Abstract

The design of rounded-edge optical waveguide lenses is presented. The lenses constructed by this method are aberration-free, rotationally symmetric geodesic lenses, where the radius and the focal length are arbitrarily given initial parameters. The rounding section of these lenses is a part of the lens; that is, without the rounding, the lens would not be aberration free. The design involves conversion of uniform refractive index rounding sections of depression lenses into outer annuli of generalized Luneberg lenses. The inner part of each generalized Luneberg lens is constructed with a technique called the annulus technique. Finally, these generalized Luneberg lenses are converted into uniform index depression lenses. The profiles of lenses so constructed are at least one-time continuously differentiable.

© 1979 Optical Society of America

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  1. M. C. Hamilton, D. A. Willie, and M. J. Micele:, "An integrated optical RF spectrum analyzer," Opt. Eng. 16, 475–478 (1977).
  2. F. Zernike, "Luneburg lens for optical waveguide use," Opt. Coinmun. 12, 379–381 (1974).
  3. W. H. Southwell, "Index profiles for generalized Luneburg lenses and their use in planar optical waveguides," J. Opt. Soc. Am. 67, 1010–1014 (1977).
  4. E. Spiller and J. S. Harper, "High resolutions lenses for optical waveguides," Appl. Opt. 13, 2105–2108 (1974).
  5. T. van Duzer, "Lenses and graded films for focusing and guiding acoustic surface waves," Proc. IEEE 58, 1230–1237 (1970).
  6. G. C. Righini, V. Russo, S. Sottini, and G. Toraldo di Francia, "Geodesic lenses for guided optical waves," Appl. Opt. 12, 1477–1481 (1973).
  7. V. E. Wood, "Effects of edge-rounding on geodesic lenses," Appl. Opt. 15, 2817–2820 (1976).
  8. D. W. Vahey and V. E. Wood (paper WE-17), "Integrated-optical corrector plates for waveguide geodesic lenses," J. Opt. Soc. Am. 67, 1393 (1977).
  9. D. Kassai, B. Chen, E. Marom, O. G. Ramer, and M. K. Barnoski, "Aberration corrected geodesic lens for IOC," paper MA-2 of Topical Meeting on Guicled Wave Optics, Salt Lake City, Utah, January 16–18, 1978, (unpublished).
  10. W. H. Southwell, "Geodesic optical waveguide lens analysis," J. Opt. Soc. Am. 67, 1293–1299 (1977).
  11. C. M. Verber, D. W. Vahey, and V. E. Wood, "Focal properties of geodesic waveguide lenses," Appl. Phys. Lett. 28, 514–516 (1976).
  12. L. P. Boivin, "Thin-film laser-to-fiber coupler," Appl. Opt. 13, 391–395 (1974).
  13. G. Toraldo di Francia, "A family of perfect configuration lenses of revolution," Opt. Acta 1, 157–163 (1955).
  14. K. S. Kunz, "Propagation of microwaves between a parallel pair of doubly curved conducting surfaces," J. Appl. Phys. 25, 642–653 (1954).
  15. D. Langwitz, Differential and Riemannian geometry (Academic, New York, 1965), p. 129.
  16. The term generalized Luneberg lens will be used for a planar index variation lens, which useful aperture is not necessarily its diameter, and its focal distance may be greater than its radius.
  17. E. Marom and O. G. Ramer, "Geodesic optical waveguide lens analysis: comment," J. Opt. Soc. Am. 69, 791–792 (1979).
  18. M. Heiblum and J. H. Harris, "Analysis of curved optical waveguides by conformal transformation," IEEE J. Quantum Electron. QE-11, 75–83 (1975).
  19. G. E. Betts, J. C. Bradley, G. E. Marx, D. C. Schubert, and H. A. Trenchard, "Axially symmetric geodesic lenses," Appl. Opt. 17, 2346–2351 (1978).
  20. B. Chen, E. Marom, and R. J. Morrison, "Diffraction-limited geodesic lens for integrated optics circuits," Appl. Phys. Lett. 33, 511–513 (1978).

1979

1978

G. E. Betts, J. C. Bradley, G. E. Marx, D. C. Schubert, and H. A. Trenchard, "Axially symmetric geodesic lenses," Appl. Opt. 17, 2346–2351 (1978).

B. Chen, E. Marom, and R. J. Morrison, "Diffraction-limited geodesic lens for integrated optics circuits," Appl. Phys. Lett. 33, 511–513 (1978).

