Abstract

A general explicit algebraic characterization of Mueller matrices is presented in terms of the non-negativity of a set of leading principal minors of the coherency matrix CA associated with the arrow form MA of a given Mueller matrix M. This result is also formulated through a set of four characteristic Stokes vectors. The particular cases of Mueller matrices with zero degree of polarizance and symmetric Mueller matrices are analyzed.

© 2014 Optical Society of America

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  1. Z.-F. Xing, J. Mod. Opt. 39, 461 (1992).
    [CrossRef]
  2. C. R. Givens and A. B. Kostinski, J. Mod. Opt. 40, 471 (1993).
    [CrossRef]
  3. S.-Y. Lu and R. A. Chipman, J. Opt. Soc. Am. A 13, 1106 (1996).
    [CrossRef]
  4. J. J. Gil, Eur. Phys. J. Appl. Phys. 40, 1 (2007).
    [CrossRef]
  5. J. J. Gil and E. Bernabéu, Opt. Acta 33, 185 (1986).
    [CrossRef]
  6. J. J. Gil, J. Opt. Soc. Am. A 17, 328 (2000).
    [CrossRef]
  7. J. J. Gil, J. Opt. Soc. Am. A 30, 701 (2013).
    [CrossRef]
  8. J. J. Gil, J. Appl. Remote Sens. 8, 081599 (2014).
  9. J. J. Gil, J. Opt. Soc. Am. A 28, 1578 (2011).
    [CrossRef]
  10. J. J. Gil and E. Bernabéu, Optik 76, 67 (1987).
  11. N. Grier Parke, “Matrix optics,” Ph.D. thesis (MIT, 1948).
  12. J. J. Gil and E. Bernabéu, Opt. Acta 32, 259 (1985).
    [CrossRef]
  13. J. J. Gil, “Determination of polarization parameters in matricial representation. Theoretical contribution and development of an automatic measurement device,” Ph.D. thesis (Fac. Ciencias, Univ. Zaragoza, 1983).
  14. S. R. Cloude, Optik 75, 26 (1986).
  15. K. Kim, L. Mandel, and E. Wolf, J. Opt. Soc. Am. A 4, 433 (1987).
    [CrossRef]
  16. J. J. Gil and I. San José, J. Opt. Soc. Am. A 30, 1078 (2013).
    [CrossRef]
  17. R. Barakat, J. Mod. Opt. 34, 1535 (1987).
    [CrossRef]
  18. A. B. Kostinski and R. C. Givens, J. Mod. Opt. 39, 1947 (1992).
    [CrossRef]
  19. R. Simon, J. Mod. Opt. 34, 569 (1987).
    [CrossRef]
  20. C. V. M. van der Mee and J. W. Hovenier, J. Math. Phys. 33, 3574 (1992).
    [CrossRef]
  21. D. I. Nagirner, Astron. Astrophys. 275, 318 (1993).
  22. A. B. Kostinski, C. R. Givens, and J. M. Kwiatkowski, Appl. Opt. 32, 1646 (1993).
    [CrossRef]
  23. C. V. M. van der Mee, J. Math. Phys. 34, 5072 (1993).
    [CrossRef]
  24. R. Sridhar and R. Simon, J. Mod. Opt. 41, 1903 (1994).
    [CrossRef]
  25. A. V. Gopala Rao, K. S. Mallesh, and Sudha, J. Mod. Opt. 45, 955 (1998).
  26. A. V. Gopala Rao, K. S. Mallesh, and Sudha, J. Mod. Opt. 45, 989 (1998).
  27. J. J. Gil, in Light Scattering from Microstructures, Lecture Notes in Physics (Springer, 2000).
  28. B. N. Simon, S. Simon, F. Gori, M. Santarsiero, R. Borghi, N. Mukunda, and R. Simon, Phys. Rev. Lett. 104, 023901 (2010).
    [CrossRef]
  29. B. N. Simon, S. Simon, N. Mukunda, F. Gori, M. Santarsiero, R. Borghi, and R. Simon, J. Opt. Soc. Am. A 27, 188 (2010).
    [CrossRef]
  30. O. Gamel and D. F. V. James, Opt. Lett. 36, 2821 (2011).
    [CrossRef]
  31. R. Ossikovski and V. Devlaminck, Opt. Lett. 39, 1216 (2014).
    [CrossRef]
  32. J. J. Gil, J. M. Correas, P. A. Melero, and C. Ferreira, Monografías Seminario MatemÆtico García de Galdeano 31, 161 (2004).
  33. I. San Jose and J. J. Gil, Opt. Commun. 284, 38 (2011).
    [CrossRef]
  34. J. J. Gil, EPJ Web of Conferences 5, 04002 (2010).
    [CrossRef]
  35. S. R. Cloude, Proc. SPIE 1166, 177 (1989).
    [CrossRef]
  36. S. R. Cloude, Polarisation: Applications in Remote Sensing (Oxford University, 2009).
  37. R. Ossikovski, J. Opt. Soc. Am. A 27, 123 (2010).
    [CrossRef]
  38. R. Ossikovski, J. Opt. Soc. Am. A 26, 1109 (2009).
    [CrossRef]
  39. S.-Y. Lu and R. A. Chipman, J. Opt. Soc. Am. A 11, 766 (1994).
    [CrossRef]

