Abstract

We analyze self-trapping of one-dimensional optical beams in photorefractive, photovoltaic media for open- and closed-circuit realizations. We show that a passive load (resistor) in the external circuit can be used for switching of dark photovoltaic solitons. Dark solitons in a short-circuited crystal can be obtained for a much smaller nonlinearity than in open-circuit conditions. Shorting the crystal affects bright solitons very little.

© 1997 Optical Society of America

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  1. In this paper, as in all our other papers on self-trapping of optical beams in photorefractive media, we use the term “soliton” in conjunction with nondiffracting self-trapped optical beams. That is, we use the broader definition of solitons that includes those in nonintegrable systems, as defined by V. E. Zakharov and B. A. Malomed, in Physical Encyclopedia, A. M. Prokhorov, ed. (Great Russian Encyclopedia, Moscow, 1994), p. 571, and also as discussed in detail by V. G. Makhankov in his review paper, Phys. Rep. 35, 1 (1978).
  2. M. Segev, B. Crosignani, A. Yariv, and B. Fischer, Phys. Rev. Lett. 68, 923 (1992).
    [CrossRef] [PubMed]
  3. B. Crosignani, M. Segev, D. Engin, P. DiPorto, A. Yariv, and G. Salamo, J. Opt. Soc. Am. B 10, 449 (1993).
    [CrossRef]
  4. 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]
  5. M. Segev, A. Yariv, G. Salamo, G. Duree, J. Shultz, B. Crosignani, P. DiPorto, and E. Sharp, Opt. Photon. News 4(12), 8 (1993).
  6. M. Segev, A. Yariv, B. Crosignani, P. DiPorto, G. Duree, G. Salamo, and E. Sharp, Opt. Lett. 19, 1296 (1994).
    [CrossRef] [PubMed]
  7. G. Duree, G. Salamo, M. Segev, A. Yariv, B. Crosignani, P. DiPorto, and E. Sharp, Opt. Lett. 19, 1195 (1994).
    [CrossRef] [PubMed]
  8. D. N. Christodoulides and M. I. Carvalho, Opt. Lett. 19, 1714 (1994).
    [CrossRef] [PubMed]
  9. M. Segev, G. Salamo, G. Duree, M. Morin, B. Crosignani, P. DiPorto, and A. Yariv, Opt. Photon. News 5(12), 9 (1994).
    [CrossRef]
  10. G. Duree, M. Morin, G. Salamo, M. Segev, A. Yariv, B. Crosignani, and P. DiPorto, Phys. Rev. Lett. 74, 1978 (1995).
    [CrossRef] [PubMed]
  11. M. Morin, G. Duree, G. Salamo, and M. Segev, Opt. Lett. 20, 2066 (1995).
    [CrossRef] [PubMed]
  12. M. Segev, G. C. Valley, B. Crosignani, P. DiPorto, and A. Yariv, Phys. Rev. Lett. 73, 3211 (1994).
    [CrossRef] [PubMed]
  13. D. N. Christodoulides and M. I. Carvalho, J. Opt. Soc. Am. B 12, 1628 (1995).
    [CrossRef]
  14. S. R. Singh and D. N. Christodoulides, Opt. Commun. 118, 569 (1995).
    [CrossRef]
  15. M. Segev, M. Shih, and G. C. Valley, J. Opt. Soc. Am. B 13, 706 (1996).
    [CrossRef]
  16. Steady-state self-focusing effects in biased photorefractive crystals were first observed by M. D. Iturbe-Castillo, P. A. Marquez-Aguilar, J. J. Sanchez-Mondragón, S. Stepanov, and V. Vysloukh, Appl. Phys. Lett. 64, 408 (1994).
    [CrossRef]
  17. Screening solitons were first observed by M. Shih, M. Segev, G. C. Valley, G. Salamo, B. Crosignani, and P. DiPorto, Electron. Lett. 31, 826 (1995).
    [CrossRef]
  18. M. Shih, P. Leach, M. Segev, M. Garrett, G. Salamo, and G. C. Valley, Opt. Lett. 21, 324 (1996).
    [CrossRef] [PubMed]
  19. K. Kos, H. Ming, G. Salamo, M. Shih, M. Segev, and G. C. Valley, Rapid Comm., Phys. Rev. E 53, R4330 (1996).
    [CrossRef]
  20. Z. Chen, M. Mitchell, M. Shih, M. Segev, M. Garrett, and G. C. Valley, Opt. Lett. 21, 629 (1996).
    [CrossRef] [PubMed]
  21. Z. Chen, M. Mitchell, and M. Segev, Opt. Lett. 21, 716 (1996).
    [CrossRef] [PubMed]
  22. M. D. Iturbe-Castillo, J. J. Sanchez-Mondragón, S. I. Stepanov, M. B. Klein, and B. A. Wechsler, Opt. Commun. 118, 515 (1995).
    [CrossRef]
  23. M. Shih, M. Segev, and G. Salamo, Opt. Lett. 21, 931 (1996).
    [CrossRef] [PubMed]
  24. M. Shih and M. Segev, Opt. Lett. 21, 1538 (1996).
    [CrossRef] [PubMed]
  25. M. Shih, Z. Chen, M. Segev, T. Coskun, and D. N. Christodoulides, Appl. Phys. Lett. 69, 4151 (1996).
    [CrossRef]
  26. H. Meng, G. Salamo, M. Shih, and M. Segev, Opt. Lett. 22, 448 (1997); W. Krolikowski and S. A. Holstrom, Opt. Lett. 22, 369 (1997); and G. C. Garcia-Quirino, M. D. Iturbe-Castillo, V. A. Vysloukh, J. J. Sanchez-Mondragon, S. I. Stepanov, G. Lugo-Martinez, and G. E. Torres-Cisneros, Opt. Lett. OPLEDP 22, 154 (1997).
    [CrossRef] [PubMed]
  27. M. Segev, G. C. Valley, S. R. Singh, M. I. Carvalho, and D. N. Christodoulides, Opt. Lett. 20, 1764 (1995).
    [CrossRef]
  28. S. R. Singh, M. I. Carvalho, and D. N. Christodoulides, Opt. Lett. 20, 2177 (1995).
