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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 19, Iss. 18 — Aug. 29, 2011
  • pp: 17086–17091

Complex Gaussian representation of statistical pulses

Sergey A. Ponomarenko  »View Author Affiliations

Optics Express, Vol. 19, Issue 18, pp. 17086-17091 (2011)

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We develop a general representation for ensembles of non-stationary random pulses in terms of statistically uncorrelated, time-delayed, frequency-shifted Gaussian pulses which are classical counterparts of coherent states of a quantum harmonic oscillator. We show that the two-time correlation function describing second-order statistics of the pulses can be expanded in terms of the complex Gaussian pulses. We also demonstrate how the novel formalism can be applied to describe recently introduced Gaussian Schell-model pulses and pulse trains generated by typical mode-locked lasers.

© 2011 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: July 8, 2011
Revised Manuscript: July 29, 2011
Manuscript Accepted: July 29, 2011
Published: August 16, 2011

Sergey A. Ponomarenko, "Complex Gaussian representation of statistical pulses," Opt. Express 19, 17086-17091 (2011)

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  1. T. Brabec and F. Krausz, “Intense few-cycle laser fields: Frontiers of nonlinear optics,” Rev. Mod. Phys. 72, 545–591 (2000). [CrossRef]
  2. E. Wolf, Introduction to the Theory of Coherence and Polarization (Cambridge University Press, 2007).
  3. L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University Press, 1995).
  4. M. Bertolotti, A. Ferrari, and L. Sereda, “Coherence properties of nonstationary polychromatic light sources,” J. Opt. Soc. Am. B 12, 341–347 (1995). [CrossRef]
  5. L. Sereda, M. Bertolotti, and A. Ferrari, “Coherence properties of nonstationary light wave fields,” J. Opt. Soc. Am. B 15, 695–705 (1998). [CrossRef]
  6. 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]
  7. B. Davis, “Measurable coherence theory for statistically periodic fields,” Phys. Rev. A 76, 043843 (2007). [CrossRef]
  8. P. Pääkkönen, J. Turunen, P. Vahimaa, A. T. Friberg, and F. Wyrowski, “Partially coherent Gaussian pulses,” Opt. Commun. 204, 53–58 (2002). [CrossRef]
  9. H. Lajunen, J. Tervo, J. Turunen, P. Vahimaa, and F. Wyrowski, “Spectral coherence properties of temporarily modulated stationary light sources,” Opt. Express 11, 1894–1899 (2003). [CrossRef] [PubMed]
  10. P. Vahimaa and J. Turunen, “Independent-elementary-pulse representation for non-stationary fields,” Opt. Express 14, 5007–5012 (2006). [CrossRef] [PubMed]
  11. Q. Lin, L. Wang, and S. Zhu, “Partially coherent light pulse and its propagation,” Opt. Commun. 219, 65–70 (2003). [CrossRef]
  12. M. Brunel and S. Coëtlemec, “Fractional-order Fourier formulation of the propagation of partially coherent light pulses,” Opt. Commun. 230, 1–5 (2004). [CrossRef]
  13. R. W. Schoonover, B. J. Davis, and P. S. Carney, “The generalized Wolf shift for cyclostationary fields,” Opt. Express 17, 4705–4711 (2009). [CrossRef] [PubMed]
  14. G. Arfken, Mathematical Methods for Physicists (Academic Press, 1970).
  15. 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. [19] for details.
  16. S. A. Ponomarenko, J. J. Greffet, and E. Wolf, “Diffusion of partially coherent beams in turbulent media,” Opt. Commun. 208, 1–8 (2002). [CrossRef]
  17. E. Wolf, “New theory of partial coherence in space-frequency domain. Part I: Spectra and cross-spectra of steady-state sources,” J. Opt. Soc. Am. 72, 343–351 (1982). [CrossRef]
  18. P. W. Milonni and J. H. Eberly, Lasers (Wiley, 1988).
  19. J. C. Diels and W. Rudolph, Ultrashort Laser Pulse Phenomena, 2nd ed. (Academic Press, 2006).

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