Abstract

The optical feature extractor is a photorefractive ring oscillator that can identify the strongest spatio-temporal component of its input space. The theoretical sections discuss the design and performance limitations of the signal extractor. A simple model of the filter’s nonlinear functioning enables the reader to go directly to the experimental section that describes the making of the filter and experimental results. The device, also called the auto-tuning filter, is 5 cm2 in size, has a 3 GHz processing bandwidth, and requires less than 5 mW of continuous optical power to operate.

© 2003 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. I. T. Jolliffe, Principal Component Analysis (Springer-Verlag, Berlin, 1996).
  2. D. Z. Anderson, V. Damiao, E. Fotheringham, D. Popovic, S. Romish, A. Sullivan, Z. Popovic, “Optical processor for X-band lens antenna arrays,” in IEEE Microwave Theory & Techniques-Symposium, Boston, Mass. (2000).
  3. P. Comon, “Independent component analysis, a new concept,” Signal Process. 36, 287–314 (1994).
    [CrossRef]
  4. P. Yeh, Introduction to Photorefractive Nonlinear Optics (Wiley Series in Pure and Applied Optics, New York, 1993).
  5. R. K. Jain, G. J. Dunning, “Spatial and temporal properties of a continuous-wave phase-conjugate resonator based on the photorefractive crystal BaTiO3,” Opt. Lett. 7, 420–422 (1982).
    [CrossRef] [PubMed]
  6. J. O. White, M. Croningolomb, B. Fischer, A. Yariv, “Coherent oscillation by self-induced gratings in the photorefractive crystal BaTiO3,” Appl. Phys. Lett. 40, 450–452 (1982).
    [CrossRef]
  7. M. Croningolomb, A. Yariv, “Plane-wave theory of non-degenerate oscillation in the linear photorefractive passive phase-conjugate mirror,” Opt. Lett. 11, 242–244 (1986).
    [CrossRef]
  8. S. K. Kwong, M. Croningolomb, A. Yariv, “Oscillation with photorefractive gain,” IEEE J. Quantum Electron. 22, 1508–1523 (1986).
    [CrossRef]
  9. L. K. Dai, Y. S. Gou, P. Yeh, C. Gu, “Photorefractive mode-coupling between two unidirectional ring oscillators,” Appl. Phys. B 53, 153–159 (1991).
    [CrossRef]
  10. G. Dalessandro, “Spatiotemporal dynamics of a unidirectional ring oscillator with photorefractive gain,” Phys. Rev. A 46, 2791–2802 (1992).
    [CrossRef]
  11. L. Dambly, H. Zeghlache, “Theory of a multimode photorefractive oscillator—quantitative results on the frequency shift,” Phys. Rev. A 49, 4043–4054 (1994).
    [CrossRef] [PubMed]
  12. M. Kaczmarek, R. W. Eason, “Conditions for efficient build-up of power in photorefractive ring cavities,” Opt. Commun. 154, 334–338 (1998).
    [CrossRef]
  13. O. Sandfuchs, J. Leonardy, F. Kaiser, M. R. Belic, “Spatio-temporal dynamics in photorefractive two-wave mixing configurations: the counterpropagating geometry and the unidirectional ring oscillator,” Chaos Solitons Fractals 10, 709–724 (1999).
  14. P. Gunter, J. P. Huignard, “Photorefractive materials and their applications,” Top. Appl. Phys. 61, 62 (1988).
  15. J. O. White, A. Yariv, “Photorefractive crystals as optical-devices, elements, and processors,” Proceedings of the Society of Photo-Optical Instrumentation Engineers 464, 7–20 (1984).
  16. S. K. Kwong, A. Yariv, M. Croningolomb, I. Ury, “Conversion of optical-path length to frequency by an interferometer using photorefractive oscillation,” Appl. Phys. Lett. 47, 460–462 (1985).
    [CrossRef]
  17. G. J. Dunning, Y. Owechko, B. H. Soffer, “Hybrid optoelectronic neural networks using a mutually pumped phase-conjugate mirror,” Opt. Lett. 16, 928–930 (1991).
    [CrossRef] [PubMed]
  18. Y. H. Ja, “A double-coupler optical fiber ring-loop resonator with degenerate 2-wave mixing,” Opt. Commun. 81, 113–122 (1991).
    [CrossRef]
  19. Y. Frauel, T. Galstyan, G. Pauliat, A. Villing, G. Roosen, “Topological map from a photorefractive self-organizing neural network,” Opt. Commun. 135, 179–188 (1997).
    [CrossRef]
  20. M. S. Petrovic, M. R. Belic, M. V. Jaric, F. Kaiser, “Optical photorefractive flip-flop oscillator,” Opt. Commun. 138, 349–353 (1997).
    [CrossRef]
  21. M. Schwab, M. Saffman, C. Denz, T. Tschudi, “Fourier control of pattern formation in an interferometric feedback configuration,” Opt. Commun. 170, 129–136 (1999).
    [CrossRef]
  22. K. M. Hung, “Optical pattern recognition using a unidirectional photorefractive oscillator coupled with an angular multiplexing volume hologram,” J. Mod. Opt. 47, 655–661 (2000).
  23. A. Desfarges-Berthelemot, V. Kermene, B. Colombeau, M. Vampouille, C. Froehly, “Intracavity beam shaping and referenceless holography,” Opt. Mat. 18, 27–35 (2001).
    [CrossRef]
  24. M. Saffman, C. Benkert, D. Z. Anderson, “Self-organizing photorefractive frequency demultiplexer,” Opt. Lett. 16, 1993–1995 (1991).
    [CrossRef] [PubMed]
  25. D. Z. Anderson, C. Benkert, V. Hebler, J. Jang, D. Montgomery, M. Saffman, “Optical implementation of a self-organizing feature extractor,” Advances in Neural Information Processing Systems IV (1992).
  26. D. Z. Anderson, M. Saffman, A. Hermanns, “Manipulating the information carried by an optical beam with reflexive photorefractive beam coupling,” J. Opt. Soc. Am. B 12, 117–123 (1995).
    [CrossRef]
  27. A. A. Zozulya, M. Saffman, D. Z. Anderson, “Stability analysis of two photorefractive ring resonator circuits: the flip-flop and the feature extractor,” J. Opt. Soc. Am. B 12, 1036–1047 (1994).
    [CrossRef]

