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Journal of the Optical Society of America

Journal of the Optical Society of America

  • Vol. 70, Iss. 8 — Aug. 1, 1980
  • pp: 944–953

Coherent optical feedback for the analog solution of partial differential equations

Jack Cederquist and Sing H. Lee  »View Author Affiliations


JOSA, Vol. 70, Issue 8, pp. 944-953 (1980)
http://dx.doi.org/10.1364/JOSA.70.000944


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Abstract

A confocal Fabry-Perot interferometer is used to produce feedback within an optical processor. The resulting confocal feedback system (CFS) has a complex-valued feedback transfer function and performs analog solution of partial differential equations (PDE’s). The CFS is interfaced to a microcomputer via a laser scanner and video electronics to create a hybrid processor, thus taking a major step toward the practical use of the CFS for the high-speed solution of PDE’s. Solutions to the three types of second-order linear PDE’s in two dimensions—elliptic, hyperbolic, and parabolic—were obtained experimentally and analyzed.

© 1980 Optical Society of America

Citation
Jack Cederquist and Sing H. Lee, "Coherent optical feedback for the analog solution of partial differential equations," J. Opt. Soc. Am. 70, 944-953 (1980)
http://www.opticsinfobase.org/josa/abstract.cfm?URI=josa-70-8-944


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References

  1. J. Cederquist and S. H. Lee, "The Use of Feedback in Optical Information Processing," Appl. Phys. 18, 311–319 (1979).
  2. R. Akins, R. Athale, and S. H. Lee, "Feedback in Analog and Digital Optical Image Processing," Opt. Eng. (to be published).
  3. M. Hercher, "The Spherical Mirror Fabry-Perot Interferometer," Appl. Opt. 7, 951–966 (1968); 7, 1336 (E) (1968).
  4. H. K. V. Lotsch, "The Confocal Resonator System," Optik 30, 1–14, 181–201, 217–233, and 563–576 (1969).
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  8. G. A. Bekey and W. J. Karplus, Hybrid Computation (Wiley, New York, 1968).
  9. S. P. McGrew, in New Concepts and Technologies in Parallel Information Processing, edited by E. R. Caianiello (Noordhoff, Leyden, 1975), pp. 55–73.
  10. N. G. Nakhodkin, A. V. Kuzmenko, V. N. Kurashov, and I. M. Pochernyaev, "Operator Method for Solving Differential Equations in a Digital Computer-Coherent Optical Device Hybrid System," Opt. Spectrosc. 40, 420–422 (1976).
  11. J. Götz, G. Häusler, A. W. Lohmann, and M. Simon, "Solving Differential Equations with TV-Optical Feedback," Proc. Int. Opt. Comput. Conf., London, 1978, pp. 179–180, IEEE Order No. CH1305-2/79/0000-0179.
  12. D. Jablonowski and S. H. Lee, "A Coherent Optical Feedback System for Optical Information Processing," Appl. Phys. 8, 51–58 (1975).
  13. J. Cederquist and S. H. Lee, "The Solution of Partial Differential Equations with Time-Varying Inhomogeneous Terms Using Coherent Optical Feedback," Proc. Int. Opt. Comput. Conf., London, 1978, pp. 181–184, IEEE Order No. CH1305-2/79/0000-0181.
  14. G. Dahlquist and Å. Björck, Numerical Methods (Prentice-Hall, Englewood Cliffs, N.J., 1974), pp. 389–392.
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  16. R. Akins and S. H. Lee, "Coherent Optical Image Amplification by an Injection-Locked Dye Amplifier at 632.8 nm," Appl. Phys. Lett. 35, 660–663 (1979).
  17. Reference 15, pp. 508–509.
  18. R. W. Hockney, Technical Report 53, Institute for Plasma Research, Stanford University, 1966 (unpublished).

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