Abstract

Isolated spots, which are spatially solitary states, are triggered at the desired positions by a control light in a nonlinear optical system with two-dimensional feedback. They exist because of the balance between isotropic transverse couplings of diffraction and an automatic regulation of feedback-loop gain owing to a simple low-cut spatial frequency filter. Self-scanning of isolated spots is caused by slight unisotropic transverse couplings without a special scanning mechanism. It provides a novel method for image display and image delay.

© 2000 Optical Society of America

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  1. M. Kreuzer, W. Balzer, and T. Tschudi, “Formation of spatial structures in bistable optical elements containing nematic liquid crystals,” Appl. Opt. 29, 579–582 (1990).
    [CrossRef] [PubMed]
  2. F. T. Arecchi, G. Giacomelli, P. L. Ramazza, and S. Residori, “Experimental evidence of chaotic itinerancy and spatiotemporal chaos in optics,” Phys. Rev. Lett. 65, 2531–2534 (1990).
    [CrossRef] [PubMed]
  3. G. D’Alessandro and W. J. Firth, “Spontaneous hexagon formation in a nonlinear optical medium with feedback mirror,” Phys. Rev. Lett. 66, 2597–2600 (1991).
    [CrossRef] [PubMed]
  4. R. Macdonald and H. J. Eichler, “Spontaneous optical pattern formation in a nematic liquid crystal with feedback mirror,” Opt. Commun. 89, 289–295 (1992).
    [CrossRef]
  5. E. Ciaramella, M. Tamburrini, and E. Santamoto, “Talbot assisted hexagonal beam patterning in a thin liquid crystal film with a single feedback mirror at negative distance,” Appl. Phys. Lett. 63, 1604–1606 (1993).
    [CrossRef]
  6. T. Honda, “Hexagonal pattern formation due to counterpropagation in KnBO3,” Opt. Lett. 18, 598–600 (1993).
    [CrossRef]
  7. P. P. Banerjee, H. L. Yu, D. A. Gregory, N. Kukhtarev, and H. J. Caufield, “Self-organization of scattering in photorefractive KNbO3 into a reconfigurable hexagonal spot array,” Opt. Lett. 20, 10–12 (1995).
    [CrossRef] [PubMed]
  8. S. A. Akhmanov, M. A. Vorontsov, V. Yu. Ivanov, A. V. Larichev, and N. I. Zheleznykh, “Controlling transverse-wave interactions in nonlinear optics: generation and interaction of spatiotemporal structures,” J. Opt. Soc. Am. B 9, 78–90 (1992).
    [CrossRef]
  9. B. Thüring, R. Neubecker, and T. Tschudi, “Transverse pattern formation in liquid crystal light valve feedback system,” Opt. Commun. 102, 111–115 (1993).
    [CrossRef]
  10. R. Neubecker, G.-L. Oppo, B. Thering, and T. Tschudi, “Pattern formation in a liquid-crystal light valve with feedback, including polarization, saturation, and internal threshold effects,” Phys. Rev. A 52, 791–808 (1994).
    [CrossRef]
  11. M. A. Vorontsov, J. C. Riklin, and G. W. Carhart, “Optical simulation of phase-distorted imaging systems: nonlinear and adaptive optics approach,” Opt. Eng. (Bellingham) 34, 3229–3238 (1995).
    [CrossRef]
  12. A. V. Mamaev and M. Saffman, “Selection of unstable patterns and control of optical turbulence by Fourier plane filtering,” Phys. Rev. Lett. 80, 3499–3502 (1998).
    [CrossRef]
  13. S. J. Jensen, M. Schwab, and C. Denz, “Manipulation, stabilization, and control of pattern formation using Fourier space filtering,” Phys. Rev. Lett. 81, 1614–1617 (1998).
    [CrossRef]
  14. G. K. Harkness, G.-L. Oppo, R. Martin, A. J. Scroggie, and W. J. Firth, “Elimination of spatiotemporal disorder by Fourier space techniques,” Phys. Rev. A 58, 2577–2585 (1998).
    [CrossRef]
  15. A. Schreiber, B. Thüring, M. Kreuzer, and T. Tshudi, “Experimental investigation of solitary structures in a nonlinear optical feedback system,” Opt. Commun. 136, 415–418 (1997).
    [CrossRef]
  16. W. J. Firth and A. J. Scroggie, “Optical bullet holes: robust controllable localized states of a nonlinear cavity,” Phys. Rev. Lett. 76, 1623–1626 (1996).
    [CrossRef] [PubMed]
  17. M. A. Vorontsov and W. B. Miller, eds., Self-Organization in Optical Systems and Applications in Information Technology (Springer-Verlag, Berlin, 1995), Chap. 2.
  18. P. L. Ramazza, S. Boccaletti, A. Giaquinta, E. Pampaloni, S. Soria, and F. T. Arecchi, “Optical pattern selection by a lateral wave-front shift,” Phys. Rev. A 54, 3472–3475 (1996).
    [CrossRef] [PubMed]
  19. Y. Hayasaki, H. Yamamoto, and N. Nishida, “Optical dependence of spatial frequency of formed patterns on focusing deviation in nonlinear optical ring resonator,” Opt. Commun. 151, 263–267 (1998).
    [CrossRef]
  20. N. Mukohzaka, N. Yoshida, H. Toyoda, Y. Kobayashi, and T. Hara, “Diffraction efficiency analysis of a parallel-aligned nematic-liquid-crystal spatial light modulator,” Appl. Opt. 33, 2804–2811 (1994).
    [CrossRef] [PubMed]

