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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. 2 — Feb. 1, 2008
  • pp: 365–370

Rotation and gyration of finite two-dimensional modes

Kurt Bernardo Wolf and Tatiana Alieva  »View Author Affiliations

JOSA A, Vol. 25, Issue 2, pp. 365-370 (2008)

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Hermite–Gauss and Laguerre–Gauss modes of a continuous optical field in two dimensions can be obtained from each other through paraxial optical setups that produce rotations in (four-dimensional) phase space. These transformations build the SU ( 2 ) Fourier group that is represented by rigid rotations of the Poincaré sphere. In finite systems, where the emitters and the sensors are in N × N square pixellated arrays, one defines corresponding finite orthonormal and complete sets of two-dimensional Kravchuk modes. Through the importation of symmetry from the continuous case, the transformations of the Fourier group are applied on the finite modes.

© 2008 Optical Society of America

OCIS Codes
(070.2580) Fourier optics and signal processing : Paraxial wave optics
(070.4560) Fourier optics and signal processing : Data processing by optical means
(080.2720) Geometric optics : Mathematical methods (general)
(110.6980) Imaging systems : Transforms
(120.4820) Instrumentation, measurement, and metrology : Optical systems
(350.6980) Other areas of optics : Transforms

ToC Category:
Fourier Optics and Signal Processing

Original Manuscript: October 2, 2007
Manuscript Accepted: November 20, 2007
Published: January 16, 2008

Kurt Bernardo Wolf and Tatiana Alieva, "Rotation and gyration of finite two-dimensional modes," J. Opt. Soc. Am. A 25, 365-370 (2008)

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