Abstract

We demonstrate self-trapping and rotation of higher-band dipole and quadruple-like gap solitons by single-site excitation in a two-dimensional square photonic lattice under self-focusing nonlinearity. Experimental results show that the second-band dipole gap solitons reside in the first photonic (Bragg reflection) gap, whereas the quadruple-like gap solitons are formed in an even higher photonic gap, resulting from modes of the third-band. Moreover, both dipole and quadruple-like gap solitons exhibit dynamical rotation around the lattice principle axes and the direction of rotation is changing periodically during propagation, provided that they are excited under appropriate initial conditions. In the latter case, the nonlinear rotation is accompanied by periodic transitions between quadruple and doubly-charged vortex states. Our numerical simulations find good agreement with the experimental observations.

© 2015 Optical Society of America

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References

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    [Crossref]
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  4. I. L. Garanovich, S. Longhi, A. A. Sukhorukov, and Y. S. Kivshar, “Light propagation and localization in modulated photonic lattices and waveguides,” Phys. Rep. 518(1-2), 1–79 (2012).
    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
  8. D. Neshev, E. Ostrovskaya, Y. Kivshar, and W. Krolikowski, “Spatial solitons in optically induced gratings,” Opt. Lett. 28(9), 710–712 (2003).
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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  19. S. Xia, D. Song, L. Tang, C. Lou, and Y. Li, “Self-trapping and oscillation of quadruple beams in high band gap of 2D photonic lattices,” Chin. Opt. Lett. 11(9), 090801 (2013).
    [Crossref]
  20. J. Yang, I. Makasyuk, A. Bezryadina, and Z. Chen, “Dipole and quadruple solitons in optically induced two-dimensional photonic lattices: theory and experiment,” Stud. Appl. Math. 113(4), 389–412 (2004).
    [Crossref]
  21. Z. Chen, A. Bezryadina, I. Makasyuk, and J. Yang, “Observation of two-dimensional lattice vector solitons,” Opt. Lett. 29(14), 1656–1658 (2004).
    [Crossref] [PubMed]
  22. D. Träger, R. Fischer, D. N. Neshev, A. A. Sukhorukov, C. Denz, W. Królikowski, and Y. S. Kivshar, “Nonlinear Bloch modes in two-dimensional photonic lattices,” Opt. Express 14(5), 1913–1923 (2006).
    [Crossref] [PubMed]
  23. A. Bezryadina, E. Eugenieva, and Z. Chen, “Self-trapping and flipping of double-charged vortices in optically induced photonic lattices,” Opt. Lett. 31(16), 2456–2458 (2006).
    [Crossref] [PubMed]
  24. E. Eugenieva, D. Song, A. Bezryadina, P. Zhang, Z. Chen, and N. B. Abraham, “Self-trapping and stabilization of doubly-charged optical vortices in two-dimensional photonic lattices,” J. Mod. Opt. 57(14–15), 1377–1387 (2010).
    [Crossref]

2013 (1)

2012 (2)

Z. Chen, M. Segev, and D. N. Christodoulides, “Optical spatial solitons: historical overview and recent advances,” Rep. Prog. Phys. 75(8), 086401 (2012).
[Crossref] [PubMed]

I. L. Garanovich, S. Longhi, A. A. Sukhorukov, and Y. S. Kivshar, “Light propagation and localization in modulated photonic lattices and waveguides,” Phys. Rep. 518(1-2), 1–79 (2012).
[Crossref]

2010 (2)

E. Eugenieva, D. Song, A. Bezryadina, P. Zhang, Z. Chen, and N. B. Abraham, “Self-trapping and stabilization of doubly-charged optical vortices in two-dimensional photonic lattices,” J. Mod. Opt. 57(14–15), 1377–1387 (2010).
[Crossref]

R. Dong, C. E. Rüter, D. Song, J. Xu, and D. Kip, “Formation of higher-band dark gap solitons in one dimensional waveguide arrays,” Opt. Express 18(26), 27493–27498 (2010).
[Crossref] [PubMed]

2008 (2)

D. Kip, C. E. Rüter, R. Dong, Z. Wang, and J. Xu, “Higher-band gap soliton formation in defocusing photonic lattices,” Opt. Lett. 33(18), 2056–2058 (2008).
[Crossref] [PubMed]

