Abstract

We demonstrate elliptical discrete solitons in an optically induced two-dimensional photonic lattice. The ellipticity of the discrete soliton results from enhanced photorefractive anisotropy and nonlocality under a nonconventional bias condition. We show that the ellipticity and orientation of the discrete solitons can be altered by changing the direction of the lattice beam and/or the bias field relative to the crystalline c-axis. Our experimental results are in good agreement with the theoretical prediction.

© 2008 Optical Society of America

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  1. For a review, see D. N. Christodoulides, F. Lederer, and Y. Silberberg, "Discretizing light behaviour in linear and nonlinear waveguide lattices," Nature 424, 817-823 (2003).
    [CrossRef] [PubMed]
  2. N. K. Efremidis, S. Sears, D. N. Christodoulides, J. W. Fleischer, and M. Segev, "Discrete solitons in photorefractive optically induced photonic lattices," Phys. Rev. E 66, 046602 (2002).
    [CrossRef]
  3. 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, 147-150 (2003).
    [CrossRef] [PubMed]
  4. D. Neshev, E. Ostrovskaya, Y. Kivshar, and W. Królikowski, "Spatial solitons in optically induced gratings," Opt. Lett. 28, 710-712 (2003).
    [CrossRef] [PubMed]
  5. H. Martin, E. D. Eugenieva, Z. Chen, and D. N. Christodoulides, "Discrete solitons and soliton-induced dislocations in partially coherent photonic lattices," Phys. Rev. Lett. 92, 123902 (2004).
    [CrossRef] [PubMed]
  6. J. W. Fleischer, T. Carmon, M. Segev, N. K. Efremidis, and D. N. Christodoulides. “Observation of discrete solitons in optically induced real time waveguide arrays,” Phys. Rev. Lett. 90, 023902 (2003).
    [CrossRef] [PubMed]
  7. 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, 1520-1531 (1995).
    [CrossRef] [PubMed]
  8. A. A. Zozulya, D. Z. Anderson, A. V. Mamaev, and M. Saffman, "Self-focusing and soliton formation in media with anisotropic nonlocal material response," Europhys. Lett. 36, 419-424 (1996).
    [CrossRef]
  9. P. Zhang, J. Zhao, C. Lou, X. Tan, Y. Gao, Q. Liu, D. Yang, J. Xu, and Z. Chen, "Elliptical solitons in nonconventionally biased photorefractive crystals," Opt. Express 15, 536-544 (2007).
    [CrossRef] [PubMed]
  10. E. D. Eugenieva, D. N. Christodoulides, and M. Segev, "Elliptic incoherent solitons in saturable nonlinear media," Opt. Lett. 25, 972-974 (2000).
    [CrossRef]
  11. O. Katz, T. Carmon, T. Schwartz, M. Segev, and D. N. Christodoulides, "Observation of elliptic incoherent spatial solitons," Opt. Lett. 29, 1248-1250 (2004).
    [CrossRef] [PubMed]
  12. J. Hudock, N. K. Efremidis, and D. N. Christodoulides, "Anisotropic diffraction and elliptic discrete solitons in two-dimensional waveguide arrays," Opt. Lett. 29, 268-270 (2004).
    [CrossRef] [PubMed]
  13. F. Ye, L. Dong, J. Wang, T. Cai, and Y. Li, "Discrete elliptic solitons in two-dimensional waveguide arrays," Chin. Opt. Lett. 3, 227-229 (2005).
  14. P. G. Kevrekidis, D. J. Frantzeskakis, R. Carretero-González, B. A. Malomed, and A. R. Bishop "Discrete solitons and vortices on anisotropic lattices," Phys. Rev. E 72, 046613 (2005).
    [CrossRef]
  15. B. Terhalle, A. S. Desyatnikov, C. Bersch, D. Träger, L. Tang, J. Imbrock, Y. S. Kivshar, and C. Denz, "Anisotropic photonic lattices and discrete solitons in photorefractive media," Appl. Phys. B 86, 399-405 (2007).
    [CrossRef]
  16. P. Zhang, S. Liu, J. Zhao, C. Lou, J. Xu, and Z. Chen, "Optically induced transition between discrete and gap solitons in a nonconventionally biased photorefractive crystal," to appear in Opt. Lett. (2008).
    [CrossRef] [PubMed]
  17. P. Zhang, Y. Ma, J. Zhao, D. Yang, and H. Xu, "One-dimensional spatial dark soliton-induced channel waveguides in lithium niobate crystal," Appl. Opt. 45, 2273-2278 (2006).
    [CrossRef] [PubMed]
  18. V. I. Petviashvili, "Equation of an extraordinary soliton," Sov. J. Plasma Phys. 2, 257-258 (1976).

