Jones Calculus
Jones Vectors
ü Linear Horizontal
1
lh = K O;
0
ü Linear Vertical
0
lv = K O;
1
ü Linear at +45 degrees
1
lp45 =
2
1
K O;
1
ü Linear at -45 degrees
1
lm45 =
K
2
1
O;
-1
ü Right Circular
rc =
1
2
K
1
O;
-Â
ü Left Circular
lc =
1
2
1
K O;
Â
ü Right Elliptical
re@ax_, ay_D :=
1
K
ax
O
- Â ay
K
ax
O
 ay
ax2 + ay2
ü Left Elliptical
le@ax_, ay_D :=
1
ax2 + ay2
Jones Matrices
ü Horizontal linear polarizer
hlp = K
1 0
O;
0 0
ü Vertical linear polarizer
vlp = K
0 0
O;
0 1
2 | JonesCalculus.nb
Optics 513 - James C. Wyant
ü Linear polarizer at + 45 degrees
lpp45 =
1
2
K
1 1
O;
1 1
ü Linear polarizer at - 45 degrees
lpm45 =
1
2
K
1 -1
O;
-1 1
ü Quarter-wave plate with fast axis vertical
qfav = ‰Â pê4 K
1 0
O;
0 -Â
ü Quarter-wave plate with fast axis horizontal
qfah = ‰-Â pê4 K
1 0
O;
0 Â
ü Retarder with fast axis vertical
rfav@f_D := ‰Â fê2
1
0
0 ‰-Â f
ü Retarder with fast axis horizontal
rfah@f_D := ‰-Â fê2
1 0
0 ‰Â f
Rotation Matrix
rot@q_D := K
Cos@qD Sin@qD
O
- Sin@qD Cos@qD
Rotated Matrix = rot@- qD R@0 °D rot@qD;
OutputPolarization = rot@- qD R@0 °D rot@qD InputPolarization;
ü Calculation of matrix of a retarder of retardation f having a fast axis at an angle q from the
horizontal
rrot@f_, q_D := FullSimplify@rot@- [email protected]@qDD;
MatrixForm@rrot@f, qDD
‰
-
Âf
2
f
2
ICos@qD2 + ‰Â f Sin@qD2 M
f
2
- Â Sin@2 qD SinA E
- Â Sin@2 qD SinA E
‰
-
Âf
2
I‰Â f Cos@qD2 + Sin@qD2 M