Abstract

The coherence properties of sunlight were first studied by Verdet around 1869 and were later examined by other scientists. However, all the previous calculations assumed that the Earth is in the far zone of the Sun, an assumption that is incorrect. An investigation of why Verdet’s result is nevertheless correct reveals a surprising property of radiation from incoherent sources.

© 2004 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |

  1. É. Verdet, Leçons d’Optique Physique, Vol. 1 (L’Imprimierie Impériale, Paris, 1869).
  2. Translation from the original French generously provided by P. S. Carney.
  3. M. Born and E. Wolf, Principles of Optics, 7th (expanded) ed. (Cambridge U. Press, Cambridge, 1999).
    [CrossRef]
  4. L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, Cambridge, 1995).
    [CrossRef]
  5. C. H. Papas, Theory of Electromagnetic Wave Propagation (Dover, New York, 1988), Sect. 4.4.
  6. G. B. Arfken and H. J. Weber, Mathematical Methods for Physicists, 5th ed. (Academic, San Diego, Calif., 2001).
  7. J. J. Greffet, private communication.

Arfken, G. B.

G. B. Arfken and H. J. Weber, Mathematical Methods for Physicists, 5th ed. (Academic, San Diego, Calif., 2001).

Born, M.

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

Greffet, J. J.

J. J. Greffet, private communication.

Mandel, L.

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

Papas, C. H.

C. H. Papas, Theory of Electromagnetic Wave Propagation (Dover, New York, 1988), Sect. 4.4.

Verdet, É.

É. Verdet, Leçons d’Optique Physique, Vol. 1 (L’Imprimierie Impériale, Paris, 1869).

Weber, H. J.

G. B. Arfken and H. J. Weber, Mathematical Methods for Physicists, 5th ed. (Academic, San Diego, Calif., 2001).

Wolf, E.

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

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

Other (7)

É. Verdet, Leçons d’Optique Physique, Vol. 1 (L’Imprimierie Impériale, Paris, 1869).

Translation from the original French generously provided by P. S. Carney.

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

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

C. H. Papas, Theory of Electromagnetic Wave Propagation (Dover, New York, 1988), Sect. 4.4.

G. B. Arfken and H. J. Weber, Mathematical Methods for Physicists, 5th ed. (Academic, San Diego, Calif., 2001).

J. J. Greffet, private communication.

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 (2)

Fig. 1
Fig. 1

Notation relating to the radiation from an incoherent spherical source.

Fig. 2
Fig. 2

Form of the spectral degree of coherence at different radial distances from a spherical source of (normalized) radius ka=100. It can be seen that, once the observation point is more than a few wavelengths away from the source domain, the functional form of the spectral degree of coherence is essentially unchanging and roughly equal to the far-zone form, calculated using the van Cittert–Zernike theorem.

Equations (14)

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

Rρhλ
πa2λr1,
Wr1,r2,ωU*r1,ωUr2,ω,
Ur,ω=lmclmhl1krYlmθ,ϕ,
Wr1,r2,ω=lmlmclm*clmhl1*kr1hl1×kr2Ylm*θ1,ϕ1Ylmθ2,ϕ2.
Was1,as2,ω=I0ωδ2s2-s1,
δ2s2-s1=lmYlm*θ1,ϕ1Ylmθ2,ϕ2.
clm*clm=δllδmmI0ωhl1ka2,
Wr1,r2,ω=lmI0ωhl1ka2hl1*kr1hl1kr2×Ylm*θ1,ϕ1Ylmθ2,ϕ2
Wr1,r2,ω=l2l+14πI0ωhl1ka2hl1*kr1hl1kr2Plcos Θ,
krkaka+12.
πa2λr1,
μrs1,rs2,ω=J12ka sinΘ/2ka sinΘ/2,

Metrics