2001 (1)

A. Desfarges-Berthelemot, V. Kermene, B. Colombeau, M. Vampouille, C. Froehly, “Intracavity beam shaping and referenceless holography,” Opt. Mat. 18, 27–35 (2001).
[CrossRef]

2000 (1)

K. M. Hung, “Optical pattern recognition using a unidirectional photorefractive oscillator coupled with an angular multiplexing volume hologram,” J. Mod. Opt. 47, 655–661 (2000).

1999 (2)

M. Schwab, M. Saffman, C. Denz, T. Tschudi, “Fourier control of pattern formation in an interferometric feedback configuration,” Opt. Commun. 170, 129–136 (1999).
[CrossRef]

O. Sandfuchs, J. Leonardy, F. Kaiser, M. R. Belic, “Spatio-temporal dynamics in photorefractive two-wave mixing configurations: the counterpropagating geometry and the unidirectional ring oscillator,” Chaos Solitons Fractals 10, 709–724 (1999).

1998 (1)

M. Kaczmarek, R. W. Eason, “Conditions for efficient build-up of power in photorefractive ring cavities,” Opt. Commun. 154, 334–338 (1998).
[CrossRef]

1997 (2)

Y. Frauel, T. Galstyan, G. Pauliat, A. Villing, G. Roosen, “Topological map from a photorefractive self-organizing neural network,” Opt. Commun. 135, 179–188 (1997).
[CrossRef]

M. S. Petrovic, M. R. Belic, M. V. Jaric, F. Kaiser, “Optical photorefractive flip-flop oscillator,” Opt. Commun. 138, 349–353 (1997).
[CrossRef]

1995 (1)

1994 (3)

A. A. Zozulya, M. Saffman, D. Z. Anderson, “Stability analysis of two photorefractive ring resonator circuits: the flip-flop and the feature extractor,” J. Opt. Soc. Am. B 12, 1036–1047 (1994).
[CrossRef]

P. Comon, “Independent component analysis, a new concept,” Signal Process. 36, 287–314 (1994).
[CrossRef]

L. Dambly, H. Zeghlache, “Theory of a multimode photorefractive oscillator—quantitative results on the frequency shift,” Phys. Rev. A 49, 4043–4054 (1994).
[CrossRef] [PubMed]

1992 (1)

G. Dalessandro, “Spatiotemporal dynamics of a unidirectional ring oscillator with photorefractive gain,” Phys. Rev. A 46, 2791–2802 (1992).
[CrossRef]

1991 (4)

L. K. Dai, Y. S. Gou, P. Yeh, C. Gu, “Photorefractive mode-coupling between two unidirectional ring oscillators,” Appl. Phys. B 53, 153–159 (1991).
[CrossRef]

Y. H. Ja, “A double-coupler optical fiber ring-loop resonator with degenerate 2-wave mixing,” Opt. Commun. 81, 113–122 (1991).
[CrossRef]

G. J. Dunning, Y. Owechko, B. H. Soffer, “Hybrid optoelectronic neural networks using a mutually pumped phase-conjugate mirror,” Opt. Lett. 16, 928–930 (1991).
[CrossRef] [PubMed]

M. Saffman, C. Benkert, D. Z. Anderson, “Self-organizing photorefractive frequency demultiplexer,” Opt. Lett. 16, 1993–1995 (1991).
[CrossRef] [PubMed]

1988 (1)

P. Gunter, J. P. Huignard, “Photorefractive materials and their applications,” Top. Appl. Phys. 61, 62 (1988).

1986 (2)

S. K. Kwong, M. Croningolomb, A. Yariv, “Oscillation with photorefractive gain,” IEEE J. Quantum Electron. 22, 1508–1523 (1986).
[CrossRef]

M. Croningolomb, A. Yariv, “Plane-wave theory of non-degenerate oscillation in the linear photorefractive passive phase-conjugate mirror,” Opt. Lett. 11, 242–244 (1986).
[CrossRef]

1985 (1)

S. K. Kwong, A. Yariv, M. Croningolomb, I. Ury, “Conversion of optical-path length to frequency by an interferometer using photorefractive oscillation,” Appl. Phys. Lett. 47, 460–462 (1985).
[CrossRef]

1984 (1)

J. O. White, A. Yariv, “Photorefractive crystals as optical-devices, elements, and processors,” Proceedings of the Society of Photo-Optical Instrumentation Engineers 464, 7–20 (1984).

1982 (2)

J. O. White, M. Croningolomb, B. Fischer, A. Yariv, “Coherent oscillation by self-induced gratings in the photorefractive crystal BaTiO3,” Appl. Phys. Lett. 40, 450–452 (1982).
[CrossRef]

R. K. Jain, G. J. Dunning, “Spatial and temporal properties of a continuous-wave phase-conjugate resonator based on the photorefractive crystal BaTiO3,” Opt. Lett. 7, 420–422 (1982).
[CrossRef] [PubMed]

Anderson, D. Z.

D. Z. Anderson, M. Saffman, A. Hermanns, “Manipulating the information carried by an optical beam with reflexive photorefractive beam coupling,” J. Opt. Soc. Am. B 12, 117–123 (1995).
[CrossRef]

A. A. Zozulya, M. Saffman, D. Z. Anderson, “Stability analysis of two photorefractive ring resonator circuits: the flip-flop and the feature extractor,” J. Opt. Soc. Am. B 12, 1036–1047 (1994).
[CrossRef]

M. Saffman, C. Benkert, D. Z. Anderson, “Self-organizing photorefractive frequency demultiplexer,” Opt. Lett. 16, 1993–1995 (1991).
[CrossRef] [PubMed]

D. Z. Anderson, C. Benkert, V. Hebler, J. Jang, D. Montgomery, M. Saffman, “Optical implementation of a self-organizing feature extractor,” Advances in Neural Information Processing Systems IV (1992).

D. Z. Anderson, V. Damiao, E. Fotheringham, D. Popovic, S. Romish, A. Sullivan, Z. Popovic, “Optical processor for X-band lens antenna arrays,” in IEEE Microwave Theory & Techniques-Symposium, Boston, Mass. (2000).

Belic, M. R.

O. Sandfuchs, J. Leonardy, F. Kaiser, M. R. Belic, “Spatio-temporal dynamics in photorefractive two-wave mixing configurations: the counterpropagating geometry and the unidirectional ring oscillator,” Chaos Solitons Fractals 10, 709–724 (1999).

M. S. Petrovic, M. R. Belic, M. V. Jaric, F. Kaiser, “Optical photorefractive flip-flop oscillator,” Opt. Commun. 138, 349–353 (1997).
[CrossRef]

Benkert, C.

M. Saffman, C. Benkert, D. Z. Anderson, “Self-organizing photorefractive frequency demultiplexer,” Opt. Lett. 16, 1993–1995 (1991).
[CrossRef] [PubMed]

D. Z. Anderson, C. Benkert, V. Hebler, J. Jang, D. Montgomery, M. Saffman, “Optical implementation of a self-organizing feature extractor,” Advances in Neural Information Processing Systems IV (1992).

Colombeau, B.

A. Desfarges-Berthelemot, V. Kermene, B. Colombeau, M. Vampouille, C. Froehly, “Intracavity beam shaping and referenceless holography,” Opt. Mat. 18, 27–35 (2001).
[CrossRef]

Comon, P.

