OSA's Digital Library

Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Vol. 20, Iss. 1 — Jan. 1, 2003
  • pp: 78–84

Coherent-mode decomposition of partially polarized, partially coherent sources

Franco Gori, Massimo Santarsiero, Raja Simon, Gemma Piquero, Riccardo Borghi, and Giorgio Guattari  »View Author Affiliations

JOSA A, Vol. 20, Issue 1, pp. 78-84 (2003)

View Full Text Article

Enhanced HTML    Acrobat PDF (160 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



It is shown that any partially polarized, partially coherent source can be expressed in terms of a suitable superposition of transverse coherent modes with orthogonal polarization states. Such modes are determined through the solution of a system of two coupled integral equations. An example, for which the modal decomposition is obtained in closed form in terms of fully linearly polarized Hermite Gaussian modes, is given.

© 2003 Optical Society of America

OCIS Codes
(030.4070) Coherence and statistical optics : Modes
(260.5430) Physical optics : Polarization

Original Manuscript: March 22, 2002
Manuscript Accepted: August 26, 2002
Published: January 1, 2003

Franco Gori, Massimo Santarsiero, Raja Simon, Gemma Piquero, Riccardo Borghi, and Giorgio Guattari, "Coherent-mode decomposition of partially polarized, partially coherent sources," J. Opt. Soc. Am. A 20, 78-84 (2003)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. L. Mandel, E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, Cambridge, UK, 1995).
  2. R. Gase, T. Gase, K. Blüthner, “Complex wave-field reconstruction by means of the Page distribution function,” Opt. Lett. 20, 2045–2047 (1995). [CrossRef] [PubMed]
  3. G. Iaconis, I. A. Walmsley, “Direct measurement of the two-point field correlation function,” Opt. Lett. 21, 1783–1785 (1996). [CrossRef] [PubMed]
  4. J. Tu, S. Tamura, “Analytic relation for recovering the mutual intensity by means of intensity information,” J. Opt. Soc. Am. A 15, 202–206 (1998). [CrossRef]
  5. J. Turunen, E. Tervonen, A. T. Friberg, “Coherence theoretic algorithm to determine the transverse-mode structure of lasers,” Opt. Lett. 14, 627–629 (1989). [CrossRef] [PubMed]
  6. E. Tervonen, J. Turunen, A. T. Friberg, “Transverse laser-mode structure determination from spatial coherence measurements: experimental results,” Appl. Phys. B 49, 409–414 (1989). [CrossRef]
  7. A. E. Siegman, S. W. Townsend, “Output beam propagation and beam quality from a multimode stable-cavity laser,” IEEE J. Quantum Electron. 29, 1212–1217 (1993). [CrossRef]
  8. B. Lü, B. Zhang, B. Cai, C. Yang, “A simple method for estimating the number of effectively oscillating modes and weighting factors of mixed mode laser beams behaving like Gaussian Schell-model beams,” Opt. Commun. 101, 49–52 (1993). [CrossRef]
  9. A. Cutolo, T. Isernia, I. Izzo, R. Pierri, L. Zeni, “Transverse mode analysis of a laser beam by near- and far-field intensity measurements,” Appl. Opt. 34, 7974–7978 (1995). [CrossRef] [PubMed]
  10. C. Martı́nez, F. Encinas-Sanz, J. Serna, P. M. Mejı́as, R. Martı́nez-Herrero, “On the parametric characterization of the transversal spatial structure of laser pulses,” Opt. Commun. 139, 299–305 (1997). [CrossRef]
  11. F. Encinas-Sanz, J. Serna, C. Martı́nez, R. Martı́nez-Herrero, P. M. Mejı́as, “Time-varying beam quality factor and mode evolution in TEA CO2 laser pulses,” IEEE J. Quantum Electron. 34, 1835–1838 (1998). [CrossRef]
  12. C. Martı́nez, J. Serna, F. Encinas-Sanz, R. Martı́nez-Herrero, P. M. Mejı́as, “Time-resolved spatial structure of TEA CO2 laser pulses,” Opt. Quantum Electron. 32, 18–30 (2000).
  13. R. Borghi, M. Santarsiero, “Modal decomposition of partially coherent flat-topped beams produced by multimode lasers,” Opt. Lett. 23, 313–315 (1998). [CrossRef]
  14. F. Gori, M. Santarsiero, R. Borghi, G. Guattari, “Intensity-based modal analysis for partially coherent beams with Hermite–Gaussian modes,” Opt. Lett. 23, 989–991 (1998). [CrossRef]
