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Journal of the Optical Society of America

Journal of the Optical Society of America

  • Vol. 67, Iss. 8 — Aug. 1, 1977
  • pp: 1010–1014

Index profiles for generalized Luneburg lenses and their use in planar optical waveguides

W. H. Southwell  »View Author Affiliations

JOSA, Vol. 67, Issue 8, pp. 1010-1014 (1977)

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An analytical approximation is derived which provides a transcendental relationship for the spherically symmetric inhomogeneous index distribution which perfectly focuses infinite objects. Using this expression, the index profiles (called generalized Luneburg lenses) were calculated for lenses having f numbers down to f/1. It is shown through a ray-tracing example that these profiles have sufficient accuracy to provide diffraction-limited performance in the optical wavelength region. It is also shown how these lenses may be utilized in a two-dimensional integrated optics waveguide. Utilizing the focusing property achieved by variations in planar waveguide thickness, circularly symmetric waveguide thickness profiles are derived which have the perfect focusing properties of the generalized Luneburg lenses.

© 1977 Optical Society of America

W. H. Southwell, "Index profiles for generalized Luneburg lenses and their use in planar optical waveguides," J. Opt. Soc. Am. 67, 1010-1014 (1977)

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  1. S. P. Morgan, "General Solution of the Luneburg Lens Problem," J. Appl. Phys. 29, 1358 (1958).
  2. R. K. Luneburg, Mathematical Theory of Optics (University of California Press, Berkeley, 1966), p. 187.
  3. M. C. Hamilton, D. A. Wille, and W. J. Miceli, "An Integrated Optical RF Spectrum Analyzer," IEEE 1976 Ultrasonic Symposium Proceedings, Annapolis, Md.
  4. D. B. Anderson, R. L. Davis, J. T. Boyd, and R. R. August, "Comparison of Optical Waveguide Lens Technologies," J. Quantum Electron., special issue on Integrated Optics, QE13, 275 (1977).
  5. F. Zernike, "Luneburg Lens for Optical Waveguide Use," Opt. Commun. 12, 379–381 (1974).
  6. W. H. Southwell, "Inhomogeneous Optical Waveguide Lens Analysis," J. Opt. Soc. Am. 67, 1004–1009 (1977).
  7. V. J. Krylov, Approximate Calculation of Integrals (Macmillian, New York, 1962), pp. 100–111 and 337–340.

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