Abstract

Steady-state dark (or bright) spatial solitons are predicted for biased photovoltaic–photorefractive materials when the diffraction of an optical beam is exactly compensated for by nonlinear self-defocusing (or self-focusing) that is due both to the photovoltaic effect and to spatially nonuniform screening of the applied field. These solitons differ from previously observed steady-state photorefractive or photovoltaic spatial solitons in their properties and experimental condition. These biased photovoltaic solitons are known as the screening-photovoltaic solitons. If the bias field is much stronger than the photovoltaic field, then the screening-photovoltaic solitons are just like the screening solitons. If the applied field is absent, they degenerate into photovoltaic solitons in the closed-circuit condition. We investigate the self-deflection process of bright screening-photovoltaic solitons by taking diffusion effects into account. By use of perturbation techniques it is found that the center of the optical beam moves on a parabolic trajectory and, moreover, that the central spatial-frequency component shifts linearly with the propagation distance. Both the spatial deflection and the angular deviation are proportional to the sum of two dimensionless quantities that are associated with the bias field and the photovoltaic field, respectively. The drift process and the photovoltaic process play an equivalent role in the self-bending process.

© 1999 Optical Society of America

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  1. M. Segev, B. Crosignani, A. Yariv, and B. Fischer, Phys. Rev. Lett. 68, 923 (1992).
    [CrossRef] [PubMed]
  2. G. C. Duree, J. L. Shultz, G. J. Salamo, M. Segev, A. Yariv, B. Crosignani, P. D. Porto, E. J. Sharp, and R. R. Neurgaonkar, Phys. Rev. Lett. 71, 533 (1993).
    [CrossRef] [PubMed]
  3. M. Morin, G. Duree, G. Salamo, and M. Segev, Opt. Lett. 20, 2066 (1995).
    [CrossRef] [PubMed]
  4. M.-F. Shih, M. Segev, G. C. Valley, G. Salamo, B. Crosignani, and P. Di Porto, Electron. Lett. 31, 826 (1995).
    [CrossRef]
  5. Z. Chen, M. Mitchell, M.-F. Shih, M. Segev, M. H. Garrett, and G. C. Valley, Opt. Lett. 21, 629 (1996).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  8. D. N. Christodoulides and M. I. Carvalho, J. Opt. Soc. Am. B 12, 1628 (1995).
    [CrossRef]
  9. M. D. Iturbe Castillo, P. A. Marquez Aguilar, J. J. Sanchez-Mondragon, S. Stepanov, and V. Vysloukh, Appl. Phys. Lett. 64, 408 (1994).
    [CrossRef]
  10. G. C. Valley, M. Segev, Bruno Crosignani, Amnon Yariv, M. M. Fejer, and M. C. Bashaw, Phys. Rev. A 50, R4457 (1994).
    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
  15. M. I. Carvalho, S. R. Singh, and D. N. Christodoulides, Opt. Commun. 120, 311 (1995).
    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]

1997 (2)

1996 (2)

1995 (7)

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

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

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

M.-F. Shih, M. Segev, G. C. Valley, G. Salamo, B. Crosignani, and P. Di Porto, 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]

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

M. I. Carvalho, S. R. Singh, and D. N. Christodoulides, Opt. Commun. 120, 311 (1995).
[CrossRef]

1994 (3)

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

M. D. Iturbe Castillo, P. A. Marquez Aguilar, J. J. Sanchez-Mondragon, S. Stepanov, and V. Vysloukh, Appl. Phys. Lett. 64, 408 (1994).
[CrossRef]

G. C. Valley, M. Segev, Bruno Crosignani, Amnon Yariv, M. M. Fejer, and M. C. Bashaw, Phys. Rev. A 50, R4457 (1994).
[CrossRef]

1993 (2)

G. C. Duree, J. L. Shultz, G. J. Salamo, M. Segev, A. Yariv, B. Crosignani, P. D. Porto, E. J. Sharp, and R. R. Neurgaonkar, Phys. Rev. Lett. 71, 533 (1993).
[CrossRef] [PubMed]

Q. W. Song, C. Zhang, and P. J. Talbot, Appl. Opt. 32, 7266 (1993).
[CrossRef] [PubMed]

1992 (1)

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

1988 (1)

1987 (1)

Y. Kodama and A. Hasegawa, IEEE J. Quantum Electron. QE-23, 510 (1987).
[CrossRef]

Bashaw, M.

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

Bashaw, M. C.

M. Segev, G. C. Valley, M. C. Bashaw, M. Taya, and M. M. Fejer, J. Opt. Soc. Am. B 14, 1772 (1997).
[CrossRef]

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

G. C. Valley, M. Segev, Bruno Crosignani, Amnon Yariv, M. M. Fejer, and M. C. Bashaw, Phys. Rev. A 50, R4457 (1994).
[CrossRef]

Blow, K. J.

Carvalho, M. I.

Chen, Z.

Christodoulides, D. N.

Crosignani, B.

M.-F. Shih, M. Segev, G. C. Valley, G. Salamo, B. Crosignani, and P. Di Porto, 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]

G. C. Duree, J. L. Shultz, G. J. Salamo, M. Segev, A. Yariv, B. Crosignani, P. D. Porto, E. J. Sharp, and R. R. Neurgaonkar, Phys. Rev. Lett. 71, 533 (1993).
[CrossRef] [PubMed]

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

Crosignani, Bruno

G. C. Valley, M. Segev, Bruno Crosignani, Amnon Yariv, M. M. Fejer, and M. C. Bashaw, Phys. Rev. A 50, R4457 (1994).
[CrossRef]

Di Porto, P.

M.-F. Shih, M. Segev, G. C. Valley, G. Salamo, B. Crosignani, and P. Di Porto, Electron. Lett. 31, 826 (1995).
[CrossRef]

Diporto, P.

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

Doran, N. J.

Duree, G.

Duree, G. C.

G. C. Duree, J. L. Shultz, G. J. Salamo, M. Segev, A. Yariv, B. Crosignani, P. D. Porto, E. J. Sharp, and R. R. Neurgaonkar, Phys. Rev. Lett. 71, 533 (1993).
[CrossRef] [PubMed]

Fejer, M. M.

M. Segev, G. C. Valley, M. C. Bashaw, M. Taya, and M. M. Fejer, J. Opt. Soc. Am. B 14, 1772 (1997).
[CrossRef]

M. Taya, M. C. Bashaw, M. M. Fejer, M. Segev, and G. C. Valley, Phys. Rev. A 52, 3095 (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, Bruno Crosignani, Amnon Yariv, M. M. Fejer, and M. C. 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. H.

Gunter, P.

Hasegawa, A.

Y. Kodama and A. Hasegawa, IEEE J. Quantum Electron. QE-23, 510 (1987).
[CrossRef]

Iturbe Castillo, M. D.

M. D. Iturbe Castillo, P. A. Marquez Aguilar, J. J. Sanchez-Mondragon, S. Stepanov, and V. Vysloukh, Appl. Phys. Lett. 64, 408 (1994).
[CrossRef]

Kodama, Y.

Y. Kodama and A. Hasegawa, IEEE J. Quantum Electron. QE-23, 510 (1987).
[CrossRef]

Leach, P.

Marquez Aguilar, P. A.

M. D. Iturbe Castillo, P. A. Marquez Aguilar, J. J. Sanchez-Mondragon, S. Stepanov, and V. Vysloukh, Appl. Phys. Lett. 64, 408 (1994).
[CrossRef]

Mitchell, M.

Montemezzani, C.

Morin, M.

Neurgaonkar, R. R.

G. C. Duree, J. L. Shultz, G. J. Salamo, M. Segev, A. Yariv, B. Crosignani, P. D. Porto, E. J. Sharp, and R. R. Neurgaonkar, Phys. Rev. Lett. 71, 533 (1993).
[CrossRef] [PubMed]

Porto, P. D.

G. C. Duree, J. L. Shultz, G. J. Salamo, M. Segev, A. Yariv, B. Crosignani, P. D. Porto, E. J. Sharp, and R. R. Neurgaonkar, Phys. Rev. Lett. 71, 533 (1993).
[CrossRef] [PubMed]

Salamo, G.

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

M.-F. Shih, M. Segev, G. C. Valley, G. Salamo, B. Crosignani, and P. Di Porto, Electron. Lett. 31, 826 (1995).
[CrossRef]

Salamo, G. J.

G. C. Duree, J. L. Shultz, G. J. Salamo, M. Segev, A. Yariv, B. Crosignani, P. D. Porto, E. J. Sharp, and R. R. Neurgaonkar, Phys. Rev. Lett. 71, 533 (1993).
[CrossRef] [PubMed]

Sanchez-Mondragon, J. J.