1998 (4)

A. V. Mamaev and M. Saffman, “Selection of unstable patterns and control of optical turbulence by Fourier plane filtering,” Phys. Rev. Lett. 80, 3499–3502 (1998).
[CrossRef]

S. J. Jensen, M. Schwab, and C. Denz, “Manipulation, stabilization, and control of pattern formation using Fourier space filtering,” Phys. Rev. Lett. 81, 1614–1617 (1998).
[CrossRef]

G. K. Harkness, G.-L. Oppo, R. Martin, A. J. Scroggie, and W. J. Firth, “Elimination of spatiotemporal disorder by Fourier space techniques,” Phys. Rev. A 58, 2577–2585 (1998).
[CrossRef]

Y. Hayasaki, H. Yamamoto, and N. Nishida, “Optical dependence of spatial frequency of formed patterns on focusing deviation in nonlinear optical ring resonator,” Opt. Commun. 151, 263–267 (1998).
[CrossRef]

1997 (1)

A. Schreiber, B. Thüring, M. Kreuzer, and T. Tshudi, “Experimental investigation of solitary structures in a nonlinear optical feedback system,” Opt. Commun. 136, 415–418 (1997).
[CrossRef]

1996 (2)

W. J. Firth and A. J. Scroggie, “Optical bullet holes: robust controllable localized states of a nonlinear cavity,” Phys. Rev. Lett. 76, 1623–1626 (1996).
[CrossRef] [PubMed]

P. L. Ramazza, S. Boccaletti, A. Giaquinta, E. Pampaloni, S. Soria, and F. T. Arecchi, “Optical pattern selection by a lateral wave-front shift,” Phys. Rev. A 54, 3472–3475 (1996).
[CrossRef] [PubMed]

1995 (2)

P. P. Banerjee, H. L. Yu, D. A. Gregory, N. Kukhtarev, and H. J. Caufield, “Self-organization of scattering in photorefractive KNbO3 into a reconfigurable hexagonal spot array,” Opt. Lett. 20, 10–12 (1995).
[CrossRef] [PubMed]

M. A. Vorontsov, J. C. Riklin, and G. W. Carhart, “Optical simulation of phase-distorted imaging systems: nonlinear and adaptive optics approach,” Opt. Eng. (Bellingham) 34, 3229–3238 (1995).
[CrossRef]

1994 (2)

N. Mukohzaka, N. Yoshida, H. Toyoda, Y. Kobayashi, and T. Hara, “Diffraction efficiency analysis of a parallel-aligned nematic-liquid-crystal spatial light modulator,” Appl. Opt. 33, 2804–2811 (1994).
[CrossRef] [PubMed]

