OSA's Digital Library

Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 20, Iss. 3 — Jan. 30, 2012
  • pp: 2548–2555

Degree of phase-space separability of statistical pulses

Sergey A. Ponomarenko  »View Author Affiliations

Optics Express, Vol. 20, Issue 3, pp. 2548-2555 (2012)

View Full Text Article

Enhanced HTML    Acrobat PDF (738 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



We introduce the concept of phase-space separability degree of statistical pulses and show how it can be determined using a bi-orthogonal decomposition of the pulse Wigner distribution. We present explicit analytical results for the case of chirped Gaussian Schell-model pulses. We also demonstrate that chirping of the pulsed source serves as a powerful tool to control coherence and phase-space separability of statistical pulses.

© 2012 OSA

OCIS Codes
(030.0030) Coherence and statistical optics : Coherence and statistical optics
(320.0320) Ultrafast optics : Ultrafast optics
(320.5550) Ultrafast optics : Pulses

ToC Category:
Coherence and Statistical Optics

Original Manuscript: December 13, 2011
Revised Manuscript: January 9, 2012
Manuscript Accepted: January 10, 2012
Published: January 19, 2012

Sergey A. Ponomarenko, "Degree of phase-space separability of statistical pulses," Opt. Express 20, 2548-2555 (2012)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. T. Brabec and F. Krausz, “Intense few-cycle laser fields: Frontiers of nonlinear optics,” Rev. Mod. Phys.72, 545–591 (2000). [CrossRef]
  2. P. Pääkkönen, J. Turunen, P. Vahimaa, A. T. Friberg, and F. Wyrowski, “Partially coherent Gaussian pulses,” Opt. Commun.204, 53–58 (2002). [CrossRef]
  3. H. Lajunen, J. Tervo, J. Turunen, P. Vahimaa, and F. Wyrowski, “Spectral coherence properties of temporarily modulated stationary light sources,” Opt. Express11, 1894–1899 (2003). [CrossRef] [PubMed]
  4. S. A. Ponomarenko, G. P. Agrawal, and E. Wolf, “Energy spectrum of a nonstationary ensemble of pulses,” Opt. Lett.29, 394–396 (2004). [CrossRef] [PubMed]
  5. V. Torres-Company, H. Lajunen, and A. T. Friberg, “Cohrence theory of noise in ultrashort pulse trains,” J. Opt. Soc. Am. B24, 1441–1450 (2007). [CrossRef]
  6. B. Davis, “Measurable coherence theory for statistically periodic fields,” Phys. Rev. A76, 043843 (2007). [CrossRef]
  7. P. Vahimaa and J. Turunen, “Independent-elementary-pulse representation for non-stationary fields,” Opt. Express14, 5007–5012 (2006). [CrossRef] [PubMed]
  8. A. T. Friberg, H. Lajunen, and V. Torres-Company, “Spectral elementary-coherence-function representation for partially coherent light pulses,” Opt. Express15, 5160–5165 (2007). [CrossRef] [PubMed]
  9. J. Ojeda-Castaneda, J. Lancis, C. M. Gomez-Sarabia, V. Torres-Company, and P. Andrés, “Ambuguity function analysis of pulse train propagation: applications to temporal Lau filtering,” J. Opt. Soc. Am. A242268–2273 (2007). [CrossRef]
  10. M. A. Alonso, “Wigner functions in optics: describing beams as ray bundles and pulses as particle ensembles,” Adv. Opt. Photon.3, 272–365 (2011). [CrossRef]
  11. S. A. Ponomarenko, “Complex Gaussian representation of statistical pulses,” Opt. Express19, 17086–17091 (2011). [CrossRef] [PubMed]
  12. G. P. Agrawal, Fiber-Optic Communication Systems, 3rd ed., (Wiley, New York, NY2002). [CrossRef]
  13. Q. Lin, L. Wang, and S. Zhu, “Partially coherent light pulse and its propagation,” Opt. Commun.219, 65–70 (2003). [CrossRef]
  14. M. Brunel and S. Coëtlemec, “Fractional-order Fourier formulation of the propagation of partially coherent light pulses,” Opt. Commun.230, 1–5 (2004). [CrossRef]
  15. H. Lajunen, V. Torres-Company, J. Lancis, E. Silvestre, and P. Andrés, “Pulse-by-pulse method to characterize partially coherent pulse propagation in instanteneous nonlonear media,” Opt. Express18, 14979–14991 (2011). [CrossRef]
  16. B. H. Kolner and M. Nazarathy, “Temporal imaging with a time lens,” Opt. Lett.14, 630–632 (1989). [CrossRef] [PubMed]
  17. Although the slowly-varying envelope approximation breaks down for few-cycle long femtosecond pulses, the decomposition into the envelope and carrier wave makes sense even in this case, see Ref. [21] for details.
  18. G. P. Agrawal, Nonlinear Fiber Optics, 4th ed. (Academic Press, Amsterdam, 2007).
  19. M. J. Bastiaans, “The Wigner distribution function applied to optical signals and systems,” Opt. Commun.25, 26–30, (1978). [CrossRef]
  20. M. J. Bastiaans, “The Wigner function and its application to first-order optics,” J. Opt. Soc. Am.69, 1710–1716 (1979). [CrossRef]
  21. J. C. Diels and W. Rudolph, Ultrashort Laser Pulse Phenomena, 2nd ed. (Academic Press, Amsterdam2006).
  22. J. Lancis, V. Torres-Company, E. Silvestre, and P. Andrés, “Space-time analogy for partially coherent plane-wave-type pulses,” Opt. Lett.30, 2973–2975 (2005). [CrossRef] [PubMed]
  23. V. Torres-Company, J. Lancis, and P. Andrés, “Space-time analogies in optics,” Prog. Opt.56, 1–80 (2011), ed. E. Wolf. [CrossRef]
  24. M. G. Raymer, M. Beck, and D. F. McAlister, “Complex wave-field reconstruction using phase-space tomography,” Phys. Rev. Lett.72, 1137–1140 (1994). [CrossRef] [PubMed]
  25. P. M. Morse and H. Feshbach, Methods of Theoretical Physics (McGraw-Hill, New York, 1953), Part I.
  26. L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University Press, 1995).
  27. M. Abramowitz and I. A. Stegan, Handbook of Mathematical Functions (Dover, New York, 1972).
  28. F. Gori, “Collett-Wolf sources and multimode lasers,” Opt. Commun.34, 301–305 (1980). [CrossRef]
  29. A. Starikov and E. Wolf, “Coherent-mode representation of Gaussian Schell-model sources and their radiation fields,” J. Opt. Soc. Am.72, 923–928 (1982). [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