Abstract

We study effective spatial and angular correlations in beams of any state of spatial coherence, and we introduce a phase-space product, Q, which takes these correlations into account. This phase-space product is shown to reduce to the conventional beam-quality factor M2 when the beam is spatially fully coherent. We also determine the lower bound for the value of Q and demonstrate that it is attained for all Gaussian Schell-model beams.

© 2001 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. J. Wu and A. D. Boerdman, J. Mod. Opt. 38, 1355 (1991).
    [CrossRef]
  2. A. Wax, S. Bali, and J. E. Thomas, Opt. Lett. 24, 1188 (1999).
    [CrossRef]
  3. M. J. Bastiaans, J. Opt. Soc. Am 69, 1710 (1979).
    [CrossRef]
  4. S. Lavi, R. Prochaska, and E. Keren, Appl. Opt. 27, 3696 (1988).
    [CrossRef] [PubMed]
  5. R. Simon, N. Mukunda, and E. C. G. Sudarshan, Opt. Commun. 65, 322 (1988).
    [CrossRef]
  6. M. J. Bastiaans, J. Opt. Soc. Am. 73, 251 (1983).
    [CrossRef]
  7. M. J. Bastiaans, J. Opt. Soc. Am. A 1, 711 (1984).
    [CrossRef]
  8. M. J. Bastiaans, J. Opt. Soc. Am. A 3, 1243 (1986).
    [CrossRef]
  9. J. Serna, R. Martinez-Herrero, and P. M. Mejias, J. Opt. Soc. Am. A 8, 1094 (1991).
    [CrossRef]
  10. G. Nemes and A. E. Siegman, J. Opt. Soc. Am. A 11, 2257 (1994).
    [CrossRef]
  11. M. Santarsiero, F. Gori, B. Borghi, G. Cincotti, and P. Vahimaa, J. Opt. Soc. Am. A 16, 106 (1999).
    [CrossRef]
  12. S. A. Ponomarenko and E. Wolf, Opt. Lett. 25, 663 (2000).
    [CrossRef]
  13. S. R. Seshadri, J. Opt. Soc. Am. A 17, 780 (2000).
    [CrossRef]
  14. A. E. Siegman, Proc. SPIE 1224, 2 (1990).
    [CrossRef]
  15. L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University Press, Cambridge, 1995).
    [CrossRef]

2000 (2)

1999 (2)

1994 (1)

1991 (2)

1990 (1)

A. E. Siegman, Proc. SPIE 1224, 2 (1990).
[CrossRef]

1988 (2)

S. Lavi, R. Prochaska, and E. Keren, Appl. Opt. 27, 3696 (1988).
[CrossRef] [PubMed]

R. Simon, N. Mukunda, and E. C. G. Sudarshan, Opt. Commun. 65, 322 (1988).
[CrossRef]

1986 (1)

1984 (1)

1983 (1)

1979 (1)

M. J. Bastiaans, J. Opt. Soc. Am 69, 1710 (1979).
[CrossRef]

Bali, S.

Bastiaans, M. J.

Boerdman, A. D.

J. Wu and A. D. Boerdman, J. Mod. Opt. 38, 1355 (1991).
[CrossRef]

Borghi, B.

Cincotti, G.

Gori, F.

Keren, E.

Lavi, S.

Mandel, L.

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

Martinez-Herrero, R.

Mejias, P. M.

Mukunda, N.

R. Simon, N. Mukunda, and E. C. G. Sudarshan, Opt. Commun. 65, 322 (1988).
[CrossRef]

Nemes, G.

Ponomarenko, S. A.

Prochaska, R.

Santarsiero, M.

Serna, J.

Seshadri, S. R.

Siegman, A. E.

Simon, R.

R. Simon, N. Mukunda, and E. C. G. Sudarshan, Opt. Commun. 65, 322 (1988).
[CrossRef]

Sudarshan, E. C. G.

R. Simon, N. Mukunda, and E. C. G. Sudarshan, Opt. Commun. 65, 322 (1988).
[CrossRef]

Thomas, J. E.

Vahimaa, P.

Wax, A.

Wolf, E.

S. A. Ponomarenko and E. Wolf, Opt. Lett. 25, 663 (2000).
[CrossRef]

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

Wu, J.

J. Wu and A. D. Boerdman, J. Mod. Opt. 38, 1355 (1991).
[CrossRef]

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (1)

Fig. 1
Fig. 1

Illustration of the notation. The point O is an origin within the region in the plane z=0, occupied by a partially coherent, statistically stationary, planar, secondary source. P1 and P2 are two points in the far zone of the source, situated in the plane z=0. OP1¯=r1s1, OP2¯=r2s2, s12=s22=1.

Equations (23)

Equations on this page are rendered with MathJax. Learn more.

δW2=d2ρ1d2ρ2ρ1-ρ22W0ρ1,ρ2,ω2d2ρ1d2ρ2W0ρ1,ρ2,ω2,
δA2=d2s1d2s2s1-s22As1,s2,ω2d2s1d2s2As1,s2,ω2.
As1,s2,ω=k4W̃0-ks1,ks2,ω,
W˜0f,f,ω=d2ρd2ρ2π2W0ρ,ρ,ω×exp-ifρ+fρ.
Q=πλδWδA.
Wcohρ1,ρ2,ω=V*ρ1,ωVρ2,ω,
δW2coh=d2ρ1d2ρ2ρ1-ρ22Iρ1Iρ2d2ρ1d2ρ2Iρ1Iρ2.
ρα=d2ρραIρd2ρIρ,
ρ2=d2ρρ2Iρd2ρIρ.
δW2coh=ρ2+ρ2-2ρ2,
δW2coh=2σI2,
Js,ω=2πk2As,s,ωcos2θ,
Acohs1,s2,ω=a*s1,ωas2,ω.
δA2coh=d2s1d2s2s1-s22Js1Js2d2s1d2s2Js1Js2.
δA2coh=2s2-s2=2σJ2,
Qcoh=2πλσIσJ,
d2ρ1d2ρ2g*̇gW0ρ1,ρ22d2ρ1d2ρ2W0ρ1,ρ220,
g=j=12ρj+αjW0ρ1,ρ2.
δW2+4α+α2k2δA20.
Q1.
ρ1-ρ2Wmin0+α01-2Wmin0=0.
Wmin0ρ1,ρ2=Aexp-γρ12+ρ22exp-βρ1ρ2,
Wmin0ρ1,ρ2=Aexp-ρ12+ρ22/4σS2×exp-ρ1-ρ22/2σg2,

Metrics