R. Neubecker, G.-L. Oppo, B. Thering, and T. Tschudi, “Pattern formation in a liquid-crystal light valve with feedback, including polarization, saturation, and internal threshold effects,” Phys. Rev. A 52, 791–808 (1994).
[CrossRef]

1993 (3)

B. Thüring, R. Neubecker, and T. Tschudi, “Transverse pattern formation in liquid crystal light valve feedback system,” Opt. Commun. 102, 111–115 (1993).
[CrossRef]

E. Ciaramella, M. Tamburrini, and E. Santamoto, “Talbot assisted hexagonal beam patterning in a thin liquid crystal film with a single feedback mirror at negative distance,” Appl. Phys. Lett. 63, 1604–1606 (1993).
[CrossRef]

T. Honda, “Hexagonal pattern formation due to counterpropagation in KnBO3,” Opt. Lett. 18, 598–600 (1993).
[CrossRef]

1992 (2)

1991 (1)

G. D’Alessandro and W. J. Firth, “Spontaneous hexagon formation in a nonlinear optical medium with feedback mirror,” Phys. Rev. Lett. 66, 2597–2600 (1991).
[CrossRef] [PubMed]

1990 (2)

M. Kreuzer, W. Balzer, and T. Tschudi, “Formation of spatial structures in bistable optical elements containing nematic liquid crystals,” Appl. Opt. 29, 579–582 (1990).
[CrossRef] [PubMed]

F. T. Arecchi, G. Giacomelli, P. L. Ramazza, and S. Residori, “Experimental evidence of chaotic itinerancy and spatiotemporal chaos in optics,” Phys. Rev. Lett. 65, 2531–2534 (1990).
[CrossRef] [PubMed]

Akhmanov, S. A.

Arecchi, F. T.

P. L. Ramazza, S. Boccaletti, A. Giaquinta, E. Pampaloni, S. Soria, and F. T. Arecchi, “Optical pattern selection by a lateral wave-front shift,” Phys. Rev. A 54, 3472–3475 (1996).
[CrossRef] [PubMed]

F. T. Arecchi, G. Giacomelli, P. L. Ramazza, and S. Residori, “Experimental evidence of chaotic itinerancy and spatiotemporal chaos in optics,” Phys. Rev. Lett. 65, 2531–2534 (1990).
[CrossRef] [PubMed]

Balzer, W.

Banerjee, P. P.

Boccaletti, S.

P. L. Ramazza, S. Boccaletti, A. Giaquinta, E. Pampaloni, S. Soria, and F. T. Arecchi, “Optical pattern selection by a lateral wave-front shift,” Phys. Rev. A 54, 3472–3475 (1996).
[CrossRef] [PubMed]

Carhart, G. W.

M. A. Vorontsov, J. C. Riklin, and G. W. Carhart, “Optical simulation of phase-distorted imaging systems: nonlinear and adaptive optics approach,” Opt. Eng. (Bellingham) 34, 3229–3238 (1995).
[CrossRef]

Caufield, H. J.

Ciaramella, E.

E. Ciaramella, M. Tamburrini, and E. Santamoto, “Talbot assisted hexagonal beam patterning in a thin liquid crystal film with a single feedback mirror at negative distance,” Appl. Phys. Lett. 63, 1604–1606 (1993).
[CrossRef]

D’Alessandro, G.

G. D’Alessandro and W. J. Firth, “Spontaneous hexagon formation in a nonlinear optical medium with feedback mirror,” Phys. Rev. Lett. 66, 2597–2600 (1991).
[CrossRef] [PubMed]

Denz, C.

S. J. Jensen, M. Schwab, and C. Denz, “Manipulation, stabilization, and control of pattern formation using Fourier space filtering,” Phys. Rev. Lett. 81, 1614–1617 (1998).
[CrossRef]

Eichler, H. J.

R. Macdonald and H. J. Eichler, “Spontaneous optical pattern formation in a nematic liquid crystal with feedback mirror,” Opt. Commun. 89, 289–295 (1992).
[CrossRef]

Firth, W. J.

