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Journal of the Optical Society of America

Journal of the Optical Society of America

  • Vol. 69, Iss. 9 — Sep. 1, 1979
  • pp: 1248–1254

General solution of the problem of perfect geodesic lenses for integrated optics

Stefano Sottini, Vera Russo, and Giancarlo C. Righini  »View Author Affiliations


JOSA, Vol. 69, Issue 9, pp. 1248-1254 (1979)
http://dx.doi.org/10.1364/JOSA.69.001248


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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

Citation
Stefano Sottini, Vera Russo, and Giancarlo C. Righini, "General solution of the problem of perfect geodesic lenses for integrated optics," J. Opt. Soc. Am. 69, 1248-1254 (1979)
http://www.opticsinfobase.org/josa/abstract.cfm?URI=josa-69-9-1248


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References

  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).
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  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).
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  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.

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