Abstract

Steady-state dark photorefractive spatial screening solitons are observed in an odd- or even-number sequence when a laser beam that contains a dark stripe generated from a phase or amplitude discontinuity in the center of the beam is launched into a biased bulk strontium barium niobate crystal. If the initial width of the dark stripe is small, only a fundamental soliton or a Y-junction soliton is generated, corresponding to the lowest order in the odd- or even-number soliton sequence. As the initial width and the bias field are increased, we observe a progressive transition from a lower-order soliton to a sequence of higher-order multiple solitons. We show that these dark solitons induce stable waveguides that can guide an intense beam of a different wavelength into multiple channels. Comparisons between experiments and theory on multiple dark spatial solitons are presented and shown to be in good agreement.

© 1997 Optical Society of America

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    [CrossRef]
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    [CrossRef] [PubMed]

1996 (14)

M. Segev, M. Shih, and G. C. Valley, J. Opt. Soc. Am. B 13, 706 (1996).
[CrossRef]

M. I. Carvalho, S. R. Singh, D. N. Christodoulides, and R. I. Joseph, Phys. Rev. E 53, R53 (1996).
[CrossRef]

W. Krolikowski, N. Akhmediev, and B. Luther-Davies, Opt. Lett. 21, 782 (1996).
[CrossRef]

Z. Chen, M. Mitchell, and M. Segev, Opt. Lett. 21, 716 (1996).
[CrossRef] [PubMed]

M. Shih, M. Segev, and G. Salamo, Opt. Lett. 21, 931 (1996).
[CrossRef] [PubMed]

M. Taya, M. Bashaw, M. M. Fejer, M. Segev, and G. C. Valley, Opt. Lett. 21, 943 (1996).
[CrossRef] [PubMed]

M. Shih and M. Segev, Opt. Lett. 21, 1538 (1996).
[CrossRef] [PubMed]

D. N. Christodoulides, S. R. Singh, M. I. Carvalho, and M. Segev, Appl. Phys. Lett. 68, 1763 (1996).
[CrossRef]

M. Chauvet, S. A. Hawkins, G. Salamo, M. Segev, D. F. Bliss, and G. Bryant, Opt. Lett. 21, 1333 (1996).
[CrossRef] [PubMed]

M. Mitchell, Z. Chen, M. Shih, and M. Segev, Phys. Rev. Lett. 77, 490 (1996).
[CrossRef] [PubMed]

Z. M. Sheng, Y. P. Cui, N. Cheng, and Y. Wei, J. Opt. Soc. Am. B 13, 584 (1996).
[CrossRef]

K. Kos, H. Ming, G. Salamo, M. Shih, M. Segev, and G. C. Valley, Phys. Rev. E 53, R4330 (1996).
[CrossRef]

Z. Chen, M. Mitchell, M. Shih, M. Segev, M. Garrett, and G. C. Valley, Opt. Lett. 21, 629 (1996).
[CrossRef] [PubMed]

A. V. Mamaev, M. Saffman, D. Z. Anderson, and A. A. Zozulya, Phys. Rev. A 54, 870 (1996). In that paper it is claimed that both bright and dark photorefractive solitons suffer from transverse instabilities and are unstable. But the experimental results presented in the same paper clearly show a “self-trapped channel of light” that does not exhibit transverse instabilities (Figs. 5d and 14b). Modulation instability was observed only when further “increasing the nonlinearity” (see discussion on page 874 there). The similarity between the experimental and the numerical results showing the development of the instability in that paper is misleading. The experimental results (Figs. 5 and 14) show sequences of output intensity distributions (at a fixed propagation distance) for different levels of applied voltages (i.e., different levels of nonlinearity), only one of which corresponds to that of a soliton (is on the existence curve), whereas the simulations (Figs. 1 and 9) show the near-field intensity evolution for different propagation distances for a fixed set of parameters (i.e., at a fixed voltage) that greatly differ from that of a soliton.
[CrossRef] [PubMed]

1995 (9)

M. Morin, G. Duree, G. Salamo, and M. Segev, Opt. Lett. 20, 2066 (1995).
[CrossRef] [PubMed]

M. Segev, G. C. Valley, S. R. Singh, M. I. Carvalho, and D. N. Christodoulides, Opt. Lett. 20, 1764 (1995).
[CrossRef]

S. R. Singh, M. I. Carvalho, and D. N. Christodoulides, Opt. Lett. 20, 2177 (1995).
[CrossRef]

G. Duree, M. Morin, G. Salamo, M. Segev, A. Yariv, B. Crosignani, P. DiPorto, and E. Sharp, Phys. Rev. Lett. 74, 1978 (1995).
[CrossRef] [PubMed]

M. D. Iturbe-Castillo, J. J. Sanchez-Mondragon, S. Stepanov, M. B. Klein, and B. A. Wechsler, Opt. Commun. 118, 515 (1995).
[CrossRef]

M. Taya, M. Bashaw, M. M. Fejer, M. Segev, and G. C. Valley, Phys. Rev. A 52, 3095 (1995).
[CrossRef] [PubMed]

M. I. Carvalho, S. R. Singh, and D. N. Christodoulides, Opt. Commun. 120, 311 (1995).
[CrossRef]

S. R. Singh and D. N. Christodoulides, Opt. Commun. 118, 569 (1995).
[CrossRef]

D. N. Christodoulides and M. I. Carvalho, J. Opt. Soc. Am. B 12, 1628 (1995).
[CrossRef]

1994 (4)

Steady-state, self-focusing in biased photorefractive media were first observed by M. D. Iturbe-Castillo, P. A. Marquez-Aguilar, J. J. Sanchez-Mondragon, S. Stepanov, and V. Vysloukh, Appl. Phys. Lett. 64, 408 (1994).
[CrossRef]