G. K. Harkness, G.-L. Oppo, R. Martin, A. J. Scroggie, and W. J. Firth, “Elimination of spatiotemporal disorder by Fourier space techniques,” Phys. Rev. A 58, 2577–2585 (1998).
[CrossRef]

W. J. Firth and A. J. Scroggie, “Optical bullet holes: robust controllable localized states of a nonlinear cavity,” Phys. Rev. Lett. 76, 1623–1626 (1996).
[CrossRef] [PubMed]

G. D’Alessandro and W. J. Firth, “Spontaneous hexagon formation in a nonlinear optical medium with feedback mirror,” Phys. Rev. Lett. 66, 2597–2600 (1991).
[CrossRef] [PubMed]

Giacomelli, G.

F. T. Arecchi, G. Giacomelli, P. L. Ramazza, and S. Residori, “Experimental evidence of chaotic itinerancy and spatiotemporal chaos in optics,” Phys. Rev. Lett. 65, 2531–2534 (1990).
[CrossRef] [PubMed]

Giaquinta, A.

P. L. Ramazza, S. Boccaletti, A. Giaquinta, E. Pampaloni, S. Soria, and F. T. Arecchi, “Optical pattern selection by a lateral wave-front shift,” Phys. Rev. A 54, 3472–3475 (1996).
[CrossRef] [PubMed]

Gregory, D. A.

Hara, T.

Harkness, G. K.

G. K. Harkness, G.-L. Oppo, R. Martin, A. J. Scroggie, and W. J. Firth, “Elimination of spatiotemporal disorder by Fourier space techniques,” Phys. Rev. A 58, 2577–2585 (1998).
[CrossRef]

Hayasaki, Y.

Y. Hayasaki, H. Yamamoto, and N. Nishida, “Optical dependence of spatial frequency of formed patterns on focusing deviation in nonlinear optical ring resonator,” Opt. Commun. 151, 263–267 (1998).
[CrossRef]

Honda, T.

Ivanov, V. Yu.

Jensen, S. J.

S. J. Jensen, M. Schwab, and C. Denz, “Manipulation, stabilization, and control of pattern formation using Fourier space filtering,” Phys. Rev. Lett. 81, 1614–1617 (1998).
[CrossRef]

Kobayashi, Y.

Kreuzer, M.

A. Schreiber, B. Thüring, M. Kreuzer, and T. Tshudi, “Experimental investigation of solitary structures in a nonlinear optical feedback system,” Opt. Commun. 136, 415–418 (1997).
[CrossRef]

M. Kreuzer, W. Balzer, and T. Tschudi, “Formation of spatial structures in bistable optical elements containing nematic liquid crystals,” Appl. Opt. 29, 579–582 (1990).
[CrossRef] [PubMed]

Kukhtarev, N.

Larichev, A. V.

Macdonald, R.

R. Macdonald and H. J. Eichler, “Spontaneous optical pattern formation in a nematic liquid crystal with feedback mirror,” Opt. Commun. 89, 289–295 (1992).
[CrossRef]

Mamaev, A. V.

A. V. Mamaev and M. Saffman, “Selection of unstable patterns and control of optical turbulence by Fourier plane filtering,” Phys. Rev. Lett. 80, 3499–3502 (1998).
[CrossRef]

Martin, R.

G. K. Harkness, G.-L. Oppo, R. Martin, A. J. Scroggie, and W. J. Firth, “Elimination of spatiotemporal disorder by Fourier space techniques,” Phys. Rev. A 58, 2577–2585 (1998).
[CrossRef]

Mukohzaka, N.

Neubecker, R.

R. Neubecker, G.-L. Oppo, B. Thering, and T. Tschudi, “Pattern formation in a liquid-crystal light valve with feedback, including polarization, saturation, and internal threshold effects,” Phys. Rev. A 52, 791–808 (1994).
[CrossRef]

B. Thüring, R. Neubecker, and T. Tschudi, “Transverse pattern formation in liquid crystal light valve feedback system,” Opt. Commun. 102, 111–115 (1993).
[CrossRef]

Nishida, N.

Y. Hayasaki, H. Yamamoto, and N. Nishida, “Optical dependence of spatial frequency of formed patterns on focusing deviation in nonlinear optical ring resonator,” Opt. Commun. 151, 263–267 (1998).
[CrossRef]

Oppo, G.-L.

