## Geometry and dynamics of squeezing in finite systems

JOSA A, Vol. 24, Issue 9, pp. 2871-2878 (2007)

http://dx.doi.org/10.1364/JOSAA.24.002871

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### Abstract

Squeezing and its inverse magnification form a one-parameter group of linear canonical transformations of continuous signals in paraxial optics. We search for corresponding unitary matrices to apply on signal vectors in *N*-point finite Hamiltonian systems. The analysis is extended to the phase space representation by means of Wigner quasi-probability distribution functions on the discrete torus and on the sphere. Together with two previous studies of the fractional Fourier and Fresnel transforms, we complete the finite counterparts of the group of linear canonical transformations.

© 2007 Optical Society of America

**OCIS Codes**

(070.2590) Fourier optics and signal processing : ABCD transforms

(070.6020) Fourier optics and signal processing : Continuous optical signal processing

(070.6760) Fourier optics and signal processing : Talbot and self-imaging effects

(080.1010) Geometric optics : Aberrations (global)

(090.1970) Holography : Diffractive optics

(200.4560) Optics in computing : Optical data processing

**ToC Category:**

Fourier optics and signal processing

**History**

Original Manuscript: April 16, 2007

Manuscript Accepted: May 23, 2007

Published: August 16, 2007

**Citation**

Kurt Bernardo Wolf and Guillermo Krötzsch, "Geometry and dynamics of squeezing in finite systems," J. Opt. Soc. Am. A **24**, 2871-2878 (2007)

http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-24-9-2871

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### References

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