## Self-trapped leaky waves in lattices: discrete and Bragg soleakons |

Optics Express, Vol. 21, Issue 17, pp. 19690-19700 (2013)

http://dx.doi.org/10.1364/OE.21.019690

Acrobat PDF (1690 KB)

### 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.

© 2013 OSA

## 1. Introduction

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

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

5. 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]

10. 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. Express **13**(6), 1780–1796 (2005). [CrossRef] [PubMed]

11. 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]

12. 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]

13. 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]

15. 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]

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

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

6. 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]

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

13. 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]

5. 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]

8. J. Feng, “Alternative scheme for studying gap solitons in an infinite periodic Kerr medium,” Opt. Lett. **18**(16), 1302–1304 (1993). [CrossRef] [PubMed]

15. 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]

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

10. 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. Express **13**(6), 1780–1796 (2005). [CrossRef] [PubMed]

17. 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]

24. 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]

17. 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]

22. 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]

24. 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]

25. 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. Topics **62**(44 Pt B), 5777–5782 (2000). [CrossRef] [PubMed]

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

24. 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]

9. 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]

26. 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]

27. A. A. Sukhorukov and Y. S. Kivshar, “Multigap discrete vector solitons,” Phys. Rev. Lett. **91**(11), 113902 (2003). [CrossRef] [PubMed]

28. 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]

29. O. Cohen, G. Bartal, H. Buljan, T. Carmon, J. W. Fleischer, M. Segev, and D. N. Christodoulides, “Observation of random-phase lattice solitons,” Nature **433**(7025), 500–503 (2005). [CrossRef] [PubMed]

30. O. Peleg, Y. Plotnik, N. Moiseyev, O. Cohen, and M. Segev, “Self-trapped leaky waves and their interactions,” Phys. Rev. A **80**(4), 041801 (2009). [CrossRef]

30. O. Peleg, Y. Plotnik, N. Moiseyev, O. Cohen, and M. Segev, “Self-trapped leaky waves and their interactions,” Phys. Rev. A **80**(4), 041801 (2009). [CrossRef]

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

32. H. C. Gurgov and O. Cohen, “Spatiotemporal pulse-train solitons,” Opt. Express **17**(9), 7052–7058 (2009). [CrossRef] [PubMed]

34. 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]

35. S. Giovanazzi, A. Gorlitz, and T. Pfau, “Ballistic expansion of a dipolar condensate,” J. Opt. B **5**(2), S208–S211 (2003). [CrossRef]

36. 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]

## 2. Leaky modes and soleakons

30. O. Peleg, Y. Plotnik, N. Moiseyev, O. Cohen, and M. Segev, “Self-trapped leaky waves and their interactions,” Phys. Rev. A **80**(4), 041801 (2009). [CrossRef]

*L*. Otherwise, the beam will not exhibit particle-like features such as collisions and therefore cannot be called a soleakon. Like solitons and breathers, soleakons should be stable to noise. Here we explore soleakons in periodic potential: lattice soleakons.

_{C}## 3. Transmission spectrum

*q*and the plane wave wave-number,

*is wave-number,*k 0 = 2 π n 0 / λ

*is the wave-length of light in vacuum and*λ = 0.5 μ m

*’s*. For a constant

*’s*. In other words, the transmission spectrum of our structure consists of a semi-infinite band that is full with propagation waves and a semi-infinite gap above it.

## 4. Model and methods

18. 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]

19. 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]

22. 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]

*u*is the normalized (maximum of

*u*is 1 at every

*z*) slowly-attenuating leaky mode of the structure

*z*. We now discuss the procedure for finding (lattice) soleakons and verify that they (approximately) solve Eq. (2) [30

**80**(4), 041801 (2009). [CrossRef]

**80**(4), 041801 (2009). [CrossRef]

*fixed*defect:

*M*leaky-mode solutions of Eq. (3) with different peak amplitudes

*M*order polynomial to the

_{th}*M*values of leakage rates

## 5. Discrete and Bragg soleakons

**80**(4), 041801 (2009). [CrossRef]

*H*(

*x*) is Heaviside step function, is 5.6

*mW*. Next, we propagated the initial beam in a linear lattice by solving Eq. (2) with

*z =*0.032

*cm =*2

*× L*]. We then calculated the nonlinear evolution of the initial beam using the ‘exact’ method. The intensity patterns at

_{C}*z =*107

*cm*(

*z =*115

*cm*(

*z*= 0 [its cross section is shown in Fig. 2(f)]. As shown, the soleakon beam attenuates faster than in the linear case. Eventually it disintegrates abruptly emitting all its localized power to the continuum. This type of dynamics was also observed for soleakons in homogeneous media [30

**80**(4), 041801 (2009). [CrossRef]

*z*= 115

*cm*). The real part of the soleakon propagation constant [red cross in Fig. 2(h)] resides within the first band. The beam power spectrum [Fig. 2(i)] consists of intense humps that correspond to the localized section and thin lines around them that are associated with the conical radiation. Finally, Fig. 2(j) shows the induced ring-barrier waveguide structure which is the 2D version of the 1D double-barrier waveguide which is known to support slowly-attenuating leaky modes.

