Abstract

The evolution of a polarized beam can be described by the differential formulation of Mueller calculus. The nondepolarizing differential Mueller matrices are well known. However, they only account for 7 out of the 16 independent parameters that are necessary to model a general anisotropic depolarizing medium. In this work we present the nine differential Mueller matrices for general depolarizing media, highlighting the physical implications of each of them. Group theory is applied to establish the relationship between the differential matrix and the set of transformation generators in the Minkowski space, of which Lorentz generators constitute a particular subgroup.

© 2011 Optical Society of America

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References

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2011 (2)

N. Ortega-Quijano, F. Fanjul-Vélez, I. Salas-García, and J. L. Arce-Diego, Proc. SPIE 7906, 790612 (2011).
[CrossRef]

N. Ortega-Quijano and J. L. Arce-Diego, Opt. Lett. 36, 1942 (2011).
[CrossRef] [PubMed]

2010 (1)

2009 (1)

2003 (1)

D. Goldstein, Polarized Light (Marcel Dekker, 2003).
[CrossRef]

1998 (1)

C. Brosseau, Polarized Light (Wiley, 1998).

1997 (1)

D. Han, Y. S. Kim, and M. E. Noz, Phys. Rev. E 56, 6065 (1997).
[CrossRef]

1996 (1)

1995 (2)

C. Brosseau, Opt. Lett. 20, 1221 (1995).
[CrossRef] [PubMed]

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University, 1995).

1994 (2)

F. Muhammad and C. S. Brown, Proc. SPIE 2265, 337 (1994).
[CrossRef]

R. Sridhar and R. Simon, J. Mod. Opt. 41, 1903 (1994).
[CrossRef]

1986 (1)

S. R. Cloude, Optik 75, 26 (1986).

1978 (1)

1948 (1)

Arce-Diego, J. L.

N. Ortega-Quijano and J. L. Arce-Diego, Opt. Lett. 36, 1942 (2011).
[CrossRef] [PubMed]

N. Ortega-Quijano, F. Fanjul-Vélez, I. Salas-García, and J. L. Arce-Diego, Proc. SPIE 7906, 790612 (2011).
[CrossRef]

Azzam, R. M. A.

Barakat, R.

Brosseau, C.

C. Brosseau, Polarized Light (Wiley, 1998).

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[CrossRef] [PubMed]

Brown, C. S.

F. Muhammad and C. S. Brown, Proc. SPIE 2265, 337 (1994).
[CrossRef]

Cloude, S. R.

S. R. Cloude, Optik 75, 26 (1986).

De Martino, A.

Devlaminck, V.

Fallet, C.

Fanjul-Vélez, F.

N. Ortega-Quijano, F. Fanjul-Vélez, I. Salas-García, and J. L. Arce-Diego, Proc. SPIE 7906, 790612 (2011).
[CrossRef]

Foldyna, M.

Goldstein, D.

D. Goldstein, Polarized Light (Marcel Dekker, 2003).
[CrossRef]

Han, D.

D. Han, Y. S. Kim, and M. E. Noz, Phys. Rev. E 56, 6065 (1997).
[CrossRef]

Jones, C. R.

Kim, Y. S.

D. Han, Y. S. Kim, and M. E. Noz, Phys. Rev. E 56, 6065 (1997).
[CrossRef]

Mandel, L.

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University, 1995).

Muhammad, F.

F. Muhammad and C. S. Brown, Proc. SPIE 2265, 337 (1994).
[CrossRef]

Noz, M. E.

D. Han, Y. S. Kim, and M. E. Noz, Phys. Rev. E 56, 6065 (1997).
[CrossRef]

Ortega-Quijano, N.

N. Ortega-Quijano, F. Fanjul-Vélez, I. Salas-García, and J. L. Arce-Diego, Proc. SPIE 7906, 790612 (2011).
[CrossRef]

N. Ortega-Quijano and J. L. Arce-Diego, Opt. Lett. 36, 1942 (2011).
[CrossRef] [PubMed]

Ossikovski, R.

Salas-García, I.

N. Ortega-Quijano, F. Fanjul-Vélez, I. Salas-García, and J. L. Arce-Diego, Proc. SPIE 7906, 790612 (2011).
[CrossRef]

Simon, R.

R. Sridhar and R. Simon, J. Mod. Opt. 41, 1903 (1994).
[CrossRef]

Sridhar, R.

R. Sridhar and R. Simon, J. Mod. Opt. 41, 1903 (1994).
[CrossRef]

Wolf, E.

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University, 1995).

