Abstract

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 <i>f</i> numbers down to <i>f</i>/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

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References

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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.

1977 (1)

1974 (1)

F. Zernike, "Luneburg Lens for Optical Waveguide Use," Opt. Commun. 12, 379–381 (1974).

1958 (1)

S. P. Morgan, "General Solution of the Luneburg Lens Problem," J. Appl. Phys. 29, 1358 (1958).

Anderson, D. B.

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).

August, R. R.

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).

Boyd, J. T.

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).

Davis, R. L.

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).

Hamilton, M. C.

M. C. Hamilton, D. A. Wille, and W. J. Miceli, "An Integrated Optical RF Spectrum Analyzer," IEEE 1976 Ultrasonic Symposium Proceedings, Annapolis, Md.

Krylov, V. J.

V. J. Krylov, Approximate Calculation of Integrals (Macmillian, New York, 1962), pp. 100–111 and 337–340.

Luneburg, R. K.

R. K. Luneburg, Mathematical Theory of Optics (University of California Press, Berkeley, 1966), p. 187.

Miceli, W. J.

M. C. Hamilton, D. A. Wille, and W. J. Miceli, "An Integrated Optical RF Spectrum Analyzer," IEEE 1976 Ultrasonic Symposium Proceedings, Annapolis, Md.

Morgan, S. P.

S. P. Morgan, "General Solution of the Luneburg Lens Problem," J. Appl. Phys. 29, 1358 (1958).

Southwell, W. H.

Wille, D. A.

M. C. Hamilton, D. A. Wille, and W. J. Miceli, "An Integrated Optical RF Spectrum Analyzer," IEEE 1976 Ultrasonic Symposium Proceedings, Annapolis, Md.

Zernike, F.

F. Zernike, "Luneburg Lens for Optical Waveguide Use," Opt. Commun. 12, 379–381 (1974).

J. Appl. Phys. (1)

S. P. Morgan, "General Solution of the Luneburg Lens Problem," J. Appl. Phys. 29, 1358 (1958).

J. Opt. Soc. Am. (1)

Opt. Commun. (1)

F. Zernike, "Luneburg Lens for Optical Waveguide Use," Opt. Commun. 12, 379–381 (1974).

Other (4)

V. J. Krylov, Approximate Calculation of Integrals (Macmillian, New York, 1962), pp. 100–111 and 337–340.

R. K. Luneburg, Mathematical Theory of Optics (University of California Press, Berkeley, 1966), p. 187.

M. C. Hamilton, D. A. Wille, and W. J. Miceli, "An Integrated Optical RF Spectrum Analyzer," IEEE 1976 Ultrasonic Symposium Proceedings, Annapolis, Md.

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).

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