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Symmetry in Lie optics

Authors
Journal
Annals of Physics
0003-4916
Publisher
Elsevier
Publication Date
Volume
172
Issue
1
Identifiers
DOI: 10.1016/0003-4916(86)90017-5
Disciplines
  • Mathematics

Abstract

Abstract Optical systems produce nonlinear canonical transformations in optical phase space. Free propagation in a homogeneous medium has Euclidean symmetry and dynamical algebras under the Poisson-Lie bracket. Refracting interfaces between homogeneous media exhibit invariants; in particular, a spherical surface possesses an so(3) symmetry algebra which allows the recursive computation of its aberration coefficients to arbitrarily high order. We present explicit results for aberration order nine.

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