2014

J. J. Gil, J. Appl. Remote Sens. 8, 081599 (2014).

R. Ossikovski and V. Devlaminck, Opt. Lett. 39, 1216 (2014).
[CrossRef]

2013

2011

2010

J. J. Gil, EPJ Web of Conferences 5, 04002 (2010).
[CrossRef]

R. Ossikovski, J. Opt. Soc. Am. A 27, 123 (2010).
[CrossRef]

B. N. Simon, S. Simon, F. Gori, M. Santarsiero, R. Borghi, N. Mukunda, and R. Simon, Phys. Rev. Lett. 104, 023901 (2010).
[CrossRef]

B. N. Simon, S. Simon, N. Mukunda, F. Gori, M. Santarsiero, R. Borghi, and R. Simon, J. Opt. Soc. Am. A 27, 188 (2010).
[CrossRef]

2009

2007

J. J. Gil, Eur. Phys. J. Appl. Phys. 40, 1 (2007).
[CrossRef]

2004

J. J. Gil, J. M. Correas, P. A. Melero, and C. Ferreira, Monografías Seminario MatemÆtico García de Galdeano 31, 161 (2004).

2000

1998

A. V. Gopala Rao, K. S. Mallesh, and Sudha, J. Mod. Opt. 45, 955 (1998).

A. V. Gopala Rao, K. S. Mallesh, and Sudha, J. Mod. Opt. 45, 989 (1998).

1996

1994

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

S.-Y. Lu and R. A. Chipman, J. Opt. Soc. Am. A 11, 766 (1994).
[CrossRef]

1993

D. I. Nagirner, Astron. Astrophys. 275, 318 (1993).

A. B. Kostinski, C. R. Givens, and J. M. Kwiatkowski, Appl. Opt. 32, 1646 (1993).
[CrossRef]

C. V. M. van der Mee, J. Math. Phys. 34, 5072 (1993).
[CrossRef]

C. R. Givens and A. B. Kostinski, J. Mod. Opt. 40, 471 (1993).
[CrossRef]

1992

Z.-F. Xing, J. Mod. Opt. 39, 461 (1992).
[CrossRef]