**80**(4), 041801 (2009). [CrossRef]

*z =*0.05

*cm =*2

*× L*]. The nonlinear propagation of the beam was than evaluated using the ‘exact’ method. The intensity patterns at

_{C}*z =*8

*cm*(

*z =*50

*cm*(

*z =*0. As shown the Bragg soleakon attenuates slower than the linear case and continues to propagate without disintegration. This results from the fact that the leakage rate of the Bragg soleakon decreases with localized power [Fig. 3(f)]. Figures 3(g)-3(h) display properties of the self-induced leaky modes corresponding to Bragg soleakon at

*z =*0. Real part of its propagation constant

## 6. Conclusion

**80**(4), 041801 (2009). [CrossRef]

## References and links

1. | A. A. Ovchinnikov, “Localized long-lived vibrational states in molecular crystals,” Zh. Exp. Theor. Phys. |

2. | W. P. Su, J. R. Schrieffer, and A. J. Heeger, “Solitons in polyacetylene,” Phys. Rev. Lett. |

3. | A. J. Sievers and S. Takeno, “Intrinsic localized modes in anharmonic crystals,” Phys. Rev. Lett. |

4. | A. S. Davydov, “The theory of contraction of proteins under their excitation,” J. Theor. Biol. |

5. | W. Chen and D. L. Mills, “Gap solitons and the nonlinear optical response of superlattices,” Phys. Rev. Lett. |

6. | D. N. Christodoulides and R. I. Joseph, “Discrete self-focusing in nonlinear arrays of coupled waveguides,” Opt. Lett. |

7. | D. N. Christodoulides and R. I. Joseph, “Slow Bragg solitons in nonlinear periodic structures,” Phys. Rev. Lett. |

8. | J. Feng, “Alternative scheme for studying gap solitons in an infinite periodic Kerr medium,” Opt. Lett. |

9. | 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. |

10. | 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. Express |

11. | M. Sato, B. E. Hubbard, and A. J. Sievers, “Colloquium: Nonlinear energy localization and its manipulation in micromechanical oscillator arrays,” Rev. Mod. Phys. |

12. | 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. |

13. | E. Trías, J. J. Mazo, and T. P. Orlando, “Discrete breathers in nonlinear lattices: experimental detection in a josephson array,” Phys. Rev. Lett. |

14. | N. K. Efremidis and D. N. Christodoulidis, “Lattice solitons in Bose-Einstein condensates,” Phys. Rev. A |

15. | 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. |

16. | F. Bloch, “Über die quantenmechanik der elektronen in kristallgittern,” Z. Phys. |

17. | H. S. Eisenberg, Y. Silberberg, R. Morandotti, A. R. Boyd, and J. S. Aitchison, “Discrete spatial optical solitons in waveguide arrays,” Phys. Rev. Lett. |

18. | 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. |

19. | 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 |

20. | D. Neshev, E. Ostrovskaya, Y. Kivshar, and W. Krolikowski, “Spatial solitons in optically induced gratings,” Opt. Lett. |

21. | 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. |

22. | A. Fratalocchi, G. Assanto, K. A. Brzdakiewicz, and M. A. Karpierz, “Discrete propagation and spatial solitons in nematic liquid crystals,” Opt. Lett. |

23. | D. Mandelik, R. Morandotti, J. S. Aitchison, and Y. Silberberg, “Gap solitons in waveguide arrays,” Phys. Rev. Lett. |

24. | N. K. Efremidis, J. Hudock, D. N. Christodoulides, J. W. Fleischer, O. Cohen, and M. Segev, “Two-dimensional optical lattice solitons,” Phys. Rev. Lett. |

25. | 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. Topics |

26. | O. Cohen, T. Schwartz, J. W. Fleischer, M. Segev, and D. N. Christodoulides, “Multiband vector lattice solitons,” Phys. Rev. Lett. |

27. | A. A. Sukhorukov and Y. S. Kivshar, “Multigap discrete vector solitons,” Phys. Rev. Lett. |

28. | 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. |

29. | O. Cohen, G. Bartal, H. Buljan, T. Carmon, J. W. Fleischer, M. Segev, and D. N. Christodoulides, “Observation of random-phase lattice solitons,” Nature |

30. | O. Peleg, Y. Plotnik, N. Moiseyev, O. Cohen, and M. Segev, “Self-trapped leaky waves and their interactions,” Phys. Rev. A |

31. | N. Moiseyev, P. R. Certain, and F. Weinhold, “Resonance properties of complex-rotated hamiltonians,” Mol. Phys. |

32. | H. C. Gurgov and O. Cohen, “Spatiotemporal pulse-train solitons,” Opt. Express |