G. K. Harkness, G.-L. Oppo, R. Martin, A. J. Scroggie, and W. J. Firth, “Elimination of spatiotemporal disorder by Fourier space techniques,” Phys. Rev. A 58, 2577–2585 (1998).
[CrossRef]

R. Neubecker, G.-L. Oppo, B. Thering, and T. Tschudi, “Pattern formation in a liquid-crystal light valve with feedback, including polarization, saturation, and internal threshold effects,” Phys. Rev. A 52, 791–808 (1994).
[CrossRef]

Pampaloni, E.

P. L. Ramazza, S. Boccaletti, A. Giaquinta, E. Pampaloni, S. Soria, and F. T. Arecchi, “Optical pattern selection by a lateral wave-front shift,” Phys. Rev. A 54, 3472–3475 (1996).
[CrossRef] [PubMed]

Ramazza, P. L.

P. L. Ramazza, S. Boccaletti, A. Giaquinta, E. Pampaloni, S. Soria, and F. T. Arecchi, “Optical pattern selection by a lateral wave-front shift,” Phys. Rev. A 54, 3472–3475 (1996).
[CrossRef] [PubMed]

F. T. Arecchi, G. Giacomelli, P. L. Ramazza, and S. Residori, “Experimental evidence of chaotic itinerancy and spatiotemporal chaos in optics,” Phys. Rev. Lett. 65, 2531–2534 (1990).
[CrossRef] [PubMed]

Residori, S.

F. T. Arecchi, G. Giacomelli, P. L. Ramazza, and S. Residori, “Experimental evidence of chaotic itinerancy and spatiotemporal chaos in optics,” Phys. Rev. Lett. 65, 2531–2534 (1990).
[CrossRef] [PubMed]

Riklin, J. C.

M. A. Vorontsov, J. C. Riklin, and G. W. Carhart, “Optical simulation of phase-distorted imaging systems: nonlinear and adaptive optics approach,” Opt. Eng. (Bellingham) 34, 3229–3238 (1995).
[CrossRef]

Saffman, M.

A. V. Mamaev and M. Saffman, “Selection of unstable patterns and control of optical turbulence by Fourier plane filtering,” Phys. Rev. Lett. 80, 3499–3502 (1998).
[CrossRef]

Santamoto, E.

E. Ciaramella, M. Tamburrini, and E. Santamoto, “Talbot assisted hexagonal beam patterning in a thin liquid crystal film with a single feedback mirror at negative distance,” Appl. Phys. Lett. 63, 1604–1606 (1993).
[CrossRef]

Schreiber, A.

A. Schreiber, B. Thüring, M. Kreuzer, and T. Tshudi, “Experimental investigation of solitary structures in a nonlinear optical feedback system,” Opt. Commun. 136, 415–418 (1997).
[CrossRef]

Schwab, M.

S. J. Jensen, M. Schwab, and C. Denz, “Manipulation, stabilization, and control of pattern formation using Fourier space filtering,” Phys. Rev. Lett. 81, 1614–1617 (1998).
[CrossRef]

Scroggie, A. J.

G. K. Harkness, G.-L. Oppo, R. Martin, A. J. Scroggie, and W. J. Firth, “Elimination of spatiotemporal disorder by Fourier space techniques,” Phys. Rev. A 58, 2577–2585 (1998).
[CrossRef]

W. J. Firth and A. J. Scroggie, “Optical bullet holes: robust controllable localized states of a nonlinear cavity,” Phys. Rev. Lett. 76, 1623–1626 (1996).
[CrossRef] [PubMed]

Soria, S.

P. L. Ramazza, S. Boccaletti, A. Giaquinta, E. Pampaloni, S. Soria, and F. T. Arecchi, “Optical pattern selection by a lateral wave-front shift,” Phys. Rev. A 54, 3472–3475 (1996).
[CrossRef] [PubMed]

Tamburrini, M.

E. Ciaramella, M. Tamburrini, and E. Santamoto, “Talbot assisted hexagonal beam patterning in a thin liquid crystal film with a single feedback mirror at negative distance,” Appl. Phys. Lett. 63, 1604–1606 (1993).
[CrossRef]

Thering, B.