P. Comon, “Independent component analysis, a new concept,” Signal Process. 36, 287–314 (1994).
[CrossRef]

Croningolomb, M.

M. Croningolomb, A. Yariv, “Plane-wave theory of non-degenerate oscillation in the linear photorefractive passive phase-conjugate mirror,” Opt. Lett. 11, 242–244 (1986).
[CrossRef]

S. K. Kwong, M. Croningolomb, A. Yariv, “Oscillation with photorefractive gain,” IEEE J. Quantum Electron. 22, 1508–1523 (1986).
[CrossRef]

S. K. Kwong, A. Yariv, M. Croningolomb, I. Ury, “Conversion of optical-path length to frequency by an interferometer using photorefractive oscillation,” Appl. Phys. Lett. 47, 460–462 (1985).
[CrossRef]

J. O. White, M. Croningolomb, B. Fischer, A. Yariv, “Coherent oscillation by self-induced gratings in the photorefractive crystal BaTiO3,” Appl. Phys. Lett. 40, 450–452 (1982).
[CrossRef]

Dai, L. K.

L. K. Dai, Y. S. Gou, P. Yeh, C. Gu, “Photorefractive mode-coupling between two unidirectional ring oscillators,” Appl. Phys. B 53, 153–159 (1991).
[CrossRef]

Dalessandro, G.

G. Dalessandro, “Spatiotemporal dynamics of a unidirectional ring oscillator with photorefractive gain,” Phys. Rev. A 46, 2791–2802 (1992).
[CrossRef]

Dambly, L.

L. Dambly, H. Zeghlache, “Theory of a multimode photorefractive oscillator—quantitative results on the frequency shift,” Phys. Rev. A 49, 4043–4054 (1994).
[CrossRef] [PubMed]

Damiao, V.

D. Z. Anderson, V. Damiao, E. Fotheringham, D. Popovic, S. Romish, A. Sullivan, Z. Popovic, “Optical processor for X-band lens antenna arrays,” in IEEE Microwave Theory & Techniques-Symposium, Boston, Mass. (2000).

Denz, C.

M. Schwab, M. Saffman, C. Denz, T. Tschudi, “Fourier control of pattern formation in an interferometric feedback configuration,” Opt. Commun. 170, 129–136 (1999).
[CrossRef]

Desfarges-Berthelemot, A.

A. Desfarges-Berthelemot, V. Kermene, B. Colombeau, M. Vampouille, C. Froehly, “Intracavity beam shaping and referenceless holography,” Opt. Mat. 18, 27–35 (2001).
[CrossRef]

Dunning, G. J.

Eason, R. W.

M. Kaczmarek, R. W. Eason, “Conditions for efficient build-up of power in photorefractive ring cavities,” Opt. Commun. 154, 334–338 (1998).
[CrossRef]

Fischer, B.

J. O. White, M. Croningolomb, B. Fischer, A. Yariv, “Coherent oscillation by self-induced gratings in the photorefractive crystal BaTiO3,” Appl. Phys. Lett. 40, 450–452 (1982).
[CrossRef]

Fotheringham, E.

D. Z. Anderson, V. Damiao, E. Fotheringham, D. Popovic, S. Romish, A. Sullivan, Z. Popovic, “Optical processor for X-band lens antenna arrays,” in IEEE Microwave Theory & Techniques-Symposium, Boston, Mass. (2000).

Frauel, Y.

Y. Frauel, T. Galstyan, G. Pauliat, A. Villing, G. Roosen, “Topological map from a photorefractive self-organizing neural network,” Opt. Commun. 135, 179–188 (1997).
[CrossRef]

Froehly, C.

A. Desfarges-Berthelemot, V. Kermene, B. Colombeau, M. Vampouille, C. Froehly, “Intracavity beam shaping and referenceless holography,” Opt. Mat. 18, 27–35 (2001).
[CrossRef]

Galstyan, T.

Y. Frauel, T. Galstyan, G. Pauliat, A. Villing, G. Roosen, “Topological map from a photorefractive self-organizing neural network,” Opt. Commun. 135, 179–188 (1997).
[CrossRef]

Gou, Y. S.

L. K. Dai, Y. S. Gou, P. Yeh, C. Gu, “Photorefractive mode-coupling between two unidirectional ring oscillators,” Appl. Phys. B 53, 153–159 (1991).
[CrossRef]

Gu, C.

L. K. Dai, Y. S. Gou, P. Yeh, C. Gu, “Photorefractive mode-coupling between two unidirectional ring oscillators,” Appl. Phys. B 53, 153–159 (1991).
[CrossRef]

Gunter, P.

P. Gunter, J. P. Huignard, “Photorefractive materials and their applications,” Top. Appl. Phys. 61, 62 (1988).

Hebler, V.

D. Z. Anderson, C. Benkert, V. Hebler, J. Jang, D. Montgomery, M. Saffman, “Optical implementation of a self-organizing feature extractor,” Advances in Neural Information Processing Systems IV (1992).

Hermanns, A.

Huignard, J. P.

P. Gunter, J. P. Huignard, “Photorefractive materials and their applications,” Top. Appl. Phys. 61, 62 (1988).

Hung, K. M.

K. M. Hung, “Optical pattern recognition using a unidirectional photorefractive oscillator coupled with an angular multiplexing volume hologram,” J. Mod. Opt. 47, 655–661 (2000).

Ja, Y. H.

Y. H. Ja, “A double-coupler optical fiber ring-loop resonator with degenerate 2-wave mixing,” Opt. Commun. 81, 113–122 (1991).
[CrossRef]

Jain, R. K.

Jang, J.

D. Z. Anderson, C. Benkert, V. Hebler, J. Jang, D. Montgomery, M. Saffman, “Optical implementation of a self-organizing feature extractor,” Advances in Neural Information Processing Systems IV (1992).

Jaric, M. V.

M. S. Petrovic, M. R. Belic, M. V. Jaric, F. Kaiser, “Optical photorefractive flip-flop oscillator,” Opt. Commun. 138, 349–353 (1997).
[CrossRef]

Jolliffe, I. T.

I. T. Jolliffe, Principal Component Analysis (Springer-Verlag, Berlin, 1996).

Kaczmarek, M.

M. Kaczmarek, R. W. Eason, “Conditions for efficient build-up of power in photorefractive ring cavities,” Opt. Commun. 154, 334–338 (1998).
[CrossRef]

Kaiser, F.

O. Sandfuchs, J. Leonardy, F. Kaiser, M. R. Belic, “Spatio-temporal dynamics in photorefractive two-wave mixing configurations: the counterpropagating geometry and the unidirectional ring oscillator,” Chaos Solitons Fractals 10, 709–724 (1999).

M. S. Petrovic, M. R. Belic, M. V. Jaric, F. Kaiser, “Optical photorefractive flip-flop oscillator,” Opt. Commun. 138, 349–353 (1997).
[CrossRef]

Kermene, V.

A. Desfarges-Berthelemot, V. Kermene, B. Colombeau, M. Vampouille, C. Froehly, “Intracavity beam shaping and referenceless holography,” Opt. Mat. 18, 27–35 (2001).
[CrossRef]

Kwong, S. K.

S. K. Kwong, M. Croningolomb, A. Yariv, “Oscillation with photorefractive gain,” IEEE J. Quantum Electron. 22, 1508–1523 (1986).
[CrossRef]

S. K. Kwong, A. Yariv, M. Croningolomb, I. Ury, “Conversion of optical-path length to frequency by an interferometer using photorefractive oscillation,” Appl. Phys. Lett. 47, 460–462 (1985).
[CrossRef]

Leonardy, J.

O. Sandfuchs, J. Leonardy, F. Kaiser, M. R. Belic, “Spatio-temporal dynamics in photorefractive two-wave mixing configurations: the counterpropagating geometry and the unidirectional ring oscillator,” Chaos Solitons Fractals 10, 709–724 (1999).

Montgomery, D.

D. Z. Anderson, C. Benkert, V. Hebler, J. Jang, D. Montgomery, M. Saffman, “Optical implementation of a self-organizing feature extractor,” Advances in Neural Information Processing Systems IV (1992).

Owechko, Y.

Pauliat, G.

Y. Frauel, T. Galstyan, G. Pauliat, A. Villing, G. Roosen, “Topological map from a photorefractive self-organizing neural network,” Opt. Commun. 135, 179–188 (1997).
[CrossRef]

Petrovic, M. S.

M. S. Petrovic, M. R. Belic, M. V. Jaric, F. Kaiser, “Optical photorefractive flip-flop oscillator,” Opt. Commun. 138, 349–353 (1997).
[CrossRef]

Popovic, D.

D. Z. Anderson, V. Damiao, E. Fotheringham, D. Popovic, S. Romish, A. Sullivan, Z. Popovic, “Optical processor for X-band lens antenna arrays,” in IEEE Microwave Theory & Techniques-Symposium, Boston, Mass. (2000).

Popovic, Z.