33. | I. B. Burgess, M. Peccianti, G. Assanto, and R. Morandotti, “Accessible light bullets via synergetic nonlinearities,” Phys. Rev. Lett. |

34. | 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. |

35. | S. Giovanazzi, A. Gorlitz, and T. Pfau, “Ballistic expansion of a dipolar condensate,” J. Opt. B |

36. | 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. |

37. | A. W. Snyder and J. D. Love, |

38. | A. R. Champneys, B. A. Malomed, and M. J. Friedman, “Thirring solitons in the presence of dispersion,” Phys. Rev. Lett. |

39. | J. Yang, B. A. Malomed, and D. J. Kaup, “Embedded solitons in second-harmonic-generating systems,” Phys. Rev. Lett. |

40. | J. Yang, “Fully localized two-dimensional embedded solitons,” Phys. Rev. A |

41. | X. Wang, Z. Chen, J. Wang, and J. Yang, “Observation of in-band lattice solitons,” Phys. Rev. Lett. |

42. | G. Agraval, |

**OCIS Codes**

(190.5940) Nonlinear optics : Self-action effects

(190.6135) Nonlinear optics : Spatial solitons

**ToC Category:**

Nonlinear Optics

**History**

Original Manuscript: May 30, 2013

Revised Manuscript: July 15, 2013

Manuscript Accepted: July 15, 2013

Published: August 14, 2013

**Citation**

Maxim Kozlov, Ofer Kfir, and Oren Cohen, "Self-trapped leaky waves in lattices: discrete and Bragg soleakons," Opt. Express **21**, 19690-19700 (2013)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-17-19690

Sort: Year | Journal | Reset

### References

- A. A. Ovchinnikov, “Localized long-lived vibrational states in molecular crystals,” Zh. Exp. Theor. Phys.57, 263–270 (1969).
- W. P. Su, J. R. Schrieffer, and A. J. Heeger, “Solitons in polyacetylene,” Phys. Rev. Lett.42(25), 1698–1701 (1979). [CrossRef]
- A. J. Sievers and S. Takeno, “Intrinsic localized modes in anharmonic crystals,” Phys. Rev. Lett.61(8), 970–973 (1988). [CrossRef] [PubMed]
- A. S. Davydov, “The theory of contraction of proteins under their excitation,” J. Theor. Biol.38(3), 559–569 (1973). [CrossRef] [PubMed]
- 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]
- 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]
- D. N. Christodoulides and R. I. Joseph, “Slow Bragg solitons in nonlinear periodic structures,” Phys. Rev. Lett.62(15), 1746–1749 (1989). [CrossRef] [PubMed]
- J. Feng, “Alternative scheme for studying gap solitons in an infinite periodic Kerr medium,” Opt. Lett.18(16), 1302–1304 (1993). [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]
- 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]
- 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]
- 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]
- 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]
- N. K. Efremidis and D. N. Christodoulidis, “Lattice solitons in Bose-Einstein condensates,” Phys. Rev. A67(6), 063608 (2003). [CrossRef]
- 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]
- F. Bloch, “Über die quantenmechanik der elektronen in kristallgittern,” Z. Phys.52, 555–600 (1928).
- 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]
- 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. Neshev, E. Ostrovskaya, Y. Kivshar, and W. Krolikowski, “Spatial solitons in optically induced gratings,” Opt. Lett.28(9), 710–712 (2003). [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]
- 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]
- D. Mandelik, R. Morandotti, J. S. Aitchison, and Y. Silberberg, “Gap solitons in waveguide arrays,” Phys. Rev. Lett.92(9), 093904 (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]
- 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]
- 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]
- 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, 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]
- 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. Moiseyev, P. R. Certain, and F. Weinhold, “Resonance properties of complex-rotated hamiltonians,” Mol. Phys.36(6), 1613–1630 (1978). [CrossRef]
- H. C. Gurgov and O. Cohen, “Spatiotemporal pulse-train solitons,” Opt. Express17(9), 7052–7058 (2009). [CrossRef] [PubMed]
- 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. 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]
- S. Giovanazzi, A. Gorlitz, and T. Pfau, “Ballistic expansion of a dipolar condensate,” J. Opt. B5(2), S208–S211 (2003). [CrossRef]
- 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]
- A. W. Snyder and J. D. Love, Optical Waveguide Theory (Chapman & Hall, 1983).
- 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]
- 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]
- J. Yang, “Fully localized two-dimensional embedded solitons,” Phys. Rev. A82(5), 053828 (2010). [CrossRef]
- X. Wang, Z. Chen, J. Wang, and J. Yang, “Observation of in-band lattice solitons,” Phys. Rev. Lett.99(24), 243901 (2007). [CrossRef] [PubMed]
- G. Agraval, Nonlinear Fiber Optics, 3rd ed. (Academic Press, 2001).

## Cited By |
Alert me when this paper is cited |

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

« Previous Article | Next Article »

OSA is a member of CrossRef.