A. B. Kostinski and R. C. Givens, J. Mod. Opt. 39, 1947 (1992).
[CrossRef]

C. V. M. van der Mee and J. W. Hovenier, J. Math. Phys. 33, 3574 (1992).
[CrossRef]

1989

S. R. Cloude, Proc. SPIE 1166, 177 (1989).
[CrossRef]

1987

K. Kim, L. Mandel, and E. Wolf, J. Opt. Soc. Am. A 4, 433 (1987).
[CrossRef]

R. Simon, J. Mod. Opt. 34, 569 (1987).
[CrossRef]

R. Barakat, J. Mod. Opt. 34, 1535 (1987).
[CrossRef]

J. J. Gil and E. Bernabéu, Optik 76, 67 (1987).

1986

J. J. Gil and E. Bernabéu, Opt. Acta 33, 185 (1986).
[CrossRef]

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

1985

J. J. Gil and E. Bernabéu, Opt. Acta 32, 259 (1985).
[CrossRef]

Barakat, R.

R. Barakat, J. Mod. Opt. 34, 1535 (1987).
[CrossRef]

Bernabéu, E.

J. J. Gil and E. Bernabéu, Optik 76, 67 (1987).

J. J. Gil and E. Bernabéu, Opt. Acta 33, 185 (1986).
[CrossRef]

J. J. Gil and E. Bernabéu, Opt. Acta 32, 259 (1985).
[CrossRef]

Borghi, R.

B. N. Simon, S. Simon, F. Gori, M. Santarsiero, R. Borghi, N. Mukunda, and R. Simon, Phys. Rev. Lett. 104, 023901 (2010).
[CrossRef]

B. N. Simon, S. Simon, N. Mukunda, F. Gori, M. Santarsiero, R. Borghi, and R. Simon, J. Opt. Soc. Am. A 27, 188 (2010).
[CrossRef]

Chipman, R. A.

Cloude, S. R.

S. R. Cloude, Proc. SPIE 1166, 177 (1989).
[CrossRef]

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

S. R. Cloude, Polarisation: Applications in Remote Sensing (Oxford University, 2009).

Correas, J. M.

J. J. Gil, J. M. Correas, P. A. Melero, and C. Ferreira, Monografías Seminario MatemÆtico García de Galdeano 31, 161 (2004).

Devlaminck, V.

Ferreira, C.

J. J. Gil, J. M. Correas, P. A. Melero, and C. Ferreira, Monografías Seminario MatemÆtico García de Galdeano 31, 161 (2004).

Gamel, O.

Gil, J. J.

J. J. Gil, J. Appl. Remote Sens. 8, 081599 (2014).

J. J. Gil and I. San José, J. Opt. Soc. Am. A 30, 1078 (2013).
[CrossRef]

J. J. Gil, J. Opt. Soc. Am. A 30, 701 (2013).
[CrossRef]

J. J. Gil, J. Opt. Soc. Am. A 28, 1578 (2011).
[CrossRef]

I. San Jose and J. J. Gil, Opt. Commun. 284, 38 (2011).
[CrossRef]

J. J. Gil, EPJ Web of Conferences 5, 04002 (2010).
[CrossRef]

J. J. Gil, Eur. Phys. J. Appl. Phys. 40, 1 (2007).
[CrossRef]

J. J. Gil, J. M. Correas, P. A. Melero, and C. Ferreira, Monografías Seminario MatemÆtico García de Galdeano 31, 161 (2004).

J. J. Gil, J. Opt. Soc. Am. A 17, 328 (2000).
[CrossRef]

J. J. Gil and E. Bernabéu, Optik 76, 67 (1987).

J. J. Gil and E. Bernabéu, Opt. Acta 33, 185 (1986).
[CrossRef]

J. J. Gil and E. Bernabéu, Opt. Acta 32, 259 (1985).
[CrossRef]

J. J. Gil, in Light Scattering from Microstructures, Lecture Notes in Physics (Springer, 2000).

J. J. Gil, “Determination of polarization parameters in matricial representation. Theoretical contribution and development of an automatic measurement device,” Ph.D. thesis (Fac. Ciencias, Univ. Zaragoza, 1983).

Givens, C. R.

Givens, R. C.

