Abstract

A novel method has been derived for efficient numerical computation of the refractive-index profiles of generalized Luneburg lenses. The integral equation for the index profile is expressed as an infinite series, and the truncation error is evaluated. For focal lengths exceeding twice the lens radius, the series converges rapidly.

© 1981 Optical Society of America

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References

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  1. D. B. Anderson, "Integrated optical spectrum analyzer: an imminent 'chip,' "IEEE Spectrum 15, 22-29 (1978).
  2. S. K. Yao, "Theoretical model of thin-film deposition profile with shadow effect," J. Appl. Phys. 50, 3390-3395 (1979).
  3. P. K. Tien, "Light waves in thin films and integrated optics," Appl. Opt. 10, 2395-2413 (1971).
  4. S. K. Yao et al., "Guided-wave optical thin-film Luneburg lenses: fabrication technique and properties," Appl. Opt. 18, 4067–4079 (1979).
  5. R. K. Luneburg, Mathematical Theory of Optics (U. of California Press, Berkeley, Calif., 1966), p. 187.
  6. S. P. Morgan, "General solution of the Luneburg lens problem," J. Appl. Phys. 29, 1358-1368 (958).
  7. W. H. Southwell, "Index profiles for generalized Luneburg lenses and their use in planar optical waveguides," J. Opt. Soc. Am. 67, 1010-1014 (1977).
  8. R. C. Weast and S. M. Selby, Handbook of Tables for Mathematics, 4th ed. (Chemical Rubber Co., Cleveland, Ohio, 1970), p. 560.
  9. E. Colombini, "Design of thin-film Luneburg lenses for maximum focal length control," Appl. Opt. (to be published).

1979

S. K. Yao, "Theoretical model of thin-film deposition profile with shadow effect," J. Appl. Phys. 50, 3390-3395 (1979).

S. K. Yao et al., "Guided-wave optical thin-film Luneburg lenses: fabrication technique and properties," Appl. Opt. 18, 4067–4079 (1979).

1978

D. B. Anderson, "Integrated optical spectrum analyzer: an imminent 'chip,' "IEEE Spectrum 15, 22-29 (1978).

1977

1971

P. K. Tien, "Light waves in thin films and integrated optics," Appl. Opt. 10, 2395-2413 (1971).

Anderson, D. B.

D. B. Anderson, "Integrated optical spectrum analyzer: an imminent 'chip,' "IEEE Spectrum 15, 22-29 (1978).

Colombini, E.

E. Colombini, "Design of thin-film Luneburg lenses for maximum focal length control," Appl. Opt. (to be published).

Luneburg, R. K.

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

Morgan, S. P.

S. P. Morgan, "General solution of the Luneburg lens problem," J. Appl. Phys. 29, 1358-1368 (958).

Selby, S. M.

R. C. Weast and S. M. Selby, Handbook of Tables for Mathematics, 4th ed. (Chemical Rubber Co., Cleveland, Ohio, 1970), p. 560.

Southwell, W. H.

Tien, P. K.

P. K. Tien, "Light waves in thin films and integrated optics," Appl. Opt. 10, 2395-2413 (1971).

Weast, R. C.

R. C. Weast and S. M. Selby, Handbook of Tables for Mathematics, 4th ed. (Chemical Rubber Co., Cleveland, Ohio, 1970), p. 560.

Yao, S. K.

S. K. Yao et al., "Guided-wave optical thin-film Luneburg lenses: fabrication technique and properties," Appl. Opt. 18, 4067–4079 (1979).

S. K. Yao, "Theoretical model of thin-film deposition profile with shadow effect," J. Appl. Phys. 50, 3390-3395 (1979).

Appl. Opt.

P. K. Tien, "Light waves in thin films and integrated optics," Appl. Opt. 10, 2395-2413 (1971).

Appl. Opt.

IEEE Spectrum

D. B. Anderson, "Integrated optical spectrum analyzer: an imminent 'chip,' "IEEE Spectrum 15, 22-29 (1978).

J. Appl. Phys.

S. K. Yao, "Theoretical model of thin-film deposition profile with shadow effect," J. Appl. Phys. 50, 3390-3395 (1979).

S. P. Morgan, "General solution of the Luneburg lens problem," J. Appl. Phys. 29, 1358-1368 (958).

J. Opt. Soc. Am.

Other

R. C. Weast and S. M. Selby, Handbook of Tables for Mathematics, 4th ed. (Chemical Rubber Co., Cleveland, Ohio, 1970), p. 560.

E. Colombini, "Design of thin-film Luneburg lenses for maximum focal length control," Appl. Opt. (to be published).

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

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