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Journal of the Optical Society of America

Journal of the Optical Society of America

  • Vol. 73, Iss. 4 — Apr. 1, 1983
  • pp: 490–494

Luneburg lens: unitary invariance and point characteristic

H. A. Buchdahl  »View Author Affiliations

JOSA, Vol. 73, Issue 4, pp. 490-494 (1983)

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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)

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  1. H. A. Buchdahl, An Introduction to Hamiltonian Optics (Cambridge U. Press, Cambridge, England, 1970).
  2. H. A. Buchdahl, "Hamiltonian optics: the point characteristic of a refracting plane," J. Opt. Soc. Am. 60, 997–1000 (1970).
  3. G. W. Forbes, "Order doubling in the determination of characteristic functions," J. Opt. Soc. Am. 72, 1097–1099 (1982).
  4. H. A. Buchdahl, "Rays in gradient-index media: separable systems," J. Opt Soc. Am. 63, 46–49 (1973).
  5. H. V. McIntosh, Group Theory and Its Applications, E. M. Loebl, ed. (Academic, New York, 1971), Vol. II, pp. 77–84.
  6. H. A. Buchdahl, "Conformal transformations and conformal invariance of optical systems," Optik 43, 259–274 (1975).
  7. Ref. 5, pp. 84–86.
  8. R. K. Luneburg, Mathematical Theory of Optics (U. California Press, Berkeley, Calif., 1964), p. 187.
  9. H. A. Buchdahl, "Characteristic functions of Robertson-Walker spaces," Gen. Rel. Grav. 3, 35–41 (1972).

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