Abstract

A dissipative photorefractive system is considered, which consists of a biased photorefractive crystal and a pump beam with a uniform spatial distribution. A signal beam couples coherently with the pump beam by codirectional degenerate two-beam coupling and hence obtains a gain. It is shown that the signal beam can evolve into a steady-state spatial bright (or dark) soliton that is a result of double balance, i.e., loss is balanced by gain, and diffraction is balanced by nonlinearity due to the spatially nonuniform screening of the applied field and to the process of two-beam coupling. Such solitons have fixed amplitude and width for fixed values of system parameters and hence are known as rigid screening (RS) solitons. RS solitons differ from previously observed screening solitons in their properties and physical origin and can exist whether the crystal possesses a focusing or a defocusing nonlinearity. If the pump beam is switched to a background illumination, RS-soliton solutions can reduce to screening-soliton solutions. Numerical simulations show that RS solitons are stable relative to small perturbations.

© 2003 Optical Society of America

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  1. M. Segev, G. C. Valley, B. Crosignani, P. D. Porto, and A. Yariv, “Steady-state spatial screening solitons in photorefractive materials with external applied field,” Phys. Rev. Lett. 73, 3211–3214 (1994).
    [CrossRef] [PubMed]
  2. Z. G. Chen, M. Mitchell, M. Shih, M. Segev, M. H. Garrett, and G. C. Valley, “Steady-state dark photorefractive screening solitons,” Opt. Lett. 21, 629–631 (1996).
    [CrossRef] [PubMed]
  3. M.-F. Shih, M. Segev, G. C. Valley, G. Salamo, B. Crosignani, and P. Di Porto, “Observation of two-dimensional steady-state photorefractive screening solitons,” Electron. Lett. 31, 826–827 (1995).
    [CrossRef]
  4. 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]
  5. M. Segev, M. Shih, and G. C. Valley, “Photorefractive screening solitons of high and low intensity,” J. Opt. Soc. Am. B 13, 706–718 (1996).
    [CrossRef]
  6. K. Kos, H. X. Meng, G. Salamo, M. Shih, M. Segev, and G. C. Valley, “One-dimensional steady-state photorefractive screening solitons,” Phys. Rev. E 53, R4330–R4333 (1996).
    [CrossRef]
  7. M. 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]
  8. Jinsong Liu and Keqing Lu, “Screening-photovoltaic spatial solitons in biased photovoltaic-photorefractive crystals and their self-deflection,” J. Opt. Soc. Am. B 16, 550–555 (1999).
    [CrossRef]
  9. Jinsong Liu, “Universal theory of state-state one-dimensional photorefractive solitons,” Chin. Phys. 10, 1037–1042 (2001).
    [CrossRef]
  10. Jinsong Liu and Hao Zhonghua, “Higher-order space charge field effects on the evolution of screening-photovoltaic spatial solitons in biased photovoltaic photorefractive crystals,” J. Opt. Soc. Am. B 19, 513–521 (2002).
    [CrossRef]
  11. Jinsong Liu and Zhonghua Hao, “Evolution of separate screening soliton pairs in a biased series photorefractive crystal circuit,” Phys. Rev. E 65, 066601 (2002).
    [CrossRef]
  12. R. Singh and D. N. Christodoulides, “Evolution of spatial optical solitons in biased photorefractive media under steady state conditions,” Opt. Commun. 118, 569–576 (1995).
    [CrossRef]
  13. C. Paré, L. Gagnon, and P.-A. Belangre, “Spatial solitary wave in a weakly saturated amplifying/absorbing medium,” Opt. Commun. 74, 228–232 (1989).
    [CrossRef]
  14. G. Khitrova, H. M. Gibbs, Y. Kawamura, H. Iwamura, T. Ikegami, J. E. Sipe, and L. Ming, “Spatial solitons in self-focusing gain medium,” Phys. Rev. Lett. 70, 920–923 (1993).
    [CrossRef] [PubMed]
  15. V. G. Kulushkin, “Gaussian light beam in a lens-like medium with a nonlinear complex susceptibility,” Sov. J. Quantum Electron. 17, 116–117 (1987).
    [CrossRef]
  16. N. N. Akhmediev and V. V. Afanasjev, “Solitons of the complex Ginzburg–Landau equation,” in Spatial Solitons, S. Trillo and W. Torruellas, eds. (Springer, Berlin, 2001).
  17. N. N. Akhmediev, V. V. Afanasjev, and J. M. Soto-Crespo, “Singularities and special soliton solutions of the cubic-quintic complex Ginzburg–Landau equation,” Phys. Rev. E 53, 1190–1201 (1996).
    [CrossRef]
  18. M. Saffman, D. Montgomery, and D. Z. Anderson, “Collapse of a transverse-mode continuum in a self-imaging photorefractively pumped ring resonator,” Opt. Lett. 19, 518–520 (1994).
    [CrossRef] [PubMed]
  19. J. M. Soto-Crespo, N. N. Akhmediev, and V. V. Afanasjev, “Stability of the pulselike solutions of the quintic complex Ginzburg–Landau equation,” J. Opt. Soc. Am. B 13, 1439–1449 (1996).
    [CrossRef]
  20. P. Yeh, “Two-wave mixing in nonlinear media,” IEEE J. Quantum Electron. 25, 484–519 (1989).
    [CrossRef]
  21. I. Oda, Y. Otani, L. Liu, and T. Yoshizawa, “Polarization effect for vibration detection using photorefractive two-wave mixing in KNSBN:Cu crystal,” Opt. Commun. 148, 95–100 (1998).
    [CrossRef]
  22. N. Bekki and K. Nozaki, “Exact solution of the generalized Ginzburg–Landau equation,” J. Phys. Soc. Jpn. 53, 1581–1582 (1984).
    [CrossRef]
  23. J. Petter, C. Weilnau, C. Denz, A. Stepken, and F. Kaiser, “Self-bending of photorefractive solitons,” Opt. Commun. 170, 291–297 (1999).
    [CrossRef]
  24. Z. G. Chen, M. Segev, T. H. Coskun, D. N. Christodoulides, and Y. S. Kivshar, “Coupled photorefractive spatial-soliton pairs,” J. Opt. Soc. Am. B 14, 3066–3077 (1997).
    [CrossRef]

2002

Jinsong Liu and Zhonghua Hao, “Evolution of separate screening soliton pairs in a biased series photorefractive crystal circuit,” Phys. Rev. E 65, 066601 (2002).
[CrossRef]

Jinsong Liu and Hao Zhonghua, “Higher-order space charge field effects on the evolution of screening-photovoltaic spatial solitons in biased photovoltaic photorefractive crystals,” J. Opt. Soc. Am. B 19, 513–521 (2002).
[CrossRef]

2001

Jinsong Liu, “Universal theory of state-state one-dimensional photorefractive solitons,” Chin. Phys. 10, 1037–1042 (2001).
[CrossRef]

1999

J. Petter, C. Weilnau, C. Denz, A. Stepken, and F. Kaiser, “Self-bending of photorefractive solitons,” Opt. Commun. 170, 291–297 (1999).
[CrossRef]

Jinsong Liu and Keqing Lu, “Screening-photovoltaic spatial solitons in biased photovoltaic-photorefractive crystals and their self-deflection,” J. Opt. Soc. Am. B 16, 550–555 (1999).
[CrossRef]

1998

I. Oda, Y. Otani, L. Liu, and T. Yoshizawa, “Polarization effect for vibration detection using photorefractive two-wave mixing in KNSBN:Cu crystal,” Opt. Commun. 148, 95–100 (1998).
[CrossRef]

1997

1996

1995

M.-F. Shih, M. Segev, G. C. Valley, G. Salamo, B. Crosignani, and P. Di Porto, “Observation of two-dimensional steady-state photorefractive screening solitons,” Electron. Lett. 31, 826–827 (1995).
[CrossRef]

R. Singh and D. N. Christodoulides, “Evolution of spatial optical solitons in biased photorefractive media under steady state conditions,” Opt. Commun. 118, 569–576 (1995).
[CrossRef]

