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Optics Express

Optics Express

  • Editor: Michael Duncan
  • Vol. 10, Iss. 16 — Aug. 12, 2002
  • pp: 716–727

Rays, beams and diffraction in a discrete phase space: Wilson bases

John M. Arnold  »View Author Affiliations

Optics Express, Vol. 10, Issue 16, pp. 716-727 (2002)

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For high-frequency fields, which can be separated into superpositions of a few distinct components with rapidly varying phases and slowly varying amplitudes, phase-space representations exhibit a strong localisation in which the coefficients are negligible over most of the phase space. This leads, potentially, to a very large reduction in the computational cost of computing propagators. Using the Windowed Fourier Transform, a number of fundamental problems from diffraction theory are studied using a representation of continuous wavefields by superpositions of beams that are continuously parameterised in phase-space and which propagate along ray trajectories. The existence of noncanonical WFT coefficients is observed, due to the nonuniqeness of the WFT. Numerical evaluations require discrete finite bases. The discrete Wilson basis is generated by a discrete sampling of the windowed Fourier Transform in the phase-space. The sampling is optimal, in the sense that the smallest number of coefficients is generated in an orthogonal basis.

© 2002 Optical Society of America

OCIS Codes
(080.2720) Geometric optics : Mathematical methods (general)
(260.1960) Physical optics : Diffraction theory

ToC Category:
Focus Issue: Rays in wave theory

Original Manuscript: June 13, 2002
Revised Manuscript: August 7, 2002
Published: August 12, 2002

John Arnold, "Rays, beams and diffraction in a discrete phase space: Wilson bases," Opt. Express 10, 716-727 (2002)

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