F. Lederer, G. I. Stegeman, D. N. Christodoulides, G. Assanto, M. Segev, and Y. Silberberg, “Discrete solitons in optics,” Phys. Rep. 463(1-3), 1–126 (2008).
[Crossref]

2007 (2)

C. Lou, X. Wang, J. Xu, Z. Chen, and J. Yang, “Nonlinear spectrum reshaping and gap-soliton-train trapping in optically induced photonic structures,” Phys. Rev. Lett. 98(21), 213903 (2007).
[Crossref] [PubMed]

Z. Shi and J. Yang, “Solitary waves bifurcated from Bloch-band edges in two-dimensional periodic media,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 75(5 Pt 2), 056602 (2007).
[Crossref] [PubMed]

2006 (2)

2005 (2)

G. Bartal, O. Manela, O. Cohen, J. W. Fleischer, and M. Segev, “Observation of second-band vortex solitons in 2D photonic lattices,” Phys. Rev. Lett. 95(5), 053904 (2005).
[Crossref] [PubMed]

F. Chen, M. Stepić, C. E. Rüter, D. Runde, D. Kip, V. Shandarov, O. Manela, and M. Segev, “Discrete diffraction and spatial gap solitons in photovoltaic LiNbO3 waveguide arrays,” Opt. Express 13(11), 4314–4324 (2005).
[Crossref] [PubMed]

2004 (5)

Z. Chen, A. Bezryadina, I. Makasyuk, and J. Yang, “Observation of two-dimensional lattice vector solitons,” Opt. Lett. 29(14), 1656–1658 (2004).
[Crossref] [PubMed]

J. Yang, I. Makasyuk, A. Bezryadina, and Z. Chen, “Dipole and quadruple solitons in optically induced two-dimensional photonic lattices: theory and experiment,” Stud. Appl. Math. 113(4), 389–412 (2004).
[Crossref]

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(12), 123902 (2004).
[Crossref] [PubMed]

D. Mandelik, R. Morandotti, J. S. Aitchison, and Y. Silberberg, “Gap solitons in waveguide arrays,” Phys. Rev. Lett. 92(9), 093904 (2004).
[Crossref] [PubMed]

D. Neshev, A. A. Sukhorukov, B. Hanna, W. Krolikowski, and Y. S. Kivshar, “Controlled generation and steering of spatial gap solitons,” Phys. Rev. Lett. 93(8), 083905 (2004).
[Crossref] [PubMed]

2003 (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(6928), 147–150 (2003).
[Crossref] [PubMed]

D. N. Christodoulides, F. Lederer, and Y. Silberberg, “Discretizing light behaviour in linear and nonlinear waveguide lattices,” Nature 424(6950), 817–823 (2003).
[Crossref] [PubMed]

D. Neshev, E. Ostrovskaya, Y. Kivshar, and W. Krolikowski, “Spatial solitons in optically induced gratings,” Opt. Lett. 28(9), 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 Stat. Nonlin. Soft Matter Phys. 66(4), 046602 (2002).
[Crossref] [PubMed]

1998 (1)

H. S. Eisenberg, Y. Silberberg, R. Morandotti, A. R. Boyd, and J. S. Aitchison, “Discrete spatial optical solitons in waveguide arrays,” Phys. Rev. Lett. 81(16), 3383–3386 (1998).
[Crossref]

Abraham, N. B.

E. Eugenieva, D. Song, A. Bezryadina, P. Zhang, Z. Chen, and N. B. Abraham, “Self-trapping and stabilization of doubly-charged optical vortices in two-dimensional photonic lattices,” J. Mod. Opt. 57(14–15), 1377–1387 (2010).
[Crossref]

Aitchison, J. S.

D. Mandelik, R. Morandotti, J. S. Aitchison, and Y. Silberberg, “Gap solitons in waveguide arrays,” Phys. Rev. Lett. 92(9), 093904 (2004).
[Crossref] [PubMed]

H. S. Eisenberg, Y. Silberberg, R. Morandotti, A. R. Boyd, and J. S. Aitchison, “Discrete spatial optical solitons in waveguide arrays,” Phys. Rev. Lett. 81(16), 3383–3386 (1998).
[Crossref]

Assanto, G.

