Abstract

We theoretically predict and experimentally observe the two-dimensional (2-D) bright solitons in a nonconventionally biased strontium barium niobate (SBN) crystal. A theory describing light propagating in an SBN crystal with a bias field along an arbitrary direction is formulated. Then the existence of 2-D bright solitons in such a crystal is numerically verified. By employing digital holography, the index changes induced by Gaussian beams in an SBN crystal under different biasing conditions are visualized. Finally, skewed elliptical solitons are experimentally demonstrated.

© 2007 Optical Society of America

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  1. M. Segev, B. Crosignani, A. Yariv, and B. Fischer, "Spatial solitons in photorefractive media," Phys. Rev. Lett. 68, 923 (1992).
    [CrossRef] [PubMed]
  2. G. I. Stegeman and M. Segev, "Optical spatial solitons and their interactions: universality and diversity," Science 286, 1518 (1999).
    [CrossRef] [PubMed]
  3. M. Shih, P. Leach, M. Segev, M. H. Garett, G. Salamo, and G. C. Valley, "Two-dimensional steady-state photorefractive screening solitons," Opt. Lett. 21, 324 (1996).
    [CrossRef] [PubMed]
  4. Z. Chen, M. Mitchell, M. Shih, M. Segev, M. H. Garrett, and G. C. Valley, "Steady-state dark photorefractive screening solitons," Opt. Lett. 21, 629 (1996).
    [CrossRef] [PubMed]
  5. W. Królikowski and S. A. Holmstrom, "Fusion and birth of spatial solitons upon collision," Opt. Lett. 22, 369 (1997).
    [CrossRef] [PubMed]
  6. J. W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, "Observation of two-dimensional discrete solitons in optically induced nonlinear photonic lattices," Nature 422, 147 (2003).
    [CrossRef] [PubMed]
  7. J. N. Malmberg, A. H. Carlsson, D. Anderson, M. Lisak, E. A. Ostrovskaya, and Yu. S. Kivshar, "Vector solitons in (2+1) dimensions," Opt. Lett. 25, 643 (2000).
    [CrossRef]
  8. Z. Chen, M. Segev, D. W. Wilson, R. E. Muller, and P. D. Maker, "Self-trapping of an optical vortex by use of the bulk photovoltaic effect," Phys. Rev. Lett. 78, 2948 (1997).
    [CrossRef]
  9. C. Crognale and L. Rosa, "Vector analysis of the space-charge field in nonconventionally biased photorefractive crystals," J. Lightwave Technol. 23, 2175 (2005).
    [CrossRef]
  10. A. Yariv and P. Yeh, Optical waves in crystals (Wiley, New York, 1984), Chap. 7.
  11. P. Zhang, Y. Ma, J. Zhao, D. X. Yang, and H. Xu, "One-dimensional spatial dark soliton-induced channel waveguides in lithium niobate crystal," Appl. Opt. 45, 2273 (2006).
    [CrossRef] [PubMed]
  12. A. A. Zozulya and D. Z. Anderson, "Propagation of an optical beam in a photorefractive medium in the presence of a photogalvanic nonlinearity or an externally applied electric field," Phys. Rev. A 51, 1520 (1995).
    [CrossRef] [PubMed]
  13. A. A. Zozulya, D. Z. Anderson, A. V. Mamaev, and M. Saffman, "Solitary attractors and low-order filamentation in anisotropic self-focusing media," Phys. Rev. A 57, 522 (1998).
    [CrossRef]
  14. V. I. Petviashvili, "Equation of an extraordinary soliton," Sov. J. Plasma Phys. 2, 257 (1976).
  15. J. Zhao, P. Zhang, J. Zhou, D. X. Yang, D. S. Yang, and E. Li, "Visualizations of light-induced refractive index changes in photorefractive crystals employing digital holography," Chin. Phys. Lett. 20, 1748 (2003).
    [CrossRef]
  16. E. D. Eugenieva, D. N. Christodoulides, and M. Segev, "Elliptic incoherent solitons in saturable nonlinear media," Opt. Lett. 25, 972 (2000).
    [CrossRef]
  17. O. Katz, T. Carmon, T. Schwartz, M. Segev, and D. N. Christodoulides, "Observation of elliptic incoherent spatial solitons," Opt. Lett. 29, 1248 (2004).
    [CrossRef] [PubMed]

