Abstract

We investigate a fundamental limitation on the measurement of spatial coherence for highly incoherent fields. We model the near-field detection scheme, required for such a measurement, with pointlike induced dipoles. We find that this fully vector model sets a characteristic length scale beyond which the spatial coherence of an optical field cannot be accurately measured. This length scale forms an uncertainty relationship with the photodetector integration time.

© 2003 Optical Society of America

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References

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  1. W. H. Carter and E. Wolf, J. Opt. Soc. Am. 65, 1067 (1975).
  2. R. Carminati and J.-J. Greffet, Phys. Rev. Lett. 82, 1660 (1999).
    [CrossRef]
  3. C. Henkel, K. Joulain, R. Carminati, and J.-J. Greffet, Opt. Commun. 186, 57 (2000).
    [CrossRef]
  4. J.-J. Greffet, R. Carminati, K. Joulain, J.-P. Mulet, S. Mainguy, and Y. Chen, Nature 416, 61 (2002).
    [CrossRef] [PubMed]
  5. C. L. Tien and G. Chen, J. Heat Transfer 116, 799 (1994).
    [CrossRef]
  6. L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, Cambridge, 1995).
    [CrossRef]
  7. J. W. Goodman, Statistical Optics (Wiley, New York, 1985).
  8. J.-J. Greffet and R. Carminati, Prog. Surf. Sci. 56, 133 (1997).
  9. C. Girard and A. Dereux, Rep. Prog. Phys. 59, 657 (1996).
    [CrossRef]
  10. E. Wolf, Opt. Lett. 8, 250 (1983).
    [CrossRef] [PubMed]
  11. D. Van Labeke and D. Barchiesi, J. Opt. Soc. Am. A 9, 732 (1992).
    [CrossRef]
  12. See, for example, T. Setälä, M. Kaivola, and A. T. Friberg, Phys. Rev. E 59, 1200 (1999).
    [CrossRef]
  13. T. Setälä, K. Blomstedt, M. Kaivola, and A. T. Friberg, Phys. Rev. E 67, 026613 (2003).
    [CrossRef]

2003 (1)

T. Setälä, K. Blomstedt, M. Kaivola, and A. T. Friberg, Phys. Rev. E 67, 026613 (2003).
[CrossRef]

2002 (1)

J.-J. Greffet, R. Carminati, K. Joulain, J.-P. Mulet, S. Mainguy, and Y. Chen, Nature 416, 61 (2002).
[CrossRef] [PubMed]

2000 (1)

C. Henkel, K. Joulain, R. Carminati, and J.-J. Greffet, Opt. Commun. 186, 57 (2000).
[CrossRef]

1999 (2)

R. Carminati and J.-J. Greffet, Phys. Rev. Lett. 82, 1660 (1999).
[CrossRef]

See, for example, T. Setälä, M. Kaivola, and A. T. Friberg, Phys. Rev. E 59, 1200 (1999).
[CrossRef]

1997 (1)

J.-J. Greffet and R. Carminati, Prog. Surf. Sci. 56, 133 (1997).

1996 (1)

C. Girard and A. Dereux, Rep. Prog. Phys. 59, 657 (1996).
[CrossRef]

1994 (1)

C. L. Tien and G. Chen, J. Heat Transfer 116, 799 (1994).
[CrossRef]

1992 (1)

1983 (1)

1975 (1)

Barchiesi, D.

Blomstedt, K.

T. Setälä, K. Blomstedt, M. Kaivola, and A. T. Friberg, Phys. Rev. E 67, 026613 (2003).
[CrossRef]

Carminati, R.

J.-J. Greffet, R. Carminati, K. Joulain, J.-P. Mulet, S. Mainguy, and Y. Chen, Nature 416, 61 (2002).
[CrossRef] [PubMed]

C. Henkel, K. Joulain, R. Carminati, and J.-J. Greffet, Opt. Commun. 186, 57 (2000).
[CrossRef]

R. Carminati and J.-J. Greffet, Phys. Rev. Lett. 82, 1660 (1999).
[CrossRef]

J.-J. Greffet and R. Carminati, Prog. Surf. Sci. 56, 133 (1997).

Carter, W. H.

Chen, G.

C. L. Tien and G. Chen, J. Heat Transfer 116, 799 (1994).
[CrossRef]

Chen, Y.

J.-J. Greffet, R. Carminati, K. Joulain, J.-P. Mulet, S. Mainguy, and Y. Chen, Nature 416, 61 (2002).
[CrossRef] [PubMed]

Dereux, A.

C. Girard and A. Dereux, Rep. Prog. Phys. 59, 657 (1996).
[CrossRef]

Friberg, A. T.

T. Setälä, K. Blomstedt, M. Kaivola, and A. T. Friberg, Phys. Rev. E 67, 026613 (2003).
[CrossRef]

See, for example, T. Setälä, M. Kaivola, and A. T. Friberg, Phys. Rev. E 59, 1200 (1999).
[CrossRef]

Girard, C.

C. Girard and A. Dereux, Rep. Prog. Phys. 59, 657 (1996).
[CrossRef]

Goodman, J. W.

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

Greffet, J.-J.

J.-J. Greffet, R. Carminati, K. Joulain, J.-P. Mulet, S. Mainguy, and Y. Chen, Nature 416, 61 (2002).
[CrossRef] [PubMed]

C. Henkel, K. Joulain, R. Carminati, and J.-J. Greffet, Opt. Commun. 186, 57 (2000).
[CrossRef]

R. Carminati and J.-J. Greffet, Phys. Rev. Lett. 82, 1660 (1999).
[CrossRef]

J.-J. Greffet and R. Carminati, Prog. Surf. Sci. 56, 133 (1997).