1977

M. C. Hamilton, D. A. Willie, and M. J. Micele:, "An integrated optical RF spectrum analyzer," Opt. Eng. 16, 475–478 (1977).

D. W. Vahey and V. E. Wood (paper WE-17), "Integrated-optical corrector plates for waveguide geodesic lenses," J. Opt. Soc. Am. 67, 1393 (1977).

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

W. H. Southwell, "Geodesic optical waveguide lens analysis," J. Opt. Soc. Am. 67, 1293–1299 (1977).

1976

V. E. Wood, "Effects of edge-rounding on geodesic lenses," Appl. Opt. 15, 2817–2820 (1976).

C. M. Verber, D. W. Vahey, and V. E. Wood, "Focal properties of geodesic waveguide lenses," Appl. Phys. Lett. 28, 514–516 (1976).

1975

M. Heiblum and J. H. Harris, "Analysis of curved optical waveguides by conformal transformation," IEEE J. Quantum Electron. QE-11, 75–83 (1975).

1974

1973

1955

G. Toraldo di Francia, "A family of perfect configuration lenses of revolution," Opt. Acta 1, 157–163 (1955).

1954

K. S. Kunz, "Propagation of microwaves between a parallel pair of doubly curved conducting surfaces," J. Appl. Phys. 25, 642–653 (1954).

Barnoski, M. K.

D. Kassai, B. Chen, E. Marom, O. G. Ramer, and M. K. Barnoski, "Aberration corrected geodesic lens for IOC," paper MA-2 of Topical Meeting on Guicled Wave Optics, Salt Lake City, Utah, January 16–18, 1978, (unpublished).

Betts, G. E.

Boivin, L. P.

Bradley, J. C.

Chen, B.

B. Chen, E. Marom, and R. J. Morrison, "Diffraction-limited geodesic lens for integrated optics circuits," Appl. Phys. Lett. 33, 511–513 (1978).

D. Kassai, B. Chen, E. Marom, O. G. Ramer, and M. K. Barnoski, "Aberration corrected geodesic lens for IOC," paper MA-2 of Topical Meeting on Guicled Wave Optics, Salt Lake City, Utah, January 16–18, 1978, (unpublished).

di Francia, G. Toraldo

G. C. Righini, V. Russo, S. Sottini, and G. Toraldo di Francia, "Geodesic lenses for guided optical waves," Appl. Opt. 12, 1477–1481 (1973).

G. Toraldo di Francia, "A family of perfect configuration lenses of revolution," Opt. Acta 1, 157–163 (1955).

Hamilton, M. C.

M. C. Hamilton, D. A. Willie, and M. J. Micele:, "An integrated optical RF spectrum analyzer," Opt. Eng. 16, 475–478 (1977).

Harper, J. S.

Harris, J. H.

M. Heiblum and J. H. Harris, "Analysis of curved optical waveguides by conformal transformation," IEEE J. Quantum Electron. QE-11, 75–83 (1975).

Heiblum, M.

M. Heiblum and J. H. Harris, "Analysis of curved optical waveguides by conformal transformation," IEEE J. Quantum Electron. QE-11, 75–83 (1975).

Kassai, D.

D. Kassai, B. Chen, E. Marom, O. G. Ramer, and M. K. Barnoski, "Aberration corrected geodesic lens for IOC," paper MA-2 of Topical Meeting on Guicled Wave Optics, Salt Lake City, Utah, January 16–18, 1978, (unpublished).

Kunz, K. S.

K. S. Kunz, "Propagation of microwaves between a parallel pair of doubly curved conducting surfaces," J. Appl. Phys. 25, 642–653 (1954).

Langwitz, D.

D. Langwitz, Differential and Riemannian geometry (Academic, New York, 1965), p. 129.

Marom, E.

E. Marom and O. G. Ramer, "Geodesic optical waveguide lens analysis: comment," J. Opt. Soc. Am. 69, 791–792 (1979).

B. Chen, E. Marom, and R. J. Morrison, "Diffraction-limited geodesic lens for integrated optics circuits," Appl. Phys. Lett. 33, 511–513 (1978).

D. Kassai, B. Chen, E. Marom, O. G. Ramer, and M. K. Barnoski, "Aberration corrected geodesic lens for IOC," paper MA-2 of Topical Meeting on Guicled Wave Optics, Salt Lake City, Utah, January 16–18, 1978, (unpublished).

Marx, G. E.

Micele, M. J.

M. C. Hamilton, D. A. Willie, and M. J. Micele:, "An integrated optical RF spectrum analyzer," Opt. Eng. 16, 475–478 (1977).