M. D. Iturbe Castillo, P. A. Marquez Aguilar, J. J. Sanchez-Mondragon, S. Stepanov, and V. Vysloukh, Appl. Phys. Lett. 64, 408 (1994).
[CrossRef]

Segev, M.

M. Segev, G. C. Valley, M. C. Bashaw, M. Taya, and M. M. Fejer, J. Opt. Soc. Am. B 14, 1772 (1997).
[CrossRef]

M.-F. Shih, P. Leach, and M. Segev, Opt. Lett. 21, 324 (1996).
[CrossRef] [PubMed]

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

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

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

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

M.-F. Shih, M. Segev, G. C. Valley, G. Salamo, B. Crosignani, and P. Di Porto, 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]

G. C. Valley, M. Segev, Bruno Crosignani, Amnon Yariv, M. M. Fejer, and M. C. Bashaw, Phys. Rev. A 50, R4457 (1994).
[CrossRef]

G. C. Duree, J. L. Shultz, G. J. Salamo, M. Segev, A. Yariv, B. Crosignani, P. D. Porto, E. J. Sharp, and R. R. Neurgaonkar, Phys. Rev. Lett. 71, 533 (1993).
[CrossRef] [PubMed]

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

Sharp, E. J.

G. C. Duree, J. L. Shultz, G. J. Salamo, M. Segev, A. Yariv, B. Crosignani, P. D. Porto, E. J. Sharp, and R. R. Neurgaonkar, Phys. Rev. Lett. 71, 533 (1993).
[CrossRef] [PubMed]

Shih, M.-F.

Shultz, J. L.

G. C. Duree, J. L. Shultz, G. J. Salamo, M. Segev, A. Yariv, B. Crosignani, P. D. Porto, E. J. Sharp, and R. R. Neurgaonkar, Phys. Rev. Lett. 71, 533 (1993).
[CrossRef] [PubMed]

Singh, S. R.

M. I. Carvalho, S. R. Singh, and D. N. Christodoulides, Opt. Commun. 120, 311 (1995).
[CrossRef]

Song, Q. W.

Stepanov, S.

M. D. Iturbe Castillo, P. A. Marquez Aguilar, J. J. Sanchez-Mondragon, S. Stepanov, and V. Vysloukh, Appl. Phys. Lett. 64, 408 (1994).
[CrossRef]

Talbot, P. J.

Taya, M.

M. Segev, G. C. Valley, M. C. Bashaw, M. Taya, and M. M. Fejer, J. Opt. Soc. Am. B 14, 1772 (1997).
[CrossRef]

M. Taya, M. C. Bashaw, M. M. Fejer, M. Segev, and G. C. Valley, Phys. Rev. A 52, 3095 (1995).
[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, G. C. Valley, M. C. Bashaw, M. Taya, and M. M. Fejer, J. Opt. Soc. Am. B 14, 1772 (1997).
[CrossRef]

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

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

M.-F. Shih, M. Segev, G. C. Valley, G. Salamo, B. Crosignani, and P. Di Porto, 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]

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, Bruno Crosignani, Amnon Yariv, M. M. Fejer, and M. C. Bashaw, Phys. Rev. A 50, R4457 (1994).
[CrossRef]

Vysloukh, V.

M. D. Iturbe Castillo, P. A. Marquez Aguilar, J. J. Sanchez-Mondragon, S. Stepanov, and V. Vysloukh, Appl. Phys. Lett. 64, 408 (1994).
[CrossRef]

Wood, D.

Yariv, A.

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

G. C. Duree, J. L. Shultz, G. J. Salamo, M. Segev, A. Yariv, B. Crosignani, P. D. Porto, E. J. Sharp, and R. R. Neurgaonkar, Phys. Rev. Lett. 71, 533 (1993).
[CrossRef] [PubMed]

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

Yariv, Amnon

G. C. Valley, M. Segev, Bruno Crosignani, Amnon Yariv, M. M. Fejer, and M. C. Bashaw, Phys. Rev. A 50, R4457 (1994).
[CrossRef]

Zhang, C.

Appl. Opt. (1)

Appl. Phys. Lett. (1)

M. D. Iturbe Castillo, P. A. Marquez Aguilar, J. J. Sanchez-Mondragon, S. Stepanov, and V. Vysloukh, Appl. Phys. Lett. 64, 408 (1994).
[CrossRef]

Electron. Lett. (1)

M.-F. Shih, M. Segev, G. C. Valley, G. Salamo, B. Crosignani, and P. Di Porto, Electron. Lett. 31, 826 (1995).
[CrossRef]

IEEE J. Quantum Electron. (1)

Y. Kodama and A. Hasegawa, IEEE J. Quantum Electron. QE-23, 510 (1987).
[CrossRef]

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

Opt. Commun. (1)

M. I. Carvalho, S. R. Singh, and D. N. Christodoulides, Opt. Commun. 120, 311 (1995).
[CrossRef]

Opt. Lett. (4)

Phys. Rev. A (3)

G. C. Valley, M. Segev, Bruno Crosignani, Amnon Yariv, M. M. Fejer, and M. C. 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]

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

Phys. Rev. Lett. (3)

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

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

G. C. Duree, J. L. Shultz, G. J. Salamo, M. Segev, A. Yariv, B. Crosignani, P. D. Porto, E. J. Sharp, and R. R. Neurgaonkar, Phys. Rev. Lett. 71, 533 (1993).
[CrossRef] [PubMed]

Other (3)

P. Gunter and J. P. Huignard, eds., Photorefractive Materi-als and Their Applications I and II (Springer-Verlag, Berlin, 1988); P. Yeh, Photorefractive Nonlinear Optics (Wiley, New York, 1993).

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.

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

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Figures (1)

Fig. 1
Fig. 1

Normalized intensity profiles of bright SP solitons calculated from Eq. (27) for ρ=10 and α=-355 and for β=±266 and 0.

Equations (37)

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

2E+(k0nˆe)2E=0,
iϕz+12kϕxx-k02(ne3reff Esc)ϕ=0,
γRnND+=si(I+Id)(ND-ND+),
Escx=e0(ND+-NA-n),
J=eμnEsc+kBTμnx+kpsi(ND-ND+)I,
Jx=0orJ=constant,
ND+=NA1+0reNAEscx,
n=si(ND-NA)γRNA(I+Id)1+0reNAEscx-1.
ND+=NA,
n=si(ND-NA)γRNA(I+Id).
n=si(ND-NA)γRNA(I+Id).
J=eμnE0+kpsi(ND-NA)I,
J=eμnE0+EpII+Id,
J=eμnEsc+KBTe ln nx+EpII+Id.
nE0+EpII+Id=nEsc+KBTe ln nx+EpII+Id.
Esc=E0I+IdI+Id+EpI-II+Id-KBTe1I+IdIx.
iUξ+12Uss-β(ρ+1)U1+|U|2-α(ρ-|U|2)U1+|U|2+γ(|U|2)sU1+|U|2=0,
iUξ+12Uss-βU1+|U|2+α|U|2U1+|U|2+γ(|U|2)sU1+|u|2=0.
iUξ+12Uss-βU1+|U|2+α|U|2U1+|U|2=0.
y¨-2νy-2βy1+ry2+2αry31+ry2=0,
ν=-β+αrln(1+r)+α,
(y˙)2=2(β+α)r[ln(1+ry2)-y2 ln(1+r)].
[2(β+α)]1/2s=±y1r1/2dyˆ[ln(1+ryˆ2)-yˆ2 ln(1+r)]1/2.
y¨-2νy-2β(ρ+1)y1+ry2-2αρ1-y21+ρy2y=0,
ν=-β.
(y˙)2=-2(β+α)(y2-1)-ρ+1ρln1+ρy21+ρ.
[-2(β+α)]1/2s=±y0dyˆ(yˆ2-1)-ρ+1ρln1+ρyˆ21+ρ1/2.
U=r1/2y[s+u(ξ)]exp(i{νξ+ω(ξ)[s+u(ξ)]+σ(ξ)})
du(ξ)dξ=-ω(ξ),
dσ(ξ)dξ=ω2(ξ)2,
dω(ξ)dξ=4γ(β+α)K(r),
K(r)=-+ds2y2(s)1+ry2(s){y2(s)In(1+r)-In[1+ry2(s)]}-+dsy2(s)-1.
ω(ξ)=4γ(β+α)K(r)ξ,
u(ξ)=-2γ(β+α)K(r)ξ2,
σ(ξ)=8[γ(β+α)K(r)]2ξ3/3.
xd=2γ(β+α)K(r)z2/(k02ne2x03),
θd=4γ(β+α)K(r)z/(k02ne2x03).

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