About the Gaussian-Schell pulse train spectrum

doi:10.1364/OE.15.002803

About the Gaussian-Schell pulse train spectrum

B. Lacaze »View Author Affiliations

Optics Express, Vol. 15, Issue 6, pp. 2803-2809 (2007)
http://dx.doi.org/10.1364/OE.15.002803

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Abstract

The Gaussian-Schell (G-S) pulse model describes variations in Gaussian shaped light pulses. Recent studies proposed random functions fitted to G-S pulses in a non-stationary context. More specifically, this paper provides a cyclo-stationary model. The associated power spectrum is derived. A correlation between pulses is shown to remove the power spectrum Gaussian character.

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

ToC Category:
Coherence and Statistical Optics

History
Original Manuscript: December 21, 2006
Revised Manuscript: February 14, 2007
Manuscript Accepted: March 3, 2007
Published: March 19, 2007

Citation
B. Lacaze, "About the Gaussian-Schell pulse train spectrum," Opt. Express 15, 2803-2809 (2007)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-15-6-2803

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References

S. B. Cavalcanti, "Theory of incoherent self-phase modulation of non-stationary pulses," New J. Phys. 419.1-19.11 (2002). [CrossRef]
L. W. CouchII, Digital and Analog Communications, (MacMillan, 1990).
H. Cramer, M. R. Leadbetter, Stationary and Related Stochastic Processes, (Wiley, 1966).
W. Feller, An Introduction to Probability Theory and its Applications, (Wiley, 1966).
A. Gardner, Introduction to Random processes with Applications to Signals and Systems, (Mc Graw Hill, 1990).
S. M. Kay, Modern Spectral Estimation, (Prentice Hall, 1988).
B. Lacaze, Processus al’eatoires pour communicatons num eriques, (Hermes, Paris, 2000).
B. Lacaze, "Calcul des spectres de puissance des processus caract`ere cyclostationnaire," Traitement du Signal, 14, 63-71 (1997).
H. Lajunen, J. Turunen, P. Vahimaa, J. Tervo, F. Wyrowski, "Spectrally partially coherent pulse trains in dispersive media," Opt. Commun. 255, 12-22 (2005). [CrossRef]
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]
Q. Lin, L. Wang, S. Zhu, "Partially coherent light pulse and its propagation," Opt. Commun. 219, 65-70 (2003). [CrossRef]
P. Paakkonen, J. Turunen, P. Vahimaa, A. Friberg, F. Wyrowski, "Partially coherent Gaussian pulses," Opt. Commun. 204, 53-58 (2002). [CrossRef]
M. Paciaroni, M. Linne, "Single-shot, two-dimensional ballistic imaging through scattering media," Appl. Opt. 43, 5100-5109 (2004). [CrossRef] [PubMed]
A. Papoulis, Probability, Random Variables and Stochastic Processes, (McGraw-Hill, 1965).
O. Pottiez, O. Deparis, R. Kiyan, P. M egret, M. Blondel, "Measurements of pulse width and amplitude jitter noises of gigahertz optical pulse trains by time-domain demodulation," Opt. Lett. 26, 1779-1781 (2001). [CrossRef]
J. G. Proakis, Digital Communications, (Mc Graw Hill, 1995).

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[1] S. B. Cavalcanti, "Theory of incoherent self-phase modulation of non-stationary pulses," New J. Phys. 419.1-19.11 (2002). [CrossRef]

[2] L. W. CouchII, Digital and Analog Communications, (MacMillan, 1990).

[3] H. Cramer, M. R. Leadbetter, Stationary and Related Stochastic Processes, (Wiley, 1966).

[4] W. Feller, An Introduction to Probability Theory and its Applications, (Wiley, 1966).

[5] A. Gardner, Introduction to Random processes with Applications to Signals and Systems, (Mc Graw Hill, 1990).

[6] S. M. Kay, Modern Spectral Estimation, (Prentice Hall, 1988).

[7] B. Lacaze, Processus al’eatoires pour communicatons num eriques, (Hermes, Paris, 2000).

[8] B. Lacaze, "Calcul des spectres de puissance des processus caract`ere cyclostationnaire," Traitement du Signal, 14, 63-71 (1997).

[9] H. Lajunen, J. Turunen, P. Vahimaa, J. Tervo, F. Wyrowski, "Spectrally partially coherent pulse trains in dispersive media," Opt. Commun. 255, 12-22 (2005). [CrossRef]

[10] 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]

[11] Q. Lin, L. Wang, S. Zhu, "Partially coherent light pulse and its propagation," Opt. Commun. 219, 65-70 (2003). [CrossRef]

[12] P. Paakkonen, J. Turunen, P. Vahimaa, A. Friberg, F. Wyrowski, "Partially coherent Gaussian pulses," Opt. Commun. 204, 53-58 (2002). [CrossRef]

[13] M. Paciaroni, M. Linne, "Single-shot, two-dimensional ballistic imaging through scattering media," Appl. Opt. 43, 5100-5109 (2004). [CrossRef] [PubMed]

[14] A. Papoulis, Probability, Random Variables and Stochastic Processes, (McGraw-Hill, 1965).

[15] O. Pottiez, O. Deparis, R. Kiyan, P. M egret, M. Blondel, "Measurements of pulse width and amplitude jitter noises of gigahertz optical pulse trains by time-domain demodulation," Opt. Lett. 26, 1779-1781 (2001). [CrossRef]

[16] J. G. Proakis, Digital Communications, (Mc Graw Hill, 1995).

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About the Gaussian-Schell pulse train spectrum