Abstract

We propose lattice soleakons: self-trapped waves that self-consistently populate slowly-attenuating leaky modes of their self-induced defects in periodic potentials. Two types, discrete and Bragg, lattice soleakons are predicted. Discrete soleakons that are supported by combination of self-focusing and self-defocusing nonlinearities propagate robustly for long propagation distances. They eventually abruptly disintegrate because they emit power to infinity at an increasing pace. In contrast, Bragg soleakons self-trap by only self-focusing nonlinearity. Also, they do not disintegrate because they emit power at a decreasing rate.

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2012 (1)

2010 (1)

J. Yang, “Fully localized two-dimensional embedded solitons,” Phys. Rev. A82(5), 053828 (2010).
[CrossRef]

2009 (4)

I. B. Burgess, M. Peccianti, G. Assanto, and R. Morandotti, “Accessible light bullets via synergetic nonlinearities,” Phys. Rev. Lett.102(20), 203903 (2009).
[CrossRef] [PubMed]

O. Peleg, Y. Plotnik, N. Moiseyev, O. Cohen, and M. Segev, “Self-trapped leaky waves and their interactions,” Phys. Rev. A80(4), 041801 (2009).
[CrossRef]

E. Kenig, B. A. Malomed, M. C. Cross, and R. Lifshitz, “Intrinsic localized modes in parametrically driven arrays of nonlinear resonators,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.80(4), 046202 (2009).
[CrossRef] [PubMed]

H. C. Gurgov and O. Cohen, “Spatiotemporal pulse-train solitons,” Opt. Express17(9), 7052–7058 (2009).
[CrossRef] [PubMed]

2007 (1)

X. Wang, Z. Chen, J. Wang, and J. Yang, “Observation of in-band lattice solitons,” Phys. Rev. Lett.99(24), 243901 (2007).
[CrossRef] [PubMed]

2006 (2)

A. Griesmaier, J. Stuhler, T. Koch, M. Fattori, T. Pfau, and S. Giovanazzi, “Comparing contact and dipolar interactions in a Bose-Einstein condensate,” Phys. Rev. Lett.97(25), 250402 (2006).
[CrossRef] [PubMed]

M. Sato, B. E. Hubbard, and A. J. Sievers, “Colloquium: Nonlinear energy localization and its manipulation in micromechanical oscillator arrays,” Rev. Mod. Phys.78(1), 137–157 (2006).
[CrossRef]

2005 (2)

O. Cohen, G. Bartal, H. Buljan, T. Carmon, J. W. Fleischer, M. Segev, and D. N. Christodoulides, “Observation of random-phase lattice solitons,” Nature433(7025), 500–503 (2005).
[CrossRef] [PubMed]

J. W. Fleischer, G. Bartal, O. Cohen, T. Schwartz, O. Manela, B. Freedman, M. Segev, H. Buljan, and N. K. Efremidis, “Spatial photonics in nonlinear waveguide arrays,” Opt. Express13(6), 1780–1796 (2005).
[CrossRef] [PubMed]

2004 (5)

A. Fratalocchi, G. Assanto, K. A. Brzdakiewicz, and M. A. Karpierz, “Discrete propagation and spatial solitons in nematic liquid crystals,” Opt. Lett.29(13), 1530–1532 (2004).
[CrossRef] [PubMed]

H. Buljan, O. Cohen, J. W. Fleischer, T. Schwartz, M. Segev, Z. H. Musslimani, N. K. Efremidis, and D. N. Christodoulides, “Random-phase solitons in nonlinear periodic lattices,” Phys. Rev. Lett.92(22), 223901 (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]

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]

B. Eiermann, Th. Anker, M. Albiez, M. Taglieber, P. Treutlein, K. P. Marzlin, and M. K. Oberthaler, “Bright Bose-Einstein gap solitons of atoms with repulsive interaction,” Phys. Rev. Lett.92(23), 230401 (2004).
[CrossRef] [PubMed]

2003 (9)

N. K. Efremidis and D. N. Christodoulidis, “Lattice solitons in Bose-Einstein condensates,” Phys. Rev. A67(6), 063608 (2003).
[CrossRef]

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(2), 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,” Nature422(6928), 147–150 (2003).
[CrossRef] [PubMed]

D. Mandelik, H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, “Observation of mutually trapped multiband optical breathers in waveguide arrays,” Phys. Rev. Lett.90(25), 253902 (2003).
[CrossRef] [PubMed]

S. Giovanazzi, A. Gorlitz, and T. Pfau, “Ballistic expansion of a dipolar condensate,” J. Opt. B5(2), S208–S211 (2003).
[CrossRef]