2007 (2)

B. Terhalle, A. S. Desyatnikov, C. Bersch, D. Träger, L. Tang, J. Imbrock, Y. S. Kivshar, and C. Denz, "Anisotropic photonic lattices and discrete solitons in photorefractive media," Appl. Phys. B 86, 399-405 (2007).
[CrossRef]

P. Zhang, J. Zhao, C. Lou, X. Tan, Y. Gao, Q. Liu, D. Yang, J. Xu, and Z. Chen, "Elliptical solitons in nonconventionally biased photorefractive crystals," Opt. Express 15, 536-544 (2007).
[CrossRef] [PubMed]

2006 (1)

2005 (2)

F. Ye, L. Dong, J. Wang, T. Cai, and Y. Li, "Discrete elliptic solitons in two-dimensional waveguide arrays," Chin. Opt. Lett. 3, 227-229 (2005).

P. G. Kevrekidis, D. J. Frantzeskakis, R. Carretero-González, B. A. Malomed, and A. R. Bishop "Discrete solitons and vortices on anisotropic lattices," Phys. Rev. E 72, 046613 (2005).
[CrossRef]

2004 (3)

2003 (4)

J. W. Fleischer, T. Carmon, M. Segev, N. K. Efremidis, and D. N. Christodoulides. “Observation of discrete solitons in optically induced real time waveguide arrays,” Phys. Rev. Lett. 90, 023902 (2003).
[CrossRef] [PubMed]

For a review, see D. N. Christodoulides, F. Lederer, and Y. Silberberg, "Discretizing light behaviour in linear and nonlinear waveguide lattices," Nature 424, 817-823 (2003).
[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, 147-150 (2003).
[CrossRef] [PubMed]

D. Neshev, E. Ostrovskaya, Y. Kivshar, and W. Królikowski, "Spatial solitons in optically induced gratings," Opt. Lett. 28, 710-712 (2003).
[CrossRef] [PubMed]

2002 (1)

N. K. Efremidis, S. Sears, D. N. Christodoulides, J. W. Fleischer, and M. Segev, "Discrete solitons in photorefractive optically induced photonic lattices," Phys. Rev. E 66, 046602 (2002).
[CrossRef]

2000 (1)

1996 (1)

A. A. Zozulya, D. Z. Anderson, A. V. Mamaev, and M. Saffman, "Self-focusing and soliton formation in media with anisotropic nonlocal material response," Europhys. Lett. 36, 419-424 (1996).
[CrossRef]

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, 1520-1531 (1995).
[CrossRef] [PubMed]

1976 (1)

V. I. Petviashvili, "Equation of an extraordinary soliton," Sov. J. Plasma Phys. 2, 257-258 (1976).

Anderson, D. Z.

A. A. Zozulya, D. Z. Anderson, A. V. Mamaev, and M. Saffman, "Self-focusing and soliton formation in media with anisotropic nonlocal material response," Europhys. Lett. 36, 419-424 (1996).
[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, 1520-1531 (1995).
[CrossRef] [PubMed]

Bersch, C.

B. Terhalle, A. S. Desyatnikov, C. Bersch, D. Träger, L. Tang, J. Imbrock, Y. S. Kivshar, and C. Denz, "Anisotropic photonic lattices and discrete solitons in photorefractive media," Appl. Phys. B 86, 399-405 (2007).
[CrossRef]

Bishop, A. R.

P. G. Kevrekidis, D. J. Frantzeskakis, R. Carretero-González, B. A. Malomed, and A. R. Bishop "Discrete solitons and vortices on anisotropic lattices," Phys. Rev. E 72, 046613 (2005).
[CrossRef]

Cai, T.

