Abstract

We develop a nonlinear theory of soliton-induced waveguides that describe a finite-amplitude probe beam guided by a spatial dark soliton in a saturable nonlinear medium. We suggest an effective way to control the interaction of these soliton-induced waveguides and also show that, in sharp contrast with scalar dark solitons, the dark-soliton waveguides can attract each other and even form stationary bound states.

© 1998 Optical Society of America

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  1. G. A. Askar’yan, Zh. Eksp. Teor. Fiz. 42, 1567 (1962) [Sov. Phys. JETP 15, 1088 (1962)].
  2. A. W. Snyder, D. J. Mitchell, L. Poladian, and F. Ladouceur, Opt. Lett. 16, 21 (1991).
    [CrossRef] [PubMed]
  3. J. T. Manassah, Opt. Lett. 16, 587 (1991).
    [CrossRef] [PubMed]
  4. R. De la Fuente, A. Barthelemy, and C. Froehly, Opt. Lett. 16, 793 (1991).
    [CrossRef] [PubMed]
  5. B. Luther-Davies and Y. Xiaoping, Opt. Lett. 17, 496, 1775 (1992).
  6. For an overview of the soliton-induced waveguides in photorefractive media see M. Shih, Z. Chen, M. Mitchell, M. Segev, H. Lee, R. S. Feigelson, and J. P. Wilde, J. Opt. Soc. Am. B 14, 3091 (1997).
    [CrossRef]
  7. Yu. S. Kivshar and B. Luther-Davies, Phys. Rep. 298, 81 (1998), and references therein.
    [CrossRef]
  8. Dark-soliton waveguides may become multimoded when the cross- and self-phase modulation coefficients are not equal; see, e.g., M. Haelterman and A. P. Sheppard, Phys. Rev. E 49, 4512 (1994).
    [CrossRef]
  9. Z. Chen, M. Segev, T. H. Coskun, D. N. Christodoulides, Yu. S. Kivshar, and V. V. Afanasjev, Opt. Lett. 21, 1821 (1996); J. Opt. Soc. Am. B 14, 3066 (1997).
    [CrossRef] [PubMed]
  10. D. N. Christodoulides, S. R. Singh, M. I. Carvalho, and M. Segev, Appl. Phys. Lett. 68, 1763 (1996).
    [CrossRef]
  11. S. V. Manakov, Zh. Exp. Teor. Fiz. 65, 505 (1973) [Sov. Phys. JETP 38, 248 (1974)].
  12. Y. Nogami and C. S. Warke, Phys. Lett. A 59, 251 (1976).
    [CrossRef]
  13. A. P. Sheppard and Yu. S. Kivshar, in Nonlinear Guided Waves and Their Applications, Vol. 15 of 1996 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1998), pp. 157–159.
  14. A. P. Sheppard and Yu. S. Kivshar, Phys. Rev. E 55, 4773 (1997).
    [CrossRef]
  15. M. I. Carvalho, S. R. Singh, D. N. Christodoulides, and R. I. Joseph, Phys. Rev. E 53, R53 (1996).
    [CrossRef]
  16. Yu. S. Kivshar and W. Krolikowski, Opt. Commun. 114, 353 (1995).
    [CrossRef]

1998 (1)

Yu. S. Kivshar and B. Luther-Davies, Phys. Rep. 298, 81 (1998), and references therein.
[CrossRef]

1997 (2)

1996 (3)

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

Z. Chen, M. Segev, T. H. Coskun, D. N. Christodoulides, Yu. S. Kivshar, and V. V. Afanasjev, Opt. Lett. 21, 1821 (1996); J. Opt. Soc. Am. B 14, 3066 (1997).
[CrossRef] [PubMed]

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

1995 (1)

Yu. S. Kivshar and W. Krolikowski, Opt. Commun. 114, 353 (1995).
[CrossRef]

1994 (1)

Dark-soliton waveguides may become multimoded when the cross- and self-phase modulation coefficients are not equal; see, e.g., M. Haelterman and A. P. Sheppard, Phys. Rev. E 49, 4512 (1994).
[CrossRef]

1992 (1)

B. Luther-Davies and Y. Xiaoping, Opt. Lett. 17, 496, 1775 (1992).

1991 (3)

1976 (1)

Y. Nogami and C. S. Warke, Phys. Lett. A 59, 251 (1976).
[CrossRef]

1973 (1)

S. V. Manakov, Zh. Exp. Teor. Fiz. 65, 505 (1973) [Sov. Phys. JETP 38, 248 (1974)].

1962 (1)

G. A. Askar’yan, Zh. Eksp. Teor. Fiz. 42, 1567 (1962) [Sov. Phys. JETP 15, 1088 (1962)].

Afanasjev, V. V.

Askar’yan, G. A.

G. A. Askar’yan, Zh. Eksp. Teor. Fiz. 42, 1567 (1962) [Sov. Phys. JETP 15, 1088 (1962)].

Barthelemy, A.

Carvalho, M. I.

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]

Chen, Z.

Christodoulides, D. N.

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

Z. Chen, M. Segev, T. H. Coskun, D. N. Christodoulides, Yu. S. Kivshar, and V. V. Afanasjev, Opt. Lett. 21, 1821 (1996); J. Opt. Soc. Am. B 14, 3066 (1997).
[CrossRef] [PubMed]

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

Coskun, T. H.

De la Fuente, R.

Feigelson, R. S.

Froehly, C.

Haelterman, M.

Dark-soliton waveguides may become multimoded when the cross- and self-phase modulation coefficients are not equal; see, e.g., M. Haelterman and A. P. Sheppard, Phys. Rev. E 49, 4512 (1994).
[CrossRef]

Joseph, R. I.

