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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. 23, Iss. 8 — Aug. 1, 2006
  • pp: 1875–1883

First-order optical systems with unimodular eigenvalues

Martin J. Bastiaans and Tatiana Alieva  »View Author Affiliations

JOSA A, Vol. 23, Issue 8, pp. 1875-1883 (2006)

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It is shown that a lossless first-order optical system whose real symplectic ray transformation matrix can be diagonalized and has only unimodular eigenvalues is similar to a separable fractional Fourier transformer in the sense that the ray transformation matrices of the unimodular system and the separable fractional Fourier transformer are related by means of a similarity transformation. Moreover, it is shown that the system that performs this similarity transformation is itself a lossless first-order optical system. Based on the fact that Hermite–Gauss functions are the eigenfunctions of a fractional Fourier transformer, the eigenfunctions of a unimodular first-order optical system can be formulated and belong to the recently introduced class of orthonormal Hermite–Gaussian-type modes. Two decompositions of a unimodular first-order optical system are considered, and one of them is used to derive an easy optical realization in more detail.

© 2006 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

ToC Category:
Fourier Optics and Optical Signal Processing

Original Manuscript: November 10, 2005
Revised Manuscript: February 7, 2006
Manuscript Accepted: February 10, 2006

Martin J. Bastiaans and Tatiana Alieva, "First-order optical systems with unimodular eigenvalues," J. Opt. Soc. Am. A 23, 1875-1883 (2006)

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