Abstract

I show that the usual definitions of entropy and degree of polarization are not relevant for nonlinear optical waves, because they would lead to the erroneous conclusion that a genuine process of reversible propagation would be characterized by an irreversible process of entropy production. To circumvent this problem, I propose appropriate definitions of entropy and degree of polarization that depend on all the statistical moments of the nonlinear wave, so that they exhibit the satisfactory property to be conserved during a reversible propagation process.

© 2004 Optical Society of America

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References

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  1. E. L. O'Neill, Introduction to Statistical Optics (Dover, New York, 1963).
  2. See, e.g., L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, New York, 1995).
    [CrossRef]
  3. C. Brosseau, Fundamentals of Polarized Light: a Statistical Optics Approach (Wiley, New York, 1998).
  4. R. Barakat, Opt. Commun. 123, 443 (1996).
    [CrossRef]
  5. Yu. P. Svirko and N. I. Zheludev, Phys. Rev. A 50, 709 (1994).
    [CrossRef] [PubMed]
  6. Yu. P. Svirko and N. I. Zheludev, Polarization of Light in Nonlinear Optics (Wiley, New York, 2000).
  7. R. Z. Sagdeev, D. A. Usikov, and G. M. Zaslavsky, Nonlinear Physics (Harwood Academic, Chur, Switzerland, 1988).
  8. A. Wehrl, Rev. Mod. Phys. 50, 221 (1978).
    [CrossRef]
  9. See, e.g., B. Crosignani, B. Daino, and P. Di Porto, J. Opt. Soc. Am. B 3, 1120 (1986).
    [CrossRef]
  10. G. P. Agrawal, Nonlinear Fiber Optics (Academic, New York, 2001).
  11. M. J. W. Hall, Phys. Rev. A 59, 2602 (1999).
    [CrossRef]

1999

M. J. W. Hall, Phys. Rev. A 59, 2602 (1999).
[CrossRef]

1996

R. Barakat, Opt. Commun. 123, 443 (1996).
[CrossRef]

1994

Yu. P. Svirko and N. I. Zheludev, Phys. Rev. A 50, 709 (1994).
[CrossRef] [PubMed]

1986

1978

A. Wehrl, Rev. Mod. Phys. 50, 221 (1978).
[CrossRef]

Agrawal, G. P.

G. P. Agrawal, Nonlinear Fiber Optics (Academic, New York, 2001).

Barakat, R.

R. Barakat, Opt. Commun. 123, 443 (1996).
[CrossRef]

Brosseau, C.

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

Crosignani, B.

Daino, B.

Di Porto, P.

Hall, M. J. W.

M. J. W. Hall, Phys. Rev. A 59, 2602 (1999).
[CrossRef]

Mandel, L.

See, e.g., L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, New York, 1995).
[CrossRef]

O'Neill, E. L.

E. L. O'Neill, Introduction to Statistical Optics (Dover, New York, 1963).

Sagdeev, R. Z.

R. Z. Sagdeev, D. A. Usikov, and G. M. Zaslavsky, Nonlinear Physics (Harwood Academic, Chur, Switzerland, 1988).

Svirko, Yu. P.

Yu. P. Svirko and N. I. Zheludev, Phys. Rev. A 50, 709 (1994).
[CrossRef] [PubMed]

Yu. P. Svirko and N. I. Zheludev, Polarization of Light in Nonlinear Optics (Wiley, New York, 2000).

Usikov, D. A.

R. Z. Sagdeev, D. A. Usikov, and G. M. Zaslavsky, Nonlinear Physics (Harwood Academic, Chur, Switzerland, 1988).

Wehrl, A.

A. Wehrl, Rev. Mod. Phys. 50, 221 (1978).
[CrossRef]

Wolf, E.

See, e.g., L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, New York, 1995).
[CrossRef]

Zaslavsky, G. M.

R. Z. Sagdeev, D. A. Usikov, and G. M. Zaslavsky, Nonlinear Physics (Harwood Academic, Chur, Switzerland, 1988).

Zheludev, N. I.

Yu. P. Svirko and N. I. Zheludev, Phys. Rev. A 50, 709 (1994).
[CrossRef] [PubMed]

Yu. P. Svirko and N. I. Zheludev, Polarization of Light in Nonlinear Optics (Wiley, New York, 2000).

J. Opt. Soc. Am. B

Opt. Commun.

R. Barakat, Opt. Commun. 123, 443 (1996).
[CrossRef]

Phys. Rev. A

Yu. P. Svirko and N. I. Zheludev, Phys. Rev. A 50, 709 (1994).
[CrossRef] [PubMed]

M. J. W. Hall, Phys. Rev. A 59, 2602 (1999).
[CrossRef]

Rev. Mod. Phys.

A. Wehrl, Rev. Mod. Phys. 50, 221 (1978).
[CrossRef]

Other

G. P. Agrawal, Nonlinear Fiber Optics (Academic, New York, 2001).

E. L. O'Neill, Introduction to Statistical Optics (Dover, New York, 1963).

See, e.g., L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, New York, 1995).
[CrossRef]

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

Yu. P. Svirko and N. I. Zheludev, Polarization of Light in Nonlinear Optics (Wiley, New York, 2000).

R. Z. Sagdeev, D. A. Usikov, and G. M. Zaslavsky, Nonlinear Physics (Harwood Academic, Chur, Switzerland, 1988).

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Figures (2)

Fig. 1
Fig. 1

(a) Stretching of probability distribution function ρ due to the nonlinear Kerr precession of the Stokes vectors on the Poincaré sphere. (b) For large propagation distances the important stretching of ρ entails s1=s2=0.

Fig. 2
Fig. 2

Evolution of (a) degree of polarization P and (b) respective entropy W of a partially polarized wave propagating in a Kerr medium [from Eq. (3)]. Initial probability distribution ρz=0,I,ϕ is assumed to be uniform for 0I1;0ϕϕmax and zero elsewhere. Note that P and W tend to the asymptotic values P*=s3=0.5 and WP*, respectively.

Equations (4)

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dsdz=ω×s,
dρdz=ρz+ωnlIρϕ=0.
P2z=s32+cos ϕϕ2+sin ϕϕ2Qz,
PNL=1-A/4π=1-expWG/4π.

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