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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 16, Iss. 22 — Oct. 27, 2008
  • pp: 18397–18405

Hilbert and Blaschke phases in the temporal coherence function of stationary broadband light

Carlos R. Fernández-Pousa, Haroldo Maestre, Adrián J. Torregrosa, and Juan Capmany  »View Author Affiliations


Optics Express, Vol. 16, Issue 22, pp. 18397-18405 (2008)
http://dx.doi.org/10.1364/OE.16.018397


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Abstract

We show that the minimal phase of the temporal coherence function γ(τ) of stationary light having a partially-coherent symmetric spectral peak can be computed as a relative logarithmic Hilbert transform of its amplitude with respect to its asymptotic behavior. The procedure is applied to experimental data from amplified spontaneous emission broadband sources in the 1.55 µm band with subpicosecond coherence times, providing examples of degrees of coherence with both minimal and non-minimal phase. In the latter case, the Blaschke phase is retrieved and the position of the Blaschke zeros determined.

© 2008 Optical Society of America

OCIS Codes
(030.1640) Coherence and statistical optics : Coherence
(030.6600) Coherence and statistical optics : Statistical optics
(100.5070) Image processing : Phase retrieval
(060.5625) Fiber optics and optical communications : Radio frequency photonics

ToC Category:
Coherence and Statistical Optics

History
Original Manuscript: July 14, 2008
Revised Manuscript: September 28, 2008
Manuscript Accepted: October 16, 2008
Published: October 24, 2008

Citation
Carlos R. Fernández-Pousa, Haroldo Maestre, Adrian J. Torregrosa, and Juan Capmany, "Hilbert and Blaschke phases in the temporal coherence function of stationary broadband light," Opt. Express 16, 18397-18405 (2008)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-22-18397


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References

  1. L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge Univ. Press, Cambridge, 1995), p. 384.
  2. J. Perina, Coherence of Light, 2nd ed. (Kluwer Ac. Pub., Dordrecht, 1985), p. 46.
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  7. Here we follow the usual Fourier convention exp(−iω t) for the temporal complex oscillation from the physics literature [1, 2]. It is the opposite to that of signal theory, which is the natural for interpreting the experimental radio-frequency measurements [5].
  8. For a reference at νa, the contour should have been completed in the lhp, resulting in a change of sign in the Hilbert phase. The Blaschke zeros would have been located in the lhp and the curves γa(τ) , corresponding to those shown in Figs. 6 and 7, would then be clockwise.
  9. H. M. Nussenzveig, "Phase problem in coherence theory," J. Math. Phys. 8, 561-572 (1967). [CrossRef]
  10. A. V. Oppenheim and R. W. Schafer, Discrete-time signal processing (Prentice-Hall, Englewood Cliffs, NJ, 1989), p. 662.
  11. R. Barakat, "Moment estimator approach to the retrieval problem in coherence theory," J. Opt. Soc. Am. 70, 688-694 (1980). [CrossRef]

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