F. Lederer, G. I. Stegeman, D. N. Christodoulides, G. Assanto, M. Segev, and Y. Silberberg, “Discrete solitons in optics,” Phys. Rep. 463(1-3), 1–126 (2008).
[Crossref]

Bartal, G.

G. Bartal, O. Manela, O. Cohen, J. W. Fleischer, and M. Segev, “Observation of second-band vortex solitons in 2D photonic lattices,” Phys. Rev. Lett. 95(5), 053904 (2005).
[Crossref] [PubMed]

Bezryadina, A.

E. Eugenieva, D. Song, A. Bezryadina, P. Zhang, Z. Chen, and N. B. Abraham, “Self-trapping and stabilization of doubly-charged optical vortices in two-dimensional photonic lattices,” J. Mod. Opt. 57(14–15), 1377–1387 (2010).
[Crossref]

A. Bezryadina, E. Eugenieva, and Z. Chen, “Self-trapping and flipping of double-charged vortices in optically induced photonic lattices,” Opt. Lett. 31(16), 2456–2458 (2006).
[Crossref] [PubMed]

Z. Chen, A. Bezryadina, I. Makasyuk, and J. Yang, “Observation of two-dimensional lattice vector solitons,” Opt. Lett. 29(14), 1656–1658 (2004).
[Crossref] [PubMed]

J. Yang, I. Makasyuk, A. Bezryadina, and Z. Chen, “Dipole and quadruple solitons in optically induced two-dimensional photonic lattices: theory and experiment,” Stud. Appl. Math. 113(4), 389–412 (2004).
[Crossref]

Boyd, A. R.

H. S. Eisenberg, Y. Silberberg, R. Morandotti, A. R. Boyd, and J. S. Aitchison, “Discrete spatial optical solitons in waveguide arrays,” Phys. Rev. Lett. 81(16), 3383–3386 (1998).
[Crossref]

Chen, F.

Chen, Z.

Z. Chen, M. Segev, and D. N. Christodoulides, “Optical spatial solitons: historical overview and recent advances,” Rep. Prog. Phys. 75(8), 086401 (2012).
[Crossref] [PubMed]

E. Eugenieva, D. Song, A. Bezryadina, P. Zhang, Z. Chen, and N. B. Abraham, “Self-trapping and stabilization of doubly-charged optical vortices in two-dimensional photonic lattices,” J. Mod. Opt. 57(14–15), 1377–1387 (2010).
[Crossref]

C. Lou, X. Wang, J. Xu, Z. Chen, and J. Yang, “Nonlinear spectrum reshaping and gap-soliton-train trapping in optically induced photonic structures,” Phys. Rev. Lett. 98(21), 213903 (2007).
[Crossref] [PubMed]

A. Bezryadina, E. Eugenieva, and Z. Chen, “Self-trapping and flipping of double-charged vortices in optically induced photonic lattices,” Opt. Lett. 31(16), 2456–2458 (2006).
[Crossref] [PubMed]

Z. Chen, A. Bezryadina, I. Makasyuk, and J. Yang, “Observation of two-dimensional lattice vector solitons,” Opt. Lett. 29(14), 1656–1658 (2004).
[Crossref] [PubMed]

J. Yang, I. Makasyuk, A. Bezryadina, and Z. Chen, “Dipole and quadruple solitons in optically induced two-dimensional photonic lattices: theory and experiment,” Stud. Appl. Math. 113(4), 389–412 (2004).
[Crossref]

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(12), 123902 (2004).
[Crossref] [PubMed]

Christodoulides, D. N.