R. Neubecker, G.-L. Oppo, B. Thering, and T. Tschudi, “Pattern formation in a liquid-crystal light valve with feedback, including polarization, saturation, and internal threshold effects,” Phys. Rev. A 52, 791–808 (1994).
[CrossRef]

Thüring, B.

A. Schreiber, B. Thüring, M. Kreuzer, and T. Tshudi, “Experimental investigation of solitary structures in a nonlinear optical feedback system,” Opt. Commun. 136, 415–418 (1997).
[CrossRef]

B. Thüring, R. Neubecker, and T. Tschudi, “Transverse pattern formation in liquid crystal light valve feedback system,” Opt. Commun. 102, 111–115 (1993).
[CrossRef]

Toyoda, H.

Tschudi, T.

R. Neubecker, G.-L. Oppo, B. Thering, and T. Tschudi, “Pattern formation in a liquid-crystal light valve with feedback, including polarization, saturation, and internal threshold effects,” Phys. Rev. A 52, 791–808 (1994).
[CrossRef]

B. Thüring, R. Neubecker, and T. Tschudi, “Transverse pattern formation in liquid crystal light valve feedback system,” Opt. Commun. 102, 111–115 (1993).
[CrossRef]

M. Kreuzer, W. Balzer, and T. Tschudi, “Formation of spatial structures in bistable optical elements containing nematic liquid crystals,” Appl. Opt. 29, 579–582 (1990).
[CrossRef] [PubMed]

Tshudi, T.

A. Schreiber, B. Thüring, M. Kreuzer, and T. Tshudi, “Experimental investigation of solitary structures in a nonlinear optical feedback system,” Opt. Commun. 136, 415–418 (1997).
[CrossRef]

Vorontsov, M. A.

M. A. Vorontsov, J. C. Riklin, and G. W. Carhart, “Optical simulation of phase-distorted imaging systems: nonlinear and adaptive optics approach,” Opt. Eng. (Bellingham) 34, 3229–3238 (1995).
[CrossRef]

S. A. Akhmanov, M. A. Vorontsov, V. Yu. Ivanov, A. V. Larichev, and N. I. Zheleznykh, “Controlling transverse-wave interactions in nonlinear optics: generation and interaction of spatiotemporal structures,” J. Opt. Soc. Am. B 9, 78–90 (1992).
[CrossRef]

Yamamoto, H.

Y. Hayasaki, H. Yamamoto, and N. Nishida, “Optical dependence of spatial frequency of formed patterns on focusing deviation in nonlinear optical ring resonator,” Opt. Commun. 151, 263–267 (1998).
[CrossRef]

Yoshida, N.

Yu, H. L.

Zheleznykh, N. I.

Appl. Opt. (2)

Appl. Phys. Lett. (1)

E. Ciaramella, M. Tamburrini, and E. Santamoto, “Talbot assisted hexagonal beam patterning in a thin liquid crystal film with a single feedback mirror at negative distance,” Appl. Phys. Lett. 63, 1604–1606 (1993).
[CrossRef]

J. Opt. Soc. Am. B (1)

Opt. Commun. (4)

B. Thüring, R. Neubecker, and T. Tschudi, “Transverse pattern formation in liquid crystal light valve feedback system,” Opt. Commun. 102, 111–115 (1993).
[CrossRef]

Y. Hayasaki, H. Yamamoto, and N. Nishida, “Optical dependence of spatial frequency of formed patterns on focusing deviation in nonlinear optical ring resonator,” Opt. Commun. 151, 263–267 (1998).
[CrossRef]

R. Macdonald and H. J. Eichler, “Spontaneous optical pattern formation in a nematic liquid crystal with feedback mirror,” Opt. Commun. 89, 289–295 (1992).
[CrossRef]

A. Schreiber, B. Thüring, M. Kreuzer, and T. Tshudi, “Experimental investigation of solitary structures in a nonlinear optical feedback system,” Opt. Commun. 136, 415–418 (1997).
[CrossRef]

Opt. Eng. (Bellingham) (1)

