OSA's Digital Library

Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Editor: Stephen A. Burns
  • Vol. 26, Iss. 6 — Jun. 1, 2009
  • pp: 1437–1443

Synthesis of electromagnetic Schell-model sources

M. Santarsiero, R. Borghi, and V. Ramírez-Sánchez  »View Author Affiliations

JOSA A, Vol. 26, Issue 6, pp. 1437-1443 (2009)

View Full Text Article

Enhanced HTML    Acrobat PDF (334 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



A procedure for the synthesis of the most general electromagnetic Schell-model light source is proposed. It makes use of the generalized van Cittert–Zernike theorem to produce the electromagnetic source starting from a primary spatially incoherent source, characterized by a suitable position-dependent polarization matrix. By resorting to the spectral decomposition of the polarization matrix, it is shown how such an incoherent source can be synthesized by using a Mach–Zehnder interferometer, with suitable amplitude transmittances placed in its arms, fed by two mutually uncorrelated laser beams. Examples are given for the case of electromagnetic Gaussian Schell-model sources.

© 2009 Optical Society of America

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

ToC Category:

Original Manuscript: February 25, 2009
Manuscript Accepted: April 12, 2009
Published: May 26, 2009

M. Santarsiero, R. Borghi, and V. Ramírez-Sánchez, "Synthesis of electromagnetic Schell-model sources," J. Opt. Soc. Am. A 26, 1437-1443 (2009)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. A. Schell, “A technique for the determination of the radiation pattern of a partially coherent aperture,” IEEE Trans. Antennas Propag. 15, 187-188 (1967). [CrossRef]
  2. L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, 1995).
  3. M. Born and E. Wolf, Principles of Optics7th (expanded) ed. (Cambridge U. Press, 1999).
  4. J. W. Goodman, “Synthetic-aperture optics,” in Progress in Optics, Vol. VIII, E.Wolf, ed. (Elsevier, 1970), pp.1-50. [CrossRef]
  5. P. de Santis, F. Gori, G. Guattari, and C. Palma, “An example of a Collett-Wolf source,” Opt. Commun. 29, 256-260 (1979). [CrossRef]
  6. R. Grella, “Synthesis of generalized Collett-Wolf sources,” J. Opt. 13, 127-131 (1982). [CrossRef]
  7. J. Deschamps, D. Courjon, and J. Bulabois, “Gaussian Schell-model sources: an example and some perspectives,” J. Opt. Soc. Am. 73, 256-261 (1983). [CrossRef]
  8. P. De Santis, F. Gori, G. Guattari, and C. Palma, “Synthesis of partially coherent fields,” J. Opt. Soc. Am. A 3, 1258-1262 (1986). [CrossRef]
  9. G. Indebetouw, “Synthesis of polychromatic light sources with arbitrary degrees of coherence: some experiments,” J. Mod. Opt. 36, 251-259 (1989). [CrossRef]
  10. J. Turunen, A. Vasara, and A. T. Friberg, “Propagation invariance and self-imaging in variable-coherence optics,” J. Opt. Soc. Am. A 8, 282-289 (1991). [CrossRef]
  11. R. Simon and N. Mukunda, “Twisted Gaussian Schell-model beams,” J. Opt. Soc. Am. A 10, 95-109 (1993). [CrossRef]
  12. A. T. Friberg, E. Tervonen, and J. Turunen, “Interpretation and experimental demonstration of twisted Gaussian Schell-model beams,” J. Opt. Soc. Am. A 11, 1818-1826 (1994). [CrossRef]
  13. R. Borghi, F. Gori, and M. Santarsiero, “Phase and amplitude retrieval in ghost diffraction from field-correlation measurements,” Phys. Rev. Lett. 96, 183901-183904 (2006). [CrossRef] [PubMed]
  14. M. Santarsiero and R. Borghi, “Measuring spatial coherence by using a reversed-wavefront Young interferometer,” Opt. Lett. 96, 183901-183904 (2006).
  15. E. Wolf, Introduction to the Theory of Coherence and Polarization of Light (Cambridge U. Press, 2007).
  16. S. R. Seshadri, “Partially coherent Gaussian Schell-model electromagnetic beam,” J. Opt. Soc. Am. A 16, 1373-1380 (1999). [CrossRef]
  17. F. Gori, M. Santarsiero, G. Piquero, R. Borghi, A. Mondello, and R. Simon, “Partially polarized Gaussian Schell-model beams,” J. Opt. A, Pure Appl. Opt. 3, 1-9 (2001). [CrossRef]
  18. D. F. V. James, “Change of polarization of light beam on propagation in free-space,” J. Opt. Soc. Am. A 11, 1641-1643 (1994). [CrossRef]