Henkel, C.

C. Henkel, K. Joulain, R. Carminati, and J.-J. Greffet, Opt. Commun. 186, 57 (2000).
[CrossRef]

Joulain, K.

J.-J. Greffet, R. Carminati, K. Joulain, J.-P. Mulet, S. Mainguy, and Y. Chen, Nature 416, 61 (2002).
[CrossRef] [PubMed]

C. Henkel, K. Joulain, R. Carminati, and J.-J. Greffet, Opt. Commun. 186, 57 (2000).
[CrossRef]

Kaivola, M.

T. Setälä, K. Blomstedt, M. Kaivola, and A. T. Friberg, Phys. Rev. E 67, 026613 (2003).
[CrossRef]

See, for example, T. Setälä, M. Kaivola, and A. T. Friberg, Phys. Rev. E 59, 1200 (1999).
[CrossRef]

Mainguy, S.

J.-J. Greffet, R. Carminati, K. Joulain, J.-P. Mulet, S. Mainguy, and Y. Chen, Nature 416, 61 (2002).
[CrossRef] [PubMed]

Mandel, L.

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

Mulet, J.-P.

J.-J. Greffet, R. Carminati, K. Joulain, J.-P. Mulet, S. Mainguy, and Y. Chen, Nature 416, 61 (2002).
[CrossRef] [PubMed]

Setälä, T.

T. Setälä, K. Blomstedt, M. Kaivola, and A. T. Friberg, Phys. Rev. E 67, 026613 (2003).
[CrossRef]

See, for example, T. Setälä, M. Kaivola, and A. T. Friberg, Phys. Rev. E 59, 1200 (1999).
[CrossRef]

Tien, C. L.

C. L. Tien and G. Chen, J. Heat Transfer 116, 799 (1994).
[CrossRef]

Van Labeke, D.

Wolf, E.

E. Wolf, Opt. Lett. 8, 250 (1983).
[CrossRef] [PubMed]

W. H. Carter and E. Wolf, J. Opt. Soc. Am. 65, 1067 (1975).

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

J. Heat Transfer (1)

C. L. Tien and G. Chen, J. Heat Transfer 116, 799 (1994).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (1)

Nature (1)

J.-J. Greffet, R. Carminati, K. Joulain, J.-P. Mulet, S. Mainguy, and Y. Chen, Nature 416, 61 (2002).
[CrossRef] [PubMed]

Opt. Commun. (1)

C. Henkel, K. Joulain, R. Carminati, and J.-J. Greffet, Opt. Commun. 186, 57 (2000).
[CrossRef]

Opt. Lett. (1)

Phys. Rev. E (2)

See, for example, T. Setälä, M. Kaivola, and A. T. Friberg, Phys. Rev. E 59, 1200 (1999).
[CrossRef]

T. Setälä, K. Blomstedt, M. Kaivola, and A. T. Friberg, Phys. Rev. E 67, 026613 (2003).
[CrossRef]

Phys. Rev. Lett. (1)

R. Carminati and J.-J. Greffet, Phys. Rev. Lett. 82, 1660 (1999).
[CrossRef]

Prog. Surf. Sci. (1)

J.-J. Greffet and R. Carminati, Prog. Surf. Sci. 56, 133 (1997).

Rep. Prog. Phys. (1)

C. Girard and A. Dereux, Rep. Prog. Phys. 59, 657 (1996).
[CrossRef]

Other (2)

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

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

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Figures (2)

Fig. 1
Fig. 1

Actual (solid curve) and measured (dashed curve) diagonal components of the degree of spectral coherence tensor versus spatial separation kR in the direction sx=1,sy=0,sz=0 for characteristic spatial coherence length kσc=0.05, characteristic polarizability length kl=0.01, where (a), (b), and (c) refer to μxx,μyy, and μzz, respectively.

Fig. 2
Fig. 2

Actual (solid line) and measured (dashed curve) width kζ at which μxx=0.5 versus kσc.

Equations (9)

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

En*r1,ωEmr2,ω=Wnmr1,r2,ωδω-ω,
μnmr1,r2,ω=Wnmr1,r2,ωWnnr1,r1,ωWmmr2,r2,ω1/2,
Enjr,ω=1αωmAr,rj,ωδnm-snsm+Br,rj,ωsnsmpmj j=1,2,
Ar,rj,ω=38πkl×expikR-1kR3+ikR2+1kR, Br,rj,ω=38πkl×expikR2kR3-2ikR2,
pn1ω=αωEnor1,ω+mAδnm-snsm+Bsnsmpm2ω, pn2ω=αωEnor2,ω+mAδnm-snsm+Bsnsmpm1ω,
mgδnm-snsm+hsnsmGδml-smsl+Hsmsl=gGδnl-snsl+hHsnsl,
pn1ω=αωmδnm-snsm1-A2Enor1,ω+AEnor2,ω+snsm1-B2Enor1,ω+BEnor2,ω, pn2ω=αωmδnm-snsm1-A2AEnor1,ω+Enor2,ω+snsm1-B2BEnor1,ω+Enor2,ω.
Wnmpr1,r2=δnm-snsm1-A221+A2UR+2ReAU0+snsm1-B221+B2VR+2ReBV0,
Wnnpr1,r2=1-snsn1-A221+A2U0+2ReAUR+snsn1-B221+B2V0+2ReBVR,

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