D. Z. Anderson, V. Damiao, E. Fotheringham, D. Popovic, S. Romish, A. Sullivan, Z. Popovic, “Optical processor for X-band lens antenna arrays,” in IEEE Microwave Theory & Techniques-Symposium, Boston, Mass. (2000).

Romish, S.

D. Z. Anderson, V. Damiao, E. Fotheringham, D. Popovic, S. Romish, A. Sullivan, Z. Popovic, “Optical processor for X-band lens antenna arrays,” in IEEE Microwave Theory & Techniques-Symposium, Boston, Mass. (2000).

Roosen, G.

Y. Frauel, T. Galstyan, G. Pauliat, A. Villing, G. Roosen, “Topological map from a photorefractive self-organizing neural network,” Opt. Commun. 135, 179–188 (1997).
[CrossRef]

Saffman, M.

Sandfuchs, O.

O. Sandfuchs, J. Leonardy, F. Kaiser, M. R. Belic, “Spatio-temporal dynamics in photorefractive two-wave mixing configurations: the counterpropagating geometry and the unidirectional ring oscillator,” Chaos Solitons Fractals 10, 709–724 (1999).

Schwab, M.

M. Schwab, M. Saffman, C. Denz, T. Tschudi, “Fourier control of pattern formation in an interferometric feedback configuration,” Opt. Commun. 170, 129–136 (1999).
[CrossRef]

Soffer, B. H.

Sullivan, A.

D. Z. Anderson, V. Damiao, E. Fotheringham, D. Popovic, S. Romish, A. Sullivan, Z. Popovic, “Optical processor for X-band lens antenna arrays,” in IEEE Microwave Theory & Techniques-Symposium, Boston, Mass. (2000).

Tschudi, T.

M. Schwab, M. Saffman, C. Denz, T. Tschudi, “Fourier control of pattern formation in an interferometric feedback configuration,” Opt. Commun. 170, 129–136 (1999).
[CrossRef]

Ury, I.

S. K. Kwong, A. Yariv, M. Croningolomb, I. Ury, “Conversion of optical-path length to frequency by an interferometer using photorefractive oscillation,” Appl. Phys. Lett. 47, 460–462 (1985).
[CrossRef]

Vampouille, M.

A. Desfarges-Berthelemot, V. Kermene, B. Colombeau, M. Vampouille, C. Froehly, “Intracavity beam shaping and referenceless holography,” Opt. Mat. 18, 27–35 (2001).
[CrossRef]

Villing, A.

Y. Frauel, T. Galstyan, G. Pauliat, A. Villing, G. Roosen, “Topological map from a photorefractive self-organizing neural network,” Opt. Commun. 135, 179–188 (1997).
[CrossRef]

White, J. O.

J. O. White, A. Yariv, “Photorefractive crystals as optical-devices, elements, and processors,” Proceedings of the Society of Photo-Optical Instrumentation Engineers 464, 7–20 (1984).

J. O. White, M. Croningolomb, B. Fischer, A. Yariv, “Coherent oscillation by self-induced gratings in the photorefractive crystal BaTiO3,” Appl. Phys. Lett. 40, 450–452 (1982).
[CrossRef]

Yariv, A.

S. K. Kwong, M. Croningolomb, A. Yariv, “Oscillation with photorefractive gain,” IEEE J. Quantum Electron. 22, 1508–1523 (1986).
[CrossRef]

M. Croningolomb, A. Yariv, “Plane-wave theory of non-degenerate oscillation in the linear photorefractive passive phase-conjugate mirror,” Opt. Lett. 11, 242–244 (1986).
[CrossRef]

S. K. Kwong, A. Yariv, M. Croningolomb, I. Ury, “Conversion of optical-path length to frequency by an interferometer using photorefractive oscillation,” Appl. Phys. Lett. 47, 460–462 (1985).
[CrossRef]

J. O. White, A. Yariv, “Photorefractive crystals as optical-devices, elements, and processors,” Proceedings of the Society of Photo-Optical Instrumentation Engineers 464, 7–20 (1984).

J. O. White, M. Croningolomb, B. Fischer, A. Yariv, “Coherent oscillation by self-induced gratings in the photorefractive crystal BaTiO3,” Appl. Phys. Lett. 40, 450–452 (1982).
[CrossRef]

Yeh, P.

L. K. Dai, Y. S. Gou, P. Yeh, C. Gu, “Photorefractive mode-coupling between two unidirectional ring oscillators,” Appl. Phys. B 53, 153–159 (1991).
[CrossRef]

P. Yeh, Introduction to Photorefractive Nonlinear Optics (Wiley Series in Pure and Applied Optics, New York, 1993).

Zeghlache, H.

