Appendix BJones and Mueller Matrices

Appendix B
Jones and Mueller Matrices

1
0

Jones matrix for free space

0
1

!
ðB:1Þ

Jones matrix for an isotropic absorbing material whose transmittance is p2
!
p 0
ðB:2Þ
0 p
!

1

0

0

0

Jones matrix for linear polarizer at 908

0
0

0
1

Jones matrix for linear polarizer at 458

1 1
2 1

1
1

Jones matrix for linear polarizer at 08

ðB:3Þ
!
ðB:4Þ

!

Jones matrix for a right circular polarizer

1 1 i
2 Ài 1

Jones matrix for a left circular polarizer

1 1

2 i

Jones matrix for a linear retarder at angle 
"

Copyright © 2003 by Marcel Dekker, Inc. All Rights Reserved.

Ài
1

ðB:5Þ
!
ðB:6Þ
!

cos2 

cos  sin 

cos  sin 

sin2 

ðB:7Þ

#
ðB:8Þ


Jones matrix for linear retarder with fast axis at angle  and retardation 

"
#
ei cos2  þ sin2  ðei À 1Þ sin  cos 
ðB:9Þ
ðei À 1Þ sin  cos  ei sin2  þ cos2 
Jones matrix for quarter wave linear retarder with fast axis at 08
"
#
0
ei=4
0
eÀi=4
0
1

Jones matrix for half-wave retarder with fast axis at 458
2

1
60
6
40
0

Mueller matrix for free space

0
1
0
0

1
0

ðB:10Þ
!
ðB:11Þ

3
0
07
7
05
1

0
0
1
0

ðB:12Þ

Mueller matrix for an isotropic absorbing material whose transmittance is k
2
3
k 0 0 0
60 k 0 07
6
7
ðB:13Þ

6
7
40 0 k 05
0

0

0

k

Mueller matrix for a linear polarizer at angle 
2
1
cos 2
sin 2
2
6
2
cos
2 sin 2
cos
2
cos
16
6
2 4 sin 2 cos 2 sin 2
sin2 2
0

0

0
2

Mueller matrix for a horizontal linear polarizer

1
16
61
240
0
2

Mueller matrix for a vertical linear polarizer

1
16
À1
6
24 0
0

0

3

07
7
7

05

ðB:14Þ

1

1
1
0
0

0
0
0
0

À1
1
0
0

3
0
07
7
05
0

0
0

0
0

ðB:15Þ

3
0
07
7
05
0
ðB:16Þ

Copyright © 2003 by Marcel Dekker, Inc. All Rights Reserved.


2

1
16
60
241
0

Mueller matrix for a linear polarizer at 458

0
0
0
0

2

1
16
60
240
1

Mueller matrix for a right circular polarizer

2

Mueller matrix for a left circular polarizer

1
16
6 0
24 0
À1

1
0
1
0

3
0
07
7

05
0

ðB:17Þ

0
0
0
0

0
0
0
0

3
1
07
7
05
1

ðB:18Þ

0
0
0
0

0

0
0
0

3
À1
0 7
7
0 5
1

ðB:19Þ

Mueller matrix for a linear retarder with fast axis at angle  and retardation 
2
3
1
0
0
0
6 0 cos2 2 þ sin2 2 cos  ð1 À cos Þ sin 2 cos 2 À sin 2 sin  7
6
7
ðB:20Þ
6
7
4 0 ð1 À cos Þ sin 2 cos 2 sin2 2 þ cos2 2 cos  cos 2 sin  5
0

sin 2 sin 

À cos 2 sin 

cos 
2

1
60
6
40
0

Linear quarter wave retarder with fast axis at 08

2
Linear half-wave retarder with fast axis at 458

Copyright © 2003 by Marcel Dekker, Inc. All Rights Reserved.

1
60
6
40
0

0
1
0
0

0
À1
0
0

3
0
07
7
15
0

ðB:21Þ

3
0 0
0 0 7
7
1 0 5
0 À1

ðB:22Þ

0
0
0
À1