Carmon, T.

O. Katz, T. Carmon, T. Schwartz, M. Segev, and D. N. Christodoulides, "Observation of elliptic incoherent spatial solitons," Opt. Lett. 29, 1248-1250 (2004).
[CrossRef] [PubMed]

J. W. Fleischer, T. Carmon, M. Segev, N. K. Efremidis, and D. N. Christodoulides. “Observation of discrete solitons in optically induced real time waveguide arrays,” Phys. Rev. Lett. 90, 023902 (2003).
[CrossRef] [PubMed]

Carretero-González, R.

P. G. Kevrekidis, D. J. Frantzeskakis, R. Carretero-González, B. A. Malomed, and A. R. Bishop "Discrete solitons and vortices on anisotropic lattices," Phys. Rev. E 72, 046613 (2005).
[CrossRef]

Chen, Z.

P. Zhang, J. Zhao, C. Lou, X. Tan, Y. Gao, Q. Liu, D. Yang, J. Xu, and Z. Chen, "Elliptical solitons in nonconventionally biased photorefractive crystals," Opt. Express 15, 536-544 (2007).
[CrossRef] [PubMed]

H. Martin, E. D. Eugenieva, Z. Chen, and D. N. Christodoulides, "Discrete solitons and soliton-induced dislocations in partially coherent photonic lattices," Phys. Rev. Lett. 92, 123902 (2004).
[CrossRef] [PubMed]

Christodoulides, D. N.

H. Martin, E. D. Eugenieva, Z. Chen, and D. N. Christodoulides, "Discrete solitons and soliton-induced dislocations in partially coherent photonic lattices," Phys. Rev. Lett. 92, 123902 (2004).
[CrossRef] [PubMed]

O. Katz, T. Carmon, T. Schwartz, M. Segev, and D. N. Christodoulides, "Observation of elliptic incoherent spatial solitons," Opt. Lett. 29, 1248-1250 (2004).
[CrossRef] [PubMed]

J. Hudock, N. K. Efremidis, and D. N. Christodoulides, "Anisotropic diffraction and elliptic discrete solitons in two-dimensional waveguide arrays," Opt. Lett. 29, 268-270 (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, 147-150 (2003).
[CrossRef] [PubMed]

For a review, see D. N. Christodoulides, F. Lederer, and Y. Silberberg, "Discretizing light behaviour in linear and nonlinear waveguide lattices," Nature 424, 817-823 (2003).
[CrossRef] [PubMed]

J. W. Fleischer, T. Carmon, M. Segev, N. K. Efremidis, and D. N. Christodoulides. “Observation of discrete solitons in optically induced real time waveguide arrays,” Phys. Rev. Lett. 90, 023902 (2003).
[CrossRef] [PubMed]

N. K. Efremidis, S. Sears, D. N. Christodoulides, J. W. Fleischer, and M. Segev, "Discrete solitons in photorefractive optically induced photonic lattices," Phys. Rev. E 66, 046602 (2002).
[CrossRef]

E. D. Eugenieva, D. N. Christodoulides, and M. Segev, "Elliptic incoherent solitons in saturable nonlinear media," Opt. Lett. 25, 972-974 (2000).
[CrossRef]

Denz, C.

B. Terhalle, A. S. Desyatnikov, C. Bersch, D. Träger, L. Tang, J. Imbrock, Y. S. Kivshar, and C. Denz, "Anisotropic photonic lattices and discrete solitons in photorefractive media," Appl. Phys. B 86, 399-405 (2007).
[CrossRef]

Desyatnikov, A. S.

B. Terhalle, A. S. Desyatnikov, C. Bersch, D. Träger, L. Tang, J. Imbrock, Y. S. Kivshar, and C. Denz, "Anisotropic photonic lattices and discrete solitons in photorefractive media," Appl. Phys. B 86, 399-405 (2007).
[CrossRef]

Dong, L.

Efremidis, N. K.

J. Hudock, N. K. Efremidis, and D. N. Christodoulides, "Anisotropic diffraction and elliptic discrete solitons in two-dimensional waveguide arrays," Opt. Lett. 29, 268-270 (2004).
[CrossRef] [PubMed]

J. W. Fleischer, T. Carmon, M. Segev, N. K. Efremidis, and D. N. Christodoulides. “Observation of discrete solitons in optically induced real time waveguide arrays,” Phys. Rev. Lett. 90, 023902 (2003).
[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, 147-150 (2003).
[CrossRef] [PubMed]

N. K. Efremidis, S. Sears, D. N. Christodoulides, J. W. Fleischer, and M. Segev, "Discrete solitons in photorefractive optically induced photonic lattices," Phys. Rev. E 66, 046602 (2002).
[CrossRef]

Eugenieva, E. D.

H. Martin, E. D. Eugenieva, Z. Chen, and D. N. Christodoulides, "Discrete solitons and soliton-induced dislocations in partially coherent photonic lattices," Phys. Rev. Lett. 92, 123902 (2004).
[CrossRef] [PubMed]

E. D. Eugenieva, D. N. Christodoulides, and M. Segev, "Elliptic incoherent solitons in saturable nonlinear media," Opt. Lett. 25, 972-974 (2000).
[CrossRef]

Fleischer, J. W.

J. W. Fleischer, T. Carmon, M. Segev, N. K. Efremidis, and D. N. Christodoulides. “Observation of discrete solitons in optically induced real time waveguide arrays,” Phys. Rev. Lett. 90, 023902 (2003).
[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, 147-150 (2003).
[CrossRef] [PubMed]

N. K. Efremidis, S. Sears, D. N. Christodoulides, J. W. Fleischer, and M. Segev, "Discrete solitons in photorefractive optically induced photonic lattices," Phys. Rev. E 66, 046602 (2002).
[CrossRef]

Frantzeskakis, D. J.

P. G. Kevrekidis, D. J. Frantzeskakis, R. Carretero-González, B. A. Malomed, and A. R. Bishop "Discrete solitons and vortices on anisotropic lattices," Phys. Rev. E 72, 046613 (2005).
[CrossRef]

Gao, Y.

Hudock, J.

Imbrock, J.

B. Terhalle, A. S. Desyatnikov, C. Bersch, D. Träger, L. Tang, J. Imbrock, Y. S. Kivshar, and C. Denz, "Anisotropic photonic lattices and discrete solitons in photorefractive media," Appl. Phys. B 86, 399-405 (2007).
[CrossRef]

Katz, O.

Kevrekidis, P. G.

P. G. Kevrekidis, D. J. Frantzeskakis, R. Carretero-González, B. A. Malomed, and A. R. Bishop "Discrete solitons and vortices on anisotropic lattices," Phys. Rev. E 72, 046613 (2005).
[CrossRef]

Kivshar, Y.

Kivshar, Y. S.

B. Terhalle, A. S. Desyatnikov, C. Bersch, D. Träger, L. Tang, J. Imbrock, Y. S. Kivshar, and C. Denz, "Anisotropic photonic lattices and discrete solitons in photorefractive media," Appl. Phys. B 86, 399-405 (2007).
[CrossRef]

Królikowski, W.

Lederer, F.

For a review, see D. N. Christodoulides, F. Lederer, and Y. Silberberg, "Discretizing light behaviour in linear and nonlinear waveguide lattices," Nature 424, 817-823 (2003).
[CrossRef] [PubMed]

Li, Y.

Liu, Q.

Lou, C.

Ma, Y.

Malomed, B. A.

P. G. Kevrekidis, D. J. Frantzeskakis, R. Carretero-González, B. A. Malomed, and A. R. Bishop "Discrete solitons and vortices on anisotropic lattices," Phys. Rev. E 72, 046613 (2005).
[CrossRef]

Mamaev, A. V.

A. A. Zozulya, D. Z. Anderson, A. V. Mamaev, and M. Saffman, "Self-focusing and soliton formation in media with anisotropic nonlocal material response," Europhys. Lett. 36, 419-424 (1996).
[CrossRef]

Martin, H.

H. Martin, E. D. Eugenieva, Z. Chen, and D. N. Christodoulides, "Discrete solitons and soliton-induced dislocations in partially coherent photonic lattices," Phys. Rev. Lett. 92, 123902 (2004).
[CrossRef] [PubMed]

Neshev, D.

Ostrovskaya, E.

Petviashvili, V. I.

V. I. Petviashvili, "Equation of an extraordinary soliton," Sov. J. Plasma Phys. 2, 257-258 (1976).

Saffman, M.

A. A. Zozulya, D. Z. Anderson, A. V. Mamaev, and M. Saffman, "Self-focusing and soliton formation in media with anisotropic nonlocal material response," Europhys. Lett. 36, 419-424 (1996).
[CrossRef]

Schwartz, T.

Sears, S.

N. K. Efremidis, S. Sears, D. N. Christodoulides, J. W. Fleischer, and M. Segev, "Discrete solitons in photorefractive optically induced photonic lattices," Phys. Rev. E 66, 046602 (2002).
[CrossRef]

Segev, M.

O. Katz, T. Carmon, T. Schwartz, M. Segev, and D. N. Christodoulides, "Observation of elliptic incoherent spatial solitons," Opt. Lett. 29, 1248-1250 (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, 147-150 (2003).
[CrossRef] [PubMed]

J. W. Fleischer, T. Carmon, M. Segev, N. K. Efremidis, and D. N. Christodoulides. “Observation of discrete solitons in optically induced real time waveguide arrays,” Phys. Rev. Lett. 90, 023902 (2003).
[CrossRef] [PubMed]

N. K. Efremidis, S. Sears, D. N. Christodoulides, J. W. Fleischer, and M. Segev, "Discrete solitons in photorefractive optically induced photonic lattices," Phys. Rev. E 66, 046602 (2002).
[CrossRef]

E. D. Eugenieva, D. N. Christodoulides, and M. Segev, "Elliptic incoherent solitons in saturable nonlinear media," Opt. Lett. 25, 972-974 (2000).
[CrossRef]

Silberberg, Y.

For a review, see D. N. Christodoulides, F. Lederer, and Y. Silberberg, "Discretizing light behaviour in linear and nonlinear waveguide lattices," Nature 424, 817-823 (2003).
[CrossRef] [PubMed]

Tan, X.

Tang, L.

B. Terhalle, A. S. Desyatnikov, C. Bersch, D. Träger, L. Tang, J. Imbrock, Y. S. Kivshar, and C. Denz, "Anisotropic photonic lattices and discrete solitons in photorefractive media," Appl. Phys. B 86, 399-405 (2007).
[CrossRef]

Terhalle, B.

B. Terhalle, A. S. Desyatnikov, C. Bersch, D. Träger, L. Tang, J. Imbrock, Y. S. Kivshar, and C. Denz, "Anisotropic photonic lattices and discrete solitons in photorefractive media," Appl. Phys. B 86, 399-405 (2007).
[CrossRef]

Träger, D.

B. Terhalle, A. S. Desyatnikov, C. Bersch, D. Träger, L. Tang, J. Imbrock, Y. S. Kivshar, and C. Denz, "Anisotropic photonic lattices and discrete solitons in photorefractive media," Appl. Phys. B 86, 399-405 (2007).
[CrossRef]

Wang, J.

Xu, H.

Xu, J.

Yang, D.

Ye, F.

Zhang, P.

Zhao, J.

Zozulya, A. A.

A. A. Zozulya, D. Z. Anderson, A. V. Mamaev, and M. Saffman, "Self-focusing and soliton formation in media with anisotropic nonlocal material response," Europhys. Lett. 36, 419-424 (1996).
[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, 1520-1531 (1995).
[CrossRef] [PubMed]

Appl. Opt. (1)

Appl. Phys. B (1)

B. Terhalle, A. S. Desyatnikov, C. Bersch, D. Träger, L. Tang, J. Imbrock, Y. S. Kivshar, and C. Denz, "Anisotropic photonic lattices and discrete solitons in photorefractive media," Appl. Phys. B 86, 399-405 (2007).
[CrossRef]

Chin. Opt. Lett. (1)

Europhys. Lett. (1)

A. A. Zozulya, D. Z. Anderson, A. V. Mamaev, and M. Saffman, "Self-focusing and soliton formation in media with anisotropic nonlocal material response," Europhys. Lett. 36, 419-424 (1996).
[CrossRef]

