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Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Editor: Stephen A. Burns
  • Vol. 24, Iss. 4 — Apr. 1, 2007
  • pp: 1063–1068

Degree of coherence for vectorial electromagnetic fields as the distance between correlation matrices

Alfredo Luis  »View Author Affiliations

JOSA A, Vol. 24, Issue 4, pp. 1063-1068 (2007)

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We assess the degree of coherence of vectorial electromagnetic fields in the space–frequency domain as the distance between the cross-spectral density matrix and the identity matrix representing completely incoherent light. This definition is compared with previous approaches. It is shown that this distance provides an upper bound for the degree of coherence and visibility for any pair of scalar waves obtained by linear combinations of the original fields. This same approach emerges when applying a previous definition of global coherence to a Young interferometer.

© 2007 Optical Society of America

OCIS Codes
(030.1640) Coherence and statistical optics : Coherence
(260.2110) Physical optics : Electromagnetic optics
(260.5430) Physical optics : Polarization

ToC Category:
Coherence and Statistical Optics

Original Manuscript: July 6, 2006
Revised Manuscript: October 12, 2006
Manuscript Accepted: November 7, 2006
Published: March 14, 2007

Alfredo Luis, "Degree of coherence for vectorial electromagnetic fields as the distance between correlation matrices," J. Opt. Soc. Am. A 24, 1063-1068 (2007)

