Abstract

A method is described, based on a recently formulated unified theory of coherence and polarization, for determining the changes that the degree of polarization, the degree of coherence, and the spectrum of a random electromagnetic beam may undergo as the beam propagates. Propagation in free space as well as in linear media, both deterministic and random, is discussed.

© 2003 Optical Society of America

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References

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  1. D. F. V. James, J. Opt. Soc. Am. A 11, 1641 (1994).
    [CrossRef]
  2. F. Gori, M. Santarsiero, S. Vaclavi, R. Borghi, G. Guattari, Pure Appl. Opt. 7, 941 (1998).
    [CrossRef]
  3. E. Wolf, “Unified theory of coherence and polarization of random electromagnetic beams,” Phys. Rev. Lett. (to be published).
  4. The so-called space-frequency formulation of second-order coherence theory used here is discussed, for example, in Ref. 5, Sec. 4.7.
  5. L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University Press, Cambridge, 1995).
    [CrossRef]
  6. Such an expression may also be readily derived in the paraxial approximation from the two Helmholtz equations that the more general 3×3 electric coherence matrix satisfies for propagation in free space (Ref., Sec. 6.6.3).
  7. E. Wolf, Phys. Rev. Lett. 56, 1370 (1986).
    [CrossRef] [PubMed]
  8. For a review of this subject up to 1996, see E. Wolf and D. F. V. James, Rep. Prog. Phys. 59, 771 (1996).
    [CrossRef]
  9. M. Born and E. Wolf, Principles of Optics (Cambridge University Press, Cambridge, 1999), 7th ed.
    [CrossRef]
  10. H. Roychowdhury and E. Wolf, “Determination of the electric cross-spectral density matrix of a random electromagnetic beam,” to be submitted to Opt. Commun.

Born, M.

M. Born and E. Wolf, Principles of Optics (Cambridge University Press, Cambridge, 1999), 7th ed.
[CrossRef]

Mandel, L.

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

Wolf, E.

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

M. Born and E. Wolf, Principles of Optics (Cambridge University Press, Cambridge, 1999), 7th ed.
[CrossRef]

Other (10)

D. F. V. James, J. Opt. Soc. Am. A 11, 1641 (1994).
[CrossRef]

F. Gori, M. Santarsiero, S. Vaclavi, R. Borghi, G. Guattari, Pure Appl. Opt. 7, 941 (1998).
[CrossRef]

E. Wolf, “Unified theory of coherence and polarization of random electromagnetic beams,” Phys. Rev. Lett. (to be published).

The so-called space-frequency formulation of second-order coherence theory used here is discussed, for example, in Ref. 5, Sec. 4.7.

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

Such an expression may also be readily derived in the paraxial approximation from the two Helmholtz equations that the more general 3×3 electric coherence matrix satisfies for propagation in free space (Ref., Sec. 6.6.3).

E. Wolf, Phys. Rev. Lett. 56, 1370 (1986).
[CrossRef] [PubMed]

For a review of this subject up to 1996, see E. Wolf and D. F. V. James, Rep. Prog. Phys. 59, 771 (1996).
[CrossRef]

M. Born and E. Wolf, Principles of Optics (Cambridge University Press, Cambridge, 1999), 7th ed.
[CrossRef]

H. Roychowdhury and E. Wolf, “Determination of the electric cross-spectral density matrix of a random electromagnetic beam,” to be submitted to Opt. Commun.

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Figures (1)

Fig. 1
Fig. 1

Illustration of the notation.

Equations (10)

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W̲̲Wijr1,r2,ω=Ei*r1,ωEjr2,ω,i,j=x,y,
μr1,r2,ω=Tr W̲̲r1,r2,ωTr W̲̲r1,r2,ωTr W̲̲r2,r2,ω,
Pr=1-4 Det W̲̲r,r,ωTr W̲̲r,r,ω2.
Sr,ω=Tr W̲̲r,r,ω.
Eir,ω=z=0Ei0ρ,ωGρ-ρ,z;ωd2ρ,
Gρ-ρ,z;ω=-ik2πzexpikρ-ρ2/2z
W̲̲r1,r2,ω=z=0W̲̲0ρ1,ρ2,ω×Kρ1-ρ1;ρ2-ρ2,z;ωd2ρ1d2ρ2,
Kρ1-ρ1;ρ2-ρ2,z;ω=G*ρ1-ρ1,z;ωGρ2-ρ2,z;ω.
W̲̲r1,r2,ω=z=0W̲̲0ρ1,ρ2,ω×Krmρ1-ρ1;ρ2-ρ2,z;ωd2ρ1d2ρ2,
Krmρ1-ρ1,z;ρ2-ρ2,ω=Gm*ρ1-ρ1,z;ωGmρ2-ρ2,z;ωrm

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