    [CrossRef]
  29. M. I. Carvalho, S. R. Singh, and D. N. Christodoulides, Phys. Rev. E 53, R53 (1996).
    [CrossRef]
  30. D. N. Christodoulides, S. R. Singh, M. I. Carvalho, and M. Segev, Appl. Phys. Lett. 68, 1763 (1996).
    [CrossRef]
  31. W. Krolikowski, N. Akhmediev, and B. Luther-Davies, Opt. Lett. 21, 782 (1996).
    [CrossRef]
  32. Z. Chen, M. Segev, T. Coskun, and D. N. Christodoulides, Opt. Lett. 21, 1436 (1996).
    [CrossRef] [PubMed]
  33. Z. Chen, M. Segev, T. Coskun, D. N. Christodoulides, Y. Kivshar, and V. V. Afanasjev, Opt. Lett. 21, 1821 (1996).
    [CrossRef] [PubMed]
  34. G. C. Valley, M. Segev, B. Crosignani, A. Yariv, M. M. Fejer, and M. Bashaw, Phys. Rev. A 50, R4457 (1994).
    [CrossRef]
  35. M. Taya, M. Bashaw, M. M. Fejer, M. Segev, and G. C. Valley, Phys. Rev. A 52, 3095 (1995).
    [CrossRef] [PubMed]
  36. M. Taya, M. C. Bashaw, M. M. Fejer, M. Segev, and G. C. Valley, Opt. Lett. 21, 943 (1996).
    [CrossRef] [PubMed]
  37. M. Chauvet, S. A. Hawkins, G. Salamo, M. Segev, D. F. Bliss, and G. Bryant, Opt. Lett. 21, 1333 (1996).
    [CrossRef] [PubMed]
  38. M. Mitchell, Z. Chen, M. Shih, and M. Segev, Phys. Rev. Lett. 77, 490 (1996).
    [CrossRef] [PubMed]
  39. D. N. Christodoulides, T. H. Coskun, M. Mitchell, and M. Segev, Phys. Rev. Lett. 78, 646 (1997).
    [CrossRef]
  40. S. Gatz and J. Herrmann, J. Opt. Soc. Am. B 8, 2296 (1991).
    [CrossRef]
  41. G. C. Valley and J. Lam, in Photorefractive Materials and Their Applications I, P. Gunter and J. P. Huignard, eds. (Springer-Verlag, New York, 1988), Chap. 3.
  42. H. J. Eichler, P. Gunter, and D. W. Pohl, Laser-Induced Dynamic Gratings (Springer-Verlag, New York, 1986).
  43. B. I. Sturman, E. Shamonina, M. Mann, and K. H. Ringhofer, J. Opt. Soc. Am. B 12, 1642 (1995).
    [CrossRef]
  44. B. I. Sturman and V. M. Fridkin, in The Photovoltaic and Photorefractive Effect in Non-Centrosymmetric Materials (Gordon & Breach, Philadelphia, Pa., 1992).
  45. We note that photovoltaic gray solitons, which propagate at some angle with respect to the optical axis z, are also pos-sible. In fact, the Y-junction solitons observed in the research reported Ref. 36 can be considered a gray pair once the channels are well separated. The theory of photovoltaic gray solitons resembles that of gray screening solitons (described in Ref. 13).
  46. More-complicated configurations can lead to tensor effects and to vector solitons, as described in Ref. 25.
  47. As explained in Ref. 44, photovoltaic current must be driven by a real optical field (photons) and cannot be driven by thermal excitations. The main argument is that the photovoltaic current is fundamentally a polar current, rather than noise in the current as Idark is. If photovoltaic dark irradiance could exist, it would permit polar currents driven by temperature and thereby perpetual-motion machines.
  48. S. Orlov, A. Yariv, and M. Segev, Appl. Phys. Lett. 68, 1610 (1996).
    [CrossRef]
  49. In fact, the most significant correction factor is to Eq. (8), which leads to self-bending effects. For screening solitons, self-bending was predicted in Ref. 14 and observed in the research reported Refs. 18, 24, 25, and 32).
  50. S. Gatz and J. Herrmann, IEEE J. Quantum. Electron. 28, 1732 (1992).
    [CrossRef]
  51. We note that a small negative offset in the induced refractive index profile Δn(ξ) caused by nonzero current is present in the closed-circuit case. This means that far away from ξ=0, Δn becomes negative. However, at u0 > 0.05 this effect is almost unnoticeable.
  52. The idea to treat solitons as the guided modes of the waveguides that they induce was pioneered by A. W. Synder and A. P. Sheppard, Opt. Lett. 18, 482 (1993) and by Y. Silberberg, “Self-induced waveguide: spatial optical solitons,” in Anisotropic and Nonlinear Optical Waveguides, G. C. Someda and G. I. Stegeman, eds. (Elsevier, Amsterdam, 1992). See also the review by A. W. Synder, D. J. Mitchell, and Y. Kivshar, Mod. Phys. Lett. B 9, 1479 (1995).
    [CrossRef]
  53. This observation is true in steady state only. We expect that, if a bright photovoltaic soliton at u0≤0.1 is switched from J=0 to J=Jmax, there will be a transient effect, because the induced refractive index Δn(ξ) has to readjust to a new offset value, as shown in Fig. 8.
  54. Switching of solitons by use of a change in a single parameter that causes large deviations in the existence curve was used in the coupled soliton pairs experiments of Refs. 32 and 33.

