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Symplectic singularities and optical diffraction

  • S. Janeczko
  • Ian Stewart
Conference paper
Part of the Lecture Notes in Mathematics book series (LNM, volume 1463)

Abstract

Singularities of symplectic mappings are important in mathematical physics; for example in optics they determine the geometry of caustics. Here we survey the structure of symplectic singularities and extend the results from mappings to symplectic relations, by making use of Lagrangian varieties (which may have singularities) in place of Lagrangian manifolds. We explain how these ideas apply to classical ray-optical diffraction: the highly singular geometry in physical space turns out to be the projection of well-behaved geometry in phase space. In particular we classify generic caustics by diffraction in a half-line aperture, and discuss diffraction at a circular obstacle.

Keywords

Canonical Variety Symplectic Manifold Symplectic Structure Lagrangian Submanifolds Symplectic Geometry 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag 1991

Authors and Affiliations

  • S. Janeczko
  • Ian Stewart

There are no affiliations available

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