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 detailwhat has just been described in outline.
© 1983 Optical Society of America
H. A. Buchdahl, "Luneburg lens: unitary invariance and point characteristic," J. Opt. Soc. Am. 73, 490-494 (1983)