1997 (1)

D. N. Christodoulides, T. H. Coskun, M. Mitchell, and M. Segev, Phys. Rev. Lett. 78, 646 (1997).
[CrossRef]

1996 (17)

M. Taya, M. C. Bashaw, M. M. Fejer, M. Segev, and G. C. Valley, Opt. Lett. 21, 943 (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]

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

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

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

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

M. Shih, Z. Chen, M. Segev, T. Coskun, and D. N. Christodoulides, Appl. Phys. Lett. 69, 4151 (1996).
[CrossRef]

M. I. Carvalho, S. R. Singh, and D. N. Christodoulides, 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]

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

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

Z. Chen, M. Segev, T. Coskun, D. N. Christodoulides, Y. Kivshar, and V. V. Afanasjev, Opt. Lett. 21, 1821 (1996).
[CrossRef] [PubMed]

M. Shih, P. Leach, M. Segev, M. Garrett, G. Salamo, and G. C. Valley, Opt. Lett. 21, 324 (1996).
[CrossRef] [PubMed]

K. Kos, H. Ming, G. Salamo, M. Shih, M. Segev, and G. C. Valley, Rapid Comm., 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]

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

S. Orlov, A. Yariv, and M. Segev, Appl. Phys. Lett. 68, 1610 (1996).
[CrossRef]

1995 (10)

B. I. Sturman, E. Shamonina, M. Mann, and K. H. Ringhofer, J. Opt. Soc. Am. B 12, 1642 (1995).
[CrossRef]

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

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

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

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

S. R. Singh and D. N. Christodoulides, Opt. Commun. 118, 569 (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]

Screening solitons were first observed by M. Shih, M. Segev, G. C. Valley, G. Salamo, B. Crosignani, and P. DiPorto, Electron. Lett. 31, 826 (1995).
[CrossRef]

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

1994 (7)

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

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]

M. Segev, A. Yariv, B. Crosignani, P. DiPorto, G. Duree, G. Salamo, and E. Sharp, Opt. Lett. 19, 1296 (1994).
[CrossRef] [PubMed]

G. Duree, G. Salamo, M. Segev, A. Yariv, B. Crosignani, P. DiPorto, and E. Sharp, Opt. Lett. 19, 1195 (1994).
[CrossRef] [PubMed]

D. N. Christodoulides and M. I. Carvalho, Opt. Lett. 19, 1714 (1994).
[CrossRef] [PubMed]

M. Segev, G. Salamo, G. Duree, M. Morin, B. Crosignani, P. DiPorto, and A. Yariv, Opt. Photon. News 5(12), 9 (1994).
[CrossRef]

1993 (3)

B. Crosignani, M. Segev, D. Engin, P. DiPorto, A. Yariv, and G. Salamo, J. Opt. Soc. Am. B 10, 449 (1993).
[CrossRef]

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, A. Yariv, G. Salamo, G. Duree, J. Shultz, B. Crosignani, P. DiPorto, and E. Sharp, Opt. Photon. News 4(12), 8 (1993).

1992 (2)

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

S. Gatz and J. Herrmann, IEEE J. Quantum. Electron. 28, 1732 (1992).
[CrossRef]

1991 (1)

1978 (1)

In this paper, as in all our other papers on self-trapping of optical beams in photorefractive media, we use the term “soliton” in conjunction with nondiffracting self-trapped optical beams. That is, we use the broader definition of solitons that includes those in nonintegrable systems, as defined by V. E. Zakharov and B. A. Malomed, in Physical Encyclopedia, A. M. Prokhorov, ed. (Great Russian Encyclopedia, Moscow, 1994), p. 571, and also as discussed in detail by V. G. Makhankov in his review paper, Phys. Rep. 35, 1 (1978).

Afanasjev, V. V.

Akhmediev, N.

Bashaw, M.

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]

Bashaw, M. C.

Bliss, D. F.

Bryant, G.

Carvalho, M. I.

Chauvet, M.

Chen, Z.

Christodoulides, D. N.

Coskun, T.

Coskun, T. H.

D. N. Christodoulides, T. H. Coskun, M. Mitchell, and M. Segev, Phys. Rev. Lett. 78, 646 (1997).
[CrossRef]

Crosignani, B.

