Abstract

Using the coherent density approach, we study the propagation dynamics of incoherent bright and dark beams in biased photorefractive crystals. We show that, under appropriate initial conditions, bright as well as darklike incoherent quasi-solitons can be established in this material system. Our numerical simulations demonstrate that the coherence properties of these beams can be significantly affected by the self-trapping process.

© 1998 Optical Society of America

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  1. A. Hasegawa, Phys. Fluids 18, 77 (1975); Phys. Fluids 20, 2155 (1977); Opt. Lett. 5, 416 (1980).
    [CrossRef]
  2. B. Gross and J. T. Manassah, Opt. Lett. 17, 166 (1992). Here the authors find that the “initial signal pulses compress and break up in cascades.” In photorefractives, no such behavior has been encountered, as a result of the noninstantaneous nature of the nonlinearity. Instead, a smooth incoherent soliton emerges.
    [CrossRef]
  3. Y. R. Shen, The Principles of Nonlinear Optics (Wiley, New York, 1984).
  4. M. Mitchell, Z. Chen, M. F. Shih, and M. Segev, Phys. Rev. Lett. 77, 490 (1996).
    [CrossRef] [PubMed]
  5. M. Segev, G. C. Valley, B. Crosignani, P. DiPorto, and A. Yariv, Phys. Rev. Lett. 73, 3211 (1994).
    [CrossRef] [PubMed]
  6. D. N. Christodoulides and M. I. Carvalho, J. Opt. Soc. Am. B 12, 1628 (1995).
    [CrossRef]
  7. D. N. Christodoulides, T. H. Coskun, M. Mitchell, and M. Segev, Phys. Rev. Lett. 78, 646 (1997).
    [CrossRef]
  8. M. Mitchell and M. Segev, Nature (London) 387, 880 (1997).
    [CrossRef]
  9. D. N. Christodoulides, T. H. Coskun, and R. I. Joseph, Opt. Lett. 22, 1080 (1997).
    [CrossRef] [PubMed]
  10. M. Mitchell, M. Segev, T. H. Coskun, and D. N. Christodoulides, Phys. Rev. Lett. 79, 4990 (1997).
    [CrossRef]
  11. B. Ya. Zel’dovich, N. F. Pilipetsky, and V. V. Shkunov, Principles of Phase Conjugation (Springer-Verlag, Berlin, 1985).
    [CrossRef]
  12. V. E. Zakharov and A. B. Shabat, Sov. Phys. JETP 37, 823 (1973); K. J. Blow and N. J. Doran, Phys. Lett. A 107, 55 (1985); Z. Chen, M. Segev, S. R. Singh, T. H. Coskun, and D. N. Christodoulides, J. Opt. Soc. Am. B 14, 1407 (1997).
    [CrossRef]

1997 (4)

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

M. Mitchell and M. Segev, Nature (London) 387, 880 (1997).
[CrossRef]

M. Mitchell, M. Segev, T. H. Coskun, and D. N. Christodoulides, Phys. Rev. Lett. 79, 4990 (1997).
[CrossRef]

D. N. Christodoulides, T. H. Coskun, and R. I. Joseph, Opt. Lett. 22, 1080 (1997).
[CrossRef] [PubMed]

1996 (1)

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

1995 (1)

1994 (1)

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

1992 (1)

1975 (1)

A. Hasegawa, Phys. Fluids 18, 77 (1975); Phys. Fluids 20, 2155 (1977); Opt. Lett. 5, 416 (1980).
[CrossRef]

1973 (1)

V. E. Zakharov and A. B. Shabat, Sov. Phys. JETP 37, 823 (1973); K. J. Blow and N. J. Doran, Phys. Lett. A 107, 55 (1985); Z. Chen, M. Segev, S. R. Singh, T. H. Coskun, and D. N. Christodoulides, J. Opt. Soc. Am. B 14, 1407 (1997).
[CrossRef]

Carvalho, M. I.

Chen, Z.

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

Christodoulides, D. N.

D. N. Christodoulides, T. H. Coskun, and R. I. Joseph, Opt. Lett. 22, 1080 (1997).
[CrossRef] [PubMed]

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

M. Mitchell, M. Segev, T. H. Coskun, and D. N. Christodoulides, Phys. Rev. Lett. 79, 4990 (1997).
[CrossRef]

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

Coskun, T. H.

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

M. Mitchell, M. Segev, T. H. Coskun, and D. N. Christodoulides, Phys. Rev. Lett. 79, 4990 (1997).
[CrossRef]

D. N. Christodoulides, T. H. Coskun, and R. I. Joseph, Opt. Lett. 22, 1080 (1997).
[CrossRef] [PubMed]

Crosignani, B.

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

DiPorto, P.

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

Gross, B.

Hasegawa, A.

