Abstract

We study temporal modulational instability of spatial discrete solitons in waveguide arrays with group velocity dispersion (GVD). For normal GVD we report existence of the strong ‘neck’-type instability specific for the discrete solitons. For anomalous GVD the instability leads to formation of the mixed discrete-continuous spatio-temporal quasi-solitons. Feasibility of experimental observation of these effects in the arrays of silicon-on-insulator waveguides is discussed.

© 2006 Optical Society of America

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References

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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
  19. J. Meier, G.I. Stegeman, D.N. Christodoulides, Y. Silberberg, R. Morandotti, H. Yang, G. Salamo, M. Sorel, and J.S. Aitchison, “Experimental observation of discrete modulational instability,” Phys. Rev. Lett. 92163902 (2004).
    [Crossref] [PubMed]
  20. D.N. Christodoulides and R.I. Joseph, “Discrete self-focusing in nonlinear arrays of coupled waveguides,” Opt. Lett. 16, 446–448 (1991).
    [Crossref] [PubMed]
  21. S. Darmanyan, I. Relke, and F. Lederer, “Instability of continuous waves and rotating solitons in waveguide arrays,” Phys. Rev. E 55, 7662–7668 (1997).
    [Crossref]
  22. M. Stepic, L. Hadzieski, and M. Skoric, “Stability of one-dimensional array solitons,” Phys. Rev. E 65, 026604 (2002).
    [Crossref]
  23. Y.V. Kartashov and L. Torner, “Surface soliton arrays,” Eur. Opt. Soc. Topical Meeting on Nonlinear Optics, TOM 6 (Paris, 2006).
  24. E.W. Laedke, K.H. Spatschek, and S.K. Turitsyn, “Stability of Discrete Solitons and Quasicollapse to Intrinsically Localized Modes,” Phys. Rev. Lett. 73, 1055–1059 (1994).
    [Crossref] [PubMed]
  25. N. Akhmediev and J.M. Soto-Crespo, “Generation of a train of three-dimensional optical solitons in a selffocusing medium,” Phys. Rev. A 47, 1358–1364 (1993).
    [Crossref] [PubMed]
  26. B. Deconinck, D.E. Pelinovsky, and J.D. Carter, “Transverse instabilities of deep-water solitary waves,” Proc. of the Royal Soc. A 462, 2039–2061 (2006).
    [Crossref]

2006 (5)

S.P. Gorza, P. Emplit, and M. Haelterman, “Observation of the snake instability of a spatially extended temporal bright soliton,” Opt. Lett. 31, 1280–1282 (2006).
[Crossref] [PubMed]

P. Dumon, G. Priem, L.R. Nunes, W. Bogaerts, D. van Thourhout, P. Bienstman, T.K. Liang, M. Tsuchiya, P. Jaenen, S. Beckx, J. Wouters, and R. Baets, “Linear and nonlinear nanophotonic devices based on silicon-oninsulator wire waveguides,” Jap. J. of Appl. Phys. 45, 6589–6602 (2006).
[Crossref]

F.N. Xia, L. Sekaric, and Y.A. Vlasov, “Mode conversion losses in silicon-on-insulator photonic wire based racetrack resonators,” Opt. Express 14, 3872–3886 (2006).
[Crossref] [PubMed]

M.A. Foster, A.C. Turner, J.E. Sharping, B.S. Schmidt, M. Lipson, and A.L. Gaeta, “Broad-band optical parametric gain on a silicon photonic chip,” Nature 441, 960–963 (2006).
[Crossref] [PubMed]

B. Deconinck, D.E. Pelinovsky, and J.D. Carter, “Transverse instabilities of deep-water solitary waves,” Proc. of the Royal Soc. A 462, 2039–2061 (2006).
[Crossref]

2005 (2)

S.D. Jenkins, D. Salerno, S. Minardi, G. Tamosauskas, T.A.B. Kennedy, and P. Di Trapani, “Quantum-noise-initiated symmetry breaking of spatial solitons,” Phys. Rev. Lett. 95, 203902 (2005).
[Crossref] [PubMed]