L. Dambly, H. Zeghlache, “Theory of a multimode photorefractive oscillator—quantitative results on the frequency shift,” Phys. Rev. A 49, 4043–4054 (1994).
[CrossRef] [PubMed]

Zozulya, A. A.

Appl. Phys. B (1)

L. K. Dai, Y. S. Gou, P. Yeh, C. Gu, “Photorefractive mode-coupling between two unidirectional ring oscillators,” Appl. Phys. B 53, 153–159 (1991).
[CrossRef]

Appl. Phys. Lett. (2)

S. K. Kwong, A. Yariv, M. Croningolomb, I. Ury, “Conversion of optical-path length to frequency by an interferometer using photorefractive oscillation,” Appl. Phys. Lett. 47, 460–462 (1985).
[CrossRef]

J. O. White, M. Croningolomb, B. Fischer, A. Yariv, “Coherent oscillation by self-induced gratings in the photorefractive crystal BaTiO3,” Appl. Phys. Lett. 40, 450–452 (1982).
[CrossRef]

Chaos Solitons Fractals (1)

O. Sandfuchs, J. Leonardy, F. Kaiser, M. R. Belic, “Spatio-temporal dynamics in photorefractive two-wave mixing configurations: the counterpropagating geometry and the unidirectional ring oscillator,” Chaos Solitons Fractals 10, 709–724 (1999).

IEEE J. Quantum Electron. (1)

S. K. Kwong, M. Croningolomb, A. Yariv, “Oscillation with photorefractive gain,” IEEE J. Quantum Electron. 22, 1508–1523 (1986).
[CrossRef]

J. Mod. Opt. (1)

K. M. Hung, “Optical pattern recognition using a unidirectional photorefractive oscillator coupled with an angular multiplexing volume hologram,” J. Mod. Opt. 47, 655–661 (2000).

J. Opt. Soc. Am. B (2)

Opt. Commun. (5)

Y. H. Ja, “A double-coupler optical fiber ring-loop resonator with degenerate 2-wave mixing,” Opt. Commun. 81, 113–122 (1991).
[CrossRef]

Y. Frauel, T. Galstyan, G. Pauliat, A. Villing, G. Roosen, “Topological map from a photorefractive self-organizing neural network,” Opt. Commun. 135, 179–188 (1997).
[CrossRef]

M. S. Petrovic, M. R. Belic, M. V. Jaric, F. Kaiser, “Optical photorefractive flip-flop oscillator,” Opt. Commun. 138, 349–353 (1997).
[CrossRef]

M. Schwab, M. Saffman, C. Denz, T. Tschudi, “Fourier control of pattern formation in an interferometric feedback configuration,” Opt. Commun. 170, 129–136 (1999).
[CrossRef]

M. Kaczmarek, R. W. Eason, “Conditions for efficient build-up of power in photorefractive ring cavities,” Opt. Commun. 154, 334–338 (1998).
[CrossRef]

Opt. Lett. (4)

Opt. Mat. (1)

A. Desfarges-Berthelemot, V. Kermene, B. Colombeau, M. Vampouille, C. Froehly, “Intracavity beam shaping and referenceless holography,” Opt. Mat. 18, 27–35 (2001).
[CrossRef]

Phys. Rev. A (2)

G. Dalessandro, “Spatiotemporal dynamics of a unidirectional ring oscillator with photorefractive gain,” Phys. Rev. A 46, 2791–2802 (1992).
[CrossRef]

L. Dambly, H. Zeghlache, “Theory of a multimode photorefractive oscillator—quantitative results on the frequency shift,” Phys. Rev. A 49, 4043–4054 (1994).
[CrossRef] [PubMed]

Proceedings of the Society of Photo-Optical Instrumentation Engineers (1)

J. O. White, A. Yariv, “Photorefractive crystals as optical-devices, elements, and processors,” Proceedings of the Society of Photo-Optical Instrumentation Engineers 464, 7–20 (1984).

Signal Process. (1)

P. Comon, “Independent component analysis, a new concept,” Signal Process. 36, 287–314 (1994).
[CrossRef]

Top. Appl. Phys. (1)

P. Gunter, J. P. Huignard, “Photorefractive materials and their applications,” Top. Appl. Phys. 61, 62 (1988).

Other (4)

I. T. Jolliffe, Principal Component Analysis (Springer-Verlag, Berlin, 1996).

D. Z. Anderson, V. Damiao, E. Fotheringham, D. Popovic, S. Romish, A. Sullivan, Z. Popovic, “Optical processor for X-band lens antenna arrays,” in IEEE Microwave Theory & Techniques-Symposium, Boston, Mass. (2000).