A. B. Kostinski and R. C. Givens, J. Mod. Opt. 39, 1947 (1992).
[CrossRef]

Gopala Rao, A. V.

A. V. Gopala Rao, K. S. Mallesh, and Sudha, J. Mod. Opt. 45, 989 (1998).

A. V. Gopala Rao, K. S. Mallesh, and Sudha, J. Mod. Opt. 45, 955 (1998).

Gori, F.

B. N. Simon, S. Simon, F. Gori, M. Santarsiero, R. Borghi, N. Mukunda, and R. Simon, Phys. Rev. Lett. 104, 023901 (2010).
[CrossRef]

B. N. Simon, S. Simon, N. Mukunda, F. Gori, M. Santarsiero, R. Borghi, and R. Simon, J. Opt. Soc. Am. A 27, 188 (2010).
[CrossRef]

Grier Parke, N.

N. Grier Parke, “Matrix optics,” Ph.D. thesis (MIT, 1948).

Hovenier, J. W.

C. V. M. van der Mee and J. W. Hovenier, J. Math. Phys. 33, 3574 (1992).
[CrossRef]

James, D. F. V.

Kim, K.

Kostinski, A. B.

A. B. Kostinski, C. R. Givens, and J. M. Kwiatkowski, Appl. Opt. 32, 1646 (1993).
[CrossRef]

C. R. Givens and A. B. Kostinski, J. Mod. Opt. 40, 471 (1993).
[CrossRef]

A. B. Kostinski and R. C. Givens, J. Mod. Opt. 39, 1947 (1992).
[CrossRef]

Kwiatkowski, J. M.

Lu, S.-Y.

Mallesh, K. S.

A. V. Gopala Rao, K. S. Mallesh, and Sudha, J. Mod. Opt. 45, 989 (1998).

A. V. Gopala Rao, K. S. Mallesh, and Sudha, J. Mod. Opt. 45, 955 (1998).

Mandel, L.

Melero, P. A.

J. J. Gil, J. M. Correas, P. A. Melero, and C. Ferreira, Monografías Seminario MatemÆtico García de Galdeano 31, 161 (2004).

Mukunda, N.

B. N. Simon, S. Simon, N. Mukunda, F. Gori, M. Santarsiero, R. Borghi, and R. Simon, J. Opt. Soc. Am. A 27, 188 (2010).
[CrossRef]

B. N. Simon, S. Simon, F. Gori, M. Santarsiero, R. Borghi, N. Mukunda, and R. Simon, Phys. Rev. Lett. 104, 023901 (2010).
[CrossRef]

Nagirner, D. I.

D. I. Nagirner, Astron. Astrophys. 275, 318 (1993).

Ossikovski, R.

San Jose, I.

I. San Jose and J. J. Gil, Opt. Commun. 284, 38 (2011).
[CrossRef]

San José, I.

Santarsiero, M.

B. N. Simon, S. Simon, N. Mukunda, F. Gori, M. Santarsiero, R. Borghi, and R. Simon, J. Opt. Soc. Am. A 27, 188 (2010).
[CrossRef]

B. N. Simon, S. Simon, F. Gori, M. Santarsiero, R. Borghi, N. Mukunda, and R. Simon, Phys. Rev. Lett. 104, 023901 (2010).
[CrossRef]

Simon, B. N.

B. N. Simon, S. Simon, F. Gori, M. Santarsiero, R. Borghi, N. Mukunda, and R. Simon, Phys. Rev. Lett. 104, 023901 (2010).
[CrossRef]

B. N. Simon, S. Simon, N. Mukunda, F. Gori, M. Santarsiero, R. Borghi, and R. Simon, J. Opt. Soc. Am. A 27, 188 (2010).
[CrossRef]

Simon, R.

