## Nonstationary elementary-field light randomly triggered by Poisson impulses |

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

http://dx.doi.org/10.1364/JOSAA.30.000932

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### Abstract

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

**History**

Original Manuscript: January 17, 2013

Manuscript Accepted: March 11, 2013

Published: April 19, 2013

**Citation**

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

http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-30-5-932

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### References

- J. W. Goodman, Statistical Optics (Wiley, 1985).
- W. A. Gardner, A. Napolitano, and L. Paura, “Cyclo-stationarity: half a century of research,” Signal Process. 86, 639–697 (2006).
- R. A. Silverman, “Locally stationary random processes,” IRE Trans. Inform. Theory 3, 182–187 (1956).
- B. J. Davis, “Observable coherence theory for statistically periodic fields,” Phys. Rev. A 76, 043843 (2007). [CrossRef]
- E. Ip and J. M. Kahn, “Power spectra of return-to-zero optical signals,” J. Lightwave Technol. 24, 1610–1618 (2006). [CrossRef]
- P. Vahimaa and J. Turunen, “Independent-elementary-pulse representation for non-stationary fields,” Opt. Express 14, 5007–5012 (2006). [CrossRef]
- J. Turunen, “Elementary-field representations in partially coherent optics,” J. Mod. Opt. 58, 509–527 (2011). [CrossRef]
- F. Gori and C. Palma, “Partially-coherent sources which give rise to highly directional beams,” Opt. Commun. 27, 185–188 (1978). [CrossRef]
- 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]
- R. Loudon, “Non-classical effects in the statistical properties of light,” Rep. Prog. Phys. 43, 913–949 (1980). [CrossRef]
- S. H. Chen and P. Tartaglia, “Light scattering from N non-interacting particles,” Opt. Commun. 6, 119–124 (1972). [CrossRef]
- M. C. Teich and B. E. A. Saleh, “Branching processes in quantum electronics,” IEEE J. Selected Topics Quantum. Electron. 6, 1450–1457 (2000). [CrossRef]
- 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]
- A. Papoulis, Probability, Random Variables, and Stochastic Processes (McGraw-Hill, 1965).
- L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University, 1995).
- W. A. Gardner, Introduction to Random Processes (Macmillan, 1986).
- A. Papoulis, Probability, Random Variables, and Stochastic Processes, 3rd ed. (McGraw-Hill, 1991).
- 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.
- H. E. Rowe, Signals and Noise in Communication Systems (Van Nostrand, 1965), Sect. 2.3.
- J. H. Eberly and K. Wódkiewicz, “The time-dependent physical spectrum of light,” J. Opt. Soc. Am. 67, 1252–1261 (1977). [CrossRef]
- 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]
- 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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