M. Segev, G. C. Valley, B. Crosignani, P. DiPorto, and A. Yariv, Phys. Rev. Lett. 73, 3211 (1994).
[CrossRef] [PubMed]

G. C. Valley, M. Segev, B. Crosignani, A. Yariv, M. M. Fejer, and M. Bashaw, Phys. Rev. A 50, R4457 (1994).
[CrossRef]

Y. S. Kivshar and X. Yang, Opt. Commun. 107, 93 (1994).
[CrossRef]

1993 (2)

G. Duree, J. L. Shultz, G. Salamo, M. Segev, A. Yariv, B. Crosignani, P. DiPorto, E. Sharp, and R. Neurgaonkar, Phys. Rev. Lett. 71, 533 (1993).
[CrossRef] [PubMed]

Y. Kivshar, IEEE J. Quantum Electron. 29, 250 (1993).
[CrossRef]

1992 (3)

B. Luther-Davies and Y. Xiaoping, Opt. Lett. 17, 496 (1992).
[CrossRef] [PubMed]

G. A. Swartzlander and C. T. Law, Phys. Rev. Lett. 69, 2503 (1992).
[CrossRef] [PubMed]

M. Segev, B. Crosignani, A. Yariv, and B. Fischer, Phys. Rev. Lett. 68, 923 (1992).
[CrossRef] [PubMed]

1991 (3)

G. R. Allan, S. R. Skinner, D. R. Andersen, and A. L. Smirl, Opt. Lett. 16, 156 (1991).
[PubMed]

S. R. Skinner, G. R. Allan, D. A. Andersen, and A. L. Smirl, IEEE J. Quantum Electron. QE-27, 2211 (1991).
[CrossRef]

G. A. Swartzlander, D. R. Andersen, J. J. Regan, H. Yin, and A. E. Kaplan, Phys. Rev. Lett. 66, 1583 (1991).
[CrossRef] [PubMed]

1990 (2)

1985 (1)

K. J. Blow and N. J. Doran, Phys. Lett. A 107, 55 (1985).
[CrossRef]

1973 (1)

V. E. Zakharov and A. B. Shabat, Sov. Phys. JETP 37, 823 (1973).

1972 (1)

V. E. Zakharov and A. B. Shabat, Sov. Phys. JETP 34, 62 (1972).

1964 (2)

R. Y. Chiao, E. Garmire, and C. H. Townes, Phys. Rev. Lett. 13, 479 (1964).
[CrossRef]

P. L. Kelley, Phys. Rev. Lett. 15, 1005 (1964).
[CrossRef]

Aitchison, J. S.

Akhmediev, N.

Allan, G. R.

G. R. Allan, S. R. Skinner, D. R. Andersen, and A. L. Smirl, Opt. Lett. 16, 156 (1991).
[PubMed]

S. R. Skinner, G. R. Allan, D. A. Andersen, and A. L. Smirl, IEEE J. Quantum Electron. QE-27, 2211 (1991).
[CrossRef]

Andersen, D. A.

S. R. Skinner, G. R. Allan, D. A. Andersen, and A. L. Smirl, IEEE J. Quantum Electron. QE-27, 2211 (1991).
[CrossRef]

Andersen, D. R.

G. A. Swartzlander, D. R. Andersen, J. J. Regan, H. Yin, and A. E. Kaplan, Phys. Rev. Lett. 66, 1583 (1991).
[CrossRef] [PubMed]

G. R. Allan, S. R. Skinner, D. R. Andersen, and A. L. Smirl, Opt. Lett. 16, 156 (1991).
[PubMed]

Anderson, D. Z.

A. V. Mamaev, M. Saffman, D. Z. Anderson, and A. A. Zozulya, Phys. Rev. A 54, 870 (1996). In that paper it is claimed that both bright and dark photorefractive solitons suffer from transverse instabilities and are unstable. But the experimental results presented in the same paper clearly show a “self-trapped channel of light” that does not exhibit transverse instabilities (Figs. 5d and 14b). Modulation instability was observed only when further “increasing the nonlinearity” (see discussion on page 874 there). The similarity between the experimental and the numerical results showing the development of the instability in that paper is misleading. The experimental results (Figs. 5 and 14) show sequences of output intensity distributions (at a fixed propagation distance) for different levels of applied voltages (i.e., different levels of nonlinearity), only one of which corresponds to that of a soliton (is on the existence curve), whereas the simulations (Figs. 1 and 9) show the near-field intensity evolution for different propagation distances for a fixed set of parameters (i.e., at a fixed voltage) that greatly differ from that of a soliton.
[CrossRef] [PubMed]

Bashaw, M.

M. Taya, M. Bashaw, M. M. Fejer, M. Segev, and G. C. Valley, Opt. Lett. 21, 943 (1996).
[CrossRef] [PubMed]

M. Taya, M. Bashaw, M. M. Fejer, M. Segev, and G. C. Valley, Phys. Rev. A 52, 3095 (1995).
[CrossRef] [PubMed]

G. C. Valley, M. Segev, B. Crosignani, A. Yariv, M. M. Fejer, and M. Bashaw, Phys. Rev. A 50, R4457 (1994).
[CrossRef]

Bliss, D. F.

Blow, K. J.

K. J. Blow and N. J. Doran, Phys. Lett. A 107, 55 (1985).
[CrossRef]

Bryant, G.

Carvalho, M. I.

