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Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Vol. 19, Iss. 12 — Dec. 1, 2002
  • pp: 2436–2444

Hamiltonian orbit structure of the set of paraxial optical systems

Sameen Ahmed Khan and Kurt Bernardo Wolf  »View Author Affiliations

JOSA A, Vol. 19, Issue 12, pp. 2436-2444 (2002)

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In the paraxial regime of three-dimensional optics, two evolution Hamiltonians are equivalent when one can be transformed to the other modulo scale by similarity through an optical system. To determine the equivalence sets of paraxial optical Hamiltonians one requires the orbit analysis of the algebra sp(4, ℜ) of 4×4 real Hamiltonian matrices. Our strategy uses instead the isomorphic algebra so(3, 2) of 5×5 matrices with metric (+1, +1, +1, -1, -1) to find four orbit regions (strata), six isolated orbits at their boundaries, and six degenerate orbits at their common point. We thus resolve the degeneracies of the eigenvalue classification.

© 2002 Optical Society of America

OCIS Codes
(000.3860) General : Mathematical methods in physics
(080.2730) Geometric optics : Matrix methods in paraxial optics

Original Manuscript: March 19, 2002
Revised Manuscript: June 19, 2002
Manuscript Accepted: June 19, 2002
Published: December 1, 2002

Sameen Ahmed Khan and Kurt Bernardo Wolf, "Hamiltonian orbit structure of the set of paraxial optical systems," J. Opt. Soc. Am. A 19, 2436-2444 (2002)

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