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Optics Letters

Optics Letters


  • Editor: Anthony J. Campillo
  • Vol. 32, Iss. 10 — May. 15, 2007
  • pp: 1226–1228

Orthonormal mode sets for the two-dimensional fractional Fourier transformation

Tatiana Alieva and Martin J. Bastiaans  »View Author Affiliations

Optics Letters, Vol. 32, Issue 10, pp. 1226-1228 (2007)

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A family of orthonormal mode sets arises when Hermite–Gauss modes propagate through lossless first-order optical systems. It is shown that the modes at the output of the system are eigenfunctions for the symmetric fractional Fourier transformation if and only if the system is described by an orthosymplectic ray transformation matrix. Essentially new orthonormal mode sets can be obtained by letting helical Laguerre–Gauss modes propagate through an antisymmetric fractional Fourier transformer. The properties of these modes and their representation on the orbital Poincaré sphere are studied.

© 2007 Optical Society of America

OCIS Codes
(070.2580) Fourier optics and signal processing : Paraxial wave optics
(070.4690) Fourier optics and signal processing : Morphological transformations
(080.2730) Geometric optics : Matrix methods in paraxial optics
(120.4820) Instrumentation, measurement, and metrology : Optical systems
(140.3300) Lasers and laser optics : Laser beam shaping

ToC Category:
Fourier Optics and Optical Signal Processing

Original Manuscript: January 16, 2007
Revised Manuscript: February 28, 2007
Manuscript Accepted: February 28, 2007
Published: April 17, 2007

Tatiana Alieva and Martin J. Bastiaans, "Orthonormal mode sets for the two-dimensional fractional Fourier transformation," Opt. Lett. 32, 1226-1228 (2007)

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