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Self-affinity in phase space.

T Alieva1, M J Bastiaans

  • 1Technische Universiteit Eindhoven, Faculteit Elektrotechniek, The Netherlands.

Journal of the Optical Society of America. A, Optics, Image Science, and Vision
|April 11, 2000
PubMed
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Researchers derived the Wigner distribution (WD) in polar coordinates using Hermite-Gauss modes. This new representation simplifies analyzing WD structure and field propagation in optical systems.

Area of Science:

  • Optics
  • Quantum Mechanics
  • Signal Processing

Background:

  • The Wigner distribution (WD) is a time-frequency representation.
  • Analyzing WD in optical systems is complex.
  • Decomposition of fields on orthogonal modes is a known technique.

Purpose of the Study:

  • Derive the Wigner distribution (WD) in polar coordinates.
  • Simplify the analysis of WD structure.
  • Describe field propagation in first-order optical systems.

Main Methods:

  • Decomposition of coherent and partially coherent fields.
  • Utilized orthogonal sets of Hermite-Gauss modes.
  • Derived the WD expression in polar coordinates.

Main Results:

Related Experiment Videos

  • Successfully derived the WD expression in polar coordinates.
  • The new representation simplifies WD structure analysis.
  • Enabled description of field propagation, including self-imaging.

Conclusions:

  • The polar coordinate WD offers a simplified analytical tool.
  • Facilitates understanding of field propagation in optical systems.
  • Provides insights into phenomena like self-imaging.