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Related Experiment Videos

Optical phase space, Wigner representation, and invariant quality parameters.

R Simon1, N Mukunda

  • 1The Institute of Mathematical Sciences, Tharamani, Chennai, India. simon@imsc.ernet.in

Journal of the Optical Society of America. A, Optics, Image Science, and Vision
|January 5, 2001
PubMed
Summary

Quantum mechanics methods, like Wigner

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Area of Science:

  • Optics and Quantum Mechanics
  • Mathematical Physics

Background:

  • Wigner's quasi-probability distribution and related quantum mechanical methods are increasingly utilized in optical applications.
  • Traditional ray and wave optics approaches have limitations in fully describing paraxial optical systems.

Purpose of the Study:

  • To explore the application of Wigner's phase-space representation in paraxial optics.
  • To analyze the behavior of intensity moments for astigmatic partially coherent beams in optical systems.
  • To investigate geometric representations and physical bounds for optical invariants.

Main Methods:

  • Utilizing Wigner's phase-space representation to bridge ray and wave optics.
  • Analyzing second-order intensity moments of astigmatic partially coherent beams.
  • Developing geometric representations for intensity moments and quality parameters.
  • Applying the optical uncertainty principle to establish bounds for invariants.

Main Results:

  • The Wigner representation effectively integrates the strengths of both ray and wave optics for paraxial systems.
  • Characterization of intensity moments for astigmatic partially coherent beams and their propagation through optical systems.
  • Demonstration of geometric representations that highlight optical quality parameters and polynomial invariants.
  • Establishment of fundamental physical limits for these invariants via the optical uncertainty principle.

Conclusions:

  • Wigner's quasi-probability distribution offers a unified framework for paraxial optics.
  • The analysis provides a comprehensive understanding of intensity moment behavior and optical invariant properties.
  • Measurement of ten intensity moments is feasible for astigmatic partially coherent beams.

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