SYMPLECTIC SINGULARITIES AND OPTICAL DIFFRACTION
UNSPECIFIED. (1991) SYMPLECTIC SINGULARITIES AND OPTICAL DIFFRACTION. LECTURE NOTES IN MATHEMATICS, 1463 . pp. 220-255. ISSN 0075-8434Full text not available from this repository.
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 Langrangian 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.
|Item Type:||Journal Article|
|Subjects:||Q Science > QA Mathematics|
|Journal or Publication Title:||LECTURE NOTES IN MATHEMATICS|
|Number of Pages:||36|
|Page Range:||pp. 220-255|
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