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Advances in Optics and Photonics

Advances in Optics and Photonics


  • Editor: Bahaa E. A. Saleh
  • Vol. 3, Iss. 4 — Dec. 31, 2011

Wigner functions in optics: describing beams as ray bundles and pulses as particle ensembles

Miguel A. Alonso  »View Author Affiliations

Advances in Optics and Photonics, Vol. 3, Issue 4, pp. 272-365 (2011)

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This tutorial gives an overview of the use of the Wigner function as a tool for modeling optical field propagation. Particular emphasis is placed on the spatial propagation of stationary fields, as well as on the propagation of pulses through dispersive media. In the first case, the Wigner function gives a representation of the field that is similar to a radiance or weight distribution for all the rays in the system, since its arguments are both position and direction. In cases in which the field is paraxial and where the system is described by a simple linear relation in the ray regime, the Wigner function is constant under propagation along rays. An equivalent property holds for optical pulse propagation in dispersive media under analogous assumptions. Several properties and applications of the Wigner function in these contexts are discussed, as is its connection with other common phase-space distributions like the ambiguity function, the spectrogram, and the Husimi, P, Q, and Kirkwood–Rihaczek functions. Also discussed are modifications to the definition of the Wigner function that allow extending the property of conservation along paths to a wider range of problems, including nonparaxial field propagation and pulse propagation within general transparent dispersive media.

© 2011 OSA

OCIS Codes
(030.5620) Coherence and statistical optics : Radiative transfer
(070.2590) Fourier optics and signal processing : ABCD transforms
(080.2730) Geometric optics : Matrix methods in paraxial optics
(080.5084) Geometric optics : Phase space methods of analysis
(070.7345) Fourier optics and signal processing : Wave propagation
(070.7425) Fourier optics and signal processing : Quasi-probability distribution functions

ToC Category:
Fourier Optics and Signal Processing

Original Manuscript: June 3, 2011
Revised Manuscript: October 4, 2011
Manuscript Accepted: October 5, 2011
Published: November 21, 2011

Virtual Issues
(2011) Advances in Optics and Photonics

Miguel A. Alonso, "Wigner functions in optics: describing beams as ray bundles and pulses as particle ensembles," Adv. Opt. Photon. 3, 272-365 (2011)

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