Abstract

We discuss the degrees of polarization (DoP) of electromagnetic beams in time and frequency domains. The mean spectral DoP corresponds to the maximal temporal DoP when unitary transformations are applied in frequency domain. We demonstrate that random unitary transformations in frequency domain cannot increase the mean spectral DoP, implying that this quantity is a useful measure of the polarization order of light beams. This leads to a classification of time-domain polarization changes into reversible and irreversible processes.

© 2012 Optical Society of America

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References

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  1. J. W. Goodman, Statistical Optics (Wiley, 1985).
  2. L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge Univ. Press, 1995).
  3. C. Brosseau, Fundamentals of Polarized Light: A Statistical Optics Approach (Wiley, 1998).
  4. T. Setälä, F. Nunziata, and A. T. Friberg, Opt. Lett. 34, 2924 (2009).
    [CrossRef]
  5. M. Lahiri, Opt. Lett. 34, 2936 (2009).
    [CrossRef]
  6. T. Setälä, F. Nunziata, and A. T. Friberg, in Information Optics and Photonics: Algorithms, Systems, and Applications, T. Fournel and B. Javidi, eds. (Springer, 2010), Chap. 16.
  7. Ph. Réfrégier, T. Setälä, and A. T. Friberg, Proc. SPIE 8171, 817102 (2011).
    [CrossRef]
  8. J. Tervo, T. Setälä, and A. T. Friberg, J. Opt. Soc. Am. A 21, 2205 (2004).
    [CrossRef]
  9. Ph. Réfrégier and A. Luis, J. Opt. Soc. Am. A 25, 2749 (2008).
    [CrossRef]
  10. Ph. Réfrégier, Opt. Lett. 37, 428 (2012).
    [CrossRef]
  11. A. Shevchenko, T. Setälä, M. Kaivola, and A. T. Friberg, New J. Phys. 11, 073004 (2009).
    [CrossRef]
  12. G. A. F. Seber, A Matrix Handbook for Statisticians (Wiley, 2008), 12.18(b).

2012 (1)

2011 (1)

Ph. Réfrégier, T. Setälä, and A. T. Friberg, Proc. SPIE 8171, 817102 (2011).
[CrossRef]

2009 (3)

2008 (1)

2004 (1)

Brosseau, C.

C. Brosseau, Fundamentals of Polarized Light: A Statistical Optics Approach (Wiley, 1998).

Friberg, A. T.

Ph. Réfrégier, T. Setälä, and A. T. Friberg, Proc. SPIE 8171, 817102 (2011).
[CrossRef]

A. Shevchenko, T. Setälä, M. Kaivola, and A. T. Friberg, New J. Phys. 11, 073004 (2009).
[CrossRef]

T. Setälä, F. Nunziata, and A. T. Friberg, Opt. Lett. 34, 2924 (2009).
[CrossRef]

J. Tervo, T. Setälä, and A. T. Friberg, J. Opt. Soc. Am. A 21, 2205 (2004).
[CrossRef]

T. Setälä, F. Nunziata, and A. T. Friberg, in Information Optics and Photonics: Algorithms, Systems, and Applications, T. Fournel and B. Javidi, eds. (Springer, 2010), Chap. 16.

Goodman, J. W.

J. W. Goodman, Statistical Optics (Wiley, 1985).

Kaivola, M.

A. Shevchenko, T. Setälä, M. Kaivola, and A. T. Friberg, New J. Phys. 11, 073004 (2009).
[CrossRef]

Lahiri, M.

Luis, A.

Mandel, L.

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

Nunziata, F.

T. Setälä, F. Nunziata, and A. T. Friberg, Opt. Lett. 34, 2924 (2009).
[CrossRef]

T. Setälä, F. Nunziata, and A. T. Friberg, in Information Optics and Photonics: Algorithms, Systems, and Applications, T. Fournel and B. Javidi, eds. (Springer, 2010), Chap. 16.

Réfrégier, Ph.

Seber, G. A. F.

G. A. F. Seber, A Matrix Handbook for Statisticians (Wiley, 2008), 12.18(b).

Setälä, T.

Ph. Réfrégier, T. Setälä, and A. T. Friberg, Proc. SPIE 8171, 817102 (2011).
[CrossRef]

A. Shevchenko, T. Setälä, M. Kaivola, and A. T. Friberg, New J. Phys. 11, 073004 (2009).
[CrossRef]

T. Setälä, F. Nunziata, and A. T. Friberg, Opt. Lett. 34, 2924 (2009).
[CrossRef]

J. Tervo, T. Setälä, and A. T. Friberg, J. Opt. Soc. Am. A 21, 2205 (2004).
[CrossRef]

T. Setälä, F. Nunziata, and A. T. Friberg, in Information Optics and Photonics: Algorithms, Systems, and Applications, T. Fournel and B. Javidi, eds. (Springer, 2010), Chap. 16.

Shevchenko, A.

A. Shevchenko, T. Setälä, M. Kaivola, and A. T. Friberg, New J. Phys. 11, 073004 (2009).
[CrossRef]

Tervo, J.

Wolf, E.

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

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

New J. Phys. (1)

A. Shevchenko, T. Setälä, M. Kaivola, and A. T. Friberg, New J. Phys. 11, 073004 (2009).
[CrossRef]

Opt. Lett. (3)

Proc. SPIE (1)

Ph. Réfrégier, T. Setälä, and A. T. Friberg, Proc. SPIE 8171, 817102 (2011).
[CrossRef]

Other (5)

G. A. F. Seber, A Matrix Handbook for Statisticians (Wiley, 2008), 12.18(b).

J. W. Goodman, Statistical Optics (Wiley, 1985).

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

C. Brosseau, Fundamentals of Polarized Light: A Statistical Optics Approach (Wiley, 1998).

T. Setälä, F. Nunziata, and A. T. Friberg, in Information Optics and Photonics: Algorithms, Systems, and Applications, T. Fournel and B. Javidi, eds. (Springer, 2010), Chap. 16.

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Equations (16)

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S(ω)=12πΓ(τ)eiωτdτ.
P2=14detΓPtr2ΓP,P2(ω)=14detS(ω)tr2S(ω),
ΓP=0S(ω)dω.
S0(ω)=λ2(ω)I+P(ω)s(ω)M,
Γ0(τ)=α(τ)I+β(τ)M,
P¯ω=0P(ω)s(ω)dω0s(ω)dω,
ΔI=I0|ΔP¯ω|/[1+P¯ω(E)],
SE(ω)=s(ω)2(1111).
SA(ω)=s(ω)2(1eiϕ(ω)eiϕ(ω)1).
P¯ω(A)=10s(ω)dω0s(ω)|eiϕ(ω)|dω<1.
SA(ω)=λ2(ω)I+P(ω)s(ω)MA(ω),
ΓP,A=α(0)I+β(0)0w(ω)MA(ω)dω,
det[0w(ω)MA(ω)dω]0.
ΔI=0[δλ1(ω)+δλ2(ω)]dω.
[I0ΔI]P¯ω(B)=I0P¯ω(A)0[δλ1(ω)δλ2(ω)]dω.
ΔI=I0(ΔP¯ω)/[1+P¯ω(E)],

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