Nature (2)

For a review, see D. N. Christodoulides, F. Lederer, and Y. Silberberg, "Discretizing light behaviour in linear and nonlinear waveguide lattices," Nature 424, 817-823 (2003).
[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, 147-150 (2003).
[CrossRef] [PubMed]

Opt. Express (1)

Opt. Lett. (4)

Phys. Rev. A (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, 1520-1531 (1995).
[CrossRef] [PubMed]

Phys. Rev. E (2)

N. K. Efremidis, S. Sears, D. N. Christodoulides, J. W. Fleischer, and M. Segev, "Discrete solitons in photorefractive optically induced photonic lattices," Phys. Rev. E 66, 046602 (2002).
[CrossRef]

P. G. Kevrekidis, D. J. Frantzeskakis, R. Carretero-González, B. A. Malomed, and A. R. Bishop "Discrete solitons and vortices on anisotropic lattices," Phys. Rev. E 72, 046613 (2005).
[CrossRef]

Phys. Rev. Lett. (2)

H. Martin, E. D. Eugenieva, Z. Chen, and D. N. Christodoulides, "Discrete solitons and soliton-induced dislocations in partially coherent photonic lattices," Phys. Rev. Lett. 92, 123902 (2004).
[CrossRef] [PubMed]

J. W. Fleischer, T. Carmon, M. Segev, N. K. Efremidis, and D. N. Christodoulides. “Observation of discrete solitons in optically induced real time waveguide arrays,” Phys. Rev. Lett. 90, 023902 (2003).
[CrossRef] [PubMed]

Sov. J. Plasma Phys. (1)

V. I. Petviashvili, "Equation of an extraordinary soliton," Sov. J. Plasma Phys. 2, 257-258 (1976).

Other (1)

P. Zhang, S. Liu, J. Zhao, C. Lou, J. Xu, and Z. Chen, "Optically induced transition between discrete and gap solitons in a nonconventionally biased photorefractive crystal," to appear in Opt. Lett. (2008).
[CrossRef] [PubMed]

Supplementary Material (2)

» Media 1: GIF (732 KB)     
» Media 2: GIF (906 KB)     

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Figures (4)

Fig. 1.
Fig. 1.

Geometry of the relative orientation of the crystalline c-axis, bias field, and lattice beam.

Fig. 2.
Fig. 2.

Refractive index distributions of optically induced photonic lattices under different conditions, where in each figure the green and purple arrow indicate the directions of the crystalline c-axis and bias field, respectively, and the number in the upper left corner corresponds to the index modulation depth at E 0 = 1.

Fig. 3.
Fig. 3.

Numerical results for discrete diffraction and self-trapped states. (a)–(b) are the output patterns of the probe beam under linear (a) and nonlinear (b) propagation obtained by beam propagation method. Animations show the corresponding evolution dynamics. (c)–(d) show soliton solutions at different peak intensities obtained with iteration method. The columns from left to right are for the cases of θe = θc = π/4; θe = 3π/4, θc = π/4; θe = 5π/8, θc = π/8; and θe = π/2, θc = 0, respectively. [Media 1][Media 2]

Fig. 4.
Fig. 4.

Experimental observations of elliptical discrete solitons. Results in (a)–(c) correspond to the cases of θe = θc = π/4; θe = 3π/4, θc = π/4; and θe = 5π/8, θc = π/8, respectively, where the left (3D intensity plots) and middle (2D transverse patterns) columns are experimental results, and the right column is from numerical simulation for comparison. The top and bottom rows in (a)–(c) show the linear and nonlinear output beam patterns, respectively.

Equations (4)

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( z i 2 2 ) B ( r ) = i ( φ x cos θ c + φ y sin θ c ) B ( r )
2 φ + φ · ln ( 1 + I ) = E 0 [ ln ( 1 + I ) x cos θ e + ln ( 1 + I ) y sin θ e ]
I = V ( x , y ) + B ( r ) 2
( β 1 2 2 ) b ( x , y ) = ( φ x cos θ c + φ y sin θ c ) b ( x , y )

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