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Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Editor: Franco Gori
  • Vol. 30, Iss. 5 — May. 1, 2013
  • pp: 932–940

Nonstationary elementary-field light randomly triggered by Poisson impulses

Carlos R. Fernández-Pousa  »View Author Affiliations

JOSA A, Vol. 30, Issue 5, pp. 932-940 (2013)

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A stochastic theory of nonstationary light describing the random emission of elementary pulses is presented. The emission is governed by a nonhomogeneous Poisson point process determined by a time-varying emission rate. The model describes, in the appropriate limits, stationary, cyclostationary, locally stationary, and pulsed radiation, and reduces to a Gaussian theory in the limit of dense emission rate. The first- and second-order coherence theories are solved after the computation of second- and fourth-order correlation functions by use of the characteristic function. The ergodicity of second-order correlations under various types of detectors is explored and a number of observables, including optical spectrum, amplitude, and intensity correlations, are analyzed.

© 2013 Optical Society of America

OCIS Codes
(000.5490) General : Probability theory, stochastic processes, and statistics
(030.1640) Coherence and statistical optics : Coherence
(030.6600) Coherence and statistical optics : Statistical optics

ToC Category:
Coherence and Statistical Optics

Original Manuscript: January 17, 2013
Manuscript Accepted: March 11, 2013
Published: April 19, 2013

Carlos R. Fernández-Pousa, "Nonstationary elementary-field light randomly triggered by Poisson impulses," J. Opt. Soc. Am. A 30, 932-940 (2013)

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  1. J. W. Goodman, Statistical Optics (Wiley, 1985).
  2. W. A. Gardner, A. Napolitano, and L. Paura, “Cyclo-stationarity: half a century of research,” Signal Process. 86, 639–697 (2006).
  3. R. A. Silverman, “Locally stationary random processes,” IRE Trans. Inform. Theory 3, 182–187 (1956).
  4. B. J. Davis, “Observable coherence theory for statistically periodic fields,” Phys. Rev. A 76, 043843 (2007). [CrossRef]
  5. E. Ip and J. M. Kahn, “Power spectra of return-to-zero optical signals,” J. Lightwave Technol. 24, 1610–1618 (2006). [CrossRef]
  6. P. Vahimaa and J. Turunen, “Independent-elementary-pulse representation for non-stationary fields,” Opt. Express 14, 5007–5012 (2006). [CrossRef]
  7. J. Turunen, “Elementary-field representations in partially coherent optics,” J. Mod. Opt. 58, 509–527 (2011). [CrossRef]
  8. F. Gori and C. Palma, “Partially-coherent sources which give rise to highly directional beams,” Opt. Commun. 27, 185–188 (1978). [CrossRef]
  9. M. Korhonen, A. T. Friberg, J. Turunen, and G. Genty, “Elementary field representation of supercontinuum,” J. Opt. Soc. Am. B 30, 21–26 (2013). [CrossRef]
  10. R. Loudon, “Non-classical effects in the statistical properties of light,” Rep. Prog. Phys. 43, 913–949 (1980). [CrossRef]
  11. S. H. Chen and P. Tartaglia, “Light scattering from N non-interacting particles,” Opt. Commun. 6, 119–124 (1972). [CrossRef]
  12. M. C. Teich and B. E. A. Saleh, “Branching processes in quantum electronics,” IEEE J. Selected Topics Quantum. Electron. 6, 1450–1457 (2000). [CrossRef]
  13. B. E. A. Saleh, D. Stoler, and M. C. Teich, “Coherence and photon statistics for optical fields generated by Poisson random emissions,” Phys. Rev. A 27, 360–374 (1983). [CrossRef]
  14. A. Papoulis, Probability, Random Variables, and Stochastic Processes (McGraw-Hill, 1965).
  15. L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University, 1995).
  16. W. A. Gardner, Introduction to Random Processes (Macmillan, 1986).
  17. A. Papoulis, Probability, Random Variables, and Stochastic Processes, 3rd ed. (McGraw-Hill, 1991).
  18. S. O. Rice, “Mathematical analysis of random noise,” Bell Systems Tech. J. 23, 282-332 (1944) and 24, 46–156 (1945). Reprinted in N. Wax, Selected Papers on Noise and Stochastic Processes (Dover, 2003), Sect. 2.5.
  19. H. E. Rowe, Signals and Noise in Communication Systems (Van Nostrand, 1965), Sect. 2.3.
  20. J. H. Eberly and K. Wódkiewicz, “The time-dependent physical spectrum of light,” J. Opt. Soc. Am. 67, 1252–1261 (1977). [CrossRef]
  21. M. Nazarathy, W. V. Sorin, D. M. Baney, and S. A. Newton, “Spectral analysis of optical mixing measurements,” J. Lightwave Technol. 7, 1083–1096 (1989). [CrossRef]
  22. S. A. Ponomarenko, G. P. Agrawal, and E. Wolf, “Energy spectrum of a nonstationary ensemble of pulses,” Opt. Lett. 29, 394–396 (2004). [CrossRef]

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