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

Screening solitons were first observed by M. Shih, M. Segev, G. C. Valley, G. Salamo, B. Crosignani, and P. DiPorto, Electron. Lett. 31, 826 (1995).
[CrossRef]

M. Segev, G. Salamo, G. Duree, M. Morin, B. Crosignani, P. DiPorto, and A. Yariv, Opt. Photon. News 5(12), 9 (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]

M. Segev, A. Yariv, B. Crosignani, P. DiPorto, G. Duree, G. Salamo, and E. Sharp, Opt. Lett. 19, 1296 (1994).
[CrossRef] [PubMed]

G. Duree, G. Salamo, M. Segev, A. Yariv, B. Crosignani, P. DiPorto, and E. Sharp, Opt. Lett. 19, 1195 (1994).
[CrossRef] [PubMed]

B. Crosignani, M. Segev, D. Engin, P. DiPorto, A. Yariv, and G. Salamo, J. Opt. Soc. Am. B 10, 449 (1993).
[CrossRef]

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, A. Yariv, G. Salamo, G. Duree, J. Shultz, B. Crosignani, P. DiPorto, and E. Sharp, Opt. Photon. News 4(12), 8 (1993).

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

DiPorto, P.

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

Screening solitons were first observed by M. Shih, M. Segev, G. C. Valley, G. Salamo, B. Crosignani, and P. DiPorto, Electron. Lett. 31, 826 (1995).
[CrossRef]

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

M. Segev, G. Salamo, G. Duree, M. Morin, B. Crosignani, P. DiPorto, and A. Yariv, Opt. Photon. News 5(12), 9 (1994).
[CrossRef]

G. Duree, G. Salamo, M. Segev, A. Yariv, B. Crosignani, P. DiPorto, and E. Sharp, Opt. Lett. 19, 1195 (1994).
[CrossRef] [PubMed]

M. Segev, A. Yariv, B. Crosignani, P. DiPorto, G. Duree, G. Salamo, and E. Sharp, Opt. Lett. 19, 1296 (1994).
[CrossRef] [PubMed]

B. Crosignani, M. Segev, D. Engin, P. DiPorto, A. Yariv, and G. Salamo, J. Opt. Soc. Am. B 10, 449 (1993).
[CrossRef]

M. Segev, A. Yariv, G. Salamo, G. Duree, J. Shultz, B. Crosignani, P. DiPorto, and E. Sharp, Opt. Photon. News 4(12), 8 (1993).

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]

Duree, G.

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

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

M. Segev, A. Yariv, B. Crosignani, P. DiPorto, G. Duree, G. Salamo, and E. Sharp, Opt. Lett. 19, 1296 (1994).
[CrossRef] [PubMed]

G. Duree, G. Salamo, M. Segev, A. Yariv, B. Crosignani, P. DiPorto, and E. Sharp, Opt. Lett. 19, 1195 (1994).
[CrossRef] [PubMed]

M. Segev, G. Salamo, G. Duree, M. Morin, B. Crosignani, P. DiPorto, and A. Yariv, Opt. Photon. News 5(12), 9 (1994).
[CrossRef]

M. Segev, A. Yariv, G. Salamo, G. Duree, J. Shultz, B. Crosignani, P. DiPorto, and E. Sharp, Opt. Photon. News 4(12), 8 (1993).

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]

Engin, D.

B. Crosignani, M. Segev, D. Engin, P. DiPorto, A. Yariv, and G. Salamo, J. Opt. Soc. Am. B 10, 449 (1993).
[CrossRef]

Fejer, M. M.

M. Taya, M. C. 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]

Garrett, M.

Gatz, S.

S. Gatz and J. Herrmann, IEEE J. Quantum. Electron. 28, 1732 (1992).
[CrossRef]

S. Gatz and J. Herrmann, J. Opt. Soc. Am. B 8, 2296 (1991).
[CrossRef]

Hawkins, S. A.

Herrmann, J.

S. Gatz and J. Herrmann, IEEE J. Quantum. Electron. 28, 1732 (1992).
[CrossRef]

S. Gatz and J. Herrmann, J. Opt. Soc. Am. B 8, 2296 (1991).
[CrossRef]

Iturbe-Castillo, M. D.

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

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

Kivshar, Y.

Klein, M. B.

M. D. Iturbe-Castillo, J. J. Sanchez-Mondragón, S. I. 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, Rapid Comm., Phys. Rev. E 53, R4330 (1996).
[CrossRef]

Krolikowski, W.

Leach, P.

Luther-Davies, B.

Malomed, B. A.

In this paper, as in all our other papers on self-trapping of optical beams in photorefractive media, we use the term “soliton” in conjunction with nondiffracting self-trapped optical beams. That is, we use the broader definition of solitons that includes those in nonintegrable systems, as defined by V. E. Zakharov and B. A. Malomed, in Physical Encyclopedia, A. M. Prokhorov, ed. (Great Russian Encyclopedia, Moscow, 1994), p. 571, and also as discussed in detail by V. G. Makhankov in his review paper, Phys. Rep. 35, 1 (1978).

Mann, M.

Marquez-Aguilar, P. A.

Steady-state self-focusing effects in biased photorefractive crystals were first observed by M. D. Iturbe-Castillo, P. A. Marquez-Aguilar, J. J. Sanchez-Mondragón, 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, Rapid Comm., Phys. Rev. E 53, R4330 (1996).
[CrossRef]

Mitchell, M.

D. N. Christodoulides, T. H. Coskun, M. Mitchell, and M. Segev, Phys. Rev. Lett. 78, 646 (1997).
[CrossRef]

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

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]

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, and P. DiPorto, Phys. Rev. Lett. 74, 1978 (1995).
[CrossRef] [PubMed]

M. Segev, G. Salamo, G. Duree, M. Morin, B. Crosignani, P. DiPorto, and A. Yariv, Opt. Photon. News 5(12), 9 (1994).
[CrossRef]

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]

Orlov, S.

S. Orlov, A. Yariv, and M. Segev, Appl. Phys. Lett. 68, 1610 (1996).
[CrossRef]

Ringhofer, K. H.

Salamo, G.

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

M. Shih, P. Leach, M. Segev, M. Garrett, G. Salamo, and G. C. Valley, Opt. Lett. 21, 324 (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]

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

Screening solitons were first observed by M. Shih, M. Segev, G. C. Valley, G. Salamo, B. Crosignani, and P. DiPorto, Electron. Lett. 31, 826 (1995).
[CrossRef]

G. Duree, M. Morin, G. Salamo, M. Segev, A. Yariv, B. Crosignani, and P. DiPorto, 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, G. Salamo, M. Segev, A. Yariv, B. Crosignani, P. DiPorto, and E. Sharp, Opt. Lett. 19, 1195 (1994).
[CrossRef] [PubMed]

M. Segev, A. Yariv, B. Crosignani, P. DiPorto, G. Duree, G. Salamo, and E. Sharp, Opt. Lett. 19, 1296 (1994).
[CrossRef] [PubMed]

M. Segev, G. Salamo, G. Duree, M. Morin, B. Crosignani, P. DiPorto, and A. Yariv, Opt. Photon. News 5(12), 9 (1994).
[CrossRef]

M. Segev, A. Yariv, G. Salamo, G. Duree, J. Shultz, B. Crosignani, P. DiPorto, and E. Sharp, Opt. Photon. News 4(12), 8 (1993).

B. Crosignani, M. Segev, D. Engin, P. DiPorto, A. Yariv, and G. Salamo, J. Opt. Soc. Am. B 10, 449 (1993).
[CrossRef]

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-Mondragón, J. J.

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

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

Segev, M.

D. N. Christodoulides, T. H. Coskun, M. Mitchell, and M. Segev, Phys. Rev. Lett. 78, 646 (1997).
[CrossRef]

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

S. Orlov, A. Yariv, and M. Segev, Appl. Phys. Lett. 68, 1610 (1996).
[CrossRef]

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

M. Shih, Z. Chen, M. Segev, T. Coskun, and D. N. Christodoulides, Appl. Phys. Lett. 69, 4151 (1996).
[CrossRef]

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

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

Z. Chen, M. Segev, T. Coskun, and D. N. Christodoulides, Opt. Lett. 21, 1436 (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]

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

M. Shih, P. Leach, M. Segev, M. Garrett, G. Salamo, and G. C. Valley, Opt. Lett. 21, 324 (1996).
[CrossRef] [PubMed]

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

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

Z. Chen, M. Segev, T. Coskun, D. N. Christodoulides, Y. Kivshar, and V. V. Afanasjev, Opt. Lett. 21, 1821 (1996).
[CrossRef] [PubMed]

Screening solitons were first observed by M. Shih, M. Segev, G. C. Valley, G. Salamo, B. Crosignani, and P. DiPorto, Electron. Lett. 31, 826 (1995).
[CrossRef]

G. Duree, M. Morin, G. Salamo, M. Segev, A. Yariv, B. Crosignani, and P. DiPorto, Phys. Rev. Lett. 74, 1978 (1995).
[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. C. Valley, M. Segev, B. Crosignani, A. Yariv, M. M. Fejer, and M. Bashaw, Phys. Rev. A 50, R4457 (1994).
[CrossRef]

G. Duree, G. Salamo, M. Segev, A. Yariv, B. Crosignani, P. DiPorto, and E. Sharp, Opt. Lett. 19, 1195 (1994).
[CrossRef] [PubMed]

M. Segev, A. Yariv, B. Crosignani, P. DiPorto, G. Duree, G. Salamo, and E. Sharp, Opt. Lett. 19, 1296 (1994).
[CrossRef] [PubMed]

M. Segev, G. Salamo, G. Duree, M. Morin, B. Crosignani, P. DiPorto, and A. Yariv, Opt. Photon. News 5(12), 9 (1994).
[CrossRef]

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

M. Segev, A. Yariv, G. Salamo, G. Duree, J. Shultz, B. Crosignani, P. DiPorto, and E. Sharp, Opt. Photon. News 4(12), 8 (1993).

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]

B. Crosignani, M. Segev, D. Engin, P. DiPorto, A. Yariv, and G. Salamo, J. Opt. Soc. Am. B 10, 449 (1993).
[CrossRef]

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

Shamonina, E.

Sharp, E.

G. Duree, G. Salamo, M. Segev, A. Yariv, B. Crosignani, P. DiPorto, and E. Sharp, Opt. Lett. 19, 1195 (1994).
[CrossRef] [PubMed]

M. Segev, A. Yariv, B. Crosignani, P. DiPorto, G. Duree, G. Salamo, and E. Sharp, Opt. Lett. 19, 1296 (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, A. Yariv, G. Salamo, G. Duree, J. Shultz, B. Crosignani, P. DiPorto, and E. Sharp, Opt. Photon. News 4(12), 8 (1993).

Shih, M.

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

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

M. Shih, P. Leach, M. Segev, M. Garrett, G. Salamo, and G. C. Valley, Opt. Lett. 21, 324 (1996).
[CrossRef] [PubMed]

M. Shih, Z. Chen, M. Segev, T. Coskun, and D. N. Christodoulides, Appl. Phys. Lett. 69, 4151 (1996).
[CrossRef]

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

M. Shih, M. Segev, and G. Salamo, Opt. Lett. 21, 931 (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. Shih and M. Segev, Opt. Lett. 21, 1538 (1996).
[CrossRef] [PubMed]

Screening solitons were first observed by M. Shih, M. Segev, G. C. Valley, G. Salamo, B. Crosignani, and P. DiPorto, Electron. Lett. 31, 826 (1995).
[CrossRef]

Shultz, J.

M. Segev, A. Yariv, G. Salamo, G. Duree, J. Shultz, B. Crosignani, P. DiPorto, and E. Sharp, Opt. Photon. News 4(12), 8 (1993).

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]

Singh, S. R.

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, and D. N. Christodoulides, Phys. Rev. E 53, R53 (1996).
[CrossRef]

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

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

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

Stepanov, S.

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

Stepanov, S. I.

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

Sturman, B. I.

Taya, M.

M. Taya, M. C. 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]

Valley, G. C.

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

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

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

M. Shih, P. Leach, M. Segev, M. Garrett, G. Salamo, and G. C. Valley, Opt. Lett. 21, 324 (1996).
[CrossRef] [PubMed]

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

Screening solitons were first observed by M. Shih, M. Segev, G. C. Valley, G. Salamo, B. Crosignani, and P. DiPorto, Electron. Lett. 31, 826 (1995).
[CrossRef]

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]

Vysloukh, V.

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

Wechsler, B. A.

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

Yariv, A.

S. Orlov, A. Yariv, and M. Segev, Appl. Phys. Lett. 68, 1610 (1996).
[CrossRef]

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

M. Segev, G. Salamo, G. Duree, M. Morin, B. Crosignani, P. DiPorto, and A. Yariv, Opt. Photon. News 5(12), 9 (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]

M. Segev, A. Yariv, B. Crosignani, P. DiPorto, G. Duree, G. Salamo, and E. Sharp, Opt. Lett. 19, 1296 (1994).
[CrossRef] [PubMed]

G. Duree, G. Salamo, M. Segev, A. Yariv, B. Crosignani, P. DiPorto, and E. Sharp, Opt. Lett. 19, 1195 (1994).
[CrossRef] [PubMed]

M. Segev, A. Yariv, G. Salamo, G. Duree, J. Shultz, B. Crosignani, P. DiPorto, and E. Sharp, Opt. Photon. News 4(12), 8 (1993).

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]

B. Crosignani, M. Segev, D. Engin, P. DiPorto, A. Yariv, and G. Salamo, J. Opt. Soc. Am. B 10, 449 (1993).
[CrossRef]

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

Zakharov, V. E.

In this paper, as in all our other papers on self-trapping of optical beams in photorefractive media, we use the term “soliton” in conjunction with nondiffracting self-trapped optical beams. That is, we use the broader definition of solitons that includes those in nonintegrable systems, as defined by V. E. Zakharov and B. A. Malomed, in Physical Encyclopedia, A. M. Prokhorov, ed. (Great Russian Encyclopedia, Moscow, 1994), p. 571, and also as discussed in detail by V. G. Makhankov in his review paper, Phys. Rep. 35, 1 (1978).

Appl. Phys. Lett. (4)

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

M. Shih, Z. Chen, M. Segev, T. Coskun, and D. N. Christodoulides, Appl. Phys. Lett. 69, 4151 (1996).
[CrossRef]

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

S. Orlov, A. Yariv, and M. Segev, Appl. Phys. Lett. 68, 1610 (1996).
[CrossRef]

Electron. Lett. (1)

Screening solitons were first observed by M. Shih, M. Segev, G. C. Valley, G. Salamo, B. Crosignani, and P. DiPorto, Electron. Lett. 31, 826 (1995).
[CrossRef]

IEEE J. Quantum. Electron. (1)

S. Gatz and J. Herrmann, IEEE J. Quantum. Electron. 28, 1732 (1992).
[CrossRef]

J. Opt. Soc. Am. B (5)

Opt. Commun. (2)

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

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

Opt. Lett. (16)

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

M. Shih, P. Leach, M. Segev, M. Garrett, G. Salamo, and G. C. Valley, Opt. Lett. 21, 324 (1996).
[CrossRef] [PubMed]

M. Segev, A. Yariv, B. Crosignani, P. DiPorto, G. Duree, G. Salamo, and E. Sharp, Opt. Lett. 19, 1296 (1994).
[CrossRef] [PubMed]

G. Duree, G. Salamo, M. Segev, A. Yariv, B. Crosignani, P. DiPorto, and E. Sharp, Opt. Lett. 19, 1195 (1994).
[CrossRef] [PubMed]

D. N. Christodoulides and M. I. Carvalho, Opt. Lett. 19, 1714 (1994).
[CrossRef] [PubMed]

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

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

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

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

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

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

Z. Chen, M. Segev, T. Coskun, D. N. Christodoulides, Y. Kivshar, and V. V. Afanasjev, Opt. Lett. 21, 1821 (1996).
[CrossRef] [PubMed]

M. Taya, M. C. Bashaw, M. M. Fejer, M. Segev, and G. C. Valley, Opt. Lett. 21, 943 (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]

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]

Opt. Photon. News (2)

M. Segev, A. Yariv, G. Salamo, G. Duree, J. Shultz, B. Crosignani, P. DiPorto, and E. Sharp, Opt. Photon. News 4(12), 8 (1993).

M. Segev, G. Salamo, G. Duree, M. Morin, B. Crosignani, P. DiPorto, and A. Yariv, Opt. Photon. News 5(12), 9 (1994).
[CrossRef]

Phys. Rep. (1)

In this paper, as in all our other papers on self-trapping of optical beams in photorefractive media, we use the term “soliton” in conjunction with nondiffracting self-trapped optical beams. That is, we use the broader definition of solitons that includes those in nonintegrable systems, as defined by V. E. Zakharov and B. A. Malomed, in Physical Encyclopedia, A. M. Prokhorov, ed. (Great Russian Encyclopedia, Moscow, 1994), p. 571, and also as discussed in detail by V. G. Makhankov in his review paper, Phys. Rep. 35, 1 (1978).

Phys. Rev. A (2)

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]

Phys. Rev. E (1)

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

Phys. Rev. Lett. (6)

M. Mitchell, Z. Chen, M. Shih, and M. Segev, Phys. Rev. Lett. 77, 490 (1996).
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D. N. Christodoulides, T. H. Coskun, M. Mitchell, and M. Segev, Phys. Rev. Lett. 78, 646 (1997).
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M. Segev, B. Crosignani, A. Yariv, and B. Fischer, Phys. Rev. Lett. 68, 923 (1992).
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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).
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G. Duree, M. Morin, G. Salamo, M. Segev, A. Yariv, B. Crosignani, and P. DiPorto, Phys. Rev. Lett. 74, 1978 (1995).
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M. Segev, G. C. Valley, B. Crosignani, P. DiPorto, and A. Yariv, Phys. Rev. Lett. 73, 3211 (1994).
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Rapid Comm., Phys. Rev. E (1)

K. Kos, H. Ming, G. Salamo, M. Shih, M. Segev, and G. C. Valley, Rapid Comm., Phys. Rev. E 53, R4330 (1996).
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Other (12)

H. Meng, G. Salamo, M. Shih, and M. Segev, Opt. Lett. 22, 448 (1997); W. Krolikowski and S. A. Holstrom, Opt. Lett. 22, 369 (1997); and G. C. Garcia-Quirino, M. D. Iturbe-Castillo, V. A. Vysloukh, J. J. Sanchez-Mondragon, S. I. Stepanov, G. Lugo-Martinez, and G. E. Torres-Cisneros, Opt. Lett. OPLEDP 22, 154 (1997).
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G. C. Valley and J. Lam, in Photorefractive Materials and Their Applications I, P. Gunter and J. P. Huignard, eds. (Springer-Verlag, New York, 1988), Chap. 3.

H. J. Eichler, P. Gunter, and D. W. Pohl, Laser-Induced Dynamic Gratings (Springer-Verlag, New York, 1986).

B. I. Sturman and V. M. Fridkin, in The Photovoltaic and Photorefractive Effect in Non-Centrosymmetric Materials (Gordon & Breach, Philadelphia, Pa., 1992).

We note that photovoltaic gray solitons, which propagate at some angle with respect to the optical axis z, are also pos-sible. In fact, the Y-junction solitons observed in the research reported Ref. 36 can be considered a gray pair once the channels are well separated. The theory of photovoltaic gray solitons resembles that of gray screening solitons (described in Ref. 13).

More-complicated configurations can lead to tensor effects and to vector solitons, as described in Ref. 25.

As explained in Ref. 44, photovoltaic current must be driven by a real optical field (photons) and cannot be driven by thermal excitations. The main argument is that the photovoltaic current is fundamentally a polar current, rather than noise in the current as Idark is. If photovoltaic dark irradiance could exist, it would permit polar currents driven by temperature and thereby perpetual-motion machines.

We note that a small negative offset in the induced refractive index profile Δn(ξ) caused by nonzero current is present in the closed-circuit case. This means that far away from ξ=0, Δn becomes negative. However, at u0 > 0.05 this effect is almost unnoticeable.

The idea to treat solitons as the guided modes of the waveguides that they induce was pioneered by A. W. Synder and A. P. Sheppard, Opt. Lett. 18, 482 (1993) and by Y. Silberberg, “Self-induced waveguide: spatial optical solitons,” in Anisotropic and Nonlinear Optical Waveguides, G. C. Someda and G. I. Stegeman, eds. (Elsevier, Amsterdam, 1992). See also the review by A. W. Synder, D. J. Mitchell, and Y. Kivshar, Mod. Phys. Lett. B 9, 1479 (1995).
[CrossRef]

This observation is true in steady state only. We expect that, if a bright photovoltaic soliton at u0≤0.1 is switched from J=0 to J=Jmax, there will be a transient effect, because the induced refractive index Δn(ξ) has to readjust to a new offset value, as shown in Fig. 8.

Switching of solitons by use of a change in a single parameter that causes large deviations in the existence curve was used in the coupled soliton pairs experiments of Refs. 32 and 33.

In fact, the most significant correction factor is to Eq. (8), which leads to self-bending effects. For screening solitons, self-bending was predicted in Ref. 14 and observed in the research reported Refs. 18, 24, 25, and 32).

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Figures (8)

Fig. 1
Fig. 1

Illustration of the electrical circuit consisting of a photovoltaic crystal (acting as a source when illuminated) and an external resistor R. 1-D, one-dimensional.

Fig. 2
Fig. 2

(a) Dark solitonlike beam of width Δx and peak intensity u2. (b) Bright solitonlike beam of width Δx and peak intensity u02.

Fig. 3
Fig. 3

Normalized intensity profile (solid curve) of the open-circuit dark photovoltaic soliton and the induced change in the refractive index [Δn(ξ)E(ξ); dashed curve], both at u=10 and J=0.

Fig. 4
Fig. 4

(a) Normalized intensity profile (solid curve) of the closed-circuit dark photovoltaic soliton and the induced change in the refractive index [Δn(ξ)E(ξ), dashed curve], both at u=10 and J=Jmax. (b) Expanded version of (a).

Fig. 5
Fig. 5

Normalized intensity profile of dark solitons at u =0.1 for both J=0 and J=Jmax. The profiles coincide everywhere.

Fig. 6
Fig. 6

Soliton existence curve for open-circuit (upper curve) and closed-circuit (lower curve) dark photovoltaic solitons. The curves show the soliton width (FWHM of the intensity, u2) in units of Δxk0nb2(reffEpr)1/2 as a function of the peak soliton amplitude u, k0 being the wave number in vacuum.

Fig. 7
Fig. 7

Soliton existence curve for open-circuit and closed-circuit bright photovoltaic solitons (the curves coincide everywhere). The curves show the soliton width (FWHM of the intensity, u2) in units of Δxk0nb2(reffEpr)1/2 as a function of peak soliton amplitude u0, k0 being the wave number in vacuum.

Fig. 8
Fig. 8

Soliton intensity waveforms u2(ξ) (solid curve) and the induced change in the refractive index [100×Δn(ξ)-E(ξ)] for u0=0.05 and J=0 and J=Jmax. The waveforms u2(ξ) coincide with each other everywhere, whereas the Δn(ξ) curves are offset by a constant parameter equal to Jmax.

Equations (33)

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(s|A|2+β)(Nd-Ndi)-γnˆNdi=0,
·Jˆ=·[qμnˆEˆ+kBTμnˆ+κeff(Nd-Ndi)|A|2=0,
·Eˆ+(q/εs)(nˆ+NA-Ndi)=0,
z-i2k2x2A(x, z)=iknbΔn(Eˆ)A(x, z),
V=--l/2l/2 Eˆ·dl=RSJˆ,
A(x, z)=u(x)exp(iΓz)Idark,
n-(1+u2)(1-N)/(rN)=0,
J=nE+(1-N)u2+ε1(dn/dξ)=const.,
(N-1/r-an)-ε2(dE/dξ)=0,
d2u/dξ2=±(Γ/b+E)u,
J=-β -l/2dl/2dE(ξ)dξ,
J=nE+(1-1/r)u2nE+u2=(1+u2)E+u2=const.
E(ξ)=J-u2(ξ)[1+u2(ξ)],
d2udξ2=±Γb+J-u2(1+u2)u.
J=-β -l/2dl/2dJ-u2(ξ)[1+u2(ξ)]dξ.
J=βldu21+u2+βld.
Jβldu2(1+u2)1+βΔxd+βld.
JβΔxdu2(1+u02)1+βld+βΔxd.
E(ξ)=-u2(ξ)[1+u2(ξ)]
E(ξ)=l[u2-u2(ξ)]-Δx(1+u2)u2(ξ)[1+u2(ξ)][(1+u2)Δx+l].
E(ξ)=Δxu02l(1+u02)-u2(ξ)[1+u2(ξ)].
u=±δ+J-u21+u2u,
p2-p02=±(δ-1)(u2-u02)+(J+1)×lnu2+1u02+1,
p02=±(J+1)u21+u2-ln(u2+1).
u=-δ+J-u21+u2u,
u=(J+1)u2-u21+u2+ln1+u21+u21/2,
u=-(u2-u2)u,
u=δ+J-u21+u2u,
u=(J+1)ln(u2+1)-u2u02ln(u02+1)1/2,
u=±[(δ+J)-(J+1)u2]u.
u=(u02/2-u2)u,
Δn(ξ)|J=0-Δn(ξ)|J=Jmax
[-E(ξ)|J=0]-[-E(ξ)|J=Jmax]=u21+u2--J-u21+u2=J1+u2,

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