Z. Chen, M. Segev, and D. N. Christodoulides, “Optical spatial solitons: historical overview and recent advances,” Rep. Prog. Phys. 75(8), 086401 (2012).
[Crossref] [PubMed]

F. Lederer, G. I. Stegeman, D. N. Christodoulides, G. Assanto, M. Segev, and Y. Silberberg, “Discrete solitons in optics,” Phys. Rep. 463(1-3), 1–126 (2008).
[Crossref]

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(12), 123902 (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(6928), 147–150 (2003).
[Crossref] [PubMed]

D. N. Christodoulides, F. Lederer, and Y. Silberberg, “Discretizing light behaviour in linear and nonlinear waveguide lattices,” Nature 424(6950), 817–823 (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 Stat. Nonlin. Soft Matter Phys. 66(4), 046602 (2002).
[Crossref] [PubMed]

Cohen, O.

G. Bartal, O. Manela, O. Cohen, J. W. Fleischer, and M. Segev, “Observation of second-band vortex solitons in 2D photonic lattices,” Phys. Rev. Lett. 95(5), 053904 (2005).
[Crossref] [PubMed]

Denz, C.

Dong, R.

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(6928), 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 Stat. Nonlin. Soft Matter Phys. 66(4), 046602 (2002).
[Crossref] [PubMed]

Eisenberg, H. S.

H. S. Eisenberg, Y. Silberberg, R. Morandotti, A. R. Boyd, and J. S. Aitchison, “Discrete spatial optical solitons in waveguide arrays,” Phys. Rev. Lett. 81(16), 3383–3386 (1998).
[Crossref]

Eugenieva, E.

E. Eugenieva, D. Song, A. Bezryadina, P. Zhang, Z. Chen, and N. B. Abraham, “Self-trapping and stabilization of doubly-charged optical vortices in two-dimensional photonic lattices,” J. Mod. Opt. 57(14–15), 1377–1387 (2010).
[Crossref]

A. Bezryadina, E. Eugenieva, and Z. Chen, “Self-trapping and flipping of double-charged vortices in optically induced photonic lattices,” Opt. Lett. 31(16), 2456–2458 (2006).
[Crossref] [PubMed]

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(12), 123902 (2004).
[Crossref] [PubMed]

Fischer, R.

Fleischer, J. W.

G. Bartal, O. Manela, O. Cohen, J. W. Fleischer, and M. Segev, “Observation of second-band vortex solitons in 2D photonic lattices,” Phys. Rev. Lett. 95(5), 053904 (2005).
[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(6928), 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 Stat. Nonlin. Soft Matter Phys. 66(4), 046602 (2002).
[Crossref] [PubMed]

Garanovich, I. L.

I. L. Garanovich, S. Longhi, A. A. Sukhorukov, and Y. S. Kivshar, “Light propagation and localization in modulated photonic lattices and waveguides,” Phys. Rep. 518(1-2), 1–79 (2012).
[Crossref]

Hanna, B.

D. Neshev, A. A. Sukhorukov, B. Hanna, W. Krolikowski, and Y. S. Kivshar, “Controlled generation and steering of spatial gap solitons,” Phys. Rev. Lett. 93(8), 083905 (2004).
[Crossref] [PubMed]

Kip, D.

Kivshar, Y.

Kivshar, Y. S.

I. L. Garanovich, S. Longhi, A. A. Sukhorukov, and Y. S. Kivshar, “Light propagation and localization in modulated photonic lattices and waveguides,” Phys. Rep. 518(1-2), 1–79 (2012).
[Crossref]

D. Träger, R. Fischer, D. N. Neshev, A. A. Sukhorukov, C. Denz, W. Królikowski, and Y. S. Kivshar, “Nonlinear Bloch modes in two-dimensional photonic lattices,” Opt. Express 14(5), 1913–1923 (2006).
[Crossref] [PubMed]

D. Neshev, A. A. Sukhorukov, B. Hanna, W. Krolikowski, and Y. S. Kivshar, “Controlled generation and steering of spatial gap solitons,” Phys. Rev. Lett. 93(8), 083905 (2004).
[Crossref] [PubMed]

Krolikowski, W.

D. Neshev, A. A. Sukhorukov, B. Hanna, W. Krolikowski, and Y. S. Kivshar, “Controlled generation and steering of spatial gap solitons,” Phys. Rev. Lett. 93(8), 083905 (2004).
[Crossref] [PubMed]

D. Neshev, E. Ostrovskaya, Y. Kivshar, and W. Krolikowski, “Spatial solitons in optically induced gratings,” Opt. Lett. 28(9), 710–712 (2003).
[Crossref] [PubMed]

Królikowski, W.

Lederer, F.

F. Lederer, G. I. Stegeman, D. N. Christodoulides, G. Assanto, M. Segev, and Y. Silberberg, “Discrete solitons in optics,” Phys. Rep. 463(1-3), 1–126 (2008).
[Crossref]

D. N. Christodoulides, F. Lederer, and Y. Silberberg, “Discretizing light behaviour in linear and nonlinear waveguide lattices,” Nature 424(6950), 817–823 (2003).
[Crossref] [PubMed]

Li, Y.

Longhi, S.

I. L. Garanovich, S. Longhi, A. A. Sukhorukov, and Y. S. Kivshar, “Light propagation and localization in modulated photonic lattices and waveguides,” Phys. Rep. 518(1-2), 1–79 (2012).
[Crossref]

Lou, C.

S. Xia, D. Song, L. Tang, C. Lou, and Y. Li, “Self-trapping and oscillation of quadruple beams in high band gap of 2D photonic lattices,” Chin. Opt. Lett. 11(9), 090801 (2013).
[Crossref]

C. Lou, X. Wang, J. Xu, Z. Chen, and J. Yang, “Nonlinear spectrum reshaping and gap-soliton-train trapping in optically induced photonic structures,” Phys. Rev. Lett. 98(21), 213903 (2007).
[Crossref] [PubMed]

Makasyuk, I.

J. Yang, I. Makasyuk, A. Bezryadina, and Z. Chen, “Dipole and quadruple solitons in optically induced two-dimensional photonic lattices: theory and experiment,” Stud. Appl. Math. 113(4), 389–412 (2004).
[Crossref]

Z. Chen, A. Bezryadina, I. Makasyuk, and J. Yang, “Observation of two-dimensional lattice vector solitons,” Opt. Lett. 29(14), 1656–1658 (2004).
[Crossref] [PubMed]

Mandelik, D.

D. Mandelik, R. Morandotti, J. S. Aitchison, and Y. Silberberg, “Gap solitons in waveguide arrays,” Phys. Rev. Lett. 92(9), 093904 (2004).
[Crossref] [PubMed]

Manela, O.

G. Bartal, O. Manela, O. Cohen, J. W. Fleischer, and M. Segev, “Observation of second-band vortex solitons in 2D photonic lattices,” Phys. Rev. Lett. 95(5), 053904 (2005).
[Crossref] [PubMed]

F. Chen, M. Stepić, C. E. Rüter, D. Runde, D. Kip, V. Shandarov, O. Manela, and M. Segev, “Discrete diffraction and spatial gap solitons in photovoltaic LiNbO3 waveguide arrays,” Opt. Express 13(11), 4314–4324 (2005).
[Crossref] [PubMed]

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(12), 123902 (2004).
[Crossref] [PubMed]

Morandotti, R.

D. Mandelik, R. Morandotti, J. S. Aitchison, and Y. Silberberg, “Gap solitons in waveguide arrays,” Phys. Rev. Lett. 92(9), 093904 (2004).
[Crossref] [PubMed]

H. S. Eisenberg, Y. Silberberg, R. Morandotti, A. R. Boyd, and J. S. Aitchison, “Discrete spatial optical solitons in waveguide arrays,” Phys. Rev. Lett. 81(16), 3383–3386 (1998).
[Crossref]

Neshev, D.

D. Neshev, A. A. Sukhorukov, B. Hanna, W. Krolikowski, and Y. S. Kivshar, “Controlled generation and steering of spatial gap solitons,” Phys. Rev. Lett. 93(8), 083905 (2004).
[Crossref] [PubMed]

D. Neshev, E. Ostrovskaya, Y. Kivshar, and W. Krolikowski, “Spatial solitons in optically induced gratings,” Opt. Lett. 28(9), 710–712 (2003).
[Crossref] [PubMed]

Neshev, D. N.

Ostrovskaya, E.

Runde, D.

Rüter, C. E.

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 Stat. Nonlin. Soft Matter Phys. 66(4), 046602 (2002).
[Crossref] [PubMed]

Segev, M.