  15. M. Santarsiero, F. Gori, R. Borghi, G. Guattari, “Evaluation of the modal structure for light beams with Hermite–Gaussian modes,” Appl. Opt. 38, 5272–5281 (1999). [CrossRef]
  16. R. Borghi, M. Santarsiero, “Modal structure analysis for a class of axially symmetric flat-topped laser beams,” IEEE J. Quantum Electron. 35, 745–750 (1999). [CrossRef]
  17. M. Santarsiero, F. Gori, R. Borghi, “Modal-weight determination for a class of multimode beams,” in Laser Beam and Optics Characterization, H. Weber, H. Laabs, eds. (Optisches Institut, Technische Universität Berlin, Berlin, 2000), pp. 161–170.
  18. X. Xue, H. Wei, A. G. Kirk, “Intensity-based modal decomposition of optical beams in terms of Hermite–Gaussian functions,” J. Opt. Soc. Am. A 17, 1086–1091 (2000). [CrossRef]
  19. H. Laabs, B. Eppich, H. Weber, “Modal decomposition of partially coherent beams using the ambiguity function,” J. Opt. Soc. Am. A 19, 497–504 (2002). [CrossRef]
  20. 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]
  21. D. F. V. James, “Polarization of light radiated by black-body sources,” Opt. Commun. 109, 209–214 (1994). [CrossRef]
  22. C. Olson, P. L. Greene, G. W. Wicks, D. G. Hall, S. Rishton, “High-order azimuthal spatial modes of concentric-circle-grating surface-emitting semiconductor lasers,” Appl. Phys. Lett. 72, 1284–1286 (1998). [CrossRef]
  23. R. Martı́nez-Herrero, P. M. Mejı́as, J. M. Movilla, “Spatial characterization of partially polarized beams,” Opt. Lett. 22, 206–208 (1997). [CrossRef]
  24. A. A. Tovar, “Production and propagation of cylindrically polarized Laguerre Gaussian laser beams,” J. Opt. Soc. Am. A 15, 2705–2711 (1998). [CrossRef]
  25. F. Gori, “Matrix treatment for partially polarized, partially coherent beams,” Opt. Lett. 23, 241 (1998). [CrossRef]
  26. F. Gori, M. Santarsiero, S. Vicalvi, R. Borghi, G. Guattari, “Beam coherence-polarization matrix,” J. Eur. Opt. Soc. A Pure Appl. Opt., 7, 941–951 (1998). [CrossRef]
  27. F. Gori, M. Santarsiero, G. Piquero, R. Borghi, A. Mondello, R. Simon, “Partially polarized Gaussian Schell-model beams,” J. Opt. Pure Appl. Opt. 3, 1–9 (2001). [CrossRef]
  28. J. Pu, B. Lu, “Focal shifts in focused nonuniformly polarized beams,” J. Opt. Soc. Am. A 18, 2760–2766 (2001). [CrossRef]
  29. F. Gori, G. Guattari, C. Palma, C. Padovani, “Specular cross-spectral density functions,” Opt. Commun. 68, 239–243 (1988). [CrossRef]
  30. S. K. Berberian, Introduction to Hilbert Space (Oxford U. Press, Oxford, UK, 1961).
  31. E. Kreyszig, Introductory Functional Analysis with Applications (Wiley, New York, 1978).
  32. M. Born, E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, Cambridge, UK, 1999).
  33. E. Wolf, “New theory of partial coherence in the space-frequency domain. Part I: Spectra and cross-spectra of steady-state sources,” J. Opt. Soc. Am. 72, 343–351 (1982). [CrossRef]
  34. C. Cohen-Tannoudji, B. Diu, F. Laloe, Quantum Mechanics (Wiley, Paris, 1977).
  35. F. Gori, M. Santarsiero, R. Borghi, G. Guattari, “The irradiance of partially polarized beams in a scalar treatment,” Opt. Commun. 163, 159–163 (1999). [CrossRef]
  36. C. Brosseau, Fundamentals of Polarized Light (Wiley, New York, 1998).
  37. F. Gori, “Collett–Wolf sources and multimode laser,” Opt. Commun. 34, 301–305 (1980). [CrossRef]
  38. A. Starikov, E. Wolf, “Coherent-mode representation of Gaussian Schell-model sources and of their radiation fields,” J. Opt. Soc. Am. 72, 923–928 (1982). [CrossRef]
  39. M. Abramowitz, I. Stegun, Handbook of Mathematical Functions (Dover, New York, 1972).
  40. F. Gori, “Mode propagation of the field generated by Collet–Wolf Schell-model sources,” Opt. Commun. 46, 149–154 (1983). [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.

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited