Abstract

We provide a detailed analysis of gray spatial optical solitons in biased photorefractive media. The properties associated with these solitons, such as their transverse velocity, spatial width, and phase profile, are obtained as functions of their normalized intensity and degree of “grayness.” By employing the stability criterion based on the renormalized field momentum, we investigate the stability regions of gray spatial photorefractive solitons. The process of the soliton Y splitting arising from an initially even field depression is quasi-analytically described by use of a Hamiltonian formalism.

© 2001 Optical Society of America

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    [CrossRef]
  35. Yu. S. Kivshar and W. Królikowski, “Instabilities of dark solitons,” Opt. Lett. 20, 1527–1529 (1995).
    [CrossRef] [PubMed]
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1999 (2)

A. N. Slavin, Yu. S. Kivshar, E. A. Ostrovskaya, and H. Benner, “Generation of spin-wave envelope dark solitons,” Phys. Rev. Lett. 82, 2583–2586 (1999).
[CrossRef]

M. Klotz, H. Meng, G. J. Salamo, M. Segev, and S. R. Montgomery, “Fixing the photorefractive soliton,” Opt. Lett. 24, 77–79 (1999).
[CrossRef]

1998 (1)

For a general overview, see Yu. S. Kivshar and B. Luther-Davies, “Dark optical solitons: physics and applications,” Phys. Rep. 298, 81–197 (1998).
[CrossRef]

1997 (5)

1996 (4)

1995 (5)

Yu. S. Kivshar and W. Królikowski, “Instabilities of dark solitons,” Opt. Lett. 20, 1527–1529 (1995).
[CrossRef] [PubMed]

M. Morin, G. Duree, G. Salamo, and M. Segev, “Waveguides formed by quasi-steady-state photorefractive spatial solitons,” Opt. Lett. 20, 2066–2068 (1995).
[CrossRef] [PubMed]

D. N. Christodoulides and M. I. Carvalho, “Bright, dark, and gray spatial soliton states in photorefractive media,” J. Opt. Soc. Am. B 12, 1628–1633 (1995).
[CrossRef]

M. Taya, M. C. Bashaw, M. M. Fejer, M. Segev, and G. C. Valley, “Observation of dark photovoltaic spatial solitons,” Phys. Rev. A 52, R3095–R3100 (1995).
[CrossRef]

M. D. Iturbe-Castillo, J. J. Sanchez-Mondragon, S. I. Stepanov, M. B. Klein, and B. A. Wechsler, “(1+1)-Dimension dark spatial solitons in photorefractive Bi12TiO20 crystal,” Opt. Commun. 118, 515–519 (1995).
[CrossRef]

1994 (2)

M. Segev, G. C. Valley, B. Crosignani, P. DiPorto, and A. Yariv, “Steady-state spatial screening solitons in photorefractive materials with external applied field,” Phys. Rev. Lett. 73, 3211–3214 (1994).
[CrossRef] [PubMed]

G. C. Valley, M. Segev, B. Crosignani, A. Yariv, M. M. Fejer, and M. Bashaw, “Dark and bright photovoltaic spatial solitons,” Phys. Rev. A 50, R4457–R4460 (1994).
[CrossRef] [PubMed]

1993 (1)

W. Królikowski, N. Akhmediev, and B. Luther-Davies, “Darker-than-black solitons: dark solitons with total phase shift greater than π,” Phys. Rev. E 48, 3980–3987 (1993).
[CrossRef]

1992 (3)

G. A. Swartzlander, Jr. and C. T. Law, “Optical vortex solitons observed in Kerr nonlinear media,” Phys. Rev. Lett. 69, 2503–2506 (1992).
[CrossRef] [PubMed]

M. Segev, B. Crosignani, A. Yariv, and B. Fischer, “Spatial solitons in photorefractive media,” Phys. Rev. Lett. 68, 923–926 (1992).
[CrossRef] [PubMed]

B. Luther-Davies and Y. Xiaoping, “Waveguides and Y junctions formed in bulk media by using dark spatial solitons,” Opt. Lett. 17, 496–498 (1992).
[CrossRef] [PubMed]

1991 (3)

G. R. Allan, S. R. Skinner, D. R. Andersen, and A. L. Smirl, “Observation of fundamental dark spatial solitons in semiconductors using picosecond pulses,” Opt. Lett. 16, 156–158 (1991).
[PubMed]

G. A. Swartzlander, Jr., D. R. Andersen, J. J. Regan, H. Yin, and A. E. Kaplan, “Spatial dark-soliton stripes and grids in self-defocusing materials,” Phys. Rev. Lett. 66, 1583–1586 (1991).
[CrossRef] [PubMed]

S. R. Skinner, G. R. Allan, D. R. Andersen, and A. L. Smirl, “Dark spatial soliton propagation in bulk ZnSe,” IEEE J. Quantum Electron. 27, 2211–2219 (1991).
[CrossRef]

1990 (1)

1988 (1)

A. M. Weiner, J. P. Heritage, R. J. Hawkins, R. N. Thurston, E. M. Kirschner, D. E. Leaird, and W. J. Tomlinson, “Experimental observation of the fundamental dark soliton in optical fibers,” Phys. Rev. Lett. 61, 2445–2448 (1988).
[CrossRef] [PubMed]

1985 (1)

K. J. Blow and N. J. Doran, “Multiple dark soliton solutions of the nonlinear Schrödinger equation,” Phys. Lett. 107A, 55–58 (1985).
[CrossRef]

1973 (1)

V. E. Zakharov and A. B. Shabat, “Interaction between solitons in a stable medium,” Sov. Phys. JETP 37, 823–828 (1973).

Akhmediev, N.

W. Królikowski, N. Akhmediev, and B. Luther-Davies, “Darker-than-black solitons: dark solitons with total phase shift greater than π,” Phys. Rev. E 48, 3980–3987 (1993).
[CrossRef]

Allan, G. R.

S. R. Skinner, G. R. Allan, D. R. Andersen, and A. L. Smirl, “Dark spatial soliton propagation in bulk ZnSe,” IEEE J. Quantum Electron. 27, 2211–2219 (1991).
[CrossRef]

G. R. Allan, S. R. Skinner, D. R. Andersen, and A. L. Smirl, “Observation of fundamental dark spatial solitons in semiconductors using picosecond pulses,” Opt. Lett. 16, 156–158 (1991).
[PubMed]

Andersen, D. R.

G. R. Allan, S. R. Skinner, D. R. Andersen, and A. L. Smirl, “Observation of fundamental dark spatial solitons in semiconductors using picosecond pulses,” Opt. Lett. 16, 156–158 (1991).
[PubMed]

G. A. Swartzlander, Jr., D. R. Andersen, J. J. Regan, H. Yin, and A. E. Kaplan, “Spatial dark-soliton stripes and grids in self-defocusing materials,” Phys. Rev. Lett. 66, 1583–1586 (1991).
[CrossRef] [PubMed]

S. R. Skinner, G. R. Allan, D. R. Andersen, and A. L. Smirl, “Dark spatial soliton propagation in bulk ZnSe,” IEEE J. Quantum Electron. 27, 2211–2219 (1991).
[CrossRef]

D. R. Andersen, D. E. Hooton, G. A. Swartzlander, Jr., and A. E. Kaplan, “Direct measurement of the transverse velocity of dark spatial solitons,” Opt. Lett. 15, 783–785 (1990).
[CrossRef] [PubMed]

Bashaw, M.

M. Segev, G. C. Valley, M. Bashaw, M. Taya, and M. M. Fejer, “Photovoltaic spatial solitons,” J. Opt. Soc. Am. B 14, 1772–1781 (1997).
[CrossRef]

G. C. Valley, M. Segev, B. Crosignani, A. Yariv, M. M. Fejer, and M. Bashaw, “Dark and bright photovoltaic spatial solitons,” Phys. Rev. A 50, R4457–R4460 (1994).
[CrossRef] [PubMed]

Bashaw, M. C.

M. Taya, M. C. Bashaw, M. M. Fejer, M. Segev, and G. C. Valley, “Y junctions arising from dark-soliton propagation in photovoltaic media,” Opt. Lett. 21, 943–945 (1996).
[CrossRef] [PubMed]

M. Taya, M. C. Bashaw, M. M. Fejer, M. Segev, and G. C. Valley, “Observation of dark photovoltaic spatial solitons,” Phys. Rev. A 52, R3095–R3100 (1995).
[CrossRef]

Benner, H.

A. N. Slavin, Yu. S. Kivshar, E. A. Ostrovskaya, and H. Benner, “Generation of spin-wave envelope dark solitons,” Phys. Rev. Lett. 82, 2583–2586 (1999).
[CrossRef]

Bian, S.

S. Bian, J. Frejlich, and K. H. Ringhofer, “Photorefractive saturable Kerr-type nonlinearity in photovoltaic crystals,” Phys. Rev. Lett. 78, 4035–4038 (1997).
[CrossRef]

Blow, K. J.

K. J. Blow and N. J. Doran, “Multiple dark soliton solutions of the nonlinear Schrödinger equation,” Phys. Lett. 107A, 55–58 (1985).
[CrossRef]

Carvalho, M. I.

Chen, Z.

Christodoulides, D. N.

Coskun, T. H.

Crosignani, B.

G. C. Valley, M. Segev, B. Crosignani, A. Yariv, M. M. Fejer, and M. Bashaw, “Dark and bright photovoltaic spatial solitons,” Phys. Rev. A 50, R4457–R4460 (1994).
[CrossRef] [PubMed]

M. Segev, G. C. Valley, B. Crosignani, P. DiPorto, and A. Yariv, “Steady-state spatial screening solitons in photorefractive materials with external applied field,” Phys. Rev. Lett. 73, 3211–3214 (1994).
[CrossRef] [PubMed]

M. Segev, B. Crosignani, A. Yariv, and B. Fischer, “Spatial solitons in photorefractive media,” Phys. Rev. Lett. 68, 923–926 (1992).
[CrossRef] [PubMed]

DiPorto, P.

M. Segev, G. C. Valley, B. Crosignani, P. DiPorto, and A. Yariv, “Steady-state spatial screening solitons in photorefractive materials with external applied field,” Phys. Rev. Lett. 73, 3211–3214 (1994).
[CrossRef] [PubMed]

Doran, N. J.

K. J. Blow and N. J. Doran, “Multiple dark soliton solutions of the nonlinear Schrödinger equation,” Phys. Lett. 107A, 55–58 (1985).
[CrossRef]

Duree, G.

Fejer, M. M.

M. Segev, G. C. Valley, M. Bashaw, M. Taya, and M. M. Fejer, “Photovoltaic spatial solitons,” J. Opt. Soc. Am. B 14, 1772–1781 (1997).
[CrossRef]

M. Taya, M. C. Bashaw, M. M. Fejer, M. Segev, and G. C. Valley, “Y junctions arising from dark-soliton propagation in photovoltaic media,” Opt. Lett. 21, 943–945 (1996).
[CrossRef] [PubMed]

M. Taya, M. C. Bashaw, M. M. Fejer, M. Segev, and G. C. Valley, “Observation of dark photovoltaic spatial solitons,” Phys. Rev. A 52, R3095–R3100 (1995).
[CrossRef]

G. C. Valley, M. Segev, B. Crosignani, A. Yariv, M. M. Fejer, and M. Bashaw, “Dark and bright photovoltaic spatial solitons,” Phys. Rev. A 50, R4457–R4460 (1994).
[CrossRef] [PubMed]

Fischer, B.

M. Segev, B. Crosignani, A. Yariv, and B. Fischer, “Spatial solitons in photorefractive media,” Phys. Rev. Lett. 68, 923–926 (1992).
[CrossRef] [PubMed]

Frejlich, J.

S. Bian, J. Frejlich, and K. H. Ringhofer, “Photorefractive saturable Kerr-type nonlinearity in photovoltaic crystals,” Phys. Rev. Lett. 78, 4035–4038 (1997).
[CrossRef]

Garrett, M. H.

Hawkins, R. J.

A. M. Weiner, J. P. Heritage, R. J. Hawkins, R. N. Thurston, E. M. Kirschner, D. E. Leaird, and W. J. Tomlinson, “Experimental observation of the fundamental dark soliton in optical fibers,” Phys. Rev. Lett. 61, 2445–2448 (1988).
[CrossRef] [PubMed]

Heritage, J. P.

A. M. Weiner, J. P. Heritage, R. J. Hawkins, R. N. Thurston, E. M. Kirschner, D. E. Leaird, and W. J. Tomlinson, “Experimental observation of the fundamental dark soliton in optical fibers,” Phys. Rev. Lett. 61, 2445–2448 (1988).
[CrossRef] [PubMed]

Hooton, D. E.

Iturbe-Castillo, M. D.

M. D. Iturbe-Castillo, J. J. Sanchez-Mondragon, S. I. Stepanov, M. B. Klein, and B. A. Wechsler, “(1+1)-Dimension dark spatial solitons in photorefractive Bi12TiO20 crystal,” Opt. Commun. 118, 515–519 (1995).
[CrossRef]

Kaplan, A. E.

G. A. Swartzlander, Jr., D. R. Andersen, J. J. Regan, H. Yin, and A. E. Kaplan, “Spatial dark-soliton stripes and grids in self-defocusing materials,” Phys. Rev. Lett. 66, 1583–1586 (1991).
[CrossRef] [PubMed]

D. R. Andersen, D. E. Hooton, G. A. Swartzlander, Jr., and A. E. Kaplan, “Direct measurement of the transverse velocity of dark spatial solitons,” Opt. Lett. 15, 783–785 (1990).
[CrossRef] [PubMed]

Kirschner, E. M.

A. M. Weiner, J. P. Heritage, R. J. Hawkins, R. N. Thurston, E. M. Kirschner, D. E. Leaird, and W. J. Tomlinson, “Experimental observation of the fundamental dark soliton in optical fibers,” Phys. Rev. Lett. 61, 2445–2448 (1988).
[CrossRef] [PubMed]

Kivshar, Yu. S.

A. N. Slavin, Yu. S. Kivshar, E. A. Ostrovskaya, and H. Benner, “Generation of spin-wave envelope dark solitons,” Phys. Rev. Lett. 82, 2583–2586 (1999).
[CrossRef]

For a general overview, see Yu. S. Kivshar and B. Luther-Davies, “Dark optical solitons: physics and applications,” Phys. Rep. 298, 81–197 (1998).
[CrossRef]

Yu. S. Kivshar and W. Królikowski, “Instabilities of dark solitons,” Opt. Lett. 20, 1527–1529 (1995).
[CrossRef] [PubMed]

Klein, M. B.

M. D. Iturbe-Castillo, J. J. Sanchez-Mondragon, S. I. Stepanov, M. B. Klein, and B. A. Wechsler, “(1+1)-Dimension dark spatial solitons in photorefractive Bi12TiO20 crystal,” Opt. Commun. 118, 515–519 (1995).
[CrossRef]

Klotz, M.

Królikowski, W.

Yu. S. Kivshar and W. Królikowski, “Instabilities of dark solitons,” Opt. Lett. 20, 1527–1529 (1995).
[CrossRef] [PubMed]

W. Królikowski, N. Akhmediev, and B. Luther-Davies, “Darker-than-black solitons: dark solitons with total phase shift greater than π,” Phys. Rev. E 48, 3980–3987 (1993).
[CrossRef]

Law, C. T.

G. A. Swartzlander, Jr. and C. T. Law, “Optical vortex solitons observed in Kerr nonlinear media,” Phys. Rev. Lett. 69, 2503–2506 (1992).
[CrossRef] [PubMed]

Leaird, D. E.

A. M. Weiner, J. P. Heritage, R. J. Hawkins, R. N. Thurston, E. M. Kirschner, D. E. Leaird, and W. J. Tomlinson, “Experimental observation of the fundamental dark soliton in optical fibers,” Phys. Rev. Lett. 61, 2445–2448 (1988).
[CrossRef] [PubMed]

Luther-Davies, B.

For a general overview, see Yu. S. Kivshar and B. Luther-Davies, “Dark optical solitons: physics and applications,” Phys. Rep. 298, 81–197 (1998).
[CrossRef]

W. Królikowski, N. Akhmediev, and B. Luther-Davies, “Darker-than-black solitons: dark solitons with total phase shift greater than π,” Phys. Rev. E 48, 3980–3987 (1993).
[CrossRef]

B. Luther-Davies and Y. Xiaoping, “Waveguides and Y junctions formed in bulk media by using dark spatial solitons,” Opt. Lett. 17, 496–498 (1992).
[CrossRef] [PubMed]

Maker, P. D.

Z. Chen, M.-F. Shih, M. Segev, D. W. Wilson, R. E. Muller, and P. D. Maker, “Steady-state vortex-screening solitons formed in biased photorefractive media,” Opt. Lett. 22, 1751–1753 (1997).
[CrossRef]

Z. Chen, M. Segev, D. W. Wilson, R. E. Muller, and P. D. Maker, “Self-trapping of an optical vortex by use of the bulk photovoltaic effect,” Phys. Rev. Lett. 78, 2948–2951 (1997).
[CrossRef]

Meng, H.

Mitchell, M.

Montgomery, S. R.

Morin, M.

Muller, R. E.

Z. Chen, M. Segev, D. W. Wilson, R. E. Muller, and P. D. Maker, “Self-trapping of an optical vortex by use of the bulk photovoltaic effect,” Phys. Rev. Lett. 78, 2948–2951 (1997).
[CrossRef]

Z. Chen, M.-F. Shih, M. Segev, D. W. Wilson, R. E. Muller, and P. D. Maker, “Steady-state vortex-screening solitons formed in biased photorefractive media,” Opt. Lett. 22, 1751–1753 (1997).
[CrossRef]

Ostrovskaya, E. A.

A. N. Slavin, Yu. S. Kivshar, E. A. Ostrovskaya, and H. Benner, “Generation of spin-wave envelope dark solitons,” Phys. Rev. Lett. 82, 2583–2586 (1999).
[CrossRef]

Regan, J. J.

G. A. Swartzlander, Jr., D. R. Andersen, J. J. Regan, H. Yin, and A. E. Kaplan, “Spatial dark-soliton stripes and grids in self-defocusing materials,” Phys. Rev. Lett. 66, 1583–1586 (1991).
[CrossRef] [PubMed]

Ringhofer, K. H.

S. Bian, J. Frejlich, and K. H. Ringhofer, “Photorefractive saturable Kerr-type nonlinearity in photovoltaic crystals,” Phys. Rev. Lett. 78, 4035–4038 (1997).
[CrossRef]

Salamo, G.

Salamo, G. J.

Sanchez-Mondragon, J. J.

M. D. Iturbe-Castillo, J. J. Sanchez-Mondragon, S. I. Stepanov, M. B. Klein, and B. A. Wechsler, “(1+1)-Dimension dark spatial solitons in photorefractive Bi12TiO20 crystal,” Opt. Commun. 118, 515–519 (1995).
[CrossRef]

Segev, M.

M. Klotz, H. Meng, G. J. Salamo, M. Segev, and S. R. Montgomery, “Fixing the photorefractive soliton,” Opt. Lett. 24, 77–79 (1999).
[CrossRef]

Z. Chen, M.-F. Shih, M. Segev, D. W. Wilson, R. E. Muller, and P. D. Maker, “Steady-state vortex-screening solitons formed in biased photorefractive media,” Opt. Lett. 22, 1751–1753 (1997).
[CrossRef]

M. Segev, G. C. Valley, M. Bashaw, M. Taya, and M. M. Fejer, “Photovoltaic spatial solitons,” J. Opt. Soc. Am. B 14, 1772–1781 (1997).
[CrossRef]

Z. Chen, M. Segev, D. W. Wilson, R. E. Muller, and P. D. Maker, “Self-trapping of an optical vortex by use of the bulk photovoltaic effect,” Phys. Rev. Lett. 78, 2948–2951 (1997).
[CrossRef]

Z. Chen, M. Segev, S. R. Singh, T. H. Coskun, and D. N. Christodoulides, “Sequential formation of multiple dark photorefractive spatial solitons: experiments and theory,” J. Opt. Soc. Am. B 14, 1407–1417 (1997).
[CrossRef]

Z. Chen, M. Mitchell, and M. Segev, “Steady-state photorefractive soliton-induced Y-junction waveguides and high-order dark spatial solitons,” Opt. Lett. 21, 716–718 (1996).
[CrossRef] [PubMed]

Z. Chen, M. Mitchell, M.-F. Shih, M. Segev, M. H. Garrett, and G. C. Valley, “Steady-state dark photorefractive screening solitons,” Opt. Lett. 21, 629–631 (1996).
[CrossRef] [PubMed]

M. Segev, M. F. Shih, and G. C. Valley, “Photorefractive screening solitons of high and low intensity,” J. Opt. Soc. Am. B 13, 706–718 (1996).
[CrossRef]

M. Taya, M. C. Bashaw, M. M. Fejer, M. Segev, and G. C. Valley, “Y junctions arising from dark-soliton propagation in photovoltaic media,” Opt. Lett. 21, 943–945 (1996).
[CrossRef] [PubMed]

M. Morin, G. Duree, G. Salamo, and M. Segev, “Waveguides formed by quasi-steady-state photorefractive spatial solitons,” Opt. Lett. 20, 2066–2068 (1995).
[CrossRef] [PubMed]

M. Taya, M. C. Bashaw, M. M. Fejer, M. Segev, and G. C. Valley, “Observation of dark photovoltaic spatial solitons,” Phys. Rev. A 52, R3095–R3100 (1995).
[CrossRef]

G. C. Valley, M. Segev, B. Crosignani, A. Yariv, M. M. Fejer, and M. Bashaw, “Dark and bright photovoltaic spatial solitons,” Phys. Rev. A 50, R4457–R4460 (1994).
[CrossRef] [PubMed]

M. Segev, G. C. Valley, B. Crosignani, P. DiPorto, and A. Yariv, “Steady-state spatial screening solitons in photorefractive materials with external applied field,” Phys. Rev. Lett. 73, 3211–3214 (1994).
[CrossRef] [PubMed]

M. Segev, B. Crosignani, A. Yariv, and B. Fischer, “Spatial solitons in photorefractive media,” Phys. Rev. Lett. 68, 923–926 (1992).
[CrossRef] [PubMed]

Shabat, A. B.

V. E. Zakharov and A. B. Shabat, “Interaction between solitons in a stable medium,” Sov. Phys. JETP 37, 823–828 (1973).

Shih, M. F.

Shih, M.-F.

Singh, S. R.

Skinner, S. R.

S. R. Skinner, G. R. Allan, D. R. Andersen, and A. L. Smirl, “Dark spatial soliton propagation in bulk ZnSe,” IEEE J. Quantum Electron. 27, 2211–2219 (1991).
[CrossRef]

G. R. Allan, S. R. Skinner, D. R. Andersen, and A. L. Smirl, “Observation of fundamental dark spatial solitons in semiconductors using picosecond pulses,” Opt. Lett. 16, 156–158 (1991).
[PubMed]

Slavin, A. N.

A. N. Slavin, Yu. S. Kivshar, E. A. Ostrovskaya, and H. Benner, “Generation of spin-wave envelope dark solitons,” Phys. Rev. Lett. 82, 2583–2586 (1999).
[CrossRef]

Smirl, A. L.

S. R. Skinner, G. R. Allan, D. R. Andersen, and A. L. Smirl, “Dark spatial soliton propagation in bulk ZnSe,” IEEE J. Quantum Electron. 27, 2211–2219 (1991).
[CrossRef]

G. R. Allan, S. R. Skinner, D. R. Andersen, and A. L. Smirl, “Observation of fundamental dark spatial solitons in semiconductors using picosecond pulses,” Opt. Lett. 16, 156–158 (1991).
[PubMed]

Stepanov, S. I.

M. D. Iturbe-Castillo, J. J. Sanchez-Mondragon, S. I. Stepanov, M. B. Klein, and B. A. Wechsler, “(1+1)-Dimension dark spatial solitons in photorefractive Bi12TiO20 crystal,” Opt. Commun. 118, 515–519 (1995).
[CrossRef]

Swartzlander Jr., G. A.

G. A. Swartzlander, Jr. and C. T. Law, “Optical vortex solitons observed in Kerr nonlinear media,” Phys. Rev. Lett. 69, 2503–2506 (1992).
[CrossRef] [PubMed]

G. A. Swartzlander, Jr., D. R. Andersen, J. J. Regan, H. Yin, and A. E. Kaplan, “Spatial dark-soliton stripes and grids in self-defocusing materials,” Phys. Rev. Lett. 66, 1583–1586 (1991).
[CrossRef] [PubMed]

D. R. Andersen, D. E. Hooton, G. A. Swartzlander, Jr., and A. E. Kaplan, “Direct measurement of the transverse velocity of dark spatial solitons,” Opt. Lett. 15, 783–785 (1990).
[CrossRef] [PubMed]

Taya, M.

Thurston, R. N.

A. M. Weiner, J. P. Heritage, R. J. Hawkins, R. N. Thurston, E. M. Kirschner, D. E. Leaird, and W. J. Tomlinson, “Experimental observation of the fundamental dark soliton in optical fibers,” Phys. Rev. Lett. 61, 2445–2448 (1988).
[CrossRef] [PubMed]

Tomlinson, W. J.

A. M. Weiner, J. P. Heritage, R. J. Hawkins, R. N. Thurston, E. M. Kirschner, D. E. Leaird, and W. J. Tomlinson, “Experimental observation of the fundamental dark soliton in optical fibers,” Phys. Rev. Lett. 61, 2445–2448 (1988).
[CrossRef] [PubMed]

Valley, G. C.

M. Segev, G. C. Valley, M. Bashaw, M. Taya, and M. M. Fejer, “Photovoltaic spatial solitons,” J. Opt. Soc. Am. B 14, 1772–1781 (1997).
[CrossRef]

M. Taya, M. C. Bashaw, M. M. Fejer, M. Segev, and G. C. Valley, “Y junctions arising from dark-soliton propagation in photovoltaic media,” Opt. Lett. 21, 943–945 (1996).
[CrossRef] [PubMed]

Z. Chen, M. Mitchell, M.-F. Shih, M. Segev, M. H. Garrett, and G. C. Valley, “Steady-state dark photorefractive screening solitons,” Opt. Lett. 21, 629–631 (1996).
[CrossRef] [PubMed]

M. Segev, M. F. Shih, and G. C. Valley, “Photorefractive screening solitons of high and low intensity,” J. Opt. Soc. Am. B 13, 706–718 (1996).
[CrossRef]

M. Taya, M. C. Bashaw, M. M. Fejer, M. Segev, and G. C. Valley, “Observation of dark photovoltaic spatial solitons,” Phys. Rev. A 52, R3095–R3100 (1995).
[CrossRef]

G. C. Valley, M. Segev, B. Crosignani, A. Yariv, M. M. Fejer, and M. Bashaw, “Dark and bright photovoltaic spatial solitons,” Phys. Rev. A 50, R4457–R4460 (1994).
[CrossRef] [PubMed]

M. Segev, G. C. Valley, B. Crosignani, P. DiPorto, and A. Yariv, “Steady-state spatial screening solitons in photorefractive materials with external applied field,” Phys. Rev. Lett. 73, 3211–3214 (1994).
[CrossRef] [PubMed]

Wechsler, B. A.

M. D. Iturbe-Castillo, J. J. Sanchez-Mondragon, S. I. Stepanov, M. B. Klein, and B. A. Wechsler, “(1+1)-Dimension dark spatial solitons in photorefractive Bi12TiO20 crystal,” Opt. Commun. 118, 515–519 (1995).
[CrossRef]

Weiner, A. M.

A. M. Weiner, J. P. Heritage, R. J. Hawkins, R. N. Thurston, E. M. Kirschner, D. E. Leaird, and W. J. Tomlinson, “Experimental observation of the fundamental dark soliton in optical fibers,” Phys. Rev. Lett. 61, 2445–2448 (1988).
[CrossRef] [PubMed]

Wilson, D. W.

Z. Chen, M.-F. Shih, M. Segev, D. W. Wilson, R. E. Muller, and P. D. Maker, “Steady-state vortex-screening solitons formed in biased photorefractive media,” Opt. Lett. 22, 1751–1753 (1997).
[CrossRef]

Z. Chen, M. Segev, D. W. Wilson, R. E. Muller, and P. D. Maker, “Self-trapping of an optical vortex by use of the bulk photovoltaic effect,” Phys. Rev. Lett. 78, 2948–2951 (1997).
[CrossRef]

Xiaoping, Y.

Yariv, A.

M. Segev, G. C. Valley, B. Crosignani, P. DiPorto, and A. Yariv, “Steady-state spatial screening solitons in photorefractive materials with external applied field,” Phys. Rev. Lett. 73, 3211–3214 (1994).
[CrossRef] [PubMed]

G. C. Valley, M. Segev, B. Crosignani, A. Yariv, M. M. Fejer, and M. Bashaw, “Dark and bright photovoltaic spatial solitons,” Phys. Rev. A 50, R4457–R4460 (1994).
[CrossRef] [PubMed]

M. Segev, B. Crosignani, A. Yariv, and B. Fischer, “Spatial solitons in photorefractive media,” Phys. Rev. Lett. 68, 923–926 (1992).
[CrossRef] [PubMed]

Yin, H.

G. A. Swartzlander, Jr., D. R. Andersen, J. J. Regan, H. Yin, and A. E. Kaplan, “Spatial dark-soliton stripes and grids in self-defocusing materials,” Phys. Rev. Lett. 66, 1583–1586 (1991).
[CrossRef] [PubMed]

Zakharov, V. E.

V. E. Zakharov and A. B. Shabat, “Interaction between solitons in a stable medium,” Sov. Phys. JETP 37, 823–828 (1973).

IEEE J. Quantum Electron. (1)

S. R. Skinner, G. R. Allan, D. R. Andersen, and A. L. Smirl, “Dark spatial soliton propagation in bulk ZnSe,” IEEE J. Quantum Electron. 27, 2211–2219 (1991).
[CrossRef]

J. Opt. Soc. Am. B (4)

Opt. Commun. (1)

M. D. Iturbe-Castillo, J. J. Sanchez-Mondragon, S. I. Stepanov, M. B. Klein, and B. A. Wechsler, “(1+1)-Dimension dark spatial solitons in photorefractive Bi12TiO20 crystal,” Opt. Commun. 118, 515–519 (1995).
[CrossRef]

Opt. Lett. (10)

Z. Chen, M.-F. Shih, M. Segev, D. W. Wilson, R. E. Muller, and P. D. Maker, “Steady-state vortex-screening solitons formed in biased photorefractive media,” Opt. Lett. 22, 1751–1753 (1997).
[CrossRef]

M. Klotz, H. Meng, G. J. Salamo, M. Segev, and S. R. Montgomery, “Fixing the photorefractive soliton,” Opt. Lett. 24, 77–79 (1999).
[CrossRef]

Z. Chen, M. Mitchell, M.-F. Shih, M. Segev, M. H. Garrett, and G. C. Valley, “Steady-state dark photorefractive screening solitons,” Opt. Lett. 21, 629–631 (1996).
[CrossRef] [PubMed]

Z. Chen, M. Mitchell, and M. Segev, “Steady-state photorefractive soliton-induced Y-junction waveguides and high-order dark spatial solitons,” Opt. Lett. 21, 716–718 (1996).
[CrossRef] [PubMed]

M. Taya, M. C. Bashaw, M. M. Fejer, M. Segev, and G. C. Valley, “Y junctions arising from dark-soliton propagation in photovoltaic media,” Opt. Lett. 21, 943–945 (1996).
[CrossRef] [PubMed]

D. R. Andersen, D. E. Hooton, G. A. Swartzlander, Jr., and A. E. Kaplan, “Direct measurement of the transverse velocity of dark spatial solitons,” Opt. Lett. 15, 783–785 (1990).
[CrossRef] [PubMed]

G. R. Allan, S. R. Skinner, D. R. Andersen, and A. L. Smirl, “Observation of fundamental dark spatial solitons in semiconductors using picosecond pulses,” Opt. Lett. 16, 156–158 (1991).
[PubMed]

B. Luther-Davies and Y. Xiaoping, “Waveguides and Y junctions formed in bulk media by using dark spatial solitons,” Opt. Lett. 17, 496–498 (1992).
[CrossRef] [PubMed]

Yu. S. Kivshar and W. Królikowski, “Instabilities of dark solitons,” Opt. Lett. 20, 1527–1529 (1995).
[CrossRef] [PubMed]

M. Morin, G. Duree, G. Salamo, and M. Segev, “Waveguides formed by quasi-steady-state photorefractive spatial solitons,” Opt. Lett. 20, 2066–2068 (1995).
[CrossRef] [PubMed]

Phys. Lett. (1)

K. J. Blow and N. J. Doran, “Multiple dark soliton solutions of the nonlinear Schrödinger equation,” Phys. Lett. 107A, 55–58 (1985).
[CrossRef]

Phys. Rep. (1)

For a general overview, see Yu. S. Kivshar and B. Luther-Davies, “Dark optical solitons: physics and applications,” Phys. Rep. 298, 81–197 (1998).
[CrossRef]

Phys. Rev. A (2)

M. Taya, M. C. Bashaw, M. M. Fejer, M. Segev, and G. C. Valley, “Observation of dark photovoltaic spatial solitons,” Phys. Rev. A 52, R3095–R3100 (1995).
[CrossRef]

G. C. Valley, M. Segev, B. Crosignani, A. Yariv, M. M. Fejer, and M. Bashaw, “Dark and bright photovoltaic spatial solitons,” Phys. Rev. A 50, R4457–R4460 (1994).
[CrossRef] [PubMed]

Phys. Rev. E (1)

W. Królikowski, N. Akhmediev, and B. Luther-Davies, “Darker-than-black solitons: dark solitons with total phase shift greater than π,” Phys. Rev. E 48, 3980–3987 (1993).
[CrossRef]

Phys. Rev. Lett. (8)

A. N. Slavin, Yu. S. Kivshar, E. A. Ostrovskaya, and H. Benner, “Generation of spin-wave envelope dark solitons,” Phys. Rev. Lett. 82, 2583–2586 (1999).
[CrossRef]

S. Bian, J. Frejlich, and K. H. Ringhofer, “Photorefractive saturable Kerr-type nonlinearity in photovoltaic crystals,” Phys. Rev. Lett. 78, 4035–4038 (1997).
[CrossRef]

A. M. Weiner, J. P. Heritage, R. J. Hawkins, R. N. Thurston, E. M. Kirschner, D. E. Leaird, and W. J. Tomlinson, “Experimental observation of the fundamental dark soliton in optical fibers,” Phys. Rev. Lett. 61, 2445–2448 (1988).
[CrossRef] [PubMed]

G. A. Swartzlander, Jr. and C. T. Law, “Optical vortex solitons observed in Kerr nonlinear media,” Phys. Rev. Lett. 69, 2503–2506 (1992).
[CrossRef] [PubMed]

Z. Chen, M. Segev, D. W. Wilson, R. E. Muller, and P. D. Maker, “Self-trapping of an optical vortex by use of the bulk photovoltaic effect,” Phys. Rev. Lett. 78, 2948–2951 (1997).
[CrossRef]

M. Segev, B. Crosignani, A. Yariv, and B. Fischer, “Spatial solitons in photorefractive media,” Phys. Rev. Lett. 68, 923–926 (1992).
[CrossRef] [PubMed]

M. Segev, G. C. Valley, B. Crosignani, P. DiPorto, and A. Yariv, “Steady-state spatial screening solitons in photorefractive materials with external applied field,” Phys. Rev. Lett. 73, 3211–3214 (1994).
[CrossRef] [PubMed]

G. A. Swartzlander, Jr., D. R. Andersen, J. J. Regan, H. Yin, and A. E. Kaplan, “Spatial dark-soliton stripes and grids in self-defocusing materials,” Phys. Rev. Lett. 66, 1583–1586 (1991).
[CrossRef] [PubMed]

Sov. Phys. JETP (1)

V. E. Zakharov and A. B. Shabat, “Interaction between solitons in a stable medium,” Sov. Phys. JETP 37, 823–828 (1973).

Other (6)

G. P. Agrawal, Nonlinear Fiber Optics, 2nd ed. (San Diego, Academic Press, 1995).

M.-F. Shih, M. Segev, G. C. Valley, G. Salamo, B. Crosignani, and P. DiPorto, “Observation of two-dimensional steady-state photorefractive screening solitons,” Electron. Lett. 31, 826–827 (1995); M.-F. Shih, P. Leach, M. Segev, M. H. Garrett, G. Salamo, and G. C. Valley, “Two-dimensional steady-state photorefractive screening solitons,” Opt. Lett. 21, 324–326 (1996).
[CrossRef] [PubMed]

G. Duree, M. Morin, G. Salamo, M. Segev, B. Crosignani, P. DiPorto, E. Sharp, and A. Yariv, “Dark photorefractive spatial solitons and photorefractive vortex solitons,” Phys. Rev. Lett. 74, 1978–1981 (1995); G. Duree, J. L. Shultz, G. Salamo, M. Segev, A. Yariv, B. Crosignani, P. DiPorto, E. Sharp, and R. R. Neurgaonkar, “Observation of self-trapping of an optical beam due to the photorefractive effect,” Phys. Rev. Lett. 71, 533–536 (1993).
[CrossRef] [PubMed]

P. Emplit, J. P. Hamaide, F. Reynaud, C. Froehly, and A. Barthelemy, “Picosecond steps and dark pulses through nonlinear single mode fibers,” Opt. Commun. 62, 374–379 (1987); D. Krökel, N. J. Halas, G. Giuliani, and D. Grischkowsky, “Dark-pulse propagation in optical fibers,” Phys. Rev. Lett. 60, 29–32 (1988).
[CrossRef] [PubMed]

M. Klotz, M. Crosser, G. J. Salamo, and M. Segev, “Fixing solitonic waveguides in photorefractive strontium barium niobate,” Technical Digest of the Topical Meeting on Nonlinear Guided Waves and Their Applications (Optical Society of America, Washington, D.C., 1999), paper ThE8.

D. E. Pelinovsky, Yu. S. Kivshar, and V. V. Afanasjev, “Instability-induced dynamics of dark solitons,” Phys. Rev. E 54, 2015–2032 (1996); I. V. Barashenkov, “Stability criterion for dark solitons,” Phys. Rev. Lett. 77, 1193–1197 (1996).
[CrossRef] [PubMed]

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Figures (9)

Fig. 1
Fig. 1

(a) Normalized intensity profile of a gray photorefractive soliton at ρ=40 and for various values of the grayness factor m; (b) associated phase profile of these gray solitons.

Fig. 2
Fig. 2

Transverse velocity v of a gray photorefractive soliton as a function of ρ and m.

Fig. 3
Fig. 3

Normalized FWHM of a gray photorefractive soliton as a function of ρ and m.

Fig. 4
Fig. 4

Phase jump of a gray soliton as a function of ρ and m.

Fig. 5
Fig. 5

(a) Normalized intensity and (b) phase profile of a gray photorefractive soliton propagating in a SBN crystal when m=0.1 and ρ=40.

Fig. 6
Fig. 6

Soliton Hamiltonian Hs/ρ as a function of ρ and m.

Fig. 7
Fig. 7

(a) Normalized intensity and (b) corresponding phase profiles as obtained from numerical simulations of the soliton Y-splitting for ρ=40 and when the spatial FWHM of the even field depression is x0=18 µm. (c) Intensity and (d) phase profiles during Y-splitting in a SBN crystal when ρ=40 and the initial FWHM of the even field depression is x0=14 µm.

Fig. 8
Fig. 8

(a) Renormalized momentum Ps/ρ of a dark or gray soliton as a function of ρ and m, (b) Ps/ρ as a function of v for various values of ρ.

Fig. 9
Fig. 9

Correction factor f for gray photorefractive solitons as a function of ρ and m.

Equations (26)

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

iϕz+12k 2ϕx2-k02(ne3r33Esc)ϕ=0,
Esc=E0I+IdI+Id.
iUξ+12 2Us2+(1+ρ)U1+|U|2=0,
iΨξ+12 2Ψs2+(1+ρ)1+|Ψ|2-1Ψ=0.
L=i2(ΨΨξ*-Ψ*Ψξ)+12ΨsΨs*+(|Ψ|2-ρ)+(1+ρ)ln(1+ρ)1+|Ψ|2,
Hˆ=12|Us|2+(1+ρ)ln(1+ρ)1+|U|2+(|U|2-ρ),
N=-ds(|U|2-ρ),
P=i2-ds(Us*U-U*Us)1-ρ|U|2=i2-ds(Us*U-U*Us)-ρ Arg U|-,
H=-ds12|Us|2+(1+ρ)ln(1+ρ)1+|U|2+(|U|2-ρ),
U(s, ξ)=A(η,ζ)exp(iαη)exp(iλζ)
iAζ+12 2Aη2+(1+ρ)A1+|A|2=0.
A=ρ1/2y(η)expiμζ-iJ0ηdηy2(η)+iΦ0,
U=ρ1/2y(η)expiμ+v22ζ+ivη-0ηdηy2(η)+iΦ0.
d2ydη2-2µy-v2y3+(1+ρ)2y1+ρy2=0.
(y)22-μy2+v22y2+(1+ρ)ρln(1+ρy2)=C,
C=-μ+v22+(1+ρ)ρln(1+ρ),
C=-μm+v22m+(1+ρ)ρln(1+mρ),
v=[2(1-μ)]1/2,
μ=11-m+m(1-m)2 (1+ρ)ρln1+mρ1+ρ.
tan θ=xz=v2ne(r33|E0|)1/2.
Hs=-ds2ρ(y2-1)+2(1+ρ)ln(1+ρ)1+ρy2,
Ps(v)=ρv-dsy(s)-1y(s)2.
|E0|=-f+f2+4W|V|2W2.
|V|=2|E0|α0sˆ(1+ρ)ds(1+|U|2)+αW2-sˆ,
f=2|E0|1/2α0sˆ(1+ρ)ds(1+|U|2)-sˆ=2|E0|1/2αm0.999(1+ρ)dy(1+ρy2)y-dyy,
f=(2|E0|)1/2αm0.999dy1+ρ1+ρy2-1×μ(y2-m)+(μ-1)1y2-1m+1+ρρln1+ρm1+ρy2-1/2.

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