Z. Chen, M. Segev, and D. N. Christodoulides, “Optical spatial solitons: historical overview and recent advances,” Rep. Prog. Phys. 75(8), 086401 (2012).
[Crossref] [PubMed]

F. Lederer, G. I. Stegeman, D. N. Christodoulides, G. Assanto, M. Segev, and Y. Silberberg, “Discrete solitons in optics,” Phys. Rep. 463(1-3), 1–126 (2008).
[Crossref]

G. Bartal, O. Manela, O. Cohen, J. W. Fleischer, and M. Segev, “Observation of second-band vortex solitons in 2D photonic lattices,” Phys. Rev. Lett. 95(5), 053904 (2005).
[Crossref] [PubMed]

F. Chen, M. Stepić, C. E. Rüter, D. Runde, D. Kip, V. Shandarov, O. Manela, and M. Segev, “Discrete diffraction and spatial gap solitons in photovoltaic LiNbO3 waveguide arrays,” Opt. Express 13(11), 4314–4324 (2005).
[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(6928), 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 Stat. Nonlin. Soft Matter Phys. 66(4), 046602 (2002).
[Crossref] [PubMed]

Shandarov, V.

Shi, Z.

Z. Shi and J. Yang, “Solitary waves bifurcated from Bloch-band edges in two-dimensional periodic media,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 75(5 Pt 2), 056602 (2007).
[Crossref] [PubMed]

Silberberg, Y.

F. Lederer, G. I. Stegeman, D. N. Christodoulides, G. Assanto, M. Segev, and Y. Silberberg, “Discrete solitons in optics,” Phys. Rep. 463(1-3), 1–126 (2008).
[Crossref]

D. Mandelik, R. Morandotti, J. S. Aitchison, and Y. Silberberg, “Gap solitons in waveguide arrays,” Phys. Rev. Lett. 92(9), 093904 (2004).
[Crossref] [PubMed]

D. N. Christodoulides, F. Lederer, and Y. Silberberg, “Discretizing light behaviour in linear and nonlinear waveguide lattices,” Nature 424(6950), 817–823 (2003).
[Crossref] [PubMed]

H. S. Eisenberg, Y. Silberberg, R. Morandotti, A. R. Boyd, and J. S. Aitchison, “Discrete spatial optical solitons in waveguide arrays,” Phys. Rev. Lett. 81(16), 3383–3386 (1998).
[Crossref]

Song, D.

Stegeman, G. I.

F. Lederer, G. I. Stegeman, D. N. Christodoulides, G. Assanto, M. Segev, and Y. Silberberg, “Discrete solitons in optics,” Phys. Rep. 463(1-3), 1–126 (2008).
[Crossref]

Stepic, M.

Sukhorukov, A. A.

I. L. Garanovich, S. Longhi, A. A. Sukhorukov, and Y. S. Kivshar, “Light propagation and localization in modulated photonic lattices and waveguides,” Phys. Rep. 518(1-2), 1–79 (2012).
[Crossref]

D. Träger, R. Fischer, D. N. Neshev, A. A. Sukhorukov, C. Denz, W. Królikowski, and Y. S. Kivshar, “Nonlinear Bloch modes in two-dimensional photonic lattices,” Opt. Express 14(5), 1913–1923 (2006).
[Crossref] [PubMed]

D. Neshev, A. A. Sukhorukov, B. Hanna, W. Krolikowski, and Y. S. Kivshar, “Controlled generation and steering of spatial gap solitons,” Phys. Rev. Lett. 93(8), 083905 (2004).
[Crossref] [PubMed]

Tang, L.

Träger, D.

Wang, X.

C. Lou, X. Wang, J. Xu, Z. Chen, and J. Yang, “Nonlinear spectrum reshaping and gap-soliton-train trapping in optically induced photonic structures,” Phys. Rev. Lett. 98(21), 213903 (2007).
[Crossref] [PubMed]

Wang, Z.

Xia, S.

Xu, J.

Yang, J.

Z. Shi and J. Yang, “Solitary waves bifurcated from Bloch-band edges in two-dimensional periodic media,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 75(5 Pt 2), 056602 (2007).
[Crossref] [PubMed]

C. Lou, X. Wang, J. Xu, Z. Chen, and J. Yang, “Nonlinear spectrum reshaping and gap-soliton-train trapping in optically induced photonic structures,” Phys. Rev. Lett. 98(21), 213903 (2007).
[Crossref] [PubMed]

J. Yang, I. Makasyuk, A. Bezryadina, and Z. Chen, “Dipole and quadruple solitons in optically induced two-dimensional photonic lattices: theory and experiment,” Stud. Appl. Math. 113(4), 389–412 (2004).
[Crossref]

Z. Chen, A. Bezryadina, I. Makasyuk, and J. Yang, “Observation of two-dimensional lattice vector solitons,” Opt. Lett. 29(14), 1656–1658 (2004).
[Crossref] [PubMed]

Zhang, P.

E. Eugenieva, D. Song, A. Bezryadina, P. Zhang, Z. Chen, and N. B. Abraham, “Self-trapping and stabilization of doubly-charged optical vortices in two-dimensional photonic lattices,” J. Mod. Opt. 57(14–15), 1377–1387 (2010).
[Crossref]

Chin. Opt. Lett. (1)

J. Mod. Opt. (1)

E. Eugenieva, D. Song, A. Bezryadina, P. Zhang, Z. Chen, and N. B. Abraham, “Self-trapping and stabilization of doubly-charged optical vortices in two-dimensional photonic lattices,” J. Mod. Opt. 57(14–15), 1377–1387 (2010).
[Crossref]

Nature (2)

D. N. Christodoulides, F. Lederer, and Y. Silberberg, “Discretizing light behaviour in linear and nonlinear waveguide lattices,” Nature 424(6950), 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(6928), 147–150 (2003).
[Crossref] [PubMed]

Opt. Express (3)

Opt. Lett. (4)

Phys. Rep. (2)

F. Lederer, G. I. Stegeman, D. N. Christodoulides, G. Assanto, M. Segev, and Y. Silberberg, “Discrete solitons in optics,” Phys. Rep. 463(1-3), 1–126 (2008).
[Crossref]

I. L. Garanovich, S. Longhi, A. A. Sukhorukov, and Y. S. Kivshar, “Light propagation and localization in modulated photonic lattices and waveguides,” Phys. Rep. 518(1-2), 1–79 (2012).
[Crossref]

Phys. Rev. E Stat. Nonlin. Soft Matter Phys. (2)

Z. Shi and J. Yang, “Solitary waves bifurcated from Bloch-band edges in two-dimensional periodic media,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 75(5 Pt 2), 056602 (2007).
[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 Stat. Nonlin. Soft Matter Phys. 66(4), 046602 (2002).
[Crossref] [PubMed]

Phys. Rev. Lett. (6)

H. S. Eisenberg, Y. Silberberg, R. Morandotti, A. R. Boyd, and J. S. Aitchison, “Discrete spatial optical solitons in waveguide arrays,” Phys. Rev. Lett. 81(16), 3383–3386 (1998).
[Crossref]

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(12), 123902 (2004).
[Crossref] [PubMed]

D. Mandelik, R. Morandotti, J. S. Aitchison, and Y. Silberberg, “Gap solitons in waveguide arrays,” Phys. Rev. Lett. 92(9), 093904 (2004).
[Crossref] [PubMed]

D. Neshev, A. A. Sukhorukov, B. Hanna, W. Krolikowski, and Y. S. Kivshar, “Controlled generation and steering of spatial gap solitons,” Phys. Rev. Lett. 93(8), 083905 (2004).
[Crossref] [PubMed]

G. Bartal, O. Manela, O. Cohen, J. W. Fleischer, and M. Segev, “Observation of second-band vortex solitons in 2D photonic lattices,” Phys. Rev. Lett. 95(5), 053904 (2005).
[Crossref] [PubMed]

C. Lou, X. Wang, J. Xu, Z. Chen, and J. Yang, “Nonlinear spectrum reshaping and gap-soliton-train trapping in optically induced photonic structures,” Phys. Rev. Lett. 98(21), 213903 (2007).
[Crossref] [PubMed]

Rep. Prog. Phys. (1)

Z. Chen, M. Segev, and D. N. Christodoulides, “Optical spatial solitons: historical overview and recent advances,” Rep. Prog. Phys. 75(8), 086401 (2012).
[Crossref] [PubMed]

Stud. Appl. Math. (1)

J. Yang, I. Makasyuk, A. Bezryadina, and Z. Chen, “Dipole and quadruple solitons in optically induced two-dimensional photonic lattices: theory and experiment,” Stud. Appl. Math. 113(4), 389–412 (2004).
[Crossref]

Other (1)

X. Wang, L. Daniel, Z. Chen, J. Wang, and J. Yang, “Nonlinear dipole rotation/oscillation in anisotropic lattices,” in Frontiers in Optics 2008/Laser Science XXIV/Plasmonics and Metamaterials/Optical Fabrication and Testing, OSA Technical Digest (CD) (Optical Society of America, 2008), paper FThD5.

Supplementary Material (2)

» Media 1: MP4 (805 KB)     
» Media 2: MP4 (1048 KB)     

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Figures (7)

Fig. 1
Fig. 1 Experimental setup: (P)BS, (polarizing) beam splitter; ID, iris diaphragm; M, mirror; SBN, strontium barium niobate crystal; SLM, phase-only spatial light modulator; AM, amplitude mask; PM, phase masks displayed in SLM to generate out-of phase dipole (left) and quadruple (right) beams. Red arrows 1, 2, 3 indicate the paths of the lattice-inducing beam, the probe beam and the reference beam, respectively.
Fig. 2
Fig. 2 Experimental (top) and numerical (bottom) results of self-trapping of dipole gap solitons. (a1), (b1) input dipole beams; (a2), (b2) linear diffractions; (a3), (b3) nonlinear outputs; and (a4), (b4) k-space spectra of (a3), (b3). Inset in (a1) shows lattice pattern with circles marking the dipole input position. Inset in (a3) shows interferogram of the corresponding nonlinear output. White dashed squares in (a4), (b4) represent the first Brillouin Zone of the square lattice.
Fig. 3
Fig. 3 Experimental results of dipole gap soliton rotation. (a), (c) input dipole beams with different orientations; (b), (d) nonlinear output of dipole gap solitons. The long thin dashed lines mark the horizontal direction, while the short thick lines illustrate the dipole orientation.
Fig. 4
Fig. 4 Simulation results of dipole soliton rotation (Media 1). (a) input dipole beam with a 10° initial angle relative to the horizontal direction; (b), (c) nonlinear output patterns of localized dipole states taken when the direction of rotation starts to reverse.
Fig. 5
Fig. 5 Experimental (top row) and numerical (bottom row) results showing the formation of third-band quadruple-like gap soliton. Shown are (a) input quadruple beam; (b) linear diffraction; (c) nonlinear output; and (d), (e) corresponding interferogram and nonlinear Fourier spectrum. The dashed and solid white squares in (e) mark the 1st and 2nd BZ, respectively. (d) is zoomed-in with respected to (c) for better visualization. Inset in (a) shows the lattice pattern with circles marking the quadruple input position.
Fig. 6
Fig. 6 Experimental results showing rotation of nonlinear localized quadruple-like gap solitons. (a), (c) the input quadruple beams with an ± 5° initial angles relative to the lattice principle axes; and (b), (d) their corresponding nonlinear outputs. The long thin dashed lines mark the direction of lattices principle axes, while the short thick lines illustrate the quadruple orientation.
Fig. 7
Fig. 7 Numerical results showing self-rotation of higher-band quadruple-like lattice soliton (Media 2). Top row: (a) input quadruple beam superimposed with the lattice pattern. (b) side-view of beam propagation to z = 180mm. Middle row: (c)-(f) nonlinear output intensities corresponding to the locations of white dashed lines in (b). From (c) to (f), z = 96mm, 121mm, 145mm, 169mm. Bottom row: corresponding interferograms of the outputs. In all figures, the inset shows the phase structure where the blue color corresponds to zero phase, the red color corresponds to π phase.

Equations (1)

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i z ψ(x,y,z)+ 1 2k 2 ψ(x,y,z)+ k n e Δ n e ψ(x,y,z)=0.

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