S. Droulias, K. Hizanidis, J. Meier, and D. Christodoulides, “X - waves in nonlinear normally dispersive waveguide arrays,” Opt. Express 13, 1827–1832 (2005).
[Crossref] [PubMed]

2004 (3)

A.B. Aceves, G. Fibich, and B. Ilan, “Gap-soliton bullets in waveguide gratings,” Physica D 189, 277–286 (2004).
[Crossref]

B.B. Baizakov, B.A. Malomed, and M. Salerno, “Multidimensional solitons in a low-dimensional periodic potential,” Phys. Rev. A 70053613 (2004).
[Crossref]

J. Meier, G.I. Stegeman, D.N. Christodoulides, Y. Silberberg, R. Morandotti, H. Yang, G. Salamo, M. Sorel, and J.S. Aitchison, “Experimental observation of discrete modulational instability,” Phys. Rev. Lett. 92163902 (2004).
[Crossref] [PubMed]

2003 (4)

S. Minardi, J. Yu, G. Blasi, A. Varanavicius, G. Valiulis, A. Berzanskis, A. Piskarskas, and P. Di Trapani “Red solitons: Evidence of spatiotemporal instability in χ(2) spatial soliton dynamics,” Phys. Rev. Lett. 91, 123901 (2003).
[Crossref] [PubMed]

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

D. Cheskis, S. Bar-Ad, R. Morandotti, J.S. Aitchison, H.S. Eisenberg, Y. Silberberg, and D. Ross, “Strong Spatiotemporal Localization in a Silica Nonlinear Waveguide Array,” Phys. Rev. Lett. 91, 223901 (2003).
[Crossref] [PubMed]

P. St.J. Russell, “Photonic crystal fibers,” Science 299, 358–362 (2003).
[Crossref] [PubMed]

2002 (2)

A.V. Buryak, P. Di Trapani, D.V. Skryabin, and S. Trillo, “Optical solitons due to quadratic nonlinearities: from basic physics to futuristic applications,” Phys. Rep. 370, 63–235 (2002).
[Crossref]

M. Stepic, L. Hadzieski, and M. Skoric, “Stability of one-dimensional array solitons,” Phys. Rev. E 65, 026604 (2002).
[Crossref]

2000 (1)

Y.S. Kivshar and D.E. Pelinovsky, “Self-focusing and transverse instabilities of solitary waves,” Phys. Rep. 331, 118–195 (2000).
[Crossref]

1997 (1)

S. Darmanyan, I. Relke, and F. Lederer, “Instability of continuous waves and rotating solitons in waveguide arrays,” Phys. Rev. E 55, 7662–7668 (1997).
[Crossref]

1994 (2)

A. B. Aceves, C. De Angelis, A. M. Rubenchik, and S. K. Turitsyn, “Multidimensional solitons in fiber arrays,” Opt. Lett. 19, 329–331 (1994).
[Crossref] [PubMed]

E.W. Laedke, K.H. Spatschek, and S.K. Turitsyn, “Stability of Discrete Solitons and Quasicollapse to Intrinsically Localized Modes,” Phys. Rev. Lett. 73, 1055–1059 (1994).
[Crossref] [PubMed]

1993 (1)

N. Akhmediev and J.M. Soto-Crespo, “Generation of a train of three-dimensional optical solitons in a selffocusing medium,” Phys. Rev. A 47, 1358–1364 (1993).
[Crossref] [PubMed]

1991 (1)

Aceves, A. B.

Aceves, A.B.

A.B. Aceves, G. Fibich, and B. Ilan, “Gap-soliton bullets in waveguide gratings,” Physica D 189, 277–286 (2004).
[Crossref]

Aitchison, J.S.