  19. E. Collett and E. Wolf, “Is complete spatial coherence necessary for the generation of highly directional light beams?” Opt. Lett. 2, 27-29 (1978). [CrossRef] [PubMed]
  20. S. R. Seshadri, “Polarization properties of partially coherent Gaussian Schell-model electromagnetic beams,” J. Appl. Phys. 87, 4084-4093 (2000). [CrossRef]
  21. T. Shirai, “Polarization properties of a class of electromagnetic GSM beams which have the same far-zone intensity distribution as a fully coherent laser beam,” Opt. Commun. 256, 197-209 (2005). [CrossRef]
  22. E. Wolf, “Unified theory of coherence and polarization of statistical electromagnetic beams,” Phys. Lett. A 312, 263-267 (2003). [CrossRef]
  23. 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]
  24. R. Martínez-Herrero, G. Piquero, and P. Mejías, “Parametric characterization of the spatial structure of partially coherent and partially polarized beams,” J. Opt. A, Pure Appl. Opt. 6, S67-S71 (2004). [CrossRef]
  25. H. Roychowdhury and E. Wolf, “Young's interference experiment with light of any state of coherence and polarization,” Opt. Commun. 252, 268-274 (2005). [CrossRef]
  26. O. Korotkova, M. Salem, A. Dogariu, and E. Wolf, “Changes in the polarization ellipse of random electromagnetic beams propagating through the turbulent atmosphere,” Waves Random Complex Media 15, 353-364 (2005). [CrossRef]
  27. H. Roychowdhury, G. Agrawal, and E. Wolf, “Changes in the spectrum, in the spectral degree of polarization, and in the spectral degree of coherence of a partially coherent beam propagating through a gradient-index fiber,” J. Opt. Soc. Am. A 23, 940-948 (2006). [CrossRef]
  28. F. Gori, M. Santarsiero, R. Borghi, and E. Wolf, “Effects of coherence on the degree of polarization in Young interference pattern,” Opt. Lett. 31, 688-690 (2006). [CrossRef] [PubMed]
  29. Y. Li, H. Lee, and E. Wolf, “Spectra, coherence and polarization in Young's interference pattern formed by stochastic electromagnetic beams,” Opt. Commun. 265, 63-72 (2006). [CrossRef]
  30. A. Luis, “Ray picture of polarization and coherence in a Young interferometer,” J. Opt. Soc. Am. A 23, 2855-2860 (2006). [CrossRef]
  31. J. X. Pu, O. Korotkova, and E. Wolf, “Polarization-induced spectral changes on propagation of stochastic electromagnetic beams,” Phys. Rev. E 75, 056610 (2007). [CrossRef]
  32. M. Santarsiero, F. Gori, R. Borghi, and G. Guattari, “Vector-mode analysis of symmetric two-point sources,” J. Opt. A, Pure Appl. Opt. 9, 593-602 (2007). [CrossRef]
  33. Y. B. Zhu, D. M. Zhao, and X. Y. Du, “Propagation of stochastic Gaussian-Schell model array beams in turbulent atmosphere,” Opt. Express 16, 18437-18442 (2008). [CrossRef] [PubMed]
  34. G. Piquero, F. Gori, P. Romanini, M. Santarsiero, R. Borghi, and A. Mondello, “Synthesis of partially polarized Gaussian Schell-model sources,” Opt. Commun. 208, 9-16 (2002). [CrossRef]
  35. T. Shirai, O. Korotkova, and E. Wolf, “A method of generating electromagnetic Gaussian Schell-model beams,” J. Opt. A, Pure Appl. Opt. 7, 232-237 (2005). [CrossRef]
  36. F. Gori, M. Santarsiero, R. Borghi, and G. Piquero, “Use of the van Cittert-Zernike theorem for partially polarized sources,” Opt. Lett. 25, 1291-1293 (2000). [CrossRef]
  37. F. Gori, M. Santarsiero, R. Borghi, and V. Ramìrez-Sànchez, “Realizability condition for electromagnetic Schell-model sources,” J. Opt. Soc. Am. A 25, 1016-1021 (2008). [CrossRef]
  38. F. Gori, “Matrix treatment for partially polarized, partially coherent beams,” Opt. Lett. 23, 41-43 (1998). [CrossRef]
  39. F. Gori, M. Santarsiero, S. Vicalvi, R. Borghi, and G. Guattari, “Beam coherence polarization matrix,” Pure Appl. Opt. 7, 941-951 (1998). [CrossRef]
  40. S. K. Berberian, Introduction to Hilbert Space (Oxford U. Press, 1961).
  41. H. Roychowdhury and O. Korotkova, “Realizability conditions for electromagnetic Gaussian Schell-model sources,” Opt. Commun. 249, 379-385 (2005). [CrossRef]

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.


Fig. 1 Fig. 2 Fig. 3

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited