Abstract

We report the existence and stability of solitons in kagome optical lattices with a defect in photorefractive crystal under focusing saturable nonlinearity. For different types of defects, solitons will exist in different gaps. For a positive defect, the solitons only exist in the semi-infinite gap and only stably exist in the low power region. For a negative defect, the solitons exist both in the semi-infinite gap and the first gap. With an increasing of the negative defect depth, the stable region in the semi-infinite will be narrowed, while solitons will be firstly unstable in the high power region of the first gap, and finally solitons will be not stable in the whole first gap.

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  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(6928), 147–150 (2003).
    [CrossRef] [PubMed]
  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]
  3. X. Wang, A. Bezryadina, Z. Chen, K. G. Makris, D. N. Christodoulides, and G. I. Stegeman, “Observation of two-dimensional surface solitons,” Phys. Rev. Lett. 98(12), 123903 (2007).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  5. Z. Chen and K. McCarthy, “Spatial soliton pixels from partially incoherent light,” Opt. Lett. 27(22), 2019–2021 (2002).
    [CrossRef]
  6. T. J. Alexander, A. S. Desyatnikov, and Y. S. Kivshar, “Multivortex solitons in triangular photonic lattices,” Opt. Lett. 32(10), 1293–1295 (2007).
    [CrossRef] [PubMed]
  7. Y. V. Kartashov, B. A. Malomed, V. A. Vysloukh, and L. Torner, “Gap solitons on a ring,” Opt. Lett. 33(24), 2949–2951 (2008).
    [CrossRef] [PubMed]
  8. Z. H. Musslimani and J. Yang, “Self-trapping of light in a two-dimensional photonic lattice,” J. Opt. Soc. Am. B 21(5), 973–981 (2004).
    [CrossRef]
  9. D. N. Neshev, T. J. Alexander, E. A. Ostrovskaya, Y. S. Kivshar, H. Martin, I. Makasyuk, and Z. Chen, “Observation of discrete vortex solitons in optically induced photonic lattices,” Phys. Rev. Lett. 92(12), 123903 (2004).
    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
  12. J. Wang and J. Yang, “Families of vortex solitons in periodic media,” Phys. Rev. A 77(3), 033834 (2008).
    [CrossRef]
  13. Z. Shi, J. Wang, Z. Chen, and J. Yang, “Linear instability of two-dimensional low-amplitude gap solitons near band edges in periodic media,” Phys. Rev. A 78(6), 063812 (2008).
    [CrossRef]
  14. E. A. Ostrovskaya and Y. S. Kivshar, “Photonic crystals for matter waves: Bose-Einstein condensates in optical lattices,” Opt. Express 12(1), 19–29 (2004).
    [CrossRef] [PubMed]
  15. J. Yang, I. Makasyuk, A. Bezryadina, and Z. Chen, “Dipole and Quadrupole Solitons in Optically Induced Two-Dimensional Photonic Lattices: Theory and Experiment,” Stud. Appl. Math. 113(4), 389–412 (2004).
    [CrossRef]
  16. J. Yang and T. I. Lakoba, “Universally-Convergent Squared-Operator Iteration Methods for Solitary Wave in General Nonlinear Wave Equation,” Stud. Appl. Math. 118(2), 153–197 (2007).
    [CrossRef]
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    [CrossRef] [PubMed]
  19. J. Wang, J. Yang, and Z. Chen, “Two-dimensional defect modes in optically induced photonic lattices,” Phys. Rev. A 76(1), 013828 (2007).
    [CrossRef]
  20. J. Yang, “Iteration methods for stability spectra of solitary waves,” J. Comput. Phys. 227(14), 6862–6876 (2008).
    [CrossRef]
  21. J. Yang and Z. Chen, “Defect solitons in photonic lattices,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 73(2), 026609 (2006).
    [CrossRef] [PubMed]

2010 (1)

2009 (2)

2008 (5)

J. Wang and J. Yang, “Families of vortex solitons in periodic media,” Phys. Rev. A 77(3), 033834 (2008).
[CrossRef]

Z. Shi, J. Wang, Z. Chen, and J. Yang, “Linear instability of two-dimensional low-amplitude gap solitons near band edges in periodic media,” Phys. Rev. A 78(6), 063812 (2008).
[CrossRef]

J. Yang, “Iteration methods for stability spectra of solitary waves,” J. Comput. Phys. 227(14), 6862–6876 (2008).
[CrossRef]