J. Meier, G.I. Stegeman, D.N. Christodoulides, Y. Silberberg, R. Morandotti, H. Yang, G. Salamo, M. Sorel, and J.S. Aitchison, “Experimental observation of discrete modulational instability,” Phys. Rev. Lett. 92163902 (2004).
[Crossref] [PubMed]

D. Cheskis, S. Bar-Ad, R. Morandotti, J.S. Aitchison, H.S. Eisenberg, Y. Silberberg, and D. Ross, “Strong Spatiotemporal Localization in a Silica Nonlinear Waveguide Array,” Phys. Rev. Lett. 91, 223901 (2003).
[Crossref] [PubMed]

Akhmediev, N.

N. Akhmediev and J.M. Soto-Crespo, “Generation of a train of three-dimensional optical solitons in a selffocusing medium,” Phys. Rev. A 47, 1358–1364 (1993).
[Crossref] [PubMed]

Baets, R.

P. Dumon, G. Priem, L.R. Nunes, W. Bogaerts, D. van Thourhout, P. Bienstman, T.K. Liang, M. Tsuchiya, P. Jaenen, S. Beckx, J. Wouters, and R. Baets, “Linear and nonlinear nanophotonic devices based on silicon-oninsulator wire waveguides,” Jap. J. of Appl. Phys. 45, 6589–6602 (2006).
[Crossref]

Baizakov, B.B.

B.B. Baizakov, B.A. Malomed, and M. Salerno, “Multidimensional solitons in a low-dimensional periodic potential,” Phys. Rev. A 70053613 (2004).
[Crossref]

Bar-Ad, S.

D. Cheskis, S. Bar-Ad, R. Morandotti, J.S. Aitchison, H.S. Eisenberg, Y. Silberberg, and D. Ross, “Strong Spatiotemporal Localization in a Silica Nonlinear Waveguide Array,” Phys. Rev. Lett. 91, 223901 (2003).
[Crossref] [PubMed]

Beckx, S.

P. Dumon, G. Priem, L.R. Nunes, W. Bogaerts, D. van Thourhout, P. Bienstman, T.K. Liang, M. Tsuchiya, P. Jaenen, S. Beckx, J. Wouters, and R. Baets, “Linear and nonlinear nanophotonic devices based on silicon-oninsulator wire waveguides,” Jap. J. of Appl. Phys. 45, 6589–6602 (2006).
[Crossref]

Berzanskis, A.

S. Minardi, J. Yu, G. Blasi, A. Varanavicius, G. Valiulis, A. Berzanskis, A. Piskarskas, and P. Di Trapani “Red solitons: Evidence of spatiotemporal instability in χ(2) spatial soliton dynamics,” Phys. Rev. Lett. 91, 123901 (2003).
[Crossref] [PubMed]

Bienstman, P.

P. Dumon, G. Priem, L.R. Nunes, W. Bogaerts, D. van Thourhout, P. Bienstman, T.K. Liang, M. Tsuchiya, P. Jaenen, S. Beckx, J. Wouters, and R. Baets, “Linear and nonlinear nanophotonic devices based on silicon-oninsulator wire waveguides,” Jap. J. of Appl. Phys. 45, 6589–6602 (2006).
[Crossref]

Blasi, G.

S. Minardi, J. Yu, G. Blasi, A. Varanavicius, G. Valiulis, A. Berzanskis, A. Piskarskas, and P. Di Trapani “Red solitons: Evidence of spatiotemporal instability in χ(2) spatial soliton dynamics,” Phys. Rev. Lett. 91, 123901 (2003).
[Crossref] [PubMed]

Bogaerts, W.

P. Dumon, G. Priem, L.R. Nunes, W. Bogaerts, D. van Thourhout, P. Bienstman, T.K. Liang, M. Tsuchiya, P. Jaenen, S. Beckx, J. Wouters, and R. Baets, “Linear and nonlinear nanophotonic devices based on silicon-oninsulator wire waveguides,” Jap. J. of Appl. Phys. 45, 6589–6602 (2006).
[Crossref]

Buryak, A.V.

A.V. Buryak, P. Di Trapani, D.V. Skryabin, and S. Trillo, “Optical solitons due to quadratic nonlinearities: from basic physics to futuristic applications,” Phys. