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Journal of the Optical Society of America A

Journal of the Optical Society of America A

| OPTICS, IMAGE SCIENCE, AND VISION

  • Vol. 12, Iss. 3 — Mar. 1, 1995
  • pp: 560–569

Coherent-mode decomposition of general anisotropic Gaussian Schell-model beams

K. Sundar, N. Mukunda, and R. Simon  »View Author Affiliations


JOSA A, Vol. 12, Issue 3, pp. 560-569 (1995)
http://dx.doi.org/10.1364/JOSAA.12.000560


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Abstract

We present a complete solution to the problem of coherent-mode decomposition of the most general anisotropic Gaussian Schell-model (AGSM) beams, which constitute a ten-parameter family. Our approach is based on symmetry considerations. Concepts and techniques familiar from the context of quantum mechanics in the two-dimensional plane are used to exploit the Sp(4, R) dynamical symmetry underlying the AGSM problem. We take advantage of the fact that the symplectic group of first-order optical system acts unitarily through the metaplectic operators on the Hilbert space of wave amplitudes over the transverse plane, and, using the Iwasawa decomposition for the metaplectic operator and the classic theorem of Williamson on the normal forms of positive definite symmetric matrices under linear canonical transformations, we demonstrate the unitary equivalence of the AGSM problem to a separable problem earlier studied by Li and Wolf [ Opt. Lett. 7, 256 ( 1982)] and Gori and Guattari [ Opt. Commun. 48, 7 ( 1983)]. This connection enables one to write down, almost by inspection, the coherent-mode decomposition of the general AGSM beam. A universal feature of the eigenvalue spectrum of the AGSM family is noted.

© 1995 Optical Society of America

History
Original Manuscript: January 10, 1994
Manuscript Accepted: March 2, 1994
Published: March 1, 1995

Citation
K. Sundar, N. Mukunda, and R. Simon, "Coherent-mode decomposition of general anisotropic Gaussian Schell-model beams," J. Opt. Soc. Am. A 12, 560-569 (1995)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-12-3-560

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