Abstract

The Hamiltonian of the Luneburg lens <i>K</i> 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, <i>K</i> 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

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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).

1982 (1)

1975 (1)

H. A. Buchdahl, "Conformal transformations and conformal invariance of optical systems," Optik 43, 259–274 (1975).

1973 (1)

H. A. Buchdahl, "Rays in gradient-index media: separable systems," J. Opt Soc. Am. 63, 46–49 (1973).

1972 (1)

H. A. Buchdahl, "Characteristic functions of Robertson-Walker spaces," Gen. Rel. Grav. 3, 35–41 (1972).

1970 (1)

Buchdahl, H. A.

H. A. Buchdahl, "Conformal transformations and conformal invariance of optical systems," Optik 43, 259–274 (1975).

H. A. Buchdahl, "Rays in gradient-index media: separable systems," J. Opt Soc. Am. 63, 46–49 (1973).

H. A. Buchdahl, "Characteristic functions of Robertson-Walker spaces," Gen. Rel. Grav. 3, 35–41 (1972).

H. A. Buchdahl, "Hamiltonian optics: the point characteristic of a refracting plane," J. Opt. Soc. Am. 60, 997–1000 (1970).

H. A. Buchdahl, An Introduction to Hamiltonian Optics (Cambridge U. Press, Cambridge, England, 1970).

Forbes, G. W.

Luneburg, R. K.

R. K. Luneburg, Mathematical Theory of Optics (U. California Press, Berkeley, Calif., 1964), p. 187.

McIntosh, H. V.

H. V. McIntosh, Group Theory and Its Applications, E. M. Loebl, ed. (Academic, New York, 1971), Vol. II, pp. 77–84.

Gen. Rel. Grav. (1)

H. A. Buchdahl, "Characteristic functions of Robertson-Walker spaces," Gen. Rel. Grav. 3, 35–41 (1972).

J. Opt Soc. Am. (1)

H. A. Buchdahl, "Rays in gradient-index media: separable systems," J. Opt Soc. Am. 63, 46–49 (1973).

J. Opt. Soc. Am. (2)

Optik (1)

H. A. Buchdahl, "Conformal transformations and conformal invariance of optical systems," Optik 43, 259–274 (1975).

Other (4)

Ref. 5, pp. 84–86.

R. K. Luneburg, Mathematical Theory of Optics (U. California Press, Berkeley, Calif., 1964), p. 187.

H. V. McIntosh, Group Theory and Its Applications, E. M. Loebl, ed. (Academic, New York, 1971), Vol. II, pp. 77–84.

H. A. Buchdahl, An Introduction to Hamiltonian Optics (Cambridge U. Press, Cambridge, England, 1970).

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