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Optics Letters

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  • Editor: Alan E. Willner
  • Vol. 34, Iss. 5 — Mar. 1, 2009
  • pp: 551–553

Symplectic-dilation mixed wavelet transform and its correspondence in quantum optics

Hong-yi Fan, Shu-guang Liu, and Li-yun Hu  »View Author Affiliations


Optics Letters, Vol. 34, Issue 5, pp. 551-553 (2009)
http://dx.doi.org/10.1364/OL.34.000551


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Abstract

The symplectic wavelet transform, which is related to the quantum optical Fresnel transform, is developed to the symplectic-dilation mixed wavelet transform (SDWT). The SDWT involves both a real-variable dilation-transform and a complex-variable symplectic transform and possesses well-behaved properties such as the Parseval theorem and the inversion formula. The entangled-coherent state representation not only underlies the SDWT but also helps to derive the corresponding quantum transform operator whose counterpart in classical optics is the lens-Fresnel mixed transform.

© 2009 Optical Society of America

OCIS Codes
(000.3860) General : Mathematical methods in physics
(070.6020) Fourier optics and signal processing : Continuous optical signal processing

ToC Category:
Fourier Optics and Signal Processing

History
Original Manuscript: September 19, 2008
Revised Manuscript: November 15, 2008
Manuscript Accepted: December 3, 2008
Published: February 18, 2009

Citation
Hong-yi Fan, Shu-guang Liu, and Li-yun Hu, "Symplectic-dilation mixed wavelet transform and its correspondence in quantum optics," Opt. Lett. 34, 551-553 (2009)
http://www.opticsinfobase.org/ol/abstract.cfm?URI=ol-34-5-551


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