2006 (1)

2005 (1)

2004 (1)

2003 (2)

J. Zhao, P. Zhang, J. Zhou, D. X. Yang, D. S. Yang, and E. Li, "Visualizations of light-induced refractive index changes in photorefractive crystals employing digital holography," Chin. Phys. Lett. 20, 1748 (2003).
[CrossRef]

J. W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, "Observation of two-dimensional discrete solitons in optically induced nonlinear photonic lattices," Nature 422, 147 (2003).
[CrossRef] [PubMed]

2000 (2)

1999 (1)

G. I. Stegeman and M. Segev, "Optical spatial solitons and their interactions: universality and diversity," Science 286, 1518 (1999).
[CrossRef] [PubMed]

1998 (1)

A. A. Zozulya, D. Z. Anderson, A. V. Mamaev, and M. Saffman, "Solitary attractors and low-order filamentation in anisotropic self-focusing media," Phys. Rev. A 57, 522 (1998).
[CrossRef]

1997 (2)

W. Królikowski and S. A. Holmstrom, "Fusion and birth of spatial solitons upon collision," Opt. Lett. 22, 369 (1997).
[CrossRef] [PubMed]

Z. Chen, M. Segev, D. W. Wilson, R. E. Muller, and P. D. Maker, "Self-trapping of an optical vortex by use of the bulk photovoltaic effect," Phys. Rev. Lett. 78, 2948 (1997).
[CrossRef]

1996 (2)

1995 (1)

A. A. Zozulya and D. Z. Anderson, "Propagation of an optical beam in a photorefractive medium in the presence of a photogalvanic nonlinearity or an externally applied electric field," Phys. Rev. A 51, 1520 (1995).
[CrossRef] [PubMed]

1992 (1)

M. Segev, B. Crosignani, A. Yariv, and B. Fischer, "Spatial solitons in photorefractive media," Phys. Rev. Lett. 68, 923 (1992).
[CrossRef] [PubMed]

1976 (1)

V. I. Petviashvili, "Equation of an extraordinary soliton," Sov. J. Plasma Phys. 2, 257 (1976).

Anderson, D.

Anderson, D. Z.

A. A. Zozulya, D. Z. Anderson, A. V. Mamaev, and M. Saffman, "Solitary attractors and low-order filamentation in anisotropic self-focusing media," Phys. Rev. A 57, 522 (1998).
[CrossRef]

A. A. Zozulya and D. Z. Anderson, "Propagation of an optical beam in a photorefractive medium in the presence of a photogalvanic nonlinearity or an externally applied electric field," Phys. Rev. A 51, 1520 (1995).
[CrossRef] [PubMed]

Carlsson, A. H.

Carmon, T.

Chen, Z.

Z. Chen, M. Segev, D. W. Wilson, R. E. Muller, and P. D. Maker, "Self-trapping of an optical vortex by use of the bulk photovoltaic effect," Phys. Rev. Lett. 78, 2948 (1997).
[CrossRef]

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

Christodoulides, D. N.

Crognale, C.

Crosignani, B.

M. Segev, B. Crosignani, A. Yariv, and B. Fischer, "Spatial solitons in photorefractive media," Phys. Rev. Lett. 68, 923 (1992).
[CrossRef] [PubMed]

Efremidis, N. K.

J. W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, "Observation of two-dimensional discrete solitons in optically induced nonlinear photonic lattices," Nature 422, 147 (2003).
[CrossRef] [PubMed]

Eugenieva, E. D.

Fischer, B.

M. Segev, B. Crosignani, A. Yariv, and B. Fischer, "Spatial solitons in photorefractive media," Phys. Rev. Lett. 68, 923 (1992).
[CrossRef] [PubMed]

Fleischer, J. W.

J. W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, "Observation of two-dimensional discrete solitons in optically induced nonlinear photonic lattices," Nature 422, 147 (2003).
[CrossRef] [PubMed]

Garett, M. H.

Garrett, M. H.

Holmstrom, S. A.

Katz, O.

Kivshar, Yu. S.

Królikowski, W.

Leach, P.

Li, E.

J. Zhao, P. Zhang, J. Zhou, D. X. Yang, D. S. Yang, and E. Li, "Visualizations of light-induced refractive index changes in photorefractive crystals employing digital holography," Chin. Phys. Lett. 20, 1748 (2003).
[CrossRef]

Lisak, M.

Ma, Y.

Maker, P. D.

Z. Chen, M. Segev, D. W. Wilson, R. E. Muller, and P. D. Maker, "Self-trapping of an optical vortex by use of the bulk photovoltaic effect," Phys. Rev. Lett. 78, 2948 (1997).
[CrossRef]

Malmberg, J. N.

Mamaev, A. V.

A. A. Zozulya, D. Z. Anderson, A. V. Mamaev, and M. Saffman, "Solitary attractors and low-order filamentation in anisotropic self-focusing media," Phys. Rev. A 57, 522 (1998).
[CrossRef]

Mitchell, M.

Muller, R. E.

Z. Chen, M. Segev, D. W. Wilson, R. E. Muller, and P. D. Maker, "Self-trapping of an optical vortex by use of the bulk photovoltaic effect," Phys. Rev. Lett. 78, 2948 (1997).
[CrossRef]

Ostrovskaya, E. A.

Petviashvili, V. I.

V. I. Petviashvili, "Equation of an extraordinary soliton," Sov. J. Plasma Phys. 2, 257 (1976).

Rosa, L.

Saffman, M.

A. A. Zozulya, D. Z. Anderson, A. V. Mamaev, and M. Saffman, "Solitary attractors and low-order filamentation in anisotropic self-focusing media," Phys. Rev. A 57, 522 (1998).
[CrossRef]

Salamo, G.

Schwartz, T.

Segev, M.

O. Katz, T. Carmon, T. Schwartz, M. Segev, and D. N. Christodoulides, "Observation of elliptic incoherent spatial solitons," Opt. Lett. 29, 1248 (2004).
[CrossRef] [PubMed]

J. W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, "Observation of two-dimensional discrete solitons in optically induced nonlinear photonic lattices," Nature 422, 147 (2003).
[CrossRef] [PubMed]

E. D. Eugenieva, D. N. Christodoulides, and M. Segev, "Elliptic incoherent solitons in saturable nonlinear media," Opt. Lett. 25, 972 (2000).
[CrossRef]

G. I. Stegeman and M. Segev, "Optical spatial solitons and their interactions: universality and diversity," Science 286, 1518 (1999).
[CrossRef] [PubMed]

Z. Chen, M. Segev, D. W. Wilson, R. E. Muller, and P. D. Maker, "Self-trapping of an optical vortex by use of the bulk photovoltaic effect," Phys. Rev. Lett. 78, 2948 (1997).
[CrossRef]

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

M. Shih, P. Leach, M. Segev, M. H. Garett, G. Salamo, and G. C. Valley, "Two-dimensional steady-state photorefractive screening solitons," Opt. Lett. 21, 324 (1996).
[CrossRef] [PubMed]

M. Segev, B. Crosignani, A. Yariv, and B. Fischer, "Spatial solitons in photorefractive media," Phys. Rev. Lett. 68, 923 (1992).
[CrossRef] [PubMed]

Shih, M.

Stegeman, G. I.

G. I. Stegeman and M. Segev, "Optical spatial solitons and their interactions: universality and diversity," Science 286, 1518 (1999).
[CrossRef] [PubMed]

Valley, G. C.

Wilson, D. W.

Z. Chen, M. Segev, D. W. Wilson, R. E. Muller, and P. D. Maker, "Self-trapping of an optical vortex by use of the bulk photovoltaic effect," Phys. Rev. Lett. 78, 2948 (1997).
[CrossRef]

Xu, H.

Yang, D. S.

J. Zhao, P. Zhang, J. Zhou, D. X. Yang, D. S. Yang, and E. Li, "Visualizations of light-induced refractive index changes in photorefractive crystals employing digital holography," Chin. Phys. Lett. 20, 1748 (2003).
[CrossRef]

Yang, D. X.

P. Zhang, Y. Ma, J. Zhao, D. X. Yang, and H. Xu, "One-dimensional spatial dark soliton-induced channel waveguides in lithium niobate crystal," Appl. Opt. 45, 2273 (2006).
[CrossRef] [PubMed]

J. Zhao, P. Zhang, J. Zhou, D. X. Yang, D. S. Yang, and E. Li, "Visualizations of light-induced refractive index changes in photorefractive crystals employing digital holography," Chin. Phys. Lett. 20, 1748 (2003).
[CrossRef]

Yariv, A.

M. Segev, B. Crosignani, A. Yariv, and B. Fischer, "Spatial solitons in photorefractive media," Phys. Rev. Lett. 68, 923 (1992).
[CrossRef] [PubMed]

Zhang, P.

P. Zhang, Y. Ma, J. Zhao, D. X. Yang, and H. Xu, "One-dimensional spatial dark soliton-induced channel waveguides in lithium niobate crystal," Appl. Opt. 45, 2273 (2006).
[CrossRef] [PubMed]

J. Zhao, P. Zhang, J. Zhou, D. X. Yang, D. S. Yang, and E. Li, "Visualizations of light-induced refractive index changes in photorefractive crystals employing digital holography," Chin. Phys. Lett. 20, 1748 (2003).
[CrossRef]

Zhao, J.

P. Zhang, Y. Ma, J. Zhao, D. X. Yang, and H. Xu, "One-dimensional spatial dark soliton-induced channel waveguides in lithium niobate crystal," Appl. Opt. 45, 2273 (2006).
[CrossRef] [PubMed]

J. Zhao, P. Zhang, J. Zhou, D. X. Yang, D. S. Yang, and E. Li, "Visualizations of light-induced refractive index changes in photorefractive crystals employing digital holography," Chin. Phys. Lett. 20, 1748 (2003).
[CrossRef]

Zhou, J.

J. Zhao, P. Zhang, J. Zhou, D. X. Yang, D. S. Yang, and E. Li, "Visualizations of light-induced refractive index changes in photorefractive crystals employing digital holography," Chin. Phys. Lett. 20, 1748 (2003).
[CrossRef]

Zozulya, A. A.

A. A. Zozulya, D. Z. Anderson, A. V. Mamaev, and M. Saffman, "Solitary attractors and low-order filamentation in anisotropic self-focusing media," Phys. Rev. A 57, 522 (1998).
[CrossRef]

A. A. Zozulya and D. Z. Anderson, "Propagation of an optical beam in a photorefractive medium in the presence of a photogalvanic nonlinearity or an externally applied electric field," Phys. Rev. A 51, 1520 (1995).
[CrossRef] [PubMed]

Appl. Opt. (1)

Chin. Phys. Lett. (1)

J. Zhao, P. Zhang, J. Zhou, D. X. Yang, D. S. Yang, and E. Li, "Visualizations of light-induced refractive index changes in photorefractive crystals employing digital holography," Chin. Phys. Lett. 20, 1748 (2003).
[CrossRef]

J. Lightwave Technol. (1)

Nature (1)

J. W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, "Observation of two-dimensional discrete solitons in optically induced nonlinear photonic lattices," Nature 422, 147 (2003).
[CrossRef] [PubMed]

Opt. Lett. (6)

Phys. Rev. A (2)

A. A. Zozulya and D. Z. Anderson, "Propagation of an optical beam in a photorefractive medium in the presence of a photogalvanic nonlinearity or an externally applied electric field," Phys. Rev. A 51, 1520 (1995).
[CrossRef] [PubMed]