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]

O. Cohen, T. Schwartz, J. W. Fleischer, M. Segev, and D. N. Christodoulides, “Multiband vector lattice solitons,” Phys. Rev. Lett.91(11), 113901 (2003).
[CrossRef] [PubMed]

A. A. Sukhorukov and Y. S. Kivshar, “Multigap discrete vector solitons,” Phys. Rev. Lett.91(11), 113902 (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]

2000 (2)

S. F. Mingaleev, Y. S. Kivshar, and R. A. Sammut, “Long-range interaction and nonlinear localized modes in photonic crystal waveguides,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics62(44 Pt B), 5777–5782 (2000).
[CrossRef] [PubMed]

E. Trías, J. J. Mazo, and T. P. Orlando, “Discrete breathers in nonlinear lattices: experimental detection in a josephson array,” Phys. Rev. Lett.84(4), 741–744 (2000).
[CrossRef] [PubMed]

1999 (1)

J. Yang, B. A. Malomed, and D. J. Kaup, “Embedded solitons in second-harmonic-generating systems,” Phys. Rev. Lett.83(10), 1958–1961 (1999).
[CrossRef]

1998 (2)

A. R. Champneys, B. A. Malomed, and M. J. Friedman, “Thirring solitons in the presence of dispersion,” Phys. Rev. Lett.80(19), 4169–4172 (1998).
[CrossRef]

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]

1993 (1)

1989 (1)

D. N. Christodoulides and R. I. Joseph, “Slow Bragg solitons in nonlinear periodic structures,” Phys. Rev. Lett.62(15), 1746–1749 (1989).
[CrossRef] [PubMed]

1988 (2)

A. J. Sievers and S. Takeno, “Intrinsic localized modes in anharmonic crystals,” Phys. Rev. Lett.61(8), 970–973 (1988).
[CrossRef] [PubMed]

D. N. Christodoulides and R. I. Joseph, “Discrete self-focusing in nonlinear arrays of coupled waveguides,” Opt. Lett.13(9), 794–796 (1988).
[CrossRef] [PubMed]

1987 (1)

W. Chen and D. L. Mills, “Gap solitons and the nonlinear optical response of superlattices,” Phys. Rev. Lett.58(2), 160–163 (1987).
[CrossRef] [PubMed]

1979 (1)

W. P. Su, J. R. Schrieffer, and A. J. Heeger, “Solitons in polyacetylene,” Phys. Rev. Lett.42(25), 1698–1701 (1979).
[CrossRef]

1978 (1)

N. Moiseyev, P. R. Certain, and F. Weinhold, “Resonance properties of complex-rotated hamiltonians,” Mol. Phys.36(6), 1613–1630 (1978).
[CrossRef]

1973 (1)

A. S. Davydov, “The theory of contraction of proteins under their excitation,” J. Theor. Biol.38(3), 559–569 (1973).
[CrossRef] [PubMed]

1969 (1)

A. A. Ovchinnikov, “Localized long-lived vibrational states in molecular crystals,” Zh. Exp. Theor. Phys.57, 263–270 (1969).

1928 (1)

F. Bloch, “Über die quantenmechanik der elektronen in kristallgittern,” Z. Phys.52, 555–600 (1928).

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]

D. Mandelik, H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, “Observation of mutually trapped multiband optical breathers in waveguide arrays,” Phys. Rev. Lett.90(25), 253902 (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]

Albiez, M.

B. Eiermann, Th. Anker, M. Albiez, M. Taglieber, P. Treutlein, K. P. Marzlin, and M. K. Oberthaler, “Bright Bose-Einstein gap solitons of atoms with repulsive interaction,” Phys. Rev. Lett.92(23), 230401 (2004).
[CrossRef] [PubMed]

Anker, Th.

B. Eiermann, Th. Anker, M. Albiez, M. Taglieber, P. Treutlein, K. P. Marzlin, and M. K. Oberthaler, “Bright Bose-Einstein gap solitons of atoms with repulsive interaction,” Phys. Rev. Lett.92(23), 230401 (2004).
[CrossRef] [PubMed]

Assanto, G.

I. B. Burgess, M. Peccianti, G. Assanto, and R. Morandotti, “Accessible light bullets via synergetic nonlinearities,” Phys. Rev. Lett.102(20), 203903 (2009).
[CrossRef] [PubMed]

A. Fratalocchi, G. Assanto, K. A. Brzdakiewicz, and M. A. Karpierz, “Discrete propagation and spatial solitons in nematic liquid crystals,” Opt. Lett.29(13), 1530–1532 (2004).
[CrossRef] [PubMed]

Bartal, G.

J. W. Fleischer, G. Bartal, O. Cohen, T. Schwartz, O. Manela, B. Freedman, M. Segev, H. Buljan, and N. K. Efremidis, “Spatial photonics in nonlinear waveguide arrays,” Opt. Express13(6), 1780–1796 (2005).
[CrossRef] [PubMed]

O. Cohen, G. Bartal, H. Buljan, T. Carmon, J. W. Fleischer, M. Segev, and D. N. Christodoulides, “Observation of random-phase lattice solitons,” Nature433(7025), 500–503 (2005).
[CrossRef] [PubMed]

Bloch, F.

F. Bloch, “Über die quantenmechanik der elektronen in kristallgittern,” Z. Phys.52, 555–600 (1928).

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]

Brzdakiewicz, K. A.

Buljan, H.

J. W. Fleischer, G. Bartal, O. Cohen, T. Schwartz, O. Manela, B. Freedman, M. Segev, H. Buljan, and N. K. Efremidis, “Spatial photonics in nonlinear waveguide arrays,” Opt. Express13(6), 1780–1796 (2005).
[CrossRef] [PubMed]

O. Cohen, G. Bartal, H. Buljan, T. Carmon, J. W. Fleischer, M. Segev, and D. N. Christodoulides, “Observation of random-phase lattice solitons,” Nature433(7025), 500–503 (2005).
[CrossRef] [PubMed]

H. Buljan, O. Cohen, J. W. Fleischer, T. Schwartz, M. Segev, Z. H. Musslimani, N. K. Efremidis, and D. N. Christodoulides, “Random-phase solitons in nonlinear periodic lattices,” Phys. Rev. Lett.92(22), 223901 (2004).
[CrossRef] [PubMed]

Burgess, I. B.

I. B. Burgess, M. Peccianti, G. Assanto, and R. Morandotti, “Accessible light bullets via synergetic nonlinearities,” Phys. Rev. Lett.102(20), 203903 (2009).
[CrossRef] [PubMed]

Carmon, T.

O. Cohen, G. Bartal, H. Buljan, T. Carmon, J. W. Fleischer, M. Segev, and D. N. Christodoulides, “Observation of random-phase lattice solitons,” Nature433(7025), 500–503 (2005).
[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(2), 023902 (2003).
[CrossRef] [PubMed]

Certain, P. R.

N. Moiseyev, P. R. Certain, and F. Weinhold, “Resonance properties of complex-rotated hamiltonians,” Mol. Phys.36(6), 1613–1630 (1978).
[CrossRef]

Champneys, A. R.

A. R. Champneys, B. A. Malomed, and M. J. Friedman, “Thirring solitons in the presence of dispersion,” Phys. Rev. Lett.80(19), 4169–4172 (1998).
[CrossRef]

Chen, W.

W. Chen and D. L. Mills, “Gap solitons and the nonlinear optical response of superlattices,” Phys. Rev. Lett.58(2), 160–163 (1987).
[CrossRef] [PubMed]

Chen, Z.

X. Wang, Z. Chen, J. Wang, and J. Yang, “Observation of in-band lattice solitons,” Phys. Rev. Lett.99(24), 243901 (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(12), 123902 (2004).
[CrossRef] [PubMed]

Christodoulides, D. N.

O. Cohen, G. Bartal, H. Buljan, T. Carmon, J. W. Fleischer, M. Segev, and D. N. Christodoulides, “Observation of random-phase lattice solitons,” Nature433(7025), 500–503 (2005).
[CrossRef] [PubMed]

H. Buljan, O. Cohen, J. W. Fleischer, T. Schwartz, M. Segev, Z. H. Musslimani, N. K. Efremidis, and D. N. Christodoulides, “Random-phase solitons in nonlinear periodic lattices,” Phys. Rev. Lett.92(22), 223901 (2004).
[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(12), 123902 (2004).
[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]

O. Cohen, T. Schwartz, J. W. Fleischer, M. Segev, and D. N. Christodoulides, “Multiband vector lattice solitons,” Phys. Rev. Lett.91(11), 113901 (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(2), 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,” Nature422(6928), 147–150 (2003).
[CrossRef] [PubMed]

D. N. Christodoulides and R. I. Joseph, “Slow Bragg solitons in nonlinear periodic structures,” Phys. Rev. Lett.62(15), 1746–1749 (1989).
[CrossRef] [PubMed]

D. N. Christodoulides and R. I. Joseph, “Discrete self-focusing in nonlinear arrays of coupled waveguides,” Opt. Lett.13(9), 794–796 (1988).
[CrossRef] [PubMed]

Christodoulidis, D. N.

N. K. Efremidis and D. N. Christodoulidis, “Lattice solitons in Bose-Einstein condensates,” Phys. Rev. A67(6), 063608 (2003).
[CrossRef]

Cohen, O.

O. Lahav, H. C. Gurgov, P. Sidorenko, O. Peleg, L. Levi, A. Fleischer, and O. Cohen, “Self-phase modulation spectral broadening in two-dimensional spatial solitons: toward three-dimensional spatiotemporal pulse-train solitons,” Opt. Lett.37(24), 5196–5198 (2012).
[CrossRef] [PubMed]

H. C. Gurgov and O. Cohen, “Spatiotemporal pulse-train solitons,” Opt. Express17(9), 7052–7058 (2009).
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J. W. Fleischer, G. Bartal, O. Cohen, T. Schwartz, O. Manela, B. Freedman, M. Segev, H. Buljan, and N. K. Efremidis, “Spatial photonics in nonlinear waveguide arrays,” Opt. Express13(6), 1780–1796 (2005).
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O. Cohen, G. Bartal, H. Buljan, T. Carmon, J. W. Fleischer, M. Segev, and D. N. Christodoulides, “Observation of random-phase lattice solitons,” Nature433(7025), 500–503 (2005).
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H. Buljan, O. Cohen, J. W. Fleischer, T. Schwartz, M. Segev, Z. H. Musslimani, N. K. Efremidis, and D. N. Christodoulides, “Random-phase solitons in nonlinear periodic lattices,” Phys. Rev. Lett.92(22), 223901 (2004).
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O. Cohen, T. Schwartz, J. W. Fleischer, M. Segev, and D. N. Christodoulides, “Multiband vector lattice solitons,” Phys. Rev. Lett.91(11), 113901 (2003).
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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).
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E. Kenig, B. A. Malomed, M. C. Cross, and R. Lifshitz, “Intrinsic localized modes in parametrically driven arrays of nonlinear resonators,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.80(4), 046202 (2009).
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A. S. Davydov, “The theory of contraction of proteins under their excitation,” J. Theor. Biol.38(3), 559–569 (1973).
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J. W. Fleischer, G. Bartal, O. Cohen, T. Schwartz, O. Manela, B. Freedman, M. Segev, H. Buljan, and N. K. Efremidis, “Spatial photonics in nonlinear waveguide arrays,” Opt. Express13(6), 1780–1796 (2005).
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H. Buljan, O. Cohen, J. W. Fleischer, T. Schwartz, M. Segev, Z. H. Musslimani, N. K. Efremidis, and D. N. Christodoulides, “Random-phase solitons in nonlinear periodic lattices,” Phys. Rev. Lett.92(22), 223901 (2004).
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J. W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, “Observation of two-dimensional discrete solitons in optically induced nonlinear photonic lattices,” Nature422(6928), 147–150 (2003).
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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).
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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(2), 023902 (2003).
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B. Eiermann, Th. Anker, M. Albiez, M. Taglieber, P. Treutlein, K. P. Marzlin, and M. K. Oberthaler, “Bright Bose-Einstein gap solitons of atoms with repulsive interaction,” Phys. Rev. Lett.92(23), 230401 (2004).
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D. Mandelik, H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, “Observation of mutually trapped multiband optical breathers in waveguide arrays,” Phys. Rev. Lett.90(25), 253902 (2003).
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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).
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Fleischer, A.

Fleischer, J. W.

J. W. Fleischer, G. Bartal, O. Cohen, T. Schwartz, O. Manela, B. Freedman, M. Segev, H. Buljan, and N. K. Efremidis, “Spatial photonics in nonlinear waveguide arrays,” Opt. Express13(6), 1780–1796 (2005).
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O. Cohen, G. Bartal, H. Buljan, T. Carmon, J. W. Fleischer, M. Segev, and D. N. Christodoulides, “Observation of random-phase lattice solitons,” Nature433(7025), 500–503 (2005).
[CrossRef] [PubMed]

H. Buljan, O. Cohen, J. W. Fleischer, T. Schwartz, M. Segev, Z. H. Musslimani, N. K. Efremidis, and D. N. Christodoulides, “Random-phase solitons in nonlinear periodic lattices,” Phys. Rev. Lett.92(22), 223901 (2004).
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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]

O. Cohen, T. Schwartz, J. W. Fleischer, M. Segev, and D. N. Christodoulides, “Multiband vector lattice solitons,” Phys. Rev. Lett.91(11), 113901 (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(2), 023902 (2003).
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J. W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, “Observation of two-dimensional discrete solitons in optically induced nonlinear photonic lattices,” Nature422(6928), 147–150 (2003).
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Freedman, B.

Friedman, M. J.

A. R. Champneys, B. A. Malomed, and M. J. Friedman, “Thirring solitons in the presence of dispersion,” Phys. Rev. Lett.80(19), 4169–4172 (1998).
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A. Griesmaier, J. Stuhler, T. Koch, M. Fattori, T. Pfau, and S. Giovanazzi, “Comparing contact and dipolar interactions in a Bose-Einstein condensate,” Phys. Rev. Lett.97(25), 250402 (2006).
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S. Giovanazzi, A. Gorlitz, and T. Pfau, “Ballistic expansion of a dipolar condensate,” J. Opt. B5(2), S208–S211 (2003).
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S. Giovanazzi, A. Gorlitz, and T. Pfau, “Ballistic expansion of a dipolar condensate,” J. Opt. B5(2), S208–S211 (2003).
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A. Griesmaier, J. Stuhler, T. Koch, M. Fattori, T. Pfau, and S. Giovanazzi, “Comparing contact and dipolar interactions in a Bose-Einstein condensate,” Phys. Rev. Lett.97(25), 250402 (2006).
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W. P. Su, J. R. Schrieffer, and A. J. Heeger, “Solitons in polyacetylene,” Phys. Rev. Lett.42(25), 1698–1701 (1979).
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M. Sato, B. E. Hubbard, and A. J. Sievers, “Colloquium: Nonlinear energy localization and its manipulation in micromechanical oscillator arrays,” Rev. Mod. Phys.78(1), 137–157 (2006).
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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).
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E. Kenig, B. A. Malomed, M. C. Cross, and R. Lifshitz, “Intrinsic localized modes in parametrically driven arrays of nonlinear resonators,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.80(4), 046202 (2009).
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Kivshar, Y. S.

A. A. Sukhorukov and Y. S. Kivshar, “Multigap discrete vector solitons,” Phys. Rev. Lett.91(11), 113902 (2003).
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S. F. Mingaleev, Y. S. Kivshar, and R. A. Sammut, “Long-range interaction and nonlinear localized modes in photonic crystal waveguides,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics62(44 Pt B), 5777–5782 (2000).
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A. Griesmaier, J. Stuhler, T. Koch, M. Fattori, T. Pfau, and S. Giovanazzi, “Comparing contact and dipolar interactions in a Bose-Einstein condensate,” Phys. Rev. Lett.97(25), 250402 (2006).
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Lahav, O.

Levi, L.

Lifshitz, R.

E. Kenig, B. A. Malomed, M. C. Cross, and R. Lifshitz, “Intrinsic localized modes in parametrically driven arrays of nonlinear resonators,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.80(4), 046202 (2009).
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E. Kenig, B. A. Malomed, M. C. Cross, and R. Lifshitz, “Intrinsic localized modes in parametrically driven arrays of nonlinear resonators,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.80(4), 046202 (2009).
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J. Yang, B. A. Malomed, and D. J. Kaup, “Embedded solitons in second-harmonic-generating systems,” Phys. Rev. Lett.83(10), 1958–1961 (1999).
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A. R. Champneys, B. A. Malomed, and M. J. Friedman, “Thirring solitons in the presence of dispersion,” Phys. Rev. Lett.80(19), 4169–4172 (1998).
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D. Mandelik, R. Morandotti, J. S. Aitchison, and Y. Silberberg, “Gap solitons in waveguide arrays,” Phys. Rev. Lett.92(9), 093904 (2004).
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D. Mandelik, H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, “Observation of mutually trapped multiband optical breathers in waveguide arrays,” Phys. Rev. Lett.90(25), 253902 (2003).
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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).
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B. Eiermann, Th. Anker, M. Albiez, M. Taglieber, P. Treutlein, K. P. Marzlin, and M. K. Oberthaler, “Bright Bose-Einstein gap solitons of atoms with repulsive interaction,” Phys. Rev. Lett.92(23), 230401 (2004).
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E. Trías, J. J. Mazo, and T. P. Orlando, “Discrete breathers in nonlinear lattices: experimental detection in a josephson array,” Phys. Rev. Lett.84(4), 741–744 (2000).
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O. Peleg, Y. Plotnik, N. Moiseyev, O. Cohen, and M. Segev, “Self-trapped leaky waves and their interactions,” Phys. Rev. A80(4), 041801 (2009).
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I. B. Burgess, M. Peccianti, G. Assanto, and R. Morandotti, “Accessible light bullets via synergetic nonlinearities,” Phys. Rev. Lett.102(20), 203903 (2009).
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D. Mandelik, R. Morandotti, J. S. Aitchison, and Y. Silberberg, “Gap solitons in waveguide arrays,” Phys. Rev. Lett.92(9), 093904 (2004).
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D. Mandelik, H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, “Observation of mutually trapped multiband optical breathers in waveguide arrays,” Phys. Rev. Lett.90(25), 253902 (2003).
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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).
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H. Buljan, O. Cohen, J. W. Fleischer, T. Schwartz, M. Segev, Z. H. Musslimani, N. K. Efremidis, and D. N. Christodoulides, “Random-phase solitons in nonlinear periodic lattices,” Phys. Rev. Lett.92(22), 223901 (2004).
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Oberthaler, M. K.

B. Eiermann, Th. Anker, M. Albiez, M. Taglieber, P. Treutlein, K. P. Marzlin, and M. K. Oberthaler, “Bright Bose-Einstein gap solitons of atoms with repulsive interaction,” Phys. Rev. Lett.92(23), 230401 (2004).
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E. Trías, J. J. Mazo, and T. P. Orlando, “Discrete breathers in nonlinear lattices: experimental detection in a josephson array,” Phys. Rev. Lett.84(4), 741–744 (2000).
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Peccianti, M.

I. B. Burgess, M. Peccianti, G. Assanto, and R. Morandotti, “Accessible light bullets via synergetic nonlinearities,” Phys. Rev. Lett.102(20), 203903 (2009).
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Peleg, O.

Pfau, T.

A. Griesmaier, J. Stuhler, T. Koch, M. Fattori, T. Pfau, and S. Giovanazzi, “Comparing contact and dipolar interactions in a Bose-Einstein condensate,” Phys. Rev. Lett.97(25), 250402 (2006).
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S. Giovanazzi, A. Gorlitz, and T. Pfau, “Ballistic expansion of a dipolar condensate,” J. Opt. B5(2), S208–S211 (2003).
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O. Peleg, Y. Plotnik, N. Moiseyev, O. Cohen, and M. Segev, “Self-trapped leaky waves and their interactions,” Phys. Rev. A80(4), 041801 (2009).
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Sammut, R. A.

S. F. Mingaleev, Y. S. Kivshar, and R. A. Sammut, “Long-range interaction and nonlinear localized modes in photonic crystal waveguides,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics62(44 Pt B), 5777–5782 (2000).
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M. Sato, B. E. Hubbard, and A. J. Sievers, “Colloquium: Nonlinear energy localization and its manipulation in micromechanical oscillator arrays,” Rev. Mod. Phys.78(1), 137–157 (2006).
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W. P. Su, J. R. Schrieffer, and A. J. Heeger, “Solitons in polyacetylene,” Phys. Rev. Lett.42(25), 1698–1701 (1979).
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Schwartz, T.

J. W. Fleischer, G. Bartal, O. Cohen, T. Schwartz, O. Manela, B. Freedman, M. Segev, H. Buljan, and N. K. Efremidis, “Spatial photonics in nonlinear waveguide arrays,” Opt. Express13(6), 1780–1796 (2005).
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H. Buljan, O. Cohen, J. W. Fleischer, T. Schwartz, M. Segev, Z. H. Musslimani, N. K. Efremidis, and D. N. Christodoulides, “Random-phase solitons in nonlinear periodic lattices,” Phys. Rev. Lett.92(22), 223901 (2004).
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O. Cohen, T. Schwartz, J. W. Fleischer, M. Segev, and D. N. Christodoulides, “Multiband vector lattice solitons,” Phys. Rev. Lett.91(11), 113901 (2003).
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O. Peleg, Y. Plotnik, N. Moiseyev, O. Cohen, and M. Segev, “Self-trapped leaky waves and their interactions,” Phys. Rev. A80(4), 041801 (2009).
[CrossRef]

J. W. Fleischer, G. Bartal, O. Cohen, T. Schwartz, O. Manela, B. Freedman, M. Segev, H. Buljan, and N. K. Efremidis, “Spatial photonics in nonlinear waveguide arrays,” Opt. Express13(6), 1780–1796 (2005).
[CrossRef] [PubMed]

O. Cohen, G. Bartal, H. Buljan, T. Carmon, J. W. Fleischer, M. Segev, and D. N. Christodoulides, “Observation of random-phase lattice solitons,” Nature433(7025), 500–503 (2005).
[CrossRef] [PubMed]

H. Buljan, O. Cohen, J. W. Fleischer, T. Schwartz, M. Segev, Z. H. Musslimani, N. K. Efremidis, and D. N. Christodoulides, “Random-phase solitons in nonlinear periodic lattices,” Phys. Rev. Lett.92(22), 223901 (2004).
[CrossRef] [PubMed]

O. Cohen, T. Schwartz, J. W. Fleischer, M. Segev, and D. N. Christodoulides, “Multiband vector lattice solitons,” Phys. Rev. Lett.91(11), 113901 (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]

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(2), 023902 (2003).
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J. W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, “Observation of two-dimensional discrete solitons in optically induced nonlinear photonic lattices,” Nature422(6928), 147–150 (2003).
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Sidorenko, P.

Sievers, A. J.

M. Sato, B. E. Hubbard, and A. J. Sievers, “Colloquium: Nonlinear energy localization and its manipulation in micromechanical oscillator arrays,” Rev. Mod. Phys.78(1), 137–157 (2006).
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A. J. Sievers and S. Takeno, “Intrinsic localized modes in anharmonic crystals,” Phys. Rev. Lett.61(8), 970–973 (1988).
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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. Mandelik, H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, “Observation of mutually trapped multiband optical breathers in waveguide arrays,” Phys. Rev. Lett.90(25), 253902 (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).
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A. Griesmaier, J. Stuhler, T. Koch, M. Fattori, T. Pfau, and S. Giovanazzi, “Comparing contact and dipolar interactions in a Bose-Einstein condensate,” Phys. Rev. Lett.97(25), 250402 (2006).
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W. P. Su, J. R. Schrieffer, and A. J. Heeger, “Solitons in polyacetylene,” Phys. Rev. Lett.42(25), 1698–1701 (1979).
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A. A. Sukhorukov and Y. S. Kivshar, “Multigap discrete vector solitons,” Phys. Rev. Lett.91(11), 113902 (2003).
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B. Eiermann, Th. Anker, M. Albiez, M. Taglieber, P. Treutlein, K. P. Marzlin, and M. K. Oberthaler, “Bright Bose-Einstein gap solitons of atoms with repulsive interaction,” Phys. Rev. Lett.92(23), 230401 (2004).
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A. J. Sievers and S. Takeno, “Intrinsic localized modes in anharmonic crystals,” Phys. Rev. Lett.61(8), 970–973 (1988).
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B. Eiermann, Th. Anker, M. Albiez, M. Taglieber, P. Treutlein, K. P. Marzlin, and M. K. Oberthaler, “Bright Bose-Einstein gap solitons of atoms with repulsive interaction,” Phys. Rev. Lett.92(23), 230401 (2004).
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E. Trías, J. J. Mazo, and T. P. Orlando, “Discrete breathers in nonlinear lattices: experimental detection in a josephson array,” Phys. Rev. Lett.84(4), 741–744 (2000).
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X. Wang, Z. Chen, J. Wang, and J. Yang, “Observation of in-band lattice solitons,” Phys. Rev. Lett.99(24), 243901 (2007).
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X. Wang, Z. Chen, J. Wang, and J. Yang, “Observation of in-band lattice solitons,” Phys. Rev. Lett.99(24), 243901 (2007).
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N. Moiseyev, P. R. Certain, and F. Weinhold, “Resonance properties of complex-rotated hamiltonians,” Mol. Phys.36(6), 1613–1630 (1978).
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J. Yang, “Fully localized two-dimensional embedded solitons,” Phys. Rev. A82(5), 053828 (2010).
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X. Wang, Z. Chen, J. Wang, and J. Yang, “Observation of in-band lattice solitons,” Phys. Rev. Lett.99(24), 243901 (2007).
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J. Opt. B (1)

S. Giovanazzi, A. Gorlitz, and T. Pfau, “Ballistic expansion of a dipolar condensate,” J. Opt. B5(2), S208–S211 (2003).
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J. Theor. Biol. (1)

A. S. Davydov, “The theory of contraction of proteins under their excitation,” J. Theor. Biol.38(3), 559–569 (1973).
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Mol. Phys. (1)

N. Moiseyev, P. R. Certain, and F. Weinhold, “Resonance properties of complex-rotated hamiltonians,” Mol. Phys.36(6), 1613–1630 (1978).
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Nature (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,” Nature422(6928), 147–150 (2003).
[CrossRef] [PubMed]

O. Cohen, G. Bartal, H. Buljan, T. Carmon, J. W. Fleischer, M. Segev, and D. N. Christodoulides, “Observation of random-phase lattice solitons,” Nature433(7025), 500–503 (2005).
[CrossRef] [PubMed]

Opt. Express (2)

Opt. Lett. (5)

Phys. Rev. A (3)

J. Yang, “Fully localized two-dimensional embedded solitons,” Phys. Rev. A82(5), 053828 (2010).
[CrossRef]

O. Peleg, Y. Plotnik, N. Moiseyev, O. Cohen, and M. Segev, “Self-trapped leaky waves and their interactions,” Phys. Rev. A80(4), 041801 (2009).
[CrossRef]

N. K. Efremidis and D. N. Christodoulidis, “Lattice solitons in Bose-Einstein condensates,” Phys. Rev. A67(6), 063608 (2003).
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Phys. Rev. E Stat. Nonlin. Soft Matter Phys. (1)

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Figures (3)

Fig. 1
Fig. 1

(a) Refractive index change in the array of slab waveguides. (b) Band structure of the array of slab waveguides. Propagation constants of linear radiation modes of the first (solid blue curves) and second (dash brown curves) band labeled by corresponding values of k y D/π . The brown region displays the gap for modes with k y =0 . Radiation modes with k y 0 reside in this gap, forming a semi-infinite band.

Fig. 2
Fig. 2

(a) Intensity profile of discrete soleakon at z = 0 (logarithmic scale); (b) Intensity profile of beam in a linear lattice ( δn=0 ) at z = 0.032cm = 2 × LC; Intensity profiles of soleakon (logarithmic scale) at z = 107cm (c) and at z = 115cm (d); (e) localized power versus propagation distance obtained by adiabatic (blue dashed curve) and exact (red solid curve) methods and for linear defect (black dash-dot curve). The input beam in the exact method corresponded to 1.0125 times the input beam in the adiabatic method; (f) Nonlinear defect vs. y in the x = 0 cross section at z = 0 (red solid curve) and z = 115cm (blue dashed curve); (g) Soleakon decay rate versus localized power; (h) Propagation constant of the discrete soleakon (red cross) on the background of linear band structure. The propagation constant of the soleakon is shifted from the upper edge of the first band downward into the first band; (i) Fourier power spectrum of the discrete soleakon wave-function (logarithmic scale). Narrow rings around the humps correspond to the radiation part of the soleakon; (j) Ring-barrier wave-guide induced by local focusing and nonlocal defocusing nonlinearities.

Fig. 3
Fig. 3

(a) Intensity profile of Bragg soleakon at z = 0 (logarithmic scale); (b) Intensity profile of beam in a linear lattice ( δn=0 ) at z = 0.05cm = 2 × LC; Intensity profiles of soleakon (logarithmic scale) at z = 8 (c) and at z = 50cm (d); (e) localized power versus propagation distance obtained by adiabatic (blue dashed curve) and exact (red solid curve) methods and for linear defect (black dash-dot curve). (f) Soleakon decay rate versus localized power; (g) Propagation constant of the Bragg soleakon (red cross) on the background of linear band structure. The propagation constant of the soleakon is shifted from the upper edge of the second band upward into the first band; (h) Fourier power spectrum of the Bragg soleakon wave-function (logarithmic scale). Narrow lines connecting hot-spots correspond to the radiation part of the soleakon. Normals (black dashed lines) point in the direction of radiation; (i) Soleakon widths x 2 = + dx + d y x 2 | ψ( x,y ) | 2 / | ψ | max 2 (blue solid curve) and y 2 = + dx + d y y 2 | ψ( x,y ) | 2 / | ψ | max 2 (red dashed curve) versus localized power; (j) Fourier power spectrum of the soleakon wave-function vs. k y at k x =π/d and z = 0 (red solid curve) and z = 50cm (blue dashed curve). Arrows point to the minimal values of resonant plane wave-numbers k yR .

Equations (6)

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β Bloch q ( k x , k y )= β Bloch q ( k x ,0 ) k y 2 / 2 k 0 ,
i ψ z + 1 2 k 0 2 ψ+ k 0 n 0 [ Δn+δn(ψ) ]ψ=0,
β(0)u(z=0,x,y)= 1 2 k 0 2 u(z=0,x,y) + k 0 n 0 { Δn+δn[ A(0)u(z=0,x,y) ] }u(z=0,x,y),
dA / dz=γ( A ) A(z),
k yR =± 2 k 0 [ β Bloch 1 ( k x , k y =0 ) β R ] .
±( k 0 / | k yR | )( β Bloch 1 ( k x , k y =0 ) / k x ).

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