B. N. Simon, S. Simon, N. Mukunda, F. Gori, M. Santarsiero, R. Borghi, and R. Simon, J. Opt. Soc. Am. A 27, 188 (2010).
[CrossRef]

B. N. Simon, S. Simon, F. Gori, M. Santarsiero, R. Borghi, N. Mukunda, and R. Simon, Phys. Rev. Lett. 104, 023901 (2010).
[CrossRef]

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

R. Simon, J. Mod. Opt. 34, 569 (1987).
[CrossRef]

Simon, S.

B. N. Simon, S. Simon, N. Mukunda, F. Gori, M. Santarsiero, R. Borghi, and R. Simon, J. Opt. Soc. Am. A 27, 188 (2010).
[CrossRef]

B. N. Simon, S. Simon, F. Gori, M. Santarsiero, R. Borghi, N. Mukunda, and R. Simon, Phys. Rev. Lett. 104, 023901 (2010).
[CrossRef]

Sridhar, R.

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

Sudha,

A. V. Gopala Rao, K. S. Mallesh, and Sudha, J. Mod. Opt. 45, 989 (1998).

A. V. Gopala Rao, K. S. Mallesh, and Sudha, J. Mod. Opt. 45, 955 (1998).

van der Mee, C. V. M.

C. V. M. van der Mee, J. Math. Phys. 34, 5072 (1993).
[CrossRef]

C. V. M. van der Mee and J. W. Hovenier, J. Math. Phys. 33, 3574 (1992).
[CrossRef]

Wolf, E.

Xing, Z.-F.

Z.-F. Xing, J. Mod. Opt. 39, 461 (1992).
[CrossRef]

Appl. Opt.

Astron. Astrophys.

D. I. Nagirner, Astron. Astrophys. 275, 318 (1993).

EPJ Web of Conferences

J. J. Gil, EPJ Web of Conferences 5, 04002 (2010).
[CrossRef]

Eur. Phys. J. Appl. Phys.

J. J. Gil, Eur. Phys. J. Appl. Phys. 40, 1 (2007).
[CrossRef]

J. Appl. Remote Sens.

J. J. Gil, J. Appl. Remote Sens. 8, 081599 (2014).

J. Math. Phys.

C. V. M. van der Mee, J. Math. Phys. 34, 5072 (1993).
[CrossRef]

C. V. M. van der Mee and J. W. Hovenier, J. Math. Phys. 33, 3574 (1992).
[CrossRef]

J. Mod. Opt.

R. Barakat, J. Mod. Opt. 34, 1535 (1987).
[CrossRef]

A. B. Kostinski and R. C. Givens, J. Mod. Opt. 39, 1947 (1992).
[CrossRef]

R. Simon, J. Mod. Opt. 34, 569 (1987).
[CrossRef]

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

A. V. Gopala Rao, K. S. Mallesh, and Sudha, J. Mod. Opt. 45, 955 (1998).

A. V. Gopala Rao, K. S. Mallesh, and Sudha, J. Mod. Opt. 45, 989 (1998).

Z.-F. Xing, J. Mod. Opt. 39, 461 (1992).
[CrossRef]

C. R. Givens and A. B. Kostinski, J. Mod. Opt. 40, 471 (1993).
[CrossRef]

J. Opt. Soc. Am. A

Monografías Seminario MatemÆtico García de Galdeano

J. J. Gil, J. M. Correas, P. A. Melero, and C. Ferreira, Monografías Seminario MatemÆtico García de Galdeano 31, 161 (2004).

Opt. Acta

J. J. Gil and E. Bernabéu, Opt. Acta 33, 185 (1986).
[CrossRef]

J. J. Gil and E. Bernabéu, Opt. Acta 32, 259 (1985).
[CrossRef]

Opt. Commun.

I. San Jose and J. J. Gil, Opt. Commun. 284, 38 (2011).
[CrossRef]

Opt. Lett.

Optik

J. J. Gil and E. Bernabéu, Optik 76, 67 (1987).

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

Phys. Rev. Lett.