A. Hasegawa, Phys. Fluids 18, 77 (1975); Phys. Fluids 20, 2155 (1977); Opt. Lett. 5, 416 (1980).
[CrossRef]

Joseph, R. I.

Manassah, J. T.

Mitchell, M.

M. Mitchell and M. Segev, Nature (London) 387, 880 (1997).
[CrossRef]

M. Mitchell, M. Segev, T. H. Coskun, and D. N. Christodoulides, Phys. Rev. Lett. 79, 4990 (1997).
[CrossRef]

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

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

Pilipetsky, N. F.

B. Ya. Zel’dovich, N. F. Pilipetsky, and V. V. Shkunov, Principles of Phase Conjugation (Springer-Verlag, Berlin, 1985).
[CrossRef]

Segev, M.

M. Mitchell and M. Segev, Nature (London) 387, 880 (1997).
[CrossRef]

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

M. Mitchell, M. Segev, T. H. Coskun, and D. N. Christodoulides, Phys. Rev. Lett. 79, 4990 (1997).
[CrossRef]

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

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

Shabat, A. B.

V. E. Zakharov and A. B. Shabat, Sov. Phys. JETP 37, 823 (1973); K. J. Blow and N. J. Doran, Phys. Lett. A 107, 55 (1985); Z. Chen, M. Segev, S. R. Singh, T. H. Coskun, and D. N. Christodoulides, J. Opt. Soc. Am. B 14, 1407 (1997).
[CrossRef]

Shen, Y. R.

Y. R. Shen, The Principles of Nonlinear Optics (Wiley, New York, 1984).

Shih, M. F.

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

Shkunov, V. V.

B. Ya. Zel’dovich, N. F. Pilipetsky, and V. V. Shkunov, Principles of Phase Conjugation (Springer-Verlag, Berlin, 1985).
[CrossRef]

Valley, G. C.

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

Yariv, A.

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

Zakharov, V. E.

V. E. Zakharov and A. B. Shabat, Sov. Phys. JETP 37, 823 (1973); K. J. Blow and N. J. Doran, Phys. Lett. A 107, 55 (1985); Z. Chen, M. Segev, S. R. Singh, T. H. Coskun, and D. N. Christodoulides, J. Opt. Soc. Am. B 14, 1407 (1997).
[CrossRef]

Zel’dovich, B. Ya.

B. Ya. Zel’dovich, N. F. Pilipetsky, and V. V. Shkunov, Principles of Phase Conjugation (Springer-Verlag, Berlin, 1985).
[CrossRef]

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

Nature (London) (1)

M. Mitchell and M. Segev, Nature (London) 387, 880 (1997).
[CrossRef]

Opt. Lett. (2)

Phys. Fluids (1)

A. Hasegawa, Phys. Fluids 18, 77 (1975); Phys. Fluids 20, 2155 (1977); Opt. Lett. 5, 416 (1980).
[CrossRef]

Phys. Rev. Lett. (4)

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

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

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

M. Mitchell, M. Segev, T. H. Coskun, and D. N. Christodoulides, Phys. Rev. Lett. 79, 4990 (1997).
[CrossRef]

Sov. Phys. JETP (1)

V. E. Zakharov and A. B. Shabat, Sov. Phys. JETP 37, 823 (1973); K. J. Blow and N. J. Doran, Phys. Lett. A 107, 55 (1985); Z. Chen, M. Segev, S. R. Singh, T. H. Coskun, and D. N. Christodoulides, J. Opt. Soc. Am. B 14, 1407 (1997).
[CrossRef]

Other (2)

Y. R. Shen, The Principles of Nonlinear Optics (Wiley, New York, 1984).

B. Ya. Zel’dovich, N. F. Pilipetsky, and V. V. Shkunov, Principles of Phase Conjugation (Springer-Verlag, Berlin, 1985).
[CrossRef]

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Figures (2)

Fig. 1
Fig. 1

(a) Propagation of a bright incoherent quasi-soliton when r=3 and at a bias of 550  V, (b) the coherence length lc of this bright soliton as function of distance, (c) intensity profile of a darklike incoherent soliton when ρ=3 and the bias is -300 V, (d) coherence length lc of the dark soliton shown in (c).

Fig. 2
Fig. 2

(a) Formation of an incoherent soliton triplet when ρ=3 and the bias is -550 V, (b) the coherence length lc of this triplet as a function of distance, (c) an incoherent gray soliton pair from even initial conditions, (d) the coherence length lc associated with this pair.

Equations (5)

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

ifz+θfx+12k2fx2-k02ne3r33E01+ρf1+INx, z=0,
INx, z=-+fx, z, θ2dθ,
fz=0, x, θ=r, ρ1/2GN1/2θϕ0x,
μ12x1, x2=1INx1, zINx2, z1/2-+fx1, z, θ×f*x2, z, θexpikθx1-x2dθ.
lcx=-+μ12x, x2dx.

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