P. Yeh, Introduction to Photorefractive Nonlinear Optics (Wiley Series in Pure and Applied Optics, New York, 1993).

D. Z. Anderson, C. Benkert, V. Hebler, J. Jang, D. Montgomery, M. Saffman, “Optical implementation of a self-organizing feature extractor,” Advances in Neural Information Processing Systems IV (1992).

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.


Figures (15)

Fig. 1
Fig. 1

Optical circuit has two output ports: one outputs the largest principal component of the input signal space and the other outputs all the other components.

Fig. 2
Fig. 2

Autotuning filter is a photorefractive ring oscillator capable of extracting the largest principal component of its input signal space.

Fig. 3
Fig. 3

Reflexive two-beam coupling enhances the intensity difference between two signals carried by a multi-mode optical beam.

Fig. 4
Fig. 4

Generic plot of the oscillating signals S 1 and S 2 in the ring versus the input signal ratio P 1/P 2 in dB.

Fig. 5
Fig. 5

Notations for the signals’ intensities at various points in the filter’s open loop.

Fig. 6
Fig. 6

Intersections of the gain curves G 1(S 1, S 2) = 1 and G 2(S 1, S 2) = 1 correspond to the steady-state solutions for the two signals in the ring, with P 1/P 2 = 1.05 and the parameter values of Gr = Gg = 10, m = 50, and T = 0.5.

Fig. 7
Fig. 7

Log-log plot of the S 1/S 2 vs. P 1/P 2 curve shows a linear region when both signals are oscillating in the ring and a rapid increase toward infinity as the input signal ratio approaches the boundary value where the weaker signal disappears. The parameter values are Gr = Gg = 10, m = 50, and T = 0.5.

Fig. 8
Fig. 8

S 1/S 2 vs. P 1/P 2 curve for Gg = 9, 10, and 11, left to right (T = 0.5, Gr = 10, m = 50).

Fig. 9
Fig. 9

S 1/S 2 vs. P 1/P 2 curve for T = 0.55, 0.50, and 0.40 left to right (Gg = Gr = 10, m = 25).

Fig. 10
Fig. 10

Left side: S 1/S 2 vs. Gr for m = 60, 55, 50, 45, and 40 from top to bottom with T = 0.5, Gg = 10, and P 1/P 2 = 0.2 dB. Right side: same values except Gg = 11.

Fig. 11
Fig. 11

Gold bar-shaped crystal. The side faces are nonparallel to avoid unwanted oscillations between them. The entrance and exit faces are cut so that the angle of incidence is Brewster’s angle (β = 22.4 deg. is Brewster’s angle in the medium).

Fig. 12
Fig. 12

Top: Photograph of the autotuning filter compared to a U.S. quarter (coin). The two central elements are the gold bar-shaped photorefractive BaTiO3 crystals. The four outer elements include two plane mirrors, a spherical mirror, and a beam splitter. Bottom: Enlargement of the computer template that is placed under the transparent substrate of the filter to serve as an alignment guide for the elements.

Fig. 13
Fig. 13

Simple model of our filter as a principal component extractor. The mixing on the left-hand side accounts for the spatially finite size of the photorefractive gratings that allows one pump beam to weakly diffract off of the other pump’s grating.

Fig. 14
Fig. 14

Experimental test bed for the autotuning filter: two acousto-optic modulators shift the optical carrier by roughly 80 MHz. The resulting frequency difference between the two shifts is a few kilohertz. These two shifted beams are the input to the autotuning filter.

Fig. 15
Fig. 15

Separation performance of the filter. The smooth gray curve shows calculated data points by use of the first principal component extraction model. The slope at the origin is 15 dB/dB. This is in contrast to the experimental data points (in black) that show a slope at the origin of 26 dB/dB.

Equations (7)

Equations on this page are rendered with MathJax. Learn more.

C˜=1P|s˜1|2s˜1s˜2*s˜1s˜N*s˜2s˜1*|s˜2|2s˜2s˜N*s˜Ns˜1*s˜Ns˜2*|s˜N|2,
C˜ij=1P s˜is˜jT,
P=i=1N |s˜i2t|T.
S1=I1S1P1 exp-Gg I1Itot+S1,
S1out=T S11+m exp-Gr S1S1+S2.
G1S1, S2=TS1+P1P1 exp-Gg I1Itot+S11+m exp-Gr*11+P2+S2S2P1 expGg*I1/Itot+S1P1+S1S1P2 expGg*I2/Itot+S2-1
Ein=M Esource=m11E1+m12E2m21E1+m22E2.

Metrics