A. A. Zozulya, D. Z. Anderson, A. V. Mamaev, and M. Saffman, "Solitary attractors and low-order filamentation in anisotropic self-focusing media," Phys. Rev. A 57, 522 (1998).
[CrossRef]

Phys. Rev. Lett. (2)

M. Segev, B. Crosignani, A. Yariv, and B. Fischer, "Spatial solitons in photorefractive media," Phys. Rev. Lett. 68, 923 (1992).
[CrossRef] [PubMed]

Z. Chen, M. Segev, D. W. Wilson, R. E. Muller, and P. D. Maker, "Self-trapping of an optical vortex by use of the bulk photovoltaic effect," Phys. Rev. Lett. 78, 2948 (1997).
[CrossRef]

Science (1)

G. I. Stegeman and M. Segev, "Optical spatial solitons and their interactions: universality and diversity," Science 286, 1518 (1999).
[CrossRef] [PubMed]

Sov. J. Plasma Phys. (1)

V. I. Petviashvili, "Equation of an extraordinary soliton," Sov. J. Plasma Phys. 2, 257 (1976).

Other (1)

A. Yariv and P. Yeh, Optical waves in crystals (Wiley, New York, 1984), Chap. 7.

Supplementary Material (1)

» Media 1: MPG (2282 KB)     

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Figures (7)

Fig. 1.
Fig. 1.

Geometry of light beam propagation in a nonconventionally biased SBN crystal.

Fig. 2.
Fig. 2.

Numerical simulations of the index changes and beam propagations in a nonconventionally biased SBN crystal. (a) Input beam; (b) Linearly diffracted beam; (c) Light-induced potential; (d)-(h) Index changes induced by the input beam shown in (a) (top), output beams after nonlinear propagations (middle), and the corresponding nonlinear index changes at z=15 (bottom) for the cases of α=0, π/4 , π/2, 3π/4, and π, respectively.

Fig. 3
Fig. 3

Simulation results for 2-D bright elliptical solitons in nonconventionally biased SBN crystal. (a)-(c) Solitons with different propagation constantβ; (d) Index changes induced by the solitons shown in (b); From the first to the third row, they are the results for α=0, π/4 and π/2, respectively. (e) Soliton maximum intensity I max versus β; (f) FWHMs of the solitons and their ratio versus I max.

Fig. 4.
Fig. 4.

Simulations of the evolutions of a Gaussian beam in a nonconventionally biased SBN crystal. (a)-(e) Linear diffracted profiles with z=0, 150, 300, 450, 600, respectively; (f)-(j) Beam profiles after nonlinear propagated with z=50, 100, 300, 450, 600, respectively; (k)-(o) Nonlinear index changes corresponding to the beam profiles in (f)-(j); (p) FWHMs of the beams versus propagation lengths z.

Fig. 5.
Fig. 5.

Measured light-induced index changes in a nonconventionally biased SBN:Cr crystal. (a)–(d) 2-D maps of index changes for α=0, π, π/2 and -π/2, respectively; (e) 3-D display of (d).

Fig. 6.
Fig. 6.

Sketch of the experimental setup for observing bright solitons in nonconventionally biased SBN crystal.

Fig. 7.
Fig. 7.

Experimental results for observing soliton formations in a nonconventionally biased SBN:Cr crystal. (a) Profile of input Gaussian beam; (b)-(d) Beam profiles observed on the rear face of the crystal for a linearly diffracted beam, and the solitons formed with α=π/2 and -π/2, respectively; (e)-(h) Output beam profiles as the bias field is increased gradually; (i)-(l) Output beam profiles as the background beam illumination is increased gradually.

Equations (4)

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( z i 2 2 ) B ( r ) = i ( φ x sin α + φ y cos α ) B ( r )
2 φ + φ ln ( 1 + B ( r ) 2 ) = y ln ( 1 + B ( r ) 2 )
( β 1 2 2 ) b x y = ( φ x sin α + φ y cos α ) b x y
2 φ + φ ln ( 1 + b x y 2 ) = y ln ( 1 + b x y 2 )

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