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]

1994

M. Segev, G. C. Valley, B. Crosignani, P. D. Porto, 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. Saffman, D. Montgomery, and D. Z. Anderson, “Collapse of a transverse-mode continuum in a self-imaging photorefractively pumped ring resonator,” Opt. Lett. 19, 518–520 (1994).
[CrossRef] [PubMed]

1993

G. Khitrova, H. M. Gibbs, Y. Kawamura, H. Iwamura, T. Ikegami, J. E. Sipe, and L. Ming, “Spatial solitons in self-focusing gain medium,” Phys. Rev. Lett. 70, 920–923 (1993).
[CrossRef] [PubMed]

1989

C. Paré, L. Gagnon, and P.-A. Belangre, “Spatial solitary wave in a weakly saturated amplifying/absorbing medium,” Opt. Commun. 74, 228–232 (1989).
[CrossRef]

P. Yeh, “Two-wave mixing in nonlinear media,” IEEE J. Quantum Electron. 25, 484–519 (1989).
[CrossRef]

1987

V. G. Kulushkin, “Gaussian light beam in a lens-like medium with a nonlinear complex susceptibility,” Sov. J. Quantum Electron. 17, 116–117 (1987).
[CrossRef]

1984

N. Bekki and K. Nozaki, “Exact solution of the generalized Ginzburg–Landau equation,” J. Phys. Soc. Jpn. 53, 1581–1582 (1984).
[CrossRef]

Afanasjev, V. V.

J. M. Soto-Crespo, N. N. Akhmediev, and V. V. Afanasjev, “Stability of the pulselike solutions of the quintic complex Ginzburg–Landau equation,” J. Opt. Soc. Am. B 13, 1439–1449 (1996).
[CrossRef]

N. N. Akhmediev, V. V. Afanasjev, and J. M. Soto-Crespo, “Singularities and special soliton solutions of the cubic-quintic complex Ginzburg–Landau equation,” Phys. Rev. E 53, 1190–1201 (1996).
[CrossRef]

Akhmediev, N. N.

N. N. Akhmediev, V. V. Afanasjev, and J. M. Soto-Crespo, “Singularities and special soliton solutions of the cubic-quintic complex Ginzburg–Landau equation,” Phys. Rev. E 53, 1190–1201 (1996).
[CrossRef]

J. M. Soto-Crespo, N. N. Akhmediev, and V. V. Afanasjev, “Stability of the pulselike solutions of the quintic complex Ginzburg–Landau equation,” J. Opt. Soc. Am. B 13, 1439–1449 (1996).
[CrossRef]

Anderson, D. Z.

Bekki, N.

N. Bekki and K. Nozaki, “Exact solution of the generalized Ginzburg–Landau equation,” J. Phys. Soc. Jpn. 53, 1581–1582 (1984).
[CrossRef]

Belangre, P.-A.

C. Paré, L. Gagnon, and P.-A. Belangre, “Spatial solitary wave in a weakly saturated amplifying/absorbing medium,” Opt. Commun. 74, 228–232 (1989).
[CrossRef]

Carvalho, M. I.

Chen, Z. G.

Christodoulides, D. N.

Coskun, T. H.

Crosignani, B.

M.-F. Shih, M. Segev, G. C. Valley, G. Salamo, B. Crosignani, and P. Di Porto, “Observation of two-dimensional steady-state photorefractive screening solitons,” Electron. Lett. 31, 826–827 (1995).
[CrossRef]

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

Denz, C.

J. Petter, C. Weilnau, C. Denz, A. Stepken, and F. Kaiser, “Self-bending of photorefractive solitons,” Opt. Commun. 170, 291–297 (1999).
[CrossRef]

Di Porto, P.

M.-F. Shih, M. Segev, G. C. Valley, G. Salamo, B. Crosignani, and P. Di Porto, “Observation of two-dimensional steady-state photorefractive screening solitons,” Electron. Lett. 31, 826–827 (1995).
[CrossRef]

Gagnon, L.

C. Paré, L. Gagnon, and P.-A. Belangre, “Spatial solitary wave in a weakly saturated amplifying/absorbing medium,” Opt. Commun. 74, 228–232 (1989).
[CrossRef]

Garrett, M. H.

Gibbs, H. M.

G. Khitrova, H. M. Gibbs, Y. Kawamura, H. Iwamura, T. Ikegami, J. E. Sipe, and L. Ming, “Spatial solitons in self-focusing gain medium,” Phys. Rev. Lett. 70, 920–923 (1993).
[CrossRef] [PubMed]

Hao, Zhonghua

Jinsong Liu and Zhonghua Hao, “Evolution of separate screening soliton pairs in a biased series photorefractive crystal circuit,” Phys. Rev. E 65, 066601 (2002).
[CrossRef]

Ikegami, T.

G. Khitrova, H. M. Gibbs, Y. Kawamura, H. Iwamura, T. Ikegami, J. E. Sipe, and L. Ming, “Spatial solitons in self-focusing gain medium,” Phys. Rev. Lett. 70, 920–923 (1993).
[CrossRef] [PubMed]

Iwamura, H.

G. Khitrova, H. M. Gibbs, Y. Kawamura, H. Iwamura, T. Ikegami, J. E. Sipe, and L. Ming, “Spatial solitons in self-focusing gain medium,” Phys. Rev. Lett. 70, 920–923 (1993).
[CrossRef] [PubMed]

Kaiser, F.

J. Petter, C. Weilnau, C. Denz, A. Stepken, and F. Kaiser, “Self-bending of photorefractive solitons,” Opt. Commun. 170, 291–297 (1999).
[CrossRef]

Kawamura, Y.

G. Khitrova, H. M. Gibbs, Y. Kawamura, H. Iwamura, T. Ikegami, J. E. Sipe, and L. Ming, “Spatial solitons in self-focusing gain medium,” Phys. Rev. Lett. 70, 920–923 (1993).
[CrossRef] [PubMed]

Khitrova, G.

G. Khitrova, H. M. Gibbs, Y. Kawamura, H. Iwamura, T. Ikegami, J. E. Sipe, and L. Ming, “Spatial solitons in self-focusing gain medium,” Phys. Rev. Lett. 70, 920–923 (1993).
[CrossRef] [PubMed]

Kivshar, Y. S.

Kos, K.

K. Kos, H. X. Meng, G. Salamo, M. Shih, M. Segev, and G. C. Valley, “One-dimensional steady-state photorefractive screening solitons,” Phys. Rev. E 53, R4330–R4333 (1996).
[CrossRef]

Kulushkin, V. G.

V. G. Kulushkin, “Gaussian light beam in a lens-like medium with a nonlinear complex susceptibility,” Sov. J. Quantum Electron. 17, 116–117 (1987).
[CrossRef]

Leach, P.

Liu, Jinsong

Liu, L.

I. Oda, Y. Otani, L. Liu, and T. Yoshizawa, “Polarization effect for vibration detection using photorefractive two-wave mixing in KNSBN:Cu crystal,” Opt. Commun. 148, 95–100 (1998).
[CrossRef]

Lu, Keqing

Meng, H. X.

K. Kos, H. X. Meng, G. Salamo, M. Shih, M. Segev, and G. C. Valley, “One-dimensional steady-state photorefractive screening solitons,” Phys. Rev. E 53, R4330–R4333 (1996).
[CrossRef]

Ming, L.

G. Khitrova, H. M. Gibbs, Y. Kawamura, H. Iwamura, T. Ikegami, J. E. Sipe, and L. Ming, “Spatial solitons in self-focusing gain medium,” Phys. Rev. Lett. 70, 920–923 (1993).
[CrossRef] [PubMed]

Mitchell, M.

Montgomery, D.

Nozaki, K.

N. Bekki and K. Nozaki, “Exact solution of the generalized Ginzburg–Landau equation,” J. Phys. Soc. Jpn. 53, 1581–1582 (1984).
[CrossRef]

Oda, I.

I. Oda, Y. Otani, L. Liu, and T. Yoshizawa, “Polarization effect for vibration detection using photorefractive two-wave mixing in KNSBN:Cu crystal,” Opt. Commun. 148, 95–100 (1998).
[CrossRef]

Otani, Y.

I. Oda, Y. Otani, L. Liu, and T. Yoshizawa, “Polarization effect for vibration detection using photorefractive two-wave mixing in KNSBN:Cu crystal,” Opt. Commun. 148, 95–100 (1998).
[CrossRef]

Paré, C.

C. Paré, L. Gagnon, and P.-A. Belangre, “Spatial solitary wave in a weakly saturated amplifying/absorbing medium,” Opt. Commun. 74, 228–232 (1989).
[CrossRef]

Petter, J.

J. Petter, C. Weilnau, C. Denz, A. Stepken, and F. Kaiser, “Self-bending of photorefractive solitons,” Opt. Commun. 170, 291–297 (1999).
[CrossRef]

Porto, P. D.

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

Saffman, M.

Salamo, G.

M. 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]

K. Kos, H. X. Meng, G. Salamo, M. Shih, M. Segev, and G. C. Valley, “One-dimensional steady-state photorefractive screening solitons,” Phys. Rev. E 53, R4330–R4333 (1996).
[CrossRef]

M.-F. Shih, M. Segev, G. C. Valley, G. Salamo, B. Crosignani, and P. Di Porto, “Observation of two-dimensional steady-state photorefractive screening solitons,” Electron. Lett. 31, 826–827 (1995).
[CrossRef]

Segev, M.

Z. G. Chen, M. Segev, T. H. Coskun, D. N. Christodoulides, and Y. S. Kivshar, “Coupled photorefractive spatial-soliton pairs,” J. Opt. Soc. Am. B 14, 3066–3077 (1997).
[CrossRef]

M. 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]

K. Kos, H. X. Meng, G. Salamo, M. Shih, M. Segev, and G. C. Valley, “One-dimensional steady-state photorefractive screening solitons,” Phys. Rev. E 53, R4330–R4333 (1996).
[CrossRef]

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

M.-F. Shih, M. Segev, G. C. Valley, G. Salamo, B. Crosignani, and P. Di Porto, “Observation of two-dimensional steady-state photorefractive screening solitons,” Electron. Lett. 31, 826–827 (1995).
[CrossRef]

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

Shih, M.

Shih, M.-F.

M.-F. Shih, M. Segev, G. C. Valley, G. Salamo, B. Crosignani, and P. Di Porto, “Observation of two-dimensional steady-state photorefractive screening solitons,” Electron. Lett. 31, 826–827 (1995).
[CrossRef]

Singh, R.

R. Singh and D. N. Christodoulides, “Evolution of spatial optical solitons in biased photorefractive media under steady state conditions,” Opt. Commun. 118, 569–576 (1995).
[CrossRef]

Sipe, J. E.

G. Khitrova, H. M. Gibbs, Y. Kawamura, H. Iwamura, T. Ikegami, J. E. Sipe, and L. Ming, “Spatial solitons in self-focusing gain medium,” Phys. Rev. Lett. 70, 920–923 (1993).
[CrossRef] [PubMed]

Soto-Crespo, J. M.

N. N. Akhmediev, V. V. Afanasjev, and J. M. Soto-Crespo, “Singularities and special soliton solutions of the cubic-quintic complex Ginzburg–Landau equation,” Phys. Rev. E 53, 1190–1201 (1996).
[CrossRef]

J. M. Soto-Crespo, N. N. Akhmediev, and V. V. Afanasjev, “Stability of the pulselike solutions of the quintic complex Ginzburg–Landau equation,” J. Opt. Soc. Am. B 13, 1439–1449 (1996).
[CrossRef]

Stepken, A.

J. Petter, C. Weilnau, C. Denz, A. Stepken, and F. Kaiser, “Self-bending of photorefractive solitons,” Opt. Commun. 170, 291–297 (1999).
[CrossRef]

Valley, G. C.

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

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

K. Kos, H. X. Meng, G. Salamo, M. Shih, M. Segev, and G. C. Valley, “One-dimensional steady-state photorefractive screening solitons,” Phys. Rev. E 53, R4330–R4333 (1996).
[CrossRef]

M. 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]

M.-F. Shih, M. Segev, G. C. Valley, G. Salamo, B. Crosignani, and P. Di Porto, “Observation of two-dimensional steady-state photorefractive screening solitons,” Electron. Lett. 31, 826–827 (1995).
[CrossRef]

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

Weilnau, C.

J. Petter, C. Weilnau, C. Denz, A. Stepken, and F. Kaiser, “Self-bending of photorefractive solitons,” Opt. Commun. 170, 291–297 (1999).
[CrossRef]

Yariv, A.

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

Yeh, P.

P. Yeh, “Two-wave mixing in nonlinear media,” IEEE J. Quantum Electron. 25, 484–519 (1989).
[CrossRef]

Yoshizawa, T.

I. Oda, Y. Otani, L. Liu, and T. Yoshizawa, “Polarization effect for vibration detection using photorefractive two-wave mixing in KNSBN:Cu crystal,” Opt. Commun. 148, 95–100 (1998).
[CrossRef]

Zhonghua, Hao

Chin. Phys.

Jinsong Liu, “Universal theory of state-state one-dimensional photorefractive solitons,” Chin. Phys. 10, 1037–1042 (2001).
[CrossRef]

Electron. Lett.

M.-F. Shih, M. Segev, G. C. Valley, G. Salamo, B. Crosignani, and P. Di Porto, “Observation of two-dimensional steady-state photorefractive screening solitons,” Electron. Lett. 31, 826–827 (1995).
[CrossRef]

IEEE J. Quantum Electron.

P. Yeh, “Two-wave mixing in nonlinear media,” IEEE J. Quantum Electron. 25, 484–519 (1989).
[CrossRef]

J. Opt. Soc. Am. B

J. Phys. Soc. Jpn.

N. Bekki and K. Nozaki, “Exact solution of the generalized Ginzburg–Landau equation,” J. Phys. Soc. Jpn. 53, 1581–1582 (1984).
[CrossRef]

Opt. Commun.

J. Petter, C. Weilnau, C. Denz, A. Stepken, and F. Kaiser, “Self-bending of photorefractive solitons,” Opt. Commun. 170, 291–297 (1999).
[CrossRef]

I. Oda, Y. Otani, L. Liu, and T. Yoshizawa, “Polarization effect for vibration detection using photorefractive two-wave mixing in KNSBN:Cu crystal,” Opt. Commun. 148, 95–100 (1998).
[CrossRef]

R. Singh and D. N. Christodoulides, “Evolution of spatial optical solitons in biased photorefractive media under steady state conditions,” Opt. Commun. 118, 569–576 (1995).
[CrossRef]

C. Paré, L. Gagnon, and P.-A. Belangre, “Spatial solitary wave in a weakly saturated amplifying/absorbing medium,” Opt. Commun. 74, 228–232 (1989).
[CrossRef]

Opt. Lett.

Phys. Rev. E

N. N. Akhmediev, V. V. Afanasjev, and J. M. Soto-Crespo, “Singularities and special soliton solutions of the cubic-quintic complex Ginzburg–Landau equation,” Phys. Rev. E 53, 1190–1201 (1996).
[CrossRef]

K. Kos, H. X. Meng, G. Salamo, M. Shih, M. Segev, and G. C. Valley, “One-dimensional steady-state photorefractive screening solitons,” Phys. Rev. E 53, R4330–R4333 (1996).
[CrossRef]

Jinsong Liu and Zhonghua Hao, “Evolution of separate screening soliton pairs in a biased series photorefractive crystal circuit,” Phys. Rev. E 65, 066601 (2002).
[CrossRef]

Phys. Rev. Lett.

G. Khitrova, H. M. Gibbs, Y. Kawamura, H. Iwamura, T. Ikegami, J. E. Sipe, and L. Ming, “Spatial solitons in self-focusing gain medium,” Phys. Rev. Lett. 70, 920–923 (1993).
[CrossRef] [PubMed]

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

Sov. J. Quantum Electron.

