Abstract

The Hamiltonian of the Luneburg lens K is invariant not merely under rotations but under a wider group of unitary transformations. This has two immediate consequences: First, by inspection one can write down ray integrals sufficient in number to describe fully the shapes and disposition of rays; second, K is one of the rare, nontrivial systems for which the point characteristic can be exhibited in closed, nonparametric form. This paper sets out in detail what has just been described in outline.

© 1983 Optical Society of America

Exact analytical solution of the generalized Luneburg lens problem

Jacek Sochacki
J. Opt. Soc. Am. 73(6) 789-795 (1983)

General solution of the non-full-aperture Luneburg lens problem

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Hamiltonian analysis of beams in an optical slab guide

Walter K. Kahn and Shuwen Yang
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Improvements of the ray trace through the generalized Luneburg lens

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Perturbations of the point characteristic

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J. Opt. Soc. Am. A 7(12) 2260-2263 (1990)