M. A. Vorontsov, J. C. Riklin, and G. W. Carhart, “Optical simulation of phase-distorted imaging systems: nonlinear and adaptive optics approach,” Opt. Eng. (Bellingham) 34, 3229–3238 (1995).
[CrossRef]

Opt. Lett. (2)

Phys. Rev. A (3)

R. Neubecker, G.-L. Oppo, B. Thering, and T. Tschudi, “Pattern formation in a liquid-crystal light valve with feedback, including polarization, saturation, and internal threshold effects,” Phys. Rev. A 52, 791–808 (1994).
[CrossRef]

G. K. Harkness, G.-L. Oppo, R. Martin, A. J. Scroggie, and W. J. Firth, “Elimination of spatiotemporal disorder by Fourier space techniques,” Phys. Rev. A 58, 2577–2585 (1998).
[CrossRef]

P. L. Ramazza, S. Boccaletti, A. Giaquinta, E. Pampaloni, S. Soria, and F. T. Arecchi, “Optical pattern selection by a lateral wave-front shift,” Phys. Rev. A 54, 3472–3475 (1996).
[CrossRef] [PubMed]

Phys. Rev. Lett. (5)

W. J. Firth and A. J. Scroggie, “Optical bullet holes: robust controllable localized states of a nonlinear cavity,” Phys. Rev. Lett. 76, 1623–1626 (1996).
[CrossRef] [PubMed]

A. V. Mamaev and M. Saffman, “Selection of unstable patterns and control of optical turbulence by Fourier plane filtering,” Phys. Rev. Lett. 80, 3499–3502 (1998).
[CrossRef]

S. J. Jensen, M. Schwab, and C. Denz, “Manipulation, stabilization, and control of pattern formation using Fourier space filtering,” Phys. Rev. Lett. 81, 1614–1617 (1998).
[CrossRef]

F. T. Arecchi, G. Giacomelli, P. L. Ramazza, and S. Residori, “Experimental evidence of chaotic itinerancy and spatiotemporal chaos in optics,” Phys. Rev. Lett. 65, 2531–2534 (1990).
[CrossRef] [PubMed]

G. D’Alessandro and W. J. Firth, “Spontaneous hexagon formation in a nonlinear optical medium with feedback mirror,” Phys. Rev. Lett. 66, 2597–2600 (1991).
[CrossRef] [PubMed]

Other (1)

M. A. Vorontsov and W. B. Miller, eds., Self-Organization in Optical Systems and Applications in Information Technology (Springer-Verlag, Berlin, 1995), Chap. 2.

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Figures (6)

Fig. 1
Fig. 1

Experimental setup. See text for description of components.

Fig. 2
Fig. 2

Nonlinear intensity property of the PAL-SLM: (a) The dots are the experimental results, and the solid curve is calculated from the approximated equation of the PAL-SLM property. The dotted curve indicates the property when the feedback-loop gain is 48% of the solid-curve case. The strong bistability in (b) and the hysteresis property in (c) are the bistabilities corresponding to the solid and the dotted curves in (a), respectively.

Fig. 3
Fig. 3

Isolated spots induced by the external single-pulsed light under the in-focus condition with application of (a) 0.7-mm PS and (b) 1.4-mm PS. (c) The isolated spots induced by the external 3×3 single-pulsed lights. (d) Negative isolated spots.

Fig. 4
Fig. 4

Isolated spots induced by the 2×2 single-pulsed lights under the out-of-focus condition: (a) t=0 s and (b) t=2 s.

Fig. 5
Fig. 5

Isolated spots self-scanning from left to right. The external lights are given the repeating pattern “A” by the sequence of the vertically parallel one-dimensional pattern. The output in (b) is after 3.0 s of the output in (a). The brightest spot on the left side in (a) is being recorded in this time.

Fig. 6
Fig. 6

Speed of the isolated spots for the lateral displacement of the optical feedback.

Equations (4)

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

τmu(r, t)/t=-u(r, t)+D2u(r, t)+fm[If(r, t)],
fm(I)=PmaxIα/(Iα+Ihα),
Iout(r, t)=KI0{1-β cos[u(r, t)+ϕ0(V0)]}/2,
If(r, t)=|(Aout(r, t)*g(r))*pZ(r, Z)|2,

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