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  1. B. Karczewski, "Degree of coherence of the electromagnetic field," Phys. Lett. 5, 191-192 (1963). [CrossRef]
  2. E. Wolf, "Unified theory of coherence and polarization of random electromagnetic fields," Phys. Lett. A 312, 263-267 (2003). [CrossRef]
  3. S. A. Ponomarenko and E. Wolf, "The spectral degree of coherence of fully spatially coherent electromagnetic beams," Opt. Commun. 227, 73-74 (2003). [CrossRef]
  4. J. Tervo, T. Setälä, and A. T. Friberg, "Degree of coherence for electromagnetic fields," Opt. Express 11, 1137-1143 (2003). [CrossRef]
  5. T. Setälä, J. Tervo, and A. T. Friberg, "Complete electromagnetic coherence in the space-frequency domain," Opt. Lett. 29, 328-330 (2004). [CrossRef]
  6. E. Wolf, "Comment on 'Complete electromagnetic coherence in the space-frequency domain'," Opt. Lett. 29, 1712 (2004). [CrossRef]
  7. T. Setälä, J. Tervo, and A. T. Friberg, "Reply to comment on 'Complete electromagnetic coherence in the space-frequency domain'," Opt. Lett. 29, 1713-1714 (2004). [CrossRef]
  8. F. Zernike, "The concept of degree of coherence and its application to optical problems," Physica (Utrecht) 5, 785-795 (1938). [CrossRef]
  9. F. Zernike, "Diffraction and optical image formation," Proc. Phys. Soc. London 61, 158-164 (1948). [CrossRef]
  10. M. Born and E. Wolf, Principles of Optics, 7th expanded ed. (Cambridge U. Press, 1999).
  11. L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, 1995).
  12. A. Luis, "Degree of polarization in quantum optics," Phys. Rev. A 66, 013806 (2002). [CrossRef]
  13. A. Luis, "Visibility for anharmonic fringes," J. Phys. A 35, 8805-8815 (2002). [CrossRef]
  14. A. Luis, "Polarization correlations in quantum optics," Opt. Commun. 216, 165-172 (2003). [CrossRef]
  15. A. Luis, "Visibility for multi-particle interference," Phys. Lett. A 314, 197-202 (2003). [CrossRef]
  16. A. Luis, "Classical and quantum polarization correlations," Phys. Rev. A 69, 023803 (2004). [CrossRef]
  17. A. Luis, "Properties of spatial-angular Stokes parameters," Opt. Commun. 251, 243-253 (2005). [CrossRef]
  18. A. Luis, "Polarization distribution and degree of polarization for three-dimensional quantum light fields," Phys. Rev. A 71, 063815 (2005). [CrossRef]
  19. A. Luis, "Degree of polarization for three-dimensional fields as a distance between correlation matrices," Opt. Commun. 253, 10-14 (2005). [CrossRef]
  20. A. Luis, "Ray picture of polarization and coherence in a Young interferometer," J. Opt. Soc. Am. A 23, 2855-2860 (2006). [CrossRef]
  21. F. Gori, M. Santarsiero, and R. Borghi, "Vector mode analysis of a Young interferometer," Opt. Lett. 31, 858-860 (2006). [CrossRef] [PubMed]
  22. J. Tervo, T. Setälä, and A. T. Friberg, "Theory of partially coherent electromagnetic fields in the space-frequency domain," J. Opt. Soc. Am. A 21, 2205-2215 (2004). [CrossRef]
  23. R. Barakat, "Degree of polarization and the principal idempotents of the coherency matrix," Opt. Commun. 23, 147-150 (1977). [CrossRef]
  24. J. C. Samson and J. V. Olson, "Generalized Stokes vectors and generalized power spectra for second-order stationary vector-processes," SIAM J. Appl. Math. 40, 137-149 (1981). [CrossRef]
  25. M. Reck, A. Zeilinger, H. J. Bernstein, and P. Bertani, "Experimental realization of any discrete unitary operator," Phys. Rev. Lett. 73, 58-61 (1994). [CrossRef] [PubMed]
  26. T. Setälä, A. Shevchenko, M. Kaivola, and A. T. Friberg, "Degree of polarization for optical near fields," Phys. Rev. E 66, 016615 (2002). [CrossRef]
  27. J. J. Gil, J. M. Correas, P. A. Melero, and C. Ferreira, "Generalized polarization algebra," in Proceedings of the 8th Conference Zaragoza-Pau of Applied Mathematics and Statistics (2003), pp. 161-167. Available on line at http://www.unizar.es/galdeano/actaslowbarpau/PDFVIII/pp161-167.pdf.
  28. T. Saastamoinen and J. Tervo, "Geometric approach to the degree of polarization for arbitrary fields," J. Mod. Opt. 51, 2039-2045 (2004). [CrossRef]
  29. J. Ellis and A. Dogariu, "Complex degree of mutual polarization," Opt. Lett. 29, 536-538 (2004). [CrossRef] [PubMed]
  30. Ch. Brosseau, Fundamentals of Polarized Light: A Statistical Optics Approach (Wiley, 1998).
  31. T. Carozzi, R. Karlsson, and J. Bergman, "Parameters characterizing electromagnetic wave polarization," Phys. Rev. E 61, 2024-2028 (2000). [CrossRef]
  32. M. R. Dennis, "Geometric interpretation of the three-dimensional coherence matrix for nonparaxial polarization," J. Opt. A, Pure Appl. Opt. 6, S26-S31 (2004). [CrossRef]
  33. S. G. Schirmer, T. Zhang, and J. V. Leavy, "Orbits of quantum states and geometry of Bloch vectors for N-level systems," J. Phys. A 37, 1389-1402 (2004). [CrossRef]
  34. R. Barakat, "Theory of the coherency matrix for light of arbitrary spectral bandwidth," J. Opt. Soc. Am. 53, 317-323 (1963). [CrossRef]
  35. P. Réfrégier and F. Goudail, "Invariant degrees of coherence of partially polarized light," Opt. Express 13, 6051-6060 (2005). [CrossRef] [PubMed]
  36. M. J. Bastiaans, "New class of uncertainty relations for partially coherent light," J. Opt. Soc. Am. A 1, 711-715 (1984). [CrossRef]
  37. H. Lajunen, J. Tervo, and P. Vahimaa, "Overall coherence and coherent-mode expansion of spectrally partially coherent plane-wave pulses," J. Opt. Soc. Am. A 21, 2117-2123 (2004). [CrossRef]
  38. H. Lajunen, P. Vahimaa, and J. Tervo, "Theory of spatially and spectrally partially coherent pulses," J. Opt. Soc. Am. A 22, 1536-1545 (2005). [CrossRef]
  39. P. Vahimaa and J. Tervo, "Unified measures for optical fields: degree of polarization and effective degree of coherence," J. Opt. A, Pure Appl. Opt. 6, S41-S44 (2004). [CrossRef]
  40. M. A. Alonso, "Radiometry and wide-angle wave fields III: partial coherence," J. Opt. Soc. Am. A 18, 2502-2511 (2001). [CrossRef]

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