V. G. Kulushkin, “Gaussian light beam in a lens-like medium with a nonlinear complex susceptibility,” Sov. J. Quantum Electron. 17, 116–117 (1987).
[CrossRef]

Other

N. N. Akhmediev and V. V. Afanasjev, “Solitons of the complex Ginzburg–Landau equation,” in Spatial Solitons, S. Trillo and W. Torruellas, eds. (Springer, Berlin, 2001).

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Figures (8)

Fig. 1
Fig. 1

Illustration of the configuration to generate and observe RS solitons in a biased PR crystal with a two-beam coupling gain. Signal and pump beams couple each other by codirectional degenerate PR two-beam coupling. C denotes the c axis of the crystal. V denotes the potential measured between the electrodes of the crystals.

Fig. 2
Fig. 2

Amplitude of a bright RS soliton as a function of bias field, E0 for α=0.23, 0.3, 0.34 (from top to bottom) with x0=25μm, θ=2°, and φ=87°.

Fig. 3
Fig. 3

Intensity FWHM varies with bias field at x0=25μm, α=0.23, θ=2°, and φ=87°. r=0.1 and ρ=0.1 are for bright and dark screening solitons, respectively.

Fig. 4
Fig. 4

Phase profiles of a RS bright and dark soliton, ϕb and ϕd. x0=25μm, α=0.23, θ=2°, and φ=87°. The solid curves denote ϕb for E0=1000, 50, 0, -500, -1000 (from top to bottom). The dashed curves denote ϕd for E0=1000, 500, 0, -50, -1000 (from top to bottom).

Fig. 5
Fig. 5

Simultaneous propagation of a RS bright soliton (intensity profiles). System parameters: α=0.46, β=22.4, g=0.5, g0=0.7, and ρ=0. Solution parameters: F=0.37, B=1.74, b=1.55×10-2, and ν=20.2.

Fig. 6
Fig. 6

Dynamical evolution toward the solitary wave (intensity profiles). System and solution parameters are the same as in Fig. 5. Input conditions: ΔF=-0.02 and ΔB=0.

Fig. 7
Fig. 7

Dynamics of the normalized peak solitary beam intensity. System and solution parameters are the same as in Fig. 5. Input conditions: ΔB=0 and ΔF=0.03, 0.02, 0.01, 0, -0.01, and -0.02 (from top to bottom).

Fig. 8
Fig. 8

Dynamics of the normalized peak solitary beam intensity. System and solution parameters are the same as in Fig. 5. Input conditions: ΔF=0 and ΔB=-0.05, -0.03, 0, 0.03, and 0.05 (from top to bottom).

Equations (14)

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n^e=ne-ne32 r33Esc+Γ0+i Γ2×ϕpϕ*(|ϕp|2+|ϕ|2)k0exp(iΔ)+c.c.
12k2ϕx2+i ϕz-k0ne32 γ33Escϕ+Γ0-i2 ΓIpIp+I ϕ
+i 12 α0ϕ=0,
i Uξ+122Us2-[(1+ρ)β-g0+ig] U1+|U|2+iαU
=0,
i Uξ+122Us2-(Pd+iG)U+(Pd+ig)U|U|2=0,
U(s, ξ)=Pd-1/2V(s, ξ)exp(-iPdξ),
i Vξ+122Vs2+V|V|2=iGV-i gPd V|V|2.
U(s, ξ)=F sech(Bs)exp{ib ln[sech(Bs)]}exp(-iνξ),
U(s, ξ)=D tanh(Hs)exp{id ln[cosh(Hs)]}exp(-iΩξ),
U(s, ξ)=rsech(rβs)exp{iβ[(r/2)-1]ξ}.
U(s, ξ)=ρtanh{-ρ(1+ρ)βs}exp[-iβ(1-ρ2)ξ].
ϕb=b ln[sech(Bs)]-[(g-α)/2]s2sWb/3.53b(ln 2±Bs)s>Wb/3.53,
ϕd=d ln[cosh(Hs)][(g-α)/3]s2sWd/3.53-d(ln 2±Hs)s>Wd/3.53,

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