Abstract

The problem of designing waveguide geodesic lenses for integrated optical processing is considered. Geodesic lenses are, at present, the best solution whenever crystals of high refractive index must be used as substrates. A good geodesic lens has to be constituted by a surface of rotation, coupled without discontinuities with the planar optical circuit. The present paper derives, by an analytical procedure, the general expression for the profile of aspherical geodesic lenses able to form perfect geometrical images of the points of two given concentric circles on each other. In particular, the equations that characterize a family of lenses having two conjugate foci external to the lens depression are given. The case of one external and one internal focus is only outlined because it is less important in practice. The advantage of this analytical method is represented by the clear theoretical approach that allows a large flexibility in the lens design without long expensive computations.

© 1979 Optical Society of America

PDF Article

References

  • View by:
  • |
  • |
  • |

  1. R. Shubert and J. H. Harris, "Optical guided-wave focusing and diffraction," J. Opt. Soc. Am. 61, 154–161 (1971).
  2. P. R. Ashley and W. S. C. Chang, "Fresnel lens in a thin-film waveguide," Appl. Phys. Lett. 33, 490–492 (1978).
  3. G. C. Righini, V. Russo, S. Sottini, and G. Toraldo di Francia, "Thin film geodesic lens," Appl. Opt. 11, 1442–1443 (1972).
  4. F. Zernike, "Luneburg lens for optical waveguide use," Opt. Commun. 12, 379–381 (1974).
  5. G. Toraldo di Francia, "Un problema sulle geodetiche delle superfici di rotazione che si presenta nella tecnica delle microonde," Atti Fondaz. Ronchi 12, 151–172 (1957).
  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. G. C. Righini, V. Russo, and S. Sottini, "A family of perfect aspherical geodesic lenses for integrated optical circuits," J. Quantum Electron. QE-15, 1–4 (1979).
  8. B. Chen, E. Marom, and R. J. Morrison, "Diffraction-limited geodesic lens for integrated optics circuits," Appl. Phys Lett. 33, 511–513 (1978).
  9. W. H. Southwell, "Geodesic Optical Waveguide Lens Analysis," J. Opt. Soc. Am. 67, 1293–1299 (1977).
  10. K. S. Kunz, "Propagation of Microwaves Between a Parallel Pair of Doubly Curved Conducting Surfaces," J. Appl. Phys. 25, 642–653 (1954).
  11. M. Bocher, An Introduction to the Study of Integral Equations (Cambridge University, Cambridge, 1909), p. 9.

1979

G. C. Righini, V. Russo, and S. Sottini, "A family of perfect aspherical geodesic lenses for integrated optical circuits," J. Quantum Electron. QE-15, 1–4 (1979).

1978

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

P. R. Ashley and W. S. C. Chang, "Fresnel lens in a thin-film waveguide," Appl. Phys. Lett. 33, 490–492 (1978).

1977

1974

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

1973

1972

1971

1957

G. Toraldo di Francia, "Un problema sulle geodetiche delle superfici di rotazione che si presenta nella tecnica delle microonde," Atti Fondaz. Ronchi 12, 151–172 (1957).

1954

K. S. Kunz, "Propagation of Microwaves Between a Parallel Pair of Doubly Curved Conducting Surfaces," J. Appl. Phys. 25, 642–653 (1954).

Ashley, P. R.

P. R. Ashley and W. S. C. Chang, "Fresnel lens in a thin-film waveguide," Appl. Phys. Lett. 33, 490–492 (1978).

Bocher, M.

M. Bocher, An Introduction to the Study of Integral Equations (Cambridge University, Cambridge, 1909), p. 9.

Chang, W. S. C.

P. R. Ashley and W. S. C. Chang, "Fresnel lens in a thin-film waveguide," Appl. Phys. Lett. 33, 490–492 (1978).

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).

di Francia, G. Toraldo

Harris, J. H.

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).

Marom, E.

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

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).

Righini, G. C.

Russo, V.

Shubert, R.

Sottini, S.

Southwell, W. H.

Zernike, F.

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

Appl. Opt.

Appl. Phys Lett.

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

Appl. Phys. Lett.

P. R. Ashley and W. S. C. Chang, "Fresnel lens in a thin-film waveguide," Appl. Phys. Lett. 33, 490–492 (1978).

Atti Fondaz. Ronchi

G. Toraldo di Francia, "Un problema sulle geodetiche delle superfici di rotazione che si presenta nella tecnica delle microonde," Atti Fondaz. Ronchi 12, 151–172 (1957).

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.

J. Quantum Electron.

G. C. Righini, V. Russo, and S. Sottini, "A family of perfect aspherical geodesic lenses for integrated optical circuits," J. Quantum Electron. QE-15, 1–4 (1979).

Opt. Commun.

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

Other

M. Bocher, An Introduction to the Study of Integral Equations (Cambridge University, Cambridge, 1909), p. 9.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.