M. I. Carvalho, S. R. Singh, D. N. Christodoulides, and R. I. Joseph, Phys. Rev. E 53, R53 (1996).
[CrossRef]

D. N. Christodoulides, S. R. Singh, M. I. Carvalho, and M. Segev, Appl. Phys. Lett. 68, 1763 (1996).
[CrossRef]

D. N. Christodoulides and M. I. Carvalho, J. Opt. Soc. Am. B 12, 1628 (1995).
[CrossRef]

M. Segev, G. C. Valley, S. R. Singh, M. I. Carvalho, and D. N. Christodoulides, Opt. Lett. 20, 1764 (1995).
[CrossRef]

S. R. Singh, M. I. Carvalho, and D. N. Christodoulides, Opt. Lett. 20, 2177 (1995).
[CrossRef]

M. I. Carvalho, S. R. Singh, and D. N. Christodoulides, Opt. Commun. 120, 311 (1995).
[CrossRef]

Chauvet, M.

Chen, Z.

Cheng, N.

Chiao, R. Y.

R. Y. Chiao, E. Garmire, and C. H. Townes, Phys. Rev. Lett. 13, 479 (1964).
[CrossRef]

Christodoulides, D. N.

D. N. Christodoulides, S. R. Singh, M. I. Carvalho, and M. Segev, Appl. Phys. Lett. 68, 1763 (1996).
[CrossRef]

M. I. Carvalho, S. R. Singh, D. N. Christodoulides, and R. I. Joseph, Phys. Rev. E 53, R53 (1996).
[CrossRef]

M. Segev, G. C. Valley, S. R. Singh, M. I. Carvalho, and D. N. Christodoulides, Opt. Lett. 20, 1764 (1995).
[CrossRef]

D. N. Christodoulides and M. I. Carvalho, J. Opt. Soc. Am. B 12, 1628 (1995).
[CrossRef]

S. R. Singh, M. I. Carvalho, and D. N. Christodoulides, Opt. Lett. 20, 2177 (1995).
[CrossRef]

M. I. Carvalho, S. R. Singh, and D. N. Christodoulides, Opt. Commun. 120, 311 (1995).
[CrossRef]

S. R. Singh and D. N. Christodoulides, Opt. Commun. 118, 569 (1995).
[CrossRef]

Crosignani, B.

G. Duree, M. Morin, G. Salamo, M. Segev, A. Yariv, B. Crosignani, P. DiPorto, and E. Sharp, Phys. Rev. Lett. 74, 1978 (1995).
[CrossRef] [PubMed]

G. C. Valley, M. Segev, B. Crosignani, A. Yariv, M. M. Fejer, and M. Bashaw, Phys. Rev. A 50, R4457 (1994).
[CrossRef]

M. Segev, G. C. Valley, B. Crosignani, P. DiPorto, and A. Yariv, Phys. Rev. Lett. 73, 3211 (1994).
[CrossRef] [PubMed]

G. Duree, J. L. Shultz, G. Salamo, M. Segev, A. Yariv, B. Crosignani, P. DiPorto, E. Sharp, and R. Neurgaonkar, Phys. Rev. Lett. 71, 533 (1993).
[CrossRef] [PubMed]

M. Segev, B. Crosignani, A. Yariv, and B. Fischer, Phys. Rev. Lett. 68, 923 (1992).
[CrossRef] [PubMed]

Cui, Y. P.

DiPorto, P.

G. Duree, M. Morin, G. Salamo, M. Segev, A. Yariv, B. Crosignani, P. DiPorto, and E. Sharp, Phys. Rev. Lett. 74, 1978 (1995).
[CrossRef] [PubMed]

M. Segev, G. C. Valley, B. Crosignani, P. DiPorto, and A. Yariv, Phys. Rev. Lett. 73, 3211 (1994).
[CrossRef] [PubMed]

G. Duree, J. L. Shultz, G. Salamo, M. Segev, A. Yariv, B. Crosignani, P. DiPorto, E. Sharp, and R. Neurgaonkar, Phys. Rev. Lett. 71, 533 (1993).
[CrossRef] [PubMed]

Doran, N. J.

K. J. Blow and N. J. Doran, Phys. Lett. A 107, 55 (1985).
[CrossRef]

Duree, G.

G. Duree, M. Morin, G. Salamo, M. Segev, A. Yariv, B. Crosignani, P. DiPorto, and E. Sharp, Phys. Rev. Lett. 74, 1978 (1995).
[CrossRef] [PubMed]

M. Morin, G. Duree, G. Salamo, and M. Segev, Opt. Lett. 20, 2066 (1995).
[CrossRef] [PubMed]

G. Duree, J. L. Shultz, G. Salamo, M. Segev, A. Yariv, B. Crosignani, P. DiPorto, E. Sharp, and R. Neurgaonkar, Phys. Rev. Lett. 71, 533 (1993).
[CrossRef] [PubMed]

Fejer, M. M.

M. Taya, M. Bashaw, M. M. Fejer, M. Segev, and G. C. Valley, Opt. Lett. 21, 943 (1996).
[CrossRef] [PubMed]

M. Taya, M. Bashaw, M. M. Fejer, M. Segev, and G. C. Valley, Phys. Rev. A 52, 3095 (1995).
[CrossRef] [PubMed]

G. C. Valley, M. Segev, B. Crosignani, A. Yariv, M. M. Fejer, and M. Bashaw, Phys. Rev. A 50, R4457 (1994).
[CrossRef]

Fischer, B.

M. Segev, B. Crosignani, A. Yariv, and B. Fischer, Phys. Rev. Lett. 68, 923 (1992).
[CrossRef] [PubMed]

Garmire, E.

R. Y. Chiao, E. Garmire, and C. H. Townes, Phys. Rev. Lett. 13, 479 (1964).
[CrossRef]

Garrett, M.

Hawkins, S. A.

Iturbe-Castillo, M. D.

M. D. Iturbe-Castillo, J. J. Sanchez-Mondragon, S. Stepanov, M. B. Klein, and B. A. Wechsler, Opt. Commun. 118, 515 (1995).
[CrossRef]

Steady-state, self-focusing in biased photorefractive media were first observed by M. D. Iturbe-Castillo, P. A. Marquez-Aguilar, J. J. Sanchez-Mondragon, S. Stepanov, and V. Vysloukh, Appl. Phys. Lett. 64, 408 (1994).
[CrossRef]

Jackel, J. L.

Joseph, R. I.

M. I. Carvalho, S. R. Singh, D. N. Christodoulides, and R. I. Joseph, Phys. Rev. E 53, R53 (1996).
[CrossRef]

Kaplan, A. E.

G. A. Swartzlander, D. R. Andersen, J. J. Regan, H. Yin, and A. E. Kaplan, Phys. Rev. Lett. 66, 1583 (1991).
[CrossRef] [PubMed]

Kelley, P. L.

P. L. Kelley, Phys. Rev. Lett. 15, 1005 (1964).
[CrossRef]

Kivshar, Y.

Y. Kivshar, IEEE J. Quantum Electron. 29, 250 (1993).
[CrossRef]

Kivshar, Y. S.

Y. S. Kivshar and X. Yang, Opt. Commun. 107, 93 (1994).
[CrossRef]

Klein, M. B.

M. D. Iturbe-Castillo, J. J. Sanchez-Mondragon, S. Stepanov, M. B. Klein, and B. A. Wechsler, Opt. Commun. 118, 515 (1995).
[CrossRef]

Kos, K.

K. Kos, H. Ming, G. Salamo, M. Shih, M. Segev, and G. C. Valley, Phys. Rev. E 53, R4330 (1996).
[CrossRef]

Krolikowski, W.

Law, C. T.

G. A. Swartzlander and C. T. Law, Phys. Rev. Lett. 69, 2503 (1992).
[CrossRef] [PubMed]

Leaird, D. E.

Luther-Davies, B.

Mamaev, A. V.

A. V. Mamaev, M. Saffman, D. Z. Anderson, and A. A. Zozulya, Phys. Rev. A 54, 870 (1996). In that paper it is claimed that both bright and dark photorefractive solitons suffer from transverse instabilities and are unstable. But the experimental results presented in the same paper clearly show a “self-trapped channel of light” that does not exhibit transverse instabilities (Figs. 5d and 14b). Modulation instability was observed only when further “increasing the nonlinearity” (see discussion on page 874 there). The similarity between the experimental and the numerical results showing the development of the instability in that paper is misleading. The experimental results (Figs. 5 and 14) show sequences of output intensity distributions (at a fixed propagation distance) for different levels of applied voltages (i.e., different levels of nonlinearity), only one of which corresponds to that of a soliton (is on the existence curve), whereas the simulations (Figs. 1 and 9) show the near-field intensity evolution for different propagation distances for a fixed set of parameters (i.e., at a fixed voltage) that greatly differ from that of a soliton.
[CrossRef] [PubMed]

Marquez-Aguilar, P. A.

Steady-state, self-focusing in biased photorefractive media were first observed by M. D. Iturbe-Castillo, P. A. Marquez-Aguilar, J. J. Sanchez-Mondragon, S. Stepanov, and V. Vysloukh, Appl. Phys. Lett. 64, 408 (1994).
[CrossRef]

Ming, H.

K. Kos, H. Ming, G. Salamo, M. Shih, M. Segev, and G. C. Valley, Phys. Rev. E 53, R4330 (1996).
[CrossRef]

Mitchell, M.

Morin, M.

M. Morin, G. Duree, G. Salamo, and M. Segev, Opt. Lett. 20, 2066 (1995).
[CrossRef] [PubMed]

G. Duree, M. Morin, G. Salamo, M. Segev, A. Yariv, B. Crosignani, P. DiPorto, and E. Sharp, Phys. Rev. Lett. 74, 1978 (1995).
[CrossRef] [PubMed]

Neurgaonkar, R.

G. Duree, J. L. Shultz, G. Salamo, M. Segev, A. Yariv, B. Crosignani, P. DiPorto, E. Sharp, and R. Neurgaonkar, Phys. Rev. Lett. 71, 533 (1993).
[CrossRef] [PubMed]

Oliver, M. K.

Regan, J. J.

G. A. Swartzlander, D. R. Andersen, J. J. Regan, H. Yin, and A. E. Kaplan, Phys. Rev. Lett. 66, 1583 (1991).
[CrossRef] [PubMed]

Saffman, M.

A. V. Mamaev, M. Saffman, D. Z. Anderson, and A. A. Zozulya, Phys. Rev. A 54, 870 (1996). In that paper it is claimed that both bright and dark photorefractive solitons suffer from transverse instabilities and are unstable. But the experimental results presented in the same paper clearly show a “self-trapped channel of light” that does not exhibit transverse instabilities (Figs. 5d and 14b). Modulation instability was observed only when further “increasing the nonlinearity” (see discussion on page 874 there). The similarity between the experimental and the numerical results showing the development of the instability in that paper is misleading. The experimental results (Figs. 5 and 14) show sequences of output intensity distributions (at a fixed propagation distance) for different levels of applied voltages (i.e., different levels of nonlinearity), only one of which corresponds to that of a soliton (is on the existence curve), whereas the simulations (Figs. 1 and 9) show the near-field intensity evolution for different propagation distances for a fixed set of parameters (i.e., at a fixed voltage) that greatly differ from that of a soliton.
[CrossRef] [PubMed]

Salamo, G.

