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Applied Optics

Applied Optics


  • Editor: James C. Wyant
  • Vol. 47, Iss. 22 — Aug. 1, 2008
  • pp: E13–E18

Unifying distribution functions: some lesser known distributions

J. R. Moya-Cessa, H. Moya-Cessa, L. R. Berriel-Valdos, O. Aguilar-Loreto, and P. Barberis-Blostein  »View Author Affiliations

Applied Optics, Vol. 47, Issue 22, pp. E13-E18 (2008)

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We show that there is a way to unify distribution functions that describe simultaneously a classical signal in space and (spatial) frequency and position and momentum for a quantum system. Probably the most well known of them is the Wigner distribution function. We show how to unify functions of the Cohen class, Rihaczek’s complex energy function, and Husimi and Glauber–Sudarshan distribution functions. We do this by showing how they may be obtained from ordered forms of creation and annihilation operators and by obtaining them in terms of expectation values in different eigenbases.

© 2008 Optical Society of America

OCIS Codes
(030.0030) Coherence and statistical optics : Coherence and statistical optics
(070.0070) Fourier optics and signal processing : Fourier optics and signal processing
(270.0270) Quantum optics : Quantum optics

ToC Category:
Novel Analytical Tools

Original Manuscript: December 10, 2007
Revised Manuscript: April 3, 2008
Manuscript Accepted: April 9, 2008
Published: April 24, 2008

J. R. Moya-Cessa, H. Moya-Cessa, L. R. Berriel-Valdos, O. Aguilar-Loreto, and P. Barberis-Blostein, "Unifying distribution functions: some lesser known distributions," Appl. Opt. 47, E13-E18 (2008)

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