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Related Experiment Videos

Uncertainty products for nonparaxial wave fields.

M A Alonso1, G W Forbes

  • 1Department of Physics, Macquarie University, Sydney, NSW, Australia. alonso@physics.mq.edu.au

Journal of the Optical Society of America. A, Optics, Image Science, and Vision
|January 5, 2001
PubMed
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We introduce new measures for spatial and directional spreads of nonparaxial waves, extending the concept of maximal localization. These measures establish fundamental limits on joint localization in coordinate and frequency space for wave fields.

Area of Science:

  • Physics
  • Optics
  • Wave Phenomena

Background:

  • Maximal localization is crucial for phase-space representations of fields.
  • This concept has not been fully explored for general wave fields.

Purpose of the Study:

  • Develop measures of spatial and directional spreads for nonparaxial waves.
  • Establish limits on joint localization in coordinate and frequency space.

Main Methods:

  • Formulate invariant measures for spatial and directional spreads.
  • Analyze nonparaxial wave fields in free space.
  • Generalize from 2D to 3D fields.

Main Results:

  • Developed translationally and rotationally invariant measures for nonparaxial wave spreads.

Related Experiment Videos

  • Demonstrated that these measures reduce to conventional ones for paraxial fields.
  • Derived an uncertainty relation limiting joint localization in coordinate and frequency space.

    • Conclusions:

    • The developed measures provide a basis for a joint localization measure analogous to the M2 factor.
    • This work extends the concept of maximal localization to general wave fields.
    • The findings have implications for understanding wave propagation and localization limits.