K. Kos, H. Ming, G. Salamo, M. Shih, M. Segev, and G. C. Valley, Phys. Rev. E 53, R4330 (1996).
[CrossRef]

M. Shih, M. Segev, and G. Salamo, Opt. Lett. 21, 931 (1996).
[CrossRef] [PubMed]

M. Chauvet, S. A. Hawkins, G. Salamo, M. Segev, D. F. Bliss, and G. Bryant, Opt. Lett. 21, 1333 (1996).
[CrossRef] [PubMed]

G. Duree, M. Morin, G. Salamo, M. Segev, A. Yariv, B. Crosignani, P. DiPorto, and E. Sharp, Phys. Rev. Lett. 74, 1978 (1995).
[CrossRef] [PubMed]

M. Morin, G. Duree, G. Salamo, and M. Segev, Opt. Lett. 20, 2066 (1995).
[CrossRef] [PubMed]

G. Duree, J. L. Shultz, G. Salamo, M. Segev, A. Yariv, B. Crosignani, P. DiPorto, E. Sharp, and R. Neurgaonkar, Phys. Rev. Lett. 71, 533 (1993).
[CrossRef] [PubMed]

Sanchez-Mondragon, J. J.

M. D. Iturbe-Castillo, J. J. Sanchez-Mondragon, S. Stepanov, M. B. Klein, and B. A. Wechsler, Opt. Commun. 118, 515 (1995).
[CrossRef]

Steady-state, self-focusing in biased photorefractive media were first observed by M. D. Iturbe-Castillo, P. A. Marquez-Aguilar, J. J. Sanchez-Mondragon, S. Stepanov, and V. Vysloukh, Appl. Phys. Lett. 64, 408 (1994).
[CrossRef]

Segev, M.

Z. Chen, M. Mitchell, and M. Segev, Opt. Lett. 21, 716 (1996).
[CrossRef] [PubMed]

Z. Chen, M. Mitchell, M. Shih, M. Segev, M. Garrett, and G. C. Valley, Opt. Lett. 21, 629 (1996).
[CrossRef] [PubMed]

M. Segev, M. Shih, and G. C. Valley, J. Opt. Soc. Am. B 13, 706 (1996).
[CrossRef]

M. Mitchell, Z. Chen, M. Shih, and M. Segev, Phys. Rev. Lett. 77, 490 (1996).
[CrossRef] [PubMed]

K. Kos, H. Ming, G. Salamo, M. Shih, M. Segev, and G. C. Valley, Phys. Rev. E 53, R4330 (1996).
[CrossRef]

D. N. Christodoulides, S. R. Singh, M. I. Carvalho, and M. Segev, Appl. Phys. Lett. 68, 1763 (1996).
[CrossRef]

M. Chauvet, S. A. Hawkins, G. Salamo, M. Segev, D. F. Bliss, and G. Bryant, Opt. Lett. 21, 1333 (1996).
[CrossRef] [PubMed]

M. Shih and M. Segev, Opt. Lett. 21, 1538 (1996).
[CrossRef] [PubMed]

M. Shih, M. Segev, and G. Salamo, Opt. Lett. 21, 931 (1996).
[CrossRef] [PubMed]

M. Taya, M. Bashaw, M. M. Fejer, M. Segev, and G. C. Valley, Opt. Lett. 21, 943 (1996).
[CrossRef] [PubMed]

M. Segev, G. C. Valley, S. R. Singh, M. I. Carvalho, and D. N. Christodoulides, Opt. Lett. 20, 1764 (1995).
[CrossRef]

M. Morin, G. Duree, G. Salamo, and M. Segev, Opt. Lett. 20, 2066 (1995).
[CrossRef] [PubMed]

M. Taya, M. Bashaw, M. M. Fejer, M. Segev, and G. C. Valley, Phys. Rev. A 52, 3095 (1995).
[CrossRef] [PubMed]

G. Duree, M. Morin, G. Salamo, M. Segev, A. Yariv, B. Crosignani, P. DiPorto, and E. Sharp, Phys. Rev. Lett. 74, 1978 (1995).
[CrossRef] [PubMed]

G. C. Valley, M. Segev, B. Crosignani, A. Yariv, M. M. Fejer, and M. Bashaw, Phys. Rev. A 50, R4457 (1994).
[CrossRef]

M. Segev, G. C. Valley, B. Crosignani, P. DiPorto, and A. Yariv, Phys. Rev. Lett. 73, 3211 (1994).
[CrossRef] [PubMed]

G. Duree, J. L. Shultz, G. Salamo, M. Segev, A. Yariv, B. Crosignani, P. DiPorto, E. Sharp, and R. Neurgaonkar, Phys. Rev. Lett. 71, 533 (1993).
[CrossRef] [PubMed]

M. Segev, B. Crosignani, A. Yariv, and B. Fischer, Phys. Rev. Lett. 68, 923 (1992).
[CrossRef] [PubMed]

Shabat, A. B.

V. E. Zakharov and A. B. Shabat, Sov. Phys. JETP 37, 823 (1973).

V. E. Zakharov and A. B. Shabat, Sov. Phys. JETP 34, 62 (1972).

Sharp, E.

G. Duree, M. Morin, G. Salamo, M. Segev, A. Yariv, B. Crosignani, P. DiPorto, and E. Sharp, Phys. Rev. Lett. 74, 1978 (1995).
[CrossRef] [PubMed]

G. Duree, J. L. Shultz, G. Salamo, M. Segev, A. Yariv, B. Crosignani, P. DiPorto, E. Sharp, and R. Neurgaonkar, Phys. Rev. Lett. 71, 533 (1993).
[CrossRef] [PubMed]

Sheng, Z. M.

Shih, M.

Shultz, J. L.

G. Duree, J. L. Shultz, G. Salamo, M. Segev, A. Yariv, B. Crosignani, P. DiPorto, E. Sharp, and R. Neurgaonkar, Phys. Rev. Lett. 71, 533 (1993).
[CrossRef] [PubMed]

Silberberg, Y.

Singh, S. R.

M. I. Carvalho, S. R. Singh, D. N. Christodoulides, and R. I. Joseph, Phys. Rev. E 53, R53 (1996).
[CrossRef]

D. N. Christodoulides, S. R. Singh, M. I. Carvalho, and M. Segev, Appl. Phys. Lett. 68, 1763 (1996).
[CrossRef]

M. Segev, G. C. Valley, S. R. Singh, M. I. Carvalho, and D. N. Christodoulides, Opt. Lett. 20, 1764 (1995).
[CrossRef]

S. R. Singh, M. I. Carvalho, and D. N. Christodoulides, Opt. Lett. 20, 2177 (1995).
[CrossRef]

S. R. Singh and D. N. Christodoulides, Opt. Commun. 118, 569 (1995).
[CrossRef]

M. I. Carvalho, S. R. Singh, and D. N. Christodoulides, Opt. Commun. 120, 311 (1995).
[CrossRef]

Skinner, S. R.

S. R. Skinner, G. R. Allan, D. A. Andersen, and A. L. Smirl, IEEE J. Quantum Electron. QE-27, 2211 (1991).
[CrossRef]

G. R. Allan, S. R. Skinner, D. R. Andersen, and A. L. Smirl, Opt. Lett. 16, 156 (1991).
[PubMed]

Smirl, A. L.

G. R. Allan, S. R. Skinner, D. R. Andersen, and A. L. Smirl, Opt. Lett. 16, 156 (1991).
[PubMed]

S. R. Skinner, G. R. Allan, D. A. Andersen, and A. L. Smirl, IEEE J. Quantum Electron. QE-27, 2211 (1991).
[CrossRef]

Smith, P. W.

Stepanov, S.

M. D. Iturbe-Castillo, J. J. Sanchez-Mondragon, S. Stepanov, M. B. Klein, and B. A. Wechsler, Opt. Commun. 118, 515 (1995).
[CrossRef]

Steady-state, self-focusing in biased photorefractive media were first observed by M. D. Iturbe-Castillo, P. A. Marquez-Aguilar, J. J. Sanchez-Mondragon, S. Stepanov, and V. Vysloukh, Appl. Phys. Lett. 64, 408 (1994).
[CrossRef]

Swartzlander, G. A.

G. A. Swartzlander and C. T. Law, Phys. Rev. Lett. 69, 2503 (1992).
[CrossRef] [PubMed]

G. A. Swartzlander, D. R. Andersen, J. J. Regan, H. Yin, and A. E. Kaplan, Phys. Rev. Lett. 66, 1583 (1991).
[CrossRef] [PubMed]

Taya, M.

M. Taya, M. Bashaw, M. M. Fejer, M. Segev, and G. C. Valley, Opt. Lett. 21, 943 (1996).
[CrossRef] [PubMed]

M. Taya, M. Bashaw, M. M. Fejer, M. Segev, and G. C. Valley, Phys. Rev. A 52, 3095 (1995).
[CrossRef] [PubMed]

Townes, C. H.

R. Y. Chiao, E. Garmire, and C. H. Townes, Phys. Rev. Lett. 13, 479 (1964).
[CrossRef]

Valley, G. C.

K. Kos, H. Ming, G. Salamo, M. Shih, M. Segev, and G. C. Valley, Phys. Rev. E 53, R4330 (1996).
[CrossRef]

M. Segev, M. Shih, and G. C. Valley, J. Opt. Soc. Am. B 13, 706 (1996).
[CrossRef]

Z. Chen, M. Mitchell, M. Shih, M. Segev, M. Garrett, and G. C. Valley, Opt. Lett. 21, 629 (1996).
[CrossRef] [PubMed]

M. Taya, M. Bashaw, M. M. Fejer, M. Segev, and G. C. Valley, Opt. Lett. 21, 943 (1996).
[CrossRef] [PubMed]

M. Segev, G. C. Valley, S. R. Singh, M. I. Carvalho, and D. N. Christodoulides, Opt. Lett. 20, 1764 (1995).
[CrossRef]

M. Taya, M. Bashaw, M. M. Fejer, M. Segev, and G. C. Valley, Phys. Rev. A 52, 3095 (1995).
[CrossRef] [PubMed]

G. C. Valley, M. Segev, B. Crosignani, A. Yariv, M. M. Fejer, and M. Bashaw, Phys. Rev. A 50, R4457 (1994).
[CrossRef]

M. Segev, G. C. Valley, B. Crosignani, P. DiPorto, and A. Yariv, Phys. Rev. Lett. 73, 3211 (1994).
[CrossRef] [PubMed]

Vogel, E. M.

Vysloukh, V.

Steady-state, self-focusing in biased photorefractive media were first observed by M. D. Iturbe-Castillo, P. A. Marquez-Aguilar, J. J. Sanchez-Mondragon, S. Stepanov, and V. Vysloukh, Appl. Phys. Lett. 64, 408 (1994).
[CrossRef]

Wechsler, B. A.

M. D. Iturbe-Castillo, J. J. Sanchez-Mondragon, S. Stepanov, M. B. Klein, and B. A. Wechsler, Opt. Commun. 118, 515 (1995).
[CrossRef]

Wei, Y.

Weiner, A. M.

Xiaoping, Y.

Yang, X.

Y. S. Kivshar and X. Yang, Opt. Commun. 107, 93 (1994).
[CrossRef]

Yariv, A.

G. Duree, M. Morin, G. Salamo, M. Segev, A. Yariv, B. Crosignani, P. DiPorto, and E. Sharp, Phys. Rev. Lett. 74, 1978 (1995).
[CrossRef] [PubMed]

G. C. Valley, M. Segev, B. Crosignani, A. Yariv, M. M. Fejer, and M. Bashaw, Phys. Rev. A 50, R4457 (1994).
[CrossRef]

M. Segev, G. C. Valley, B. Crosignani, P. DiPorto, and A. Yariv, Phys. Rev. Lett. 73, 3211 (1994).
[CrossRef] [PubMed]

G. Duree, J. L. Shultz, G. Salamo, M. Segev, A. Yariv, B. Crosignani, P. DiPorto, E. Sharp, and R. Neurgaonkar, Phys. Rev. Lett. 71, 533 (1993).
[CrossRef] [PubMed]

M. Segev, B. Crosignani, A. Yariv, and B. Fischer, Phys. Rev. Lett. 68, 923 (1992).
[CrossRef] [PubMed]

Yin, H.

G. A. Swartzlander, D. R. Andersen, J. J. Regan, H. Yin, and A. E. Kaplan, Phys. Rev. Lett. 66, 1583 (1991).
[CrossRef] [PubMed]

Zakharov, V. E.

V. E. Zakharov and A. B. Shabat, Sov. Phys. JETP 37, 823 (1973).

V. E. Zakharov and A. B. Shabat, Sov. Phys. JETP 34, 62 (1972).

Zozulya, A. A.

A. V. Mamaev, M. Saffman, D. Z. Anderson, and A. A. Zozulya, Phys. Rev. A 54, 870 (1996). In that paper it is claimed that both bright and dark photorefractive solitons suffer from transverse instabilities and are unstable. But the experimental results presented in the same paper clearly show a “self-trapped channel of light” that does not exhibit transverse instabilities (Figs. 5d and 14b). Modulation instability was observed only when further “increasing the nonlinearity” (see discussion on page 874 there). The similarity between the experimental and the numerical results showing the development of the instability in that paper is misleading. The experimental results (Figs. 5 and 14) show sequences of output intensity distributions (at a fixed propagation distance) for different levels of applied voltages (i.e., different levels of nonlinearity), only one of which corresponds to that of a soliton (is on the existence curve), whereas the simulations (Figs. 1 and 9) show the near-field intensity evolution for different propagation distances for a fixed set of parameters (i.e., at a fixed voltage) that greatly differ from that of a soliton.
[CrossRef] [PubMed]

Appl. Phys. Lett. (2)

Steady-state, self-focusing in biased photorefractive media were first observed by M. D. Iturbe-Castillo, P. A. Marquez-Aguilar, J. J. Sanchez-Mondragon, S. Stepanov, and V. Vysloukh, Appl. Phys. Lett. 64, 408 (1994).
[CrossRef]

D. N. Christodoulides, S. R. Singh, M. I. Carvalho, and M. Segev, Appl. Phys. Lett. 68, 1763 (1996).
[CrossRef]

IEEE J. Quantum Electron. (2)

Y. Kivshar, IEEE J. Quantum Electron. 29, 250 (1993).
[CrossRef]

S. R. Skinner, G. R. Allan, D. A. Andersen, and A. L. Smirl, IEEE J. Quantum Electron. QE-27, 2211 (1991).
[CrossRef]

J. Opt. Soc. Am. B (3)

Opt. Commun. (4)

M. I. Carvalho, S. R. Singh, and D. N. Christodoulides, Opt. Commun. 120, 311 (1995).
[CrossRef]

S. R. Singh and D. N. Christodoulides, Opt. Commun. 118, 569 (1995).
[CrossRef]

M. D. Iturbe-Castillo, J. J. Sanchez-Mondragon, S. Stepanov, M. B. Klein, and B. A. Wechsler, Opt. Commun. 118, 515 (1995).
[CrossRef]

Y. S. Kivshar and X. Yang, Opt. Commun. 107, 93 (1994).
[CrossRef]

Opt. Lett. (14)

Phys. Lett. A (1)

K. J. Blow and N. J. Doran, Phys. Lett. A 107, 55 (1985).
[CrossRef]

Phys. Rev. A (3)

G. C. Valley, M. Segev, B. Crosignani, A. Yariv, M. M. Fejer, and M. Bashaw, Phys. Rev. A 50, R4457 (1994).
[CrossRef]

M. Taya, M. Bashaw, M. M. Fejer, M. Segev, and G. C. Valley, Phys. Rev. A 52, 3095 (1995).
[CrossRef] [PubMed]

A. V. Mamaev, M. Saffman, D. Z. Anderson, and A. A. Zozulya, Phys. Rev. A 54, 870 (1996). In that paper it is claimed that both bright and dark photorefractive solitons suffer from transverse instabilities and are unstable. But the experimental results presented in the same paper clearly show a “self-trapped channel of light” that does not exhibit transverse instabilities (Figs. 5d and 14b). Modulation instability was observed only when further “increasing the nonlinearity” (see discussion on page 874 there). The similarity between the experimental and the numerical results showing the development of the instability in that paper is misleading. The experimental results (Figs. 5 and 14) show sequences of output intensity distributions (at a fixed propagation distance) for different levels of applied voltages (i.e., different levels of nonlinearity), only one of which corresponds to that of a soliton (is on the existence curve), whereas the simulations (Figs. 1 and 9) show the near-field intensity evolution for different propagation distances for a fixed set of parameters (i.e., at a fixed voltage) that greatly differ from that of a soliton.
[CrossRef] [PubMed]

Phys. Rev. E (2)

M. I. Carvalho, S. R. Singh, D. N. Christodoulides, and R. I. Joseph, Phys. Rev. E 53, R53 (1996).
[CrossRef]

K. Kos, H. Ming, G. Salamo, M. Shih, M. Segev, and G. C. Valley, Phys. Rev. E 53, R4330 (1996).
[CrossRef]

Phys. Rev. Lett. (9)

G. Duree, M. Morin, G. Salamo, M. Segev, A. Yariv, B. Crosignani, P. DiPorto, and E. Sharp, Phys. Rev. Lett. 74, 1978 (1995).
[CrossRef] [PubMed]

M. Segev, B. Crosignani, A. Yariv, and B. Fischer, Phys. Rev. Lett. 68, 923 (1992).
[CrossRef] [PubMed]

G. Duree, J. L. Shultz, G. Salamo, M. Segev, A. Yariv, B. Crosignani, P. DiPorto, E. Sharp, and R. Neurgaonkar, Phys. Rev. Lett. 71, 533 (1993).
[CrossRef] [PubMed]

M. Segev, G. C. Valley, B. Crosignani, P. DiPorto, and A. Yariv, Phys. Rev. Lett. 73, 3211 (1994).
[CrossRef] [PubMed]

P. L. Kelley, Phys. Rev. Lett. 15, 1005 (1964).
[CrossRef]

G. A. Swartzlander, D. R. Andersen, J. J. Regan, H. Yin, and A. E. Kaplan, Phys. Rev. Lett. 66, 1583 (1991).
[CrossRef] [PubMed]

G. A. Swartzlander and C. T. Law, Phys. Rev. Lett. 69, 2503 (1992).
[CrossRef] [PubMed]

R. Y. Chiao, E. Garmire, and C. H. Townes, Phys. Rev. Lett. 13, 479 (1964).
[CrossRef]

M. Mitchell, Z. Chen, M. Shih, and M. Segev, Phys. Rev. Lett. 77, 490 (1996).
[CrossRef] [PubMed]

Sov. Phys. JETP (2)

V. E. Zakharov and A. B. Shabat, Sov. Phys. JETP 34, 62 (1972).

V. E. Zakharov and A. B. Shabat, Sov. Phys. JETP 37, 823 (1973).

Other (2)

M. Shih, M. Segev, G. C. Valley, G. Salamo, B. Crosignani, and P. DiPorto, Electron. Lett. 31, 826 (1995); Opt. Lett. 21, 324 (1996).
[CrossRef]

Z. Chen, M. Segev, T. H. Coskun, and D. N. Christodoulides, Opt. Lett. 21, 1436 (1996); Opt. Lett. 21, 1821 (1996).
[CrossRef] [PubMed]

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Figures (10)

Fig. 1
Fig. 1

Schematic description of the formation of photorefractive dark solitons from different initial conditions. (a) Fundamental dark soliton from an odd initial condition (phase jump). (b) Y-junction dark soliton pair from an even initial condition (amplitude jump).

Fig. 2
Fig. 2

Existence curve of a fundamental dark photorefractive soliton: normalized soliton width Δξ as a function of u. Solid curve, analytic theory of one-dimensional fundamental dark screening solitons; filled circles, experimental measurements.

Fig. 3
Fig. 3

Experimental setup.

Fig. 4
Fig. 4

(a) Photographs and (b) horizontal beam profiles taken from the exit face of the crystal, showing an odd-number sequence of dark soliton stripes formed from an odd initial condition.

Fig. 5
Fig. 5

(a) Photographs and (b) horizontal beam profiles taken from the exit face of the crystal showing an even-number sequence of dark soliton stripes formed from an even initial condition.

Fig. 6
Fig. 6

(a) Photographs and (b) horizontal beam profiles taken from the exit face of the crystal showing the guidance of a red (HeNe) laser beam into the multiple channels induced by the dark solitons of the first three orders.

Fig. 7
Fig. 7

Dark solitons from odd initial conditions (numerical simulation). (a) Propagation of a 7-µm, fundamental dark soliton in biased SBN. (b) A 28-µm wide dark notch splits into three, dark soliton stripes. (c) A 58-µm wide dark notch splits into five dark soliton stripes.

Fig. 8
Fig. 8

Dark solitons from even initial conditions (numerical simulation). (a) Propagation of an 18-µm, dark notch in biased SBN that shows the formation of a Y-junction soliton pair. (b) A 36.5-µm wide, dark notch splits into four, dark soliton stripes. (c) A 65-µm wide, dark notch splits into six, dark soliton stripes.

Fig. 9
Fig. 9

Plot of the separation distance between the two branches of a Y-junction pair after 5 mm of propagation in the crystal as a function of input notch width. Crosses: numerical simulations. Circles: experimental measurements.

Fig. 10
Fig. 10

Numerical simulation showing that a small quadratic phase chirp introduced in an amplitude notch reduces the separation between the two branches of a Y-junction pair. Solid curves are beam profiles taken after 5 mm of propagation in the crystal. Dashed curves indicate the input. (a) Without the quadratic phase. (b) With the quadratic phase.

Equations (5)

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

Aζ-iAξξ=iη(ζ)|A|2+1A,
Γbu-uξξ=u2+1u2+1u.
uξξ-1-u2+1u2+1u=0.
u(0)=0,
dudξ(0)=[(1+u2)ln(1+u2)-u2]1/2.

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