K. J. H. Law, H. Susanto, and P. G. Kevrekidis, “Solitons and vortices in honeycomb defocusing photonic lattices,” Phys. Rev. A 78(3), 033802 (2008).
[CrossRef]

Y. V. Kartashov, B. A. Malomed, V. A. Vysloukh, and L. Torner, “Gap solitons on a ring,” Opt. Lett. 33(24), 2949–2951 (2008).
[CrossRef] [PubMed]

2007 (5)

T. J. Alexander, A. S. Desyatnikov, and Y. S. Kivshar, “Multivortex solitons in triangular photonic lattices,” Opt. Lett. 32(10), 1293–1295 (2007).
[CrossRef] [PubMed]

J. Yang and T. I. Lakoba, “Universally-Convergent Squared-Operator Iteration Methods for Solitary Wave in General Nonlinear Wave Equation,” Stud. Appl. Math. 118(2), 153–197 (2007).
[CrossRef]

J. Wang, J. Yang, and Z. Chen, “Two-dimensional defect modes in optically induced photonic lattices,” Phys. Rev. A 76(1), 013828 (2007).
[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]

X. Wang, A. Bezryadina, Z. Chen, K. G. Makris, D. N. Christodoulides, and G. I. Stegeman, “Observation of two-dimensional surface solitons,” Phys. Rev. Lett. 98(12), 123903 (2007).
[CrossRef] [PubMed]

2006 (1)

J. Yang and Z. Chen, “Defect solitons in photonic lattices,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 73(2), 026609 (2006).
[CrossRef] [PubMed]

2004 (4)

E. A. Ostrovskaya and Y. S. Kivshar, “Photonic crystals for matter waves: Bose-Einstein condensates in optical lattices,” Opt. Express 12(1), 19–29 (2004).
[CrossRef] [PubMed]

Z. H. Musslimani and J. Yang, “Self-trapping of light in a two-dimensional photonic lattice,” J. Opt. Soc. Am. B 21(5), 973–981 (2004).
[CrossRef]

D. N. Neshev, T. J. Alexander, E. A. Ostrovskaya, Y. S. Kivshar, H. Martin, I. Makasyuk, and Z. Chen, “Observation of discrete vortex solitons in optically induced photonic lattices,” Phys. Rev. Lett. 92(12), 123903 (2004).
[CrossRef] [PubMed]

J. Yang, I. Makasyuk, A. Bezryadina, and Z. Chen, “Dipole and Quadrupole Solitons in Optically Induced Two-Dimensional Photonic Lattices: Theory and Experiment,” Stud. Appl. Math. 113(4), 389–412 (2004).
[CrossRef]

2003 (2)

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, J. Hudock, D. N. Christodoulides, J. W. Fleischer, O. Cohen, and M. Segev, “Two-dimensional optical lattice solitons,” Phys. Rev. Lett. 91(21), 213906 (2003).
[CrossRef] [PubMed]

2002 (1)

Alexander, T. J.

T. J. Alexander, A. S. Desyatnikov, and Y. S. Kivshar, “Multivortex solitons in triangular photonic lattices,” Opt. Lett. 32(10), 1293–1295 (2007).
[CrossRef] [PubMed]

D. N. Neshev, T. J. Alexander, E. A. Ostrovskaya, Y. S. Kivshar, H. Martin, I. Makasyuk, and Z. Chen, “Observation of discrete vortex solitons in optically induced photonic lattices,” Phys. Rev. Lett. 92(12), 123903 (2004).
[CrossRef] [PubMed]

Bezryadina, A.

X. Wang, A. Bezryadina, Z. Chen, K. G. Makris, D. N. Christodoulides, and G. I. Stegeman, “Observation of two-dimensional surface solitons,” Phys. Rev. Lett. 98(12), 123903 (2007).
[CrossRef] [PubMed]

J. Yang, I. Makasyuk, A. Bezryadina, and Z. Chen, “Dipole and Quadrupole Solitons in Optically Induced Two-Dimensional Photonic Lattices: Theory and Experiment,” Stud. Appl. Math. 113(4), 389–412 (2004).
[CrossRef]

Bishop, A. R.

K. J. H. Law, A. Saxena, P. G. Kevrekidis, and A. R. Bishop, “Localized strctures in kagome lattices,” Phys. Rev. A 79(5), 053818 (2009).
[CrossRef]

Chen, W. H.

Chen, Z.

Z. Shi, J. Wang, Z. Chen, and J. Yang, “Linear instability of two-dimensional low-amplitude gap solitons near band edges in periodic media,” Phys. Rev. A 78(6), 063812 (2008).
[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]

J. Wang, J. Yang, and Z. Chen, “Two-dimensional defect modes in optically induced photonic lattices,” Phys. Rev. A 76(1), 013828 (2007).
[CrossRef]

X. Wang, A. Bezryadina, Z. Chen, K. G. Makris, D. N. Christodoulides, and G. I. Stegeman, “Observation of two-dimensional surface solitons,” Phys. Rev. Lett. 98(12), 123903 (2007).
[CrossRef] [PubMed]

J. Yang and Z. Chen, “Defect solitons in photonic lattices,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 73(2), 026609 (2006).
[CrossRef] [PubMed]

J. Yang, I. Makasyuk, A. Bezryadina, and Z. Chen, “Dipole and Quadrupole Solitons in Optically Induced Two-Dimensional Photonic Lattices: Theory and Experiment,” Stud. Appl. Math. 113(4), 389–412 (2004).
[CrossRef]

D. N. Neshev, T. J. Alexander, E. A. Ostrovskaya, Y. S. Kivshar, H. Martin, I. Makasyuk, and Z. Chen, “Observation of discrete vortex solitons in optically induced photonic lattices,” Phys. Rev. Lett. 92(12), 123903 (2004).
[CrossRef] [PubMed]

Z. Chen and K. McCarthy, “Spatial soliton pixels from partially incoherent light,” Opt. Lett. 27(22), 2019–2021 (2002).
[CrossRef]

Christodoulides, D. N.

X. Wang, A. Bezryadina, Z. Chen, K. G. Makris, D. N. Christodoulides, and G. I. Stegeman, “Observation of two-dimensional surface solitons,” Phys. Rev. Lett. 98(12), 123903 (2007).
[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, J. Hudock, D. N. Christodoulides, J. W. Fleischer, O. Cohen, and M. Segev, “Two-dimensional optical lattice solitons,” Phys. Rev. Lett. 91(21), 213906 (2003).
[CrossRef] [PubMed]

Cohen, O.

N. K. Efremidis, J. Hudock, D. N. Christodoulides, J. W. Fleischer, O. Cohen, and M. Segev, “Two-dimensional optical lattice solitons,” Phys. Rev. Lett. 91(21), 213906 (2003).
[CrossRef] [PubMed]

Desyatnikov, A. S.

Dreisow, F.

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, J. Hudock, D. N. Christodoulides, J. W. Fleischer, O. Cohen, and M. Segev, “Two-dimensional optical lattice solitons,” Phys. Rev. Lett. 91(21), 213906 (2003).
[CrossRef] [PubMed]

Fleischer, J. W.

N. K. Efremidis, J. Hudock, D. N. Christodoulides, J. W. Fleischer, O. Cohen, and M. Segev, “Two-dimensional optical lattice solitons,” Phys. Rev. Lett. 91(21), 213906 (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]

Heinrich, M.

Hudock, J.

N. K. Efremidis, J. Hudock, D. N. Christodoulides, J. W. Fleischer, O. Cohen, and M. Segev, “Two-dimensional optical lattice solitons,” Phys. Rev. Lett. 91(21), 213906 (2003).
[CrossRef] [PubMed]

Kartashov, Y. V.

Kevrekidis, P. G.

K. J. H. Law, A. Saxena, P. G. Kevrekidis, and A. R. Bishop, “Localized strctures in kagome lattices,” Phys. Rev. A 79(5), 053818 (2009).
[CrossRef]

K. J. H. Law, H. Susanto, and P. G. Kevrekidis, “Solitons and vortices in honeycomb defocusing photonic lattices,” Phys. Rev. A 78(3), 033802 (2008).
[CrossRef]

Kivshar, Y. S.

Lakoba, T. I.

J. Yang and T. I. Lakoba, “Universally-Convergent Squared-Operator Iteration Methods for Solitary Wave in General Nonlinear Wave Equation,” Stud. Appl. Math. 118(2), 153–197 (2007).
[CrossRef]

Law, K. J. H.

K. J. H. Law, A. Saxena, P. G. Kevrekidis, and A. R. Bishop, “Localized strctures in kagome lattices,” Phys. Rev. A 79(5), 053818 (2009).
[CrossRef]

K. J. H. Law, H. Susanto, and P. G. Kevrekidis, “Solitons and vortices in honeycomb defocusing photonic lattices,” Phys. Rev. A 78(3), 033802 (2008).
[CrossRef]

Lederer, F.

Li, R. H.

Lou, C.

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 Quadrupole Solitons in Optically Induced Two-Dimensional Photonic Lattices: Theory and Experiment,” Stud. Appl. Math. 113(4), 389–412 (2004).
[CrossRef]

D. N. Neshev, T. J. Alexander, E. A. Ostrovskaya, Y. S. Kivshar, H. Martin, I. Makasyuk, and Z. Chen, “Observation of discrete vortex solitons in optically induced photonic lattices,” Phys. Rev. Lett. 92(12), 123903 (2004).
[CrossRef] [PubMed]

Makris, K. G.

X. Wang, A. Bezryadina, Z. Chen, K. G. Makris, D. N. Christodoulides, and G. I. Stegeman, “Observation of two-dimensional surface solitons,” Phys. Rev. Lett. 98(12), 123903 (2007).
[CrossRef] [PubMed]

Malomed, B. A.

Martin, H.

D. N. Neshev, T. J. Alexander, E. A. Ostrovskaya, Y. S. Kivshar, H. Martin, I. Makasyuk, and Z. Chen, “Observation of discrete vortex solitons in optically induced photonic lattices,” Phys. Rev. Lett. 92(12), 123903 (2004).
[CrossRef] [PubMed]

McCarthy, K.

Musslimani, Z. H.

Neshev, D. N.

D. N. Neshev, T. J. Alexander, E. A. Ostrovskaya, Y. S. Kivshar, H. Martin, I. Makasyuk, and Z. Chen, “Observation of discrete vortex solitons in optically induced photonic lattices,” Phys. Rev. Lett. 92(12), 123903 (2004).
[CrossRef] [PubMed]

Nolte, S.

Ostrovskaya, E. A.

E. A. Ostrovskaya and Y. S. Kivshar, “Photonic crystals for matter waves: Bose-Einstein condensates in optical lattices,” Opt. Express 12(1), 19–29 (2004).
[CrossRef] [PubMed]

D. N. Neshev, T. J. Alexander, E. A. Ostrovskaya, Y. S. Kivshar, H. Martin, I. Makasyuk, and Z. Chen, “Observation of discrete vortex solitons in optically induced photonic lattices,” Phys. Rev. Lett. 92(12), 123903 (2004).
[CrossRef] [PubMed]

Pertsch, T.

Saxena, A.

K. J. H. Law, A. Saxena, P. G. Kevrekidis, and A. R. Bishop, “Localized strctures in kagome lattices,” Phys. Rev. A 79(5), 053818 (2009).
[CrossRef]

Segev, M.

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, J. Hudock, D. N. Christodoulides, J. W. Fleischer, O. Cohen, and M. Segev, “Two-dimensional optical lattice solitons,” Phys. Rev. Lett. 91(21), 213906 (2003).
[CrossRef] [PubMed]

Shi, Z.

Z. Shi, J. Wang, Z. Chen, and J. Yang, “Linear instability of two-dimensional low-amplitude gap solitons near band edges in periodic media,” Phys. Rev. A 78(6), 063812 (2008).
[CrossRef]

Stegeman, G. I.

X. Wang, A. Bezryadina, Z. Chen, K. G. Makris, D. N. Christodoulides, and G. I. Stegeman, “Observation of two-dimensional surface solitons,” Phys. Rev. Lett. 98(12), 123903 (2007).
[CrossRef] [PubMed]

Susanto, H.

K. J. H. Law, H. Susanto, and P. G. Kevrekidis, “Solitons and vortices in honeycomb defocusing photonic lattices,” Phys. Rev. A 78(3), 033802 (2008).
[CrossRef]

Szameit, A.

Torner, L.

Tünnermann, A.

Vysloukh, V. A.

Wang, J.

Z. Shi, J. Wang, Z. Chen, and J. Yang, “Linear instability of two-dimensional low-amplitude gap solitons near band edges in periodic media,” Phys. Rev. A 78(6), 063812 (2008).
[CrossRef]

J. Wang and J. Yang, “Families of vortex solitons in periodic media,” Phys. Rev. A 77(3), 033834 (2008).
[CrossRef]

J. Wang, J. Yang, and Z. Chen, “Two-dimensional defect modes in optically induced photonic lattices,” Phys. Rev. A 76(1), 013828 (2007).
[CrossRef]

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]

X. Wang, A. Bezryadina, Z. Chen, K. G. Makris, D. N. Christodoulides, and G. I. Stegeman, “Observation of two-dimensional surface solitons,” Phys. Rev. Lett. 98(12), 123903 (2007).
[CrossRef] [PubMed]

Wu, T. W.

Xu, J.

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]

Yang, J.

J. Wang and J. Yang, “Families of vortex solitons in periodic media,” Phys. Rev. A 77(3), 033834 (2008).
[CrossRef]

Z. Shi, J. Wang, Z. Chen, and J. Yang, “Linear instability of two-dimensional low-amplitude gap solitons near band edges in periodic media,” Phys. Rev. A 78(6), 063812 (2008).
[CrossRef]

J. Yang, “Iteration methods for stability spectra of solitary waves,” J. Comput. Phys. 227(14), 6862–6876 (2008).
[CrossRef]

J. Yang and T. I. Lakoba, “Universally-Convergent Squared-Operator Iteration Methods for Solitary Wave in General Nonlinear Wave Equation,” Stud. Appl. Math. 118(2), 153–197 (2007).
[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]

J. Wang, J. Yang, and Z. Chen, “Two-dimensional defect modes in optically induced photonic lattices,” Phys. Rev. A 76(1), 013828 (2007).
[CrossRef]

J. Yang and Z. Chen, “Defect solitons in photonic lattices,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 73(2), 026609 (2006).
[CrossRef] [PubMed]

Z. H. Musslimani and J. Yang, “Self-trapping of light in a two-dimensional photonic lattice,” J. Opt. Soc. Am. B 21(5), 973–981 (2004).
[CrossRef]

J. Yang, I. Makasyuk, A. Bezryadina, and Z. Chen, “Dipole and Quadrupole Solitons in Optically Induced Two-Dimensional Photonic Lattices: Theory and Experiment,” Stud. Appl. Math. 113(4), 389–412 (2004).
[CrossRef]

Zhu, X.

J. Comput. Phys. (1)

J. Yang, “Iteration methods for stability spectra of solitary waves,” J. Comput. Phys. 227(14), 6862–6876 (2008).
[CrossRef]

J. Opt. Soc. Am. B (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(6928), 147–150 (2003).
[CrossRef] [PubMed]

Opt. Express (2)

Opt. Lett. (4)

Phys. Rev. A (5)

J. Wang, J. Yang, and Z. Chen, “Two-dimensional defect modes in optically induced photonic lattices,” Phys. Rev. A 76(1), 013828 (2007).
[CrossRef]

K. J. H. Law, H. Susanto, and P. G. Kevrekidis, “Solitons and vortices in honeycomb defocusing photonic lattices,” Phys. Rev. A 78(3), 033802 (2008).
[CrossRef]

K. J. H. Law, A. Saxena, P. G. Kevrekidis, and A. R. Bishop, “Localized strctures in kagome lattices,” Phys. Rev. A 79(5), 053818 (2009).
[CrossRef]

J. Wang and J. Yang, “Families of vortex solitons in periodic media,” Phys. Rev. A 77(3), 033834 (2008).
[CrossRef]

Z. Shi, J. Wang, Z. Chen, and J. Yang, “Linear instability of two-dimensional low-amplitude gap solitons near band edges in periodic media,” Phys. Rev. A 78(6), 063812 (2008).
[CrossRef]

Phys. Rev. E Stat. Nonlin. Soft Matter Phys. (1)

J. Yang and Z. Chen, “Defect solitons in photonic lattices,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 73(2), 026609 (2006).
[CrossRef] [PubMed]

Phys. Rev. Lett. (4)

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]

X. Wang, A. Bezryadina, Z. Chen, K. G. Makris, D. N. Christodoulides, and G. I. Stegeman, “Observation of two-dimensional surface solitons,” Phys. Rev. Lett. 98(12), 123903 (2007).
[CrossRef] [PubMed]

N. K. Efremidis, J. Hudock, D. N. Christodoulides, J. W. Fleischer, O. Cohen, and M. Segev, “Two-dimensional optical lattice solitons,” Phys. Rev. Lett. 91(21), 213906 (2003).
[CrossRef] [PubMed]