B. N. Simon, S. Simon, F. Gori, M. Santarsiero, R. Borghi, N. Mukunda, and R. Simon, Phys. Rev. Lett. 104, 023901 (2010).
[CrossRef]

Proc. SPIE

S. R. Cloude, Proc. SPIE 1166, 177 (1989).
[CrossRef]

Other

S. R. Cloude, Polarisation: Applications in Remote Sensing (Oxford University, 2009).

J. J. Gil, in Light Scattering from Microstructures, Lecture Notes in Physics (Springer, 2000).

N. Grier Parke, “Matrix optics,” Ph.D. thesis (MIT, 1948).

J. J. Gil, “Determination of polarization parameters in matricial representation. Theoretical contribution and development of an automatic measurement device,” Ph.D. thesis (Fac. Ciencias, Univ. Zaragoza, 1983).

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Equations (17)

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M=m00(1DTPm^);m^1m00(m11m12m13m21m22m23m31m32m33);D1m00(m01,m02,m03)T,P1m00(m10,m20,m30)T,
PΔ=(D2+P2+m^22)/3,
PP(D2+P2)/2,PSm^2/3.
M=i=1npiMJi;i=1npi=1,
H(M)=14k,l=03mkl(σkσl),
mkl=tr[(σkσl)H].
4C(M)=(m00+m11+m22+m33m01+m10i(m23m32)m02+m20+i(m13m31)m03+m30i(m12m21)m01+m10+i(m23m32)m00+m11m22m33m12+m21+i(m03m30)m13+m31i(m02m20)m02+m20i(m13m31)m12+m21i(m03m30)m00m11+m22m33m23+m32+i(m01m10)m03+m30+i(m12m21)m13+m31+i(m02m20)m23+m32i(m01m10)m00m11m22+m33).
cii=14tr(MMWi);MW0diag(1,1,1,1),MW1diag(1,1,1,1),MW2diag(1,1,1,1),MW3diag(1,1,1,1),
m^=mROmlmRI;mRi1=mRiT(i=I,O),mldiag(l1,l2,l3),
MRi=(10T0mRi),(i=I,O),
MA(M)MROTMMRIT=m00(1DTmRITmROTPmROTm^mRIT)m00(1DATPAdiag(l1,l2,l3));l1l2l30,
4CA(M)=m00(4c0DA1+PA1DA2+PA2DA3+PA3DA1+PA14c1i(DA3PA3)i(DA2PA2)DA2+PA2i(DA3PA3)4c2i(DA1PA1)DA3+PA3i(DA2PA2)i(DA1PA1)4c3);4c01+l1+l2+l3,4c11+l1l2l3,4c21l1+l2l3,4c31l1l2+l3.
m00(1+D)1,m00(1+P)1,
m000,16c0c1(DA1+PA1)216c0c1c2c2(DA1+PA1)2+c1(DA2+PA2)2+c3(DA3PA3)216c0c1c2c3+116(D2P2)2c0c1(DA1PA1)2+c2c3(DA1+PA1)2+c0c2(DA2PA2)2+c1c3(DA2+PA2)2+c0c3(DA3PA3)2+c1c2(DA3+PA3)2.
sc0[m00000],sc1[4c0c1DA1+PA100],sc2[4c0c1c2c2(DA1+PA1)c1(DA2+PA2)c3(DA3PA3)],sc3[256c0c1c2c3+(D2P2)24c0c1(DA1PA1)2+c2c3(DA1+PA1)24c0c2(DA2PA2)2+c1c3(DA2+PA2)24c0c3(DA3PA3)2+c1c2(DA3+PA3)2].
sc0[m00000],sc1[c0c1000],sc2[c0c1c2000],sc3[2c0c1c2c3c2c3DA1c1c3DA2c1c2DA3].
sc0=(m00,0,0,0)T,sc1=cosθ(1,1,0,0)T,sc2=sc3=0.

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