OSA's Digital Library

Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Vol. 22, Iss. 8 — Aug. 1, 2005
  • pp: 1536–1545

Theory of spatially and spectrally partially coherent pulses

Hanna Lajunen, Pasi Vahimaa, and Jani Tervo  »View Author Affiliations

JOSA A, Vol. 22, Issue 8, pp. 1536-1545 (2005)

View Full Text Article

Enhanced HTML    Acrobat PDF (153 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



A coherent-mode representation for spatially and spectrally partially coherent pulses is derived both in the space–frequency domain and in the space–time domain. It is shown that both the cross-spectral density and the mutual coherence function of partially coherent pulses can be expressed as a sum of spatially and spectrally and temporally completely coherent modes. The concept of the effective degree of coherence for nonstationary fields is introduced. As an application of the theory, the propagation of Gaussian Schell-model pulsed beams in the space–frequency domain is considered and their coherent-mode representation is presented.

© 2005 Optical Society of America

OCIS Codes
(030.1640) Coherence and statistical optics : Coherence
(030.6600) Coherence and statistical optics : Statistical optics
(320.5550) Ultrafast optics : Pulses

Original Manuscript: December 17, 2004
Manuscript Accepted: February 2, 2005
Published: August 1, 2005

Hanna Lajunen, Jani Tervo, and Pasi Vahimaa, "Theory of spatially and spectrally partially coherent pulses," J. Opt. Soc. Am. A 22, 1536-1545 (2005)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. L. Mandel, E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, 1995). [CrossRef]
  2. B. Cairns, E. Wolf, “The instantaneous cross-spectral density of non-stationary wavefields,” Opt. Commun. 62, 215–218 (1986). [CrossRef]
  3. M. Bertolotti, A. Ferrari, L. Sereda, “Coherence properties of nonstationary polychromatic light sources,” J. Opt. Soc. Am. B 12, 341–347 (1995). [CrossRef]
  4. L. Sereda, M. Bertolotti, A. Ferrari, “Coherence properties of nonstationary light wave fields,” J. Opt. Soc. Am. A 15, 695–705 (1998). [CrossRef]
  5. M. Bertolotti, L. Sereda, A. Ferrari, “Application of the spectral representation of stochastic process to the study of nonstationary light radiation: a tutorial,” Pure Appl. Opt. 6, 153–171 (1997). [CrossRef]
  6. P. Pääkkönen, J. Turunen, P. Vahimaa, A. T. Friberg, F. Wyrowski, “Partially coherent Gaussian pulses,” Opt. Commun. 204, 53–58 (2002). [CrossRef]
  7. S. A. Ponomarenko, G. P. Agrawal, E. Wolf, “Energy spectrum of a nonstationary ensemble of pulses,” Opt. Lett. 29, 394–396 (2004). [CrossRef] [PubMed]
  8. H. Lajunen, J. Tervo, J. Turunen, P. Vahimaa, F. Wyrowski, “Spectral coherence properties of temporally modulated stationary light sources,” Opt. Express 11, 1894–1899 (2003). [CrossRef] [PubMed]
  9. H. Lajunen, J. Tervo, 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]
  10. H. Lajunen, J. Turunen, P. Vahimaa, J. Tervo, F. Wyrowski, “Spectrally partially coherent pulse trains in dispersive media,” submitted to Opt. Commun..
  11. M. J. Bastiaans, “New class of uncertainty relations for partially coherent light,” J. Opt. Soc. Am. A 1, 711–715 (1984). [CrossRef]
  12. P. Vahimaa, 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]
  13. I. P. Christov, “Propagation of partially coherent light pulses,” Opt. Acta 33, 63–77 (1986). [CrossRef]
  14. L. Wang, Q. Lin, H. Chen, S. Zhu, “Propagation of partially coherent pulsed beams in the spatiotemporal domain,” Phys. Rev. E 67, 056612 (2003). [CrossRef]
  15. G. B. Arfken, H. J. Weber, Mathematical Methods for Physicists (Academic, 2001).
  16. E. Wolf, “New spectral representation of random sources and of the partially coherent fields that they generate,” Opt. Commun. 38, 3–6 (1981). [CrossRef]
  17. 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]
  18. E. Wolf, “New theory of partial coherence in the space–frequency domain. Part II: steady-state fields and higher-order correlations,” J. Opt. Soc. Am. A 3, 76–85 (1986). [CrossRef]
  19. G. S. Agarwal, E. Wolf, “Higher-order coherence functions in the space–frequency domain,” J. Mod. Opt. 40, 1489–1496 (1993). [CrossRef]
  20. F. Gori, M. Santarsiero, R. Simon, G. Piquero, R. Borghi, G. Guattari, “Coherent-mode decomposition of partially polarized, partially coherent sources,” J. Opt. Soc. Am. A 20, 78–84 (2003). [CrossRef]
  21. J. Tervo, T. Setälä, A. T. Friberg, “Theory of partially coherent electromagnetic fields in the space–frequency domain,” J. Opt. Soc. Am. A 21, 2205–2215 (2004). [CrossRef]
  22. L. Mandel, E. Wolf, “Complete coherence in the space–frequency domain,” Opt. Commun. 36, 247–249 (1981). [CrossRef]
  23. T. Setälä, J. Tervo, A. T. Friberg, “Complete electromagnetic coherence in the space–frequency domain,” Opt. Lett. 29, 328–330 (2004). [CrossRef]
  24. F. Riesz, B. Sz.-Nagy, Functional Analysis (Ungar, 1978), p. 245.
  25. A. T. Friberg, R. J. Sudol, “Propagation parameters of Gaussian Schell-model beams,” Opt. Commun. 41, 383–387 (1982). [CrossRef]
  26. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1996).
  27. R. W. Ziolkowski, J. B. Judkins, “Propagation characteristics of ultrawide-bandwidth pulsed Gaussian beams,” J. Opt. Soc. Am. A 9, 2021–2030 (1992). [CrossRef]
  28. E. Wolf, “Invariance of the spectrum of light on propagation,” Phys. Rev. Lett. 56, 1370–1372 (1986). [CrossRef] [PubMed]
  29. Z. Dačić, E. Wolf, “Changes in the spectrum of a partially coherent light beam propagating in free space,” J. Opt. Soc. Am. A 5, 1118–1126 (1988). [CrossRef]
  30. Z. Wang, Z. Zhang, Z. Xu, Q. Lin, “Spectral and temporal properties of ultrashort light pulse in the far zone,” Opt. Commun. 123, 5–10 (1996). [CrossRef]
  31. G. P. Agrawal, “Spectrum-induced changes in diffraction of pulsed optical beams,” Opt. Commun. 157, 52–56 (1998). [CrossRef]
  32. F. Gori, “Collett–Wolf sources and multimode lasers,” Opt. Commun. 34, 301–305 (1980). [CrossRef]
  33. 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]
  34. F. Gori, “Mode propagation of the field generated by Collett–Wolf Schell-model sources,” Opt. Commun. 34, 301–305 (1980). [CrossRef]
  35. A. E. Siegman, Lasers (University Science, 1986).

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