Abstract

We analyze theoretically and generate experimentally two-dimensional nonlinear lattices with periodic phase modulation in a photorefractive medium. The light-induced periodically modulated nonlinear refractive index is highly anisotropic and nonlocal, and it depends on the lattice orientation relative to the crystal axis. We discuss the stability of such induced photonic structures and their guiding properties.

© 2005 Optical Society of America

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References

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  1. Yu. S. Kivshar and G. P. Agrawal, Optical Solitons:?from Fibers to Photonic Crystals (Academic, San Diego, Calif., 2003).
  2. J. W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, Nature 422, 147 (2003).
    [CrossRef] [PubMed]
  3. Z. Chen and K. McCarthy, Opt. Lett. 27, 2019 (2002).
    [CrossRef]
  4. A. S. Desyatnikov, E. A. Ostrovskaya, Yu. S. Kivshar, and C. Denz, Phys. Rev. Lett. 91, 153902 (2003).
    [CrossRef]
  5. D. Neshev, Yu. S. Kivshar, H. Martin, and Z. G. Chen, Opt. Lett. 29, 486 (2004).
    [CrossRef] [PubMed]
  6. S. Minardi, S. Sapone, W. Chinaglia, P. Di Trapani, and A. Berzanskis, Opt. Lett. 25, 326 (2000).
    [CrossRef]
  7. J. Petter, J. Schröder, D. Träger, and C. Denz, Opt. Lett. 28, 438 (2003).
    [CrossRef] [PubMed]
  8. H. Martin, E. D. Eugenieva, Z. Chen, and D. N. Christodoulides, Phys. Rev. Lett. 92, 123902 (2004).
    [CrossRef]
  9. M. Petrovi?, D. Träger, A. Strini?, M. Beli?, J. Schröder, and C. Denz, Phys. Rev. E 68, 055601R (2003).
    [CrossRef]
  10. Y. V. Kartashov, V. A. Visloukh, and L. Torner, Phys. Rev. E 68, 015603 (2003).
    [CrossRef]
  11. A. A. Zozulya, D. Z. Anderson, A. V. Mamaev, and M. Saffman, Phys. Rev. A 57, 522 (1997).
    [CrossRef]
  12. Z. Chen, H. Martin, E. D. Eugenieva, J. Xu, and A. Bezryadina, Phys. Rev. Lett. 92, 143902 (2004).
    [CrossRef]

2004 (3)

D. Neshev, Yu. S. Kivshar, H. Martin, and Z. G. Chen, Opt. Lett. 29, 486 (2004).
[CrossRef] [PubMed]

H. Martin, E. D. Eugenieva, Z. Chen, and D. N. Christodoulides, Phys. Rev. Lett. 92, 123902 (2004).
[CrossRef]

Z. Chen, H. Martin, E. D. Eugenieva, J. Xu, and A. Bezryadina, Phys. Rev. Lett. 92, 143902 (2004).
[CrossRef]

2003 (5)

A. S. Desyatnikov, E. A. Ostrovskaya, Yu. S. Kivshar, and C. Denz, Phys. Rev. Lett. 91, 153902 (2003).
[CrossRef]

J. Petter, J. Schröder, D. Träger, and C. Denz, Opt. Lett. 28, 438 (2003).
[CrossRef] [PubMed]

M. Petrovi?, D. Träger, A. Strini?, M. Beli?, J. Schröder, and C. Denz, Phys. Rev. E 68, 055601R (2003).
[CrossRef]

Y. V. Kartashov, V. A. Visloukh, and L. Torner, Phys. Rev. E 68, 015603 (2003).
[CrossRef]

J. W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, Nature 422, 147 (2003).
[CrossRef] [PubMed]

2002 (1)

2000 (1)

1997 (1)

A. A. Zozulya, D. Z. Anderson, A. V. Mamaev, and M. Saffman, Phys. Rev. A 57, 522 (1997).
[CrossRef]

Agrawal, G. P.

Yu. S. Kivshar and G. P. Agrawal, Optical Solitons:?from Fibers to Photonic Crystals (Academic, San Diego, Calif., 2003).

Anderson, D. Z.

A. A. Zozulya, D. Z. Anderson, A. V. Mamaev, and M. Saffman, Phys. Rev. A 57, 522 (1997).
[CrossRef]

Belic, M.

M. Petrovi?, D. Träger, A. Strini?, M. Beli?, J. Schröder, and C. Denz, Phys. Rev. E 68, 055601R (2003).
[CrossRef]

Berzanskis, A.

Bezryadina, A.

Z. Chen, H. Martin, E. D. Eugenieva, J. Xu, and A. Bezryadina, Phys. Rev. Lett. 92, 143902 (2004).
[CrossRef]

Chen, Z.

Z. Chen, H. Martin, E. D. Eugenieva, J. Xu, and A. Bezryadina, Phys. Rev. Lett. 92, 143902 (2004).
[CrossRef]

H. Martin, E. D. Eugenieva, Z. Chen, and D. N. Christodoulides, Phys. Rev. Lett. 92, 123902 (2004).
[CrossRef]

Z. Chen and K. McCarthy, Opt. Lett. 27, 2019 (2002).
[CrossRef]

Chen, Z. G.

Chinaglia, W.

Christodoulides, D. N.

H. Martin, E. D. Eugenieva, Z. Chen, and D. N. Christodoulides, Phys. Rev. Lett. 92, 123902 (2004).
[CrossRef]

J. W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, Nature 422, 147 (2003).
[CrossRef] [PubMed]

Denz, C.

A. S. Desyatnikov, E. A. Ostrovskaya, Yu. S. Kivshar, and C. Denz, Phys. Rev. Lett. 91, 153902 (2003).
[CrossRef]

M. Petrovi?, D. Träger, A. Strini?, M. Beli?, J. Schröder, and C. Denz, Phys. Rev. E 68, 055601R (2003).
[CrossRef]

J. Petter, J. Schröder, D. Träger, and C. Denz, Opt. Lett. 28, 438 (2003).
[CrossRef] [PubMed]

Desyatnikov, A. S.

A. S. Desyatnikov, E. A. Ostrovskaya, Yu. S. Kivshar, and C. Denz, Phys. Rev. Lett. 91, 153902 (2003).
[CrossRef]

Di Trapani, P.

Efremidis, N. K.

J. W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, Nature 422, 147 (2003).
[CrossRef] [PubMed]

Eugenieva, E. D.

H. Martin, E. D. Eugenieva, Z. Chen, and D. N. Christodoulides, Phys. Rev. Lett. 92, 123902 (2004).
[CrossRef]

Z. Chen, H. Martin, E. D. Eugenieva, J. Xu, and A. Bezryadina, Phys. Rev. Lett. 92, 143902 (2004).
[CrossRef]

Fleischer, J. W.

J. W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, Nature 422, 147 (2003).
[CrossRef] [PubMed]

Kartashov, Y. V.

Y. V. Kartashov, V. A. Visloukh, and L. Torner, Phys. Rev. E 68, 015603 (2003).
[CrossRef]

Kivshar, Yu. S.

D. Neshev, Yu. S. Kivshar, H. Martin, and Z. G. Chen, Opt. Lett. 29, 486 (2004).
[CrossRef] [PubMed]

A. S. Desyatnikov, E. A. Ostrovskaya, Yu. S. Kivshar, and C. Denz, Phys. Rev. Lett. 91, 153902 (2003).
[CrossRef]

Yu. S. Kivshar and G. P. Agrawal, Optical Solitons:?from Fibers to Photonic Crystals (Academic, San Diego, Calif., 2003).

Mamaev, A. V.

A. A. Zozulya, D. Z. Anderson, A. V. Mamaev, and M. Saffman, Phys. Rev. A 57, 522 (1997).
[CrossRef]

Martin, H.

Z. Chen, H. Martin, E. D. Eugenieva, J. Xu, and A. Bezryadina, Phys. Rev. Lett. 92, 143902 (2004).
[CrossRef]

H. Martin, E. D. Eugenieva, Z. Chen, and D. N. Christodoulides, Phys. Rev. Lett. 92, 123902 (2004).
[CrossRef]

D. Neshev, Yu. S. Kivshar, H. Martin, and Z. G. Chen, Opt. Lett. 29, 486 (2004).
[CrossRef] [PubMed]

McCarthy, K.

Minardi, S.

Neshev, D.

Ostrovskaya, E. A.

A. S. Desyatnikov, E. A. Ostrovskaya, Yu. S. Kivshar, and C. Denz, Phys. Rev. Lett. 91, 153902 (2003).
[CrossRef]

Petrovic, M.

M. Petrovi?, D. Träger, A. Strini?, M. Beli?, J. Schröder, and C. Denz, Phys. Rev. E 68, 055601R (2003).
[CrossRef]

Petter, J.

Saffman, M.

A. A. Zozulya, D. Z. Anderson, A. V. Mamaev, and M. Saffman, Phys. Rev. A 57, 522 (1997).
[CrossRef]

Sapone, S.

Schröder, J.

J. Petter, J. Schröder, D. Träger, and C. Denz, Opt. Lett. 28, 438 (2003).
[CrossRef] [PubMed]

M. Petrovi?, D. Träger, A. Strini?, M. Beli?, J. Schröder, and C. Denz, Phys. Rev. E 68, 055601R (2003).
[CrossRef]

Segev, M.

J. W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, Nature 422, 147 (2003).
[CrossRef] [PubMed]

Strinic, A.

M. Petrovi?, D. Träger, A. Strini?, M. Beli?, J. Schröder, and C. Denz, Phys. Rev. E 68, 055601R (2003).
[CrossRef]

Torner, L.

Y. V. Kartashov, V. A. Visloukh, and L. Torner, Phys. Rev. E 68, 015603 (2003).
[CrossRef]

Träger, D.

J. Petter, J. Schröder, D. Träger, and C. Denz, Opt. Lett. 28, 438 (2003).
[CrossRef] [PubMed]

M. Petrovi?, D. Träger, A. Strini?, M. Beli?, J. Schröder, and C. Denz, Phys. Rev. E 68, 055601R (2003).
[CrossRef]

Visloukh, V. A.

Y. V. Kartashov, V. A. Visloukh, and L. Torner, Phys. Rev. E 68, 015603 (2003).
[CrossRef]

Xu, J.

Z. Chen, H. Martin, E. D. Eugenieva, J. Xu, and A. Bezryadina, Phys. Rev. Lett. 92, 143902 (2004).
[CrossRef]

Zozulya, A. A.

A. A. Zozulya, D. Z. Anderson, A. V. Mamaev, and M. Saffman, Phys. Rev. A 57, 522 (1997).
[CrossRef]

Nature (1)

J. W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, Nature 422, 147 (2003).
[CrossRef] [PubMed]

Opt. Lett. (4)

Phys. Rev. A (1)

A. A. Zozulya, D. Z. Anderson, A. V. Mamaev, and M. Saffman, Phys. Rev. A 57, 522 (1997).
[CrossRef]

Phys. Rev. E (2)

M. Petrovi?, D. Träger, A. Strini?, M. Beli?, J. Schröder, and C. Denz, Phys. Rev. E 68, 055601R (2003).
[CrossRef]

Y. V. Kartashov, V. A. Visloukh, and L. Torner, Phys. Rev. E 68, 015603 (2003).
[CrossRef]

Phys. Rev. Lett. (3)

A. S. Desyatnikov, E. A. Ostrovskaya, Yu. S. Kivshar, and C. Denz, Phys. Rev. Lett. 91, 153902 (2003).
[CrossRef]

H. Martin, E. D. Eugenieva, Z. Chen, and D. N. Christodoulides, Phys. Rev. Lett. 92, 123902 (2004).
[CrossRef]

Z. Chen, H. Martin, E. D. Eugenieva, J. Xu, and A. Bezryadina, Phys. Rev. Lett. 92, 143902 (2004).
[CrossRef]

Other (1)

Yu. S. Kivshar and G. P. Agrawal, Optical Solitons:?from Fibers to Photonic Crystals (Academic, San Diego, Calif., 2003).

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Figures (3)

Fig. 1
Fig. 1

(a) Square and (b) diamond self-trapped stationary periodic patterns in the model in Eqs. (1, 2, 3) at Γ = 1 . Families of nonlinear waves are summarized in (c) and (d); solid (dashed) curves correspond to the square (diamond) patterns. Both lines for A, P, and max ( x φ ) coincide in (c). Horizontal dotted lines in (d) correspond to the linear limit Γ 0 .

Fig. 2
Fig. 2

Numerical results for the propagation of (a) square and (b) diamond self-trapped patterns for Γ = 11.8 in the low-saturation regime with A 1 and k = 0.5 . Intensities of the lattice wave (LW) and the probe wave it guides (GW) are shown after propagation of z ̃ 23 mm . On the input the lattice is perturbed by 20% of the random noise, and the probe is a broad Gaussian beam.

Fig. 3
Fig. 3

Experimental results for the (a) square and (b) diamond lattices. Left to right, output intensities of the lattice after linear and nonlinear propagation and output of a guided plane wave.

Equations (4)

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i z E + 2 E + n ( I ) E = 0 ,
n ( I ) = Γ x φ ,
2 φ + φ ln ( 1 + I ) = x ln ( 1 + I ) .
k U + 2 U + Γ x φ U = 0 .

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