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Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Editor: Stephen A. Burns
  • Vol. 25, Iss. 4 — Apr. 1, 2008
  • pp: 974–978

Eigenfunctions of the complex fractional Fourier transform obtained in the context of quantum optics

Hong-Yi Fan, Li-yun Hu, and Ji-suo Wang  »View Author Affiliations

JOSA A, Vol. 25, Issue 4, pp. 974-978 (2008)

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We employ the recently established basis (the two-variable Hermite–Gaussian function) of the generalized Bargmann space (BGBS) [ Phys. Lett. A 303, 311 (2002) ] to study the generalized form of the fractional Fourier transform (FRFT). By using the technique of integration within an ordered product of operators and the bipartite entangled-state representations, we derive the generalized generating function of the BGBS with which the undecomposable kernel of the two-dimensional FRFT [also named complex fractional Fourier transform (CFRFT)] is obtained. This approach naturally shows that the BGBS is just the eigenfunction of the CFRFT.

© 2008 Optical Society of America

OCIS Codes
(270.6570) Quantum optics : Squeezed states
(070.2575) Fourier optics and signal processing : Fractional Fourier transforms

ToC Category:
Fourier Optics and Signal Processing

Original Manuscript: December 21, 2007
Manuscript Accepted: February 15, 2008
Published: March 26, 2008

Hong-Yi Fan, Li-yun Hu, and Ji-suo Wang, "Eigenfunctions of the complex fractional Fourier transform obtained in the context of quantum optics," J. Opt. Soc. Am. A 25, 974-978 (2008)

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