Morrison, R. J.

B. Chen, E. Marom, and R. J. Morrison, "Diffraction-limited geodesic lens for integrated optics circuits," Appl. Phys. Lett. 33, 511–513 (1978).

Ramer, O. G.

E. Marom and O. G. Ramer, "Geodesic optical waveguide lens analysis: comment," J. Opt. Soc. Am. 69, 791–792 (1979).

D. Kassai, B. Chen, E. Marom, O. G. Ramer, and M. K. Barnoski, "Aberration corrected geodesic lens for IOC," paper MA-2 of Topical Meeting on Guicled Wave Optics, Salt Lake City, Utah, January 16–18, 1978, (unpublished).

Righini, G. C.

Russo, V.

Schubert, D. C.

Sottini, S.

Southwell, W. H.

Spiller, E.

Trenchard, H. A.

Vahey, D. W.

D. W. Vahey and V. E. Wood (paper WE-17), "Integrated-optical corrector plates for waveguide geodesic lenses," J. Opt. Soc. Am. 67, 1393 (1977).

C. M. Verber, D. W. Vahey, and V. E. Wood, "Focal properties of geodesic waveguide lenses," Appl. Phys. Lett. 28, 514–516 (1976).

van Duzer, T.

T. van Duzer, "Lenses and graded films for focusing and guiding acoustic surface waves," Proc. IEEE 58, 1230–1237 (1970).

Verber, C. M.

C. M. Verber, D. W. Vahey, and V. E. Wood, "Focal properties of geodesic waveguide lenses," Appl. Phys. Lett. 28, 514–516 (1976).

Willie, D. A.

M. C. Hamilton, D. A. Willie, and M. J. Micele:, "An integrated optical RF spectrum analyzer," Opt. Eng. 16, 475–478 (1977).

Wood, V. E.

D. W. Vahey and V. E. Wood (paper WE-17), "Integrated-optical corrector plates for waveguide geodesic lenses," J. Opt. Soc. Am. 67, 1393 (1977).

C. M. Verber, D. W. Vahey, and V. E. Wood, "Focal properties of geodesic waveguide lenses," Appl. Phys. Lett. 28, 514–516 (1976).

V. E. Wood, "Effects of edge-rounding on geodesic lenses," Appl. Opt. 15, 2817–2820 (1976).

Zernike, F.

F. Zernike, "Luneburg lens for optical waveguide use," Opt. Coinmun. 12, 379–381 (1974).

Appl. Opt.

Appl. Phys. Lett.

C. M. Verber, D. W. Vahey, and V. E. Wood, "Focal properties of geodesic waveguide lenses," Appl. Phys. Lett. 28, 514–516 (1976).

B. Chen, E. Marom, and R. J. Morrison, "Diffraction-limited geodesic lens for integrated optics circuits," Appl. Phys. Lett. 33, 511–513 (1978).

IEEE J. Quantum Electron.

M. Heiblum and J. H. Harris, "Analysis of curved optical waveguides by conformal transformation," IEEE J. Quantum Electron. QE-11, 75–83 (1975).

J. Appl. Phys.

K. S. Kunz, "Propagation of microwaves between a parallel pair of doubly curved conducting surfaces," J. Appl. Phys. 25, 642–653 (1954).

J. Opt. Soc. Am.

Opt. Acta

G. Toraldo di Francia, "A family of perfect configuration lenses of revolution," Opt. Acta 1, 157–163 (1955).

Opt. Coinmun.

F. Zernike, "Luneburg lens for optical waveguide use," Opt. Coinmun. 12, 379–381 (1974).

Opt. Eng.

M. C. Hamilton, D. A. Willie, and M. J. Micele:, "An integrated optical RF spectrum analyzer," Opt. Eng. 16, 475–478 (1977).

Other

D. Langwitz, Differential and Riemannian geometry (Academic, New York, 1965), p. 129.

The term generalized Luneberg lens will be used for a planar index variation lens, which useful aperture is not necessarily its diameter, and its focal distance may be greater than its radius.

T. van Duzer, "Lenses and graded films for focusing and guiding acoustic surface waves," Proc. IEEE 58, 1230–1237 (1970).

D. Kassai, B. Chen, E. Marom, O. G. Ramer, and M. K. Barnoski, "Aberration corrected geodesic lens for IOC," paper MA-2 of Topical Meeting on Guicled Wave Optics, Salt Lake City, Utah, January 16–18, 1978, (unpublished).

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