyle->{Red,Opacity[0.2]},BoxRatios->{2,1,1}],
ParametricPlot3D[Evaluate[{x,E3y[x,0],0}*v+{x,0,0}*(1-v)],{x,0,xlength},{v,0,1},Mesh->None,PlotStyle->{Blue,Opacity[0.2]},BoxRatios->{2,1,1}]]

θ=0.5
xlength=15;
Show[ParametricPlot3D[{x,E3y[x,0],E3z[x,0]},{x,0,xlength},BoxRatios->{2,1,1},PlotStyle->{Black,AbsoluteThickness[4]},ViewPoint->{20*Sin[θ],-20*Cos[θ],2},ImageSize->{600,600}],
Graphics3D[{Black,Line[{{0,0,0},{xlength,0,0}}],
Black,Arrowheads[0.012],AbsoluteThickness[1],Table[Arrow[{{i,0,0},{i,E3y[i,0],E3z[i,0]}}],{i,0,xlength,0.4}]}]]

Manipulate[
xlength=15;
Show[ParametricPlot3D[{x,E3y[x,0],E3z[x,0]},{x,0,xlength},BoxRatios->{2,1,1},PlotStyle->{Black,AbsoluteThickness[4]},ViewPoint->{20*Sin[θ],-20*Cos[θ],2},ImageSize->{600,600}],
Graphics3D[{Black,Line[{{0,0,0},{xlength,0,0}}],
Black,Arrowheads[0.012],AbsoluteThickness[1],Table[Arrow[{{i,0,0},{i,E3y[i,0],E3z[i,0]}}],{i,0,xlength,0.4}]}]],{θ,0,π/2}]

New Feb 2019

δ=π/2;
E3y[x_,t_]:=Cos[x-2*π*t]
E3z[x_,t_]:=Cos[x-2*π*t+δ]

Show[ParametricPlot3D[{{x,0,E3z[x,0]},{x,E3y[x,0],0}},{x,0,10},BoxRatios->{2,1,1},PlotStyle->{{Red,AbsoluteThickness[2]},{Blue,AbsoluteThickness[2]}},ImageSize->600],
Graphics3D[{Black,Line[{{0,0,0},{10,0,0}}],Arrowheads[0.015],AbsoluteThickness[1],
Red,Table[Arrow[{{i,0,0},{i,0,E3z[i,0]}}],{i,0,10,0.4}],
Blue,Table[Arrow[{{i,0,0},{i,E3y[i,0],0}}],{i,0,10,0.4}]}],ParametricPlot3D[Evaluate[{x,0,E3z[x,0]}*v+{x,0,0}*(1-v)],{x,0,10},{v,0,1},Mesh->None,PlotStyle->{Red,Opacity[0.2]},BoxRatios->{2,1,1}],
ParametricPlot3D[Evaluate[{x,E3y[x,0],0}*v+{x,0,0}*(1-v)],{x,0,10},{v,0,1},Mesh->None,PlotStyle->{Blue,Opacity[0.2]},BoxRatios->{2,1,1}]]

xlength=15;
Show[ParametricPlot3D[{{x,0,E3z[x,0]},{x,E3y[x,0],0},{x,E3y[x,0],E3z[x,0]}},{x,0,xlength},BoxRatios->{2,1,1},PlotStyle->{{Red,AbsoluteThickness[0.5]},{Blue,AbsoluteThickness[0.5]},{Black,AbsoluteThickness[4]}},ImageSize->600],
Graphics3D[{Black,Line[{{0,0,0},{xlength,0,0}}],Arrowheads[0.006],AbsoluteThickness[0.5],
Red,Table[Arrow[{{i,0,0},{i,0,E3z[i,0]}}],{i,0,xlength,0.4}],
Blue,Table[Arrow[{{i,0,0},{i,E3y[i,0],0}}],{i,0,xlength,0.4}],
Black,Arrowheads[0.012],AbsoluteThickness[1],Table[Arrow[{{i,0,0},{i,E3y[i,0],E3z[i,0]}}],{i,0,xlength,0.4}]}],ParametricPlot3D[Evaluate[{x,0,E3z[x,0]}*v+{x,0,0}*(1-v)],{x,0,xlength},{v,0,1},Mesh->None,PlotStyle->{Red,Opacity[0.2]},BoxRatios->{2,1,1}],
ParametricPlot3D[Evaluate[{x,E3y[x,0],0}*v+{x,0,0}*(1-v)],{x,0,xlength},{v,0,1},Mesh->None,PlotStyle->{Blue,Opacity[0.2]},BoxRatios->{2,1,1}]]

θ=0.5;
xlength=15;
Show[ParametricPlot3D[{x,E3y[x,0],E3z[x,0]},{x,0,xlength},BoxRatios->{2,1,1},PlotStyle->{Black,AbsoluteThickness[4]},ViewPoint->{20*Sin[θ],-20*Cos[θ],2},ImageSize->{600,600}],
Graphics3D[{Black,Line[{{0,0,0},{xlength,0,0}}],
Black,Arrowheads[0.012],AbsoluteThickness[1],Table[Arrow[{{i,0,0},{i,E3y[i,0],E3z[i,0]}}],{i,0,xlength,0.4}]}]]

Manipulate[ParametricPlot[{E3y[0,t],E3z[0,t]},{t,0,1},Epilog->{AbsoluteThickness[4],Red,Arrowheads[0.1],Arrow[{{0,0},{E3y[0,t],E3z[0,t]}}]}],{t,0,1}]