D. N. Neshev, T. J. Alexander, E. A. Ostrovskaya, Y. S. Kivshar, H. Martin, I. Makasyuk, and Z. Chen, “Observation of discrete vortex solitons in optically induced photonic lattices,” Phys. Rev. Lett. 92(12), 123903 (2004).
[CrossRef] [PubMed]

Stud. Appl. Math. (2)

J. Yang, I. Makasyuk, A. Bezryadina, and Z. Chen, “Dipole and Quadrupole Solitons in Optically Induced Two-Dimensional Photonic Lattices: Theory and Experiment,” Stud. Appl. Math. 113(4), 389–412 (2004).
[CrossRef]

J. Yang and T. I. Lakoba, “Universally-Convergent Squared-Operator Iteration Methods for Solitary Wave in General Nonlinear Wave Equation,” Stud. Appl. Math. 118(2), 153–197 (2007).
[CrossRef]

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Figures (6)

Fig. 1
Fig. 1

(Color online) (a) Band structure of kagome lattices (blank region corresponds to Bloch band). (b) The kagome lattices with a negative defect (ε = −0.5). (c) The kagome lattices with a positive defect (ε = 0.5).

Fig. 2
Fig. 2

(Color online) ε = 0. (a) Power diagram of gap solitons (blue regions correspond to Bloch bands). (b) Re(δ) versus constant μ for gap solitons. (c) Profile (|u|) of gap soliton for μ = 4.6 (point A). Its profile (|u|) at (d) z = 100 and (e) z = 200. (f) Profile (|u|) of gap soliton for μ = 6.3 (point B). Its profile (|u|) at (g) z = 100 and (h) z = 200.

Fig. 3
Fig. 3

(Color online) ε = 0. (a) Profile (|u|) of DS for μ = 2.5 (point C). Its profile (|u|) at (b) z = 100 and (c) z = 200. (d) Profile (|u|) of DS for μ = 6.33. Its profile (|u|) at (e) z = 100 and (f) z = 200.

Fig. 4
Fig. 4

(Color online) ε = −0.5. (a) Power diagram of DSs (blue regions correspond to Bloch bands). (b) Re(δ) versus constant μ for negative DSs. (c) Profile (|u|) of DS for μ = 5.0 (point A). Its profile (|u|) at (d) z = 100 and (e) z = 200. (f) Profile (|u|) of DS for μ = 6.16 (point B). Its profile (|u|) at (g) z = 100 and (h) z = 200.

Fig. 5
Fig. 5

(Color online) ε = −0.5. (a) Profile (|u|) of DS for μ = 3.5. Its profile (|u|) at (b) z = 100, and (c) z = 200. (d) Profile (|u|) of DS for μ = 7.0. Its profile (|u|) at (e) z = 100 and (f) z = 200. (g) Profile (|u|) of DS for μ = 7.5. Its profile (|u|) at (h) z = 100 and (i) z = 200.

Fig. 6
Fig. 6

(Color online) ε = 0.5. (a) Power diagram of DSs (blue regions correspond to Bloch bands, the dashed line represents the unstable regions and the solid line represents the stable regions). (b) Re(δ) versus constant μ for positive DSs. (c) Profile (|u|) of DS for μ = 3.0 (point A). Its profile (|u|) at (d) z = 100 and (e) z = 200. (f) Profile (|u|) of DS for μ = 2.2 (point B). Its profile (|u|) at (g) z = 100 and (h) z = 200.

Equations (5)

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i U z + 2 U x 2 + 2 U y 2 E 0 1 + I L + | U | 2 U = 0 ,
I = V 0 | 2 × exp ( i k p y / h ) cos ( p k y / h ) × exp ( i k y / h ) + exp [ i k y / ( 2 h ) i ( 3 / 2 ) k x ] + exp [ i k y / ( 2 h ) + i k x ( 3 / 2 ) | 2 ,
I L = I × { 1 + ε exp [ ( 4 x 2 + 3 y 2 ) ] 4 / 128 ] } .
2 u x 2 + 2 u y 2 E 0 1 + I L + | u | 2 u = μ u .
{ δ v = i ( 2 w x 2 + 2 w y 2 + μ w E 0 1 + I L + u 2 w ) , δ w = i ( 2 v x 2 + 2 v y 2 + μ v E 0 1 + I L + u 2 v + 2 E 0 u 2 ( 1 + I L + u 2 ) 2 v ) .

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