J. Mod. Opt. (1)

R. Sridhar and R. Simon, J. Mod. Opt. 41, 1903 (1994).
[CrossRef]

J. Opt. Soc. Am. (2)

J. Opt. Soc. Am. A (2)

Opt. Lett. (3)

Optik (1)

S. R. Cloude, Optik 75, 26 (1986).

Phys. Rev. E (1)

D. Han, Y. S. Kim, and M. E. Noz, Phys. Rev. E 56, 6065 (1997).
[CrossRef]

Proc. SPIE (2)

F. Muhammad and C. S. Brown, Proc. SPIE 2265, 337 (1994).
[CrossRef]

N. Ortega-Quijano, F. Fanjul-Vélez, I. Salas-García, and J. L. Arce-Diego, Proc. SPIE 7906, 790612 (2011).
[CrossRef]

Other (3)

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University, 1995).

C. Brosseau, Polarized Light (Wiley, 1998).

D. Goldstein, Polarized Light (Marcel Dekker, 2003).
[CrossRef]

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Equations (31)

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d S / d z = m S ,
m = lim Δ z 0 [ ( M z , Δ z I ) / Δ z ] ,
M = exp ( m z ) .
m 1 = κ i K i = κ i I ,
m 2 = κ q K q = κ q [ 0 1 0 0 ; 1 0 0 0 ; 0 0 0 0 ; 0 0 0 0 ] ,
m 3 = κ u K u = κ u [ 0 0 1 0 ; 0 0 0 0 ; 1 0 0 0 ; 0 0 0 0 ] ,
m 4 = κ v K v = κ v [ 0 0 0 1 ; 0 0 0 0 ; 0 0 0 0 ; 1 0 0 0 ] ,
m 5 = η q H q = η q [ 0 0 0 0 ; 0 0 0 0 ; 0 0 0 1 ; 0 0 1 0 ] ,
m 6 = η u H u = η u [ 0 0 0 0 ; 0 0 0 1 ; 0 0 0 0 ; 0 1 0 0 ] ,
m 7 = η v H v = η v [ 0 0 0 0 ; 0 0 1 0 ; 0 1 0 0 ; 0 0 0 0 ] ,
m nd = n = 1 7 m n = [ κ i κ q κ u κ v κ q κ i η v η u κ u η v κ i η q κ v η u η q κ i ] .
Λ ( 1 / 2 , 1 / 2 ) = exp ( j = 1 3 κ j K j + η j H j ) ,
S = Λ ( 1 / 2 , 1 / 2 ) S ,
diag [ 1 , 1 , 1 , exp ( κ i , v ) ] ,
m 8 = κ i , q D q = κ i , q · diag [ 0 , 1 , 0 , 0 ] ,
m 9 = κ i , u D u = κ i , u · diag [ 0 , 0 , 1 , 0 ] ,
m 10 = κ i , v D v = κ i , v · diag [ 0 , 0 , 0 , 1 ] .
K q = [ 0 1 0 0 ; 1 0 0 0 ; 0 0 0 0 ; 0 0 0 0 ] ,
K u = [ 0 0 1 0 ; 0 0 0 0 ; 1 0 0 0 ; 0 0 0 0 ] ,
K v = [ 0 0 0 1 ; 0 0 0 0 ; 0 0 0 0 ; 1 0 0 0 ] ,
H q = [ 0 0 0 0 ; 0 0 0 0 ; 0 0 0 1 ; 0 0 1 0 ] ,
H u = [ 0 0 0 0 ; 0 0 0 1 ; 0 0 0 0 ; 0 1 0 0 ] ,
H v = [ 0 0 0 0 ; 0 0 1 0 ; 0 1 0 0 ; 0 0 0 0 ] .
G = [ 1 0 0 0 0 A + a q 2 ( 1 A ) a q a u ( 1 A ) a q a v ( 1 A ) 0 a q a u ( 1 A ) A + a u 2 ( 1 A ) a u a v ( 1 A ) 0 a q a v ( 1 A ) a u a v ( 1 A ) A + a v 2 ( 1 A ) ] ,
m 11 = κ q K q ,
m 12 = κ u K u ,
m 13 = κ v K v ,
m 14 = η q H q ,
m 15 = η u H u ,
m 16 = η v H v ,
m = n = 1 16 m n = [ κ i κ q + κ q κ u + κ u κ v + κ v κ q κ q κ i κ i , q η v + η v η u + η u κ u κ u η v + η v κ i κ i , u η q + η q κ v κ v η u + η u η q + η q κ i κ i , v ] .

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