Abstract

We examine the properties of the recently introduced degrees of coherence regarding the phase correlations of the optical field. It is seen that some of these quantities are straightforwardly related to the limits of complete dependence and complete independence of phases, which were used as the extremes of complete coherence and complete incoherence by Zernike in 1938. Certain other coherence measures are not in agreement with these limits in all situations. Our results elucidate the physical meaning of coherence in electromagnetic fields.

© 2012 Optical Society of America

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References

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  1. F. Zernike, Physica 5, 785 (1938).
    [CrossRef]
  2. L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge Univ., 1995).
  3. E. Wolf, Phys. Lett. A 312, 263 (2003).
    [CrossRef]
  4. E. Wolf, Opt. Lett. 29, 1712 (2004).
    [CrossRef]
  5. O. Korotkova and E. Wolf, J. Opt. Soc. Am. A 21, 2382 (2004).
    [CrossRef]
  6. J. Tervo, T. Setälä, and A. T. Friberg, Opt. Express 11, 1137 (2003).
    [CrossRef]
  7. Ph. Réfrégier and F. Goudail, Opt. Express 13, 6051 (2005).
    [CrossRef]
  8. A. Luis, J. Opt. Soc. Am. A 24, 1063 (2007).
    [CrossRef]
  9. T. Setälä, J. Tervo, and A. T. Friberg, Opt. Lett. 29, 328 (2004).
    [CrossRef]
  10. T. Setälä, J. Tervo, and A. T. Friberg, Opt. Lett. 29, 1713 (2004).
    [CrossRef]
  11. B. Karczewski, Phys. Lett. 5, 191 (1963).
    [CrossRef]
  12. B. Karczewski, Nuovo Cimento 30, 906 (1963).
    [CrossRef]
  13. T. Setälä, J. Tervo, and A. T. Friberg, Opt. Lett. 31, 2208 (2006).
    [CrossRef]
  14. T. Setälä, J. Tervo, and A. T. Friberg, Opt. Lett. 31, 2669 (2006).
    [CrossRef]

2007 (1)

2006 (2)

2005 (1)

2004 (4)

2003 (2)

1963 (2)

B. Karczewski, Phys. Lett. 5, 191 (1963).
[CrossRef]

B. Karczewski, Nuovo Cimento 30, 906 (1963).
[CrossRef]

1938 (1)

F. Zernike, Physica 5, 785 (1938).
[CrossRef]

Friberg, A. T.

Goudail, F.

Karczewski, B.

B. Karczewski, Nuovo Cimento 30, 906 (1963).
[CrossRef]

B. Karczewski, Phys. Lett. 5, 191 (1963).
[CrossRef]

Korotkova, O.

Luis, A.

Mandel, L.

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

Réfrégier, Ph.

Setälä, T.

Tervo, J.

Wolf, E.

O. Korotkova and E. Wolf, J. Opt. Soc. Am. A 21, 2382 (2004).
[CrossRef]

E. Wolf, Opt. Lett. 29, 1712 (2004).
[CrossRef]

E. Wolf, Phys. Lett. A 312, 263 (2003).
[CrossRef]

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

Zernike, F.

F. Zernike, Physica 5, 785 (1938).
[CrossRef]

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Equations (18)

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Γ12=U1*U2=A1A2exp[i(ϕ2ϕ1)],
γ12=|U1*U2|A1A2=|exp[i(ϕ2ϕ1)]|,
E1=[A1xexp(iϕ1x)A1yexp(iϕ1y)],E2=[A2xexp(iϕ2x)A2yexp(iϕ2y)],
Γmn=Em*EnT=[AmxAnxexp(iΦmnxx)AmxAnyexp(iΦmnxy)AmyAnxexp(iΦmnyx)AmyAnyexp(iΦmnyy)],
μ12=[tr(Γ12Γ12)I1I2]1/2,
μ12=[pqA1p2A2q2|exp(iΦ12pq)|2pqA1p2A2q2]1/2,
ξ12=trΓ12I1I2
M12=Γ111/2Γ12Γ221/2.
Γmn=Im1/2In1/2am*anT,
am=Im1/2[Amxexp(iψmx)Amyexp(iψmy)]
Γmm1/2=Im1/2am*amT.
M12=a1*a2T=U1ΣU2,
Um=Im1/2[Amxexp(iψmx)Amyexp(iψmy)Amyexp(iψmy)Amxexp(iψmx)]
Σ=[1000]
D12=43[tr(N122)(trN12)214],
N12=[Γ11Γ12Γ12Γ22]
N12=[Γ1100Γ22],
D12=(I1I2)2+2I12P12+2I22P223(I1+I2)2,

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