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

Kivshar, Yu. S.

Yu. S. Kivshar and B. Luther-Davies, Phys. Rep. 298, 81 (1998), and references therein.
[CrossRef]

A. P. Sheppard and Yu. S. Kivshar, Phys. Rev. E 55, 4773 (1997).
[CrossRef]

Z. Chen, M. Segev, T. H. Coskun, D. N. Christodoulides, Yu. S. Kivshar, and V. V. Afanasjev, Opt. Lett. 21, 1821 (1996); J. Opt. Soc. Am. B 14, 3066 (1997).
[CrossRef] [PubMed]

Yu. S. Kivshar and W. Krolikowski, Opt. Commun. 114, 353 (1995).
[CrossRef]

A. P. Sheppard and Yu. S. Kivshar, in Nonlinear Guided Waves and Their Applications, Vol. 15 of 1996 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1998), pp. 157–159.

Krolikowski, W.

Yu. S. Kivshar and W. Krolikowski, Opt. Commun. 114, 353 (1995).
[CrossRef]

Ladouceur, F.

Lee, H.

Luther-Davies, B.

Yu. S. Kivshar and B. Luther-Davies, Phys. Rep. 298, 81 (1998), and references therein.
[CrossRef]

B. Luther-Davies and Y. Xiaoping, Opt. Lett. 17, 496, 1775 (1992).

Manakov, S. V.

S. V. Manakov, Zh. Exp. Teor. Fiz. 65, 505 (1973) [Sov. Phys. JETP 38, 248 (1974)].

Manassah, J. T.

Mitchell, D. J.

Mitchell, M.

Nogami, Y.

Y. Nogami and C. S. Warke, Phys. Lett. A 59, 251 (1976).
[CrossRef]

Poladian, L.

Segev, M.

Sheppard, A. P.

A. P. Sheppard and Yu. S. Kivshar, Phys. Rev. E 55, 4773 (1997).
[CrossRef]

Dark-soliton waveguides may become multimoded when the cross- and self-phase modulation coefficients are not equal; see, e.g., M. Haelterman and A. P. Sheppard, Phys. Rev. E 49, 4512 (1994).
[CrossRef]

A. P. Sheppard and Yu. S. Kivshar, in Nonlinear Guided Waves and Their Applications, Vol. 15 of 1996 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1998), pp. 157–159.

Shih, M.

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

Snyder, A. W.

Warke, C. S.

Y. Nogami and C. S. Warke, Phys. Lett. A 59, 251 (1976).
[CrossRef]

Wilde, J. P.

Xiaoping, Y.

B. Luther-Davies and Y. Xiaoping, Opt. Lett. 17, 496, 1775 (1992).

Appl. Phys. Lett. (1)

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

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

Opt. Commun. (1)

Yu. S. Kivshar and W. Krolikowski, Opt. Commun. 114, 353 (1995).
[CrossRef]

Opt. Lett. (5)

Phys. Lett. A (1)

Y. Nogami and C. S. Warke, Phys. Lett. A 59, 251 (1976).
[CrossRef]

Phys. Rep. (1)

Yu. S. Kivshar and B. Luther-Davies, Phys. Rep. 298, 81 (1998), and references therein.
[CrossRef]

Phys. Rev. E (3)

Dark-soliton waveguides may become multimoded when the cross- and self-phase modulation coefficients are not equal; see, e.g., M. Haelterman and A. P. Sheppard, Phys. Rev. E 49, 4512 (1994).
[CrossRef]

A. P. Sheppard and Yu. S. Kivshar, Phys. Rev. E 55, 4773 (1997).
[CrossRef]

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

Zh. Eksp. Teor. Fiz. (1)

G. A. Askar’yan, Zh. Eksp. Teor. Fiz. 42, 1567 (1962) [Sov. Phys. JETP 15, 1088 (1962)].

Zh. Exp. Teor. Fiz. (1)

S. V. Manakov, Zh. Exp. Teor. Fiz. 65, 505 (1973) [Sov. Phys. JETP 38, 248 (1974)].

Other (1)

A. P. Sheppard and Yu. S. Kivshar, in Nonlinear Guided Waves and Their Applications, Vol. 15 of 1996 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1998), pp. 157–159.

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Figures (4)

Fig. 1
Fig. 1

Bifurcation of a one-component dark soliton usx for three values of s, shown as the dependence of the complimentary power Pc on the propagation constant λ. Examples of two-component localized solutions are shown for s=0.2.

Fig. 2
Fig. 2

Evolution of the dark-soliton waveguide without the guided mode for s=0.5. (a) Soliton profiles at z=0 (thick curve) and z=100 (thin curve) for λ=0.95. (b) Amplitude of the additional gray-soliton pair g versus λ measured at z=100. Dashed line, amplitude of the gray soliton in (a).

Fig. 3
Fig. 3

Examples of two-soliton bound states in model (2): (a) s=0.4 and λ=0.55, (b) s=0.5 and λ=0.55, (c) s=0.5 and λ=0.65.

Fig. 4
Fig. 4

Interaction between two dark-soliton waveguides guiding bright components (a) in phase and (b) out of phase.

Equations (5)

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

iUz+122Ux2+β1+ρU1+U2+W2=0,iWz+122Wx2+β1+ρW1+U2+W2=0.
iuz+122ux2-u2+w2u1+su2+w2+u=0,iwz+122wx2-u2+w2w1+su2+w2+λw=0,
12d2wdx2-us21+sus2w+λw=0.
Pc=-+dxux2+wx2-1-s-1,
Ueffx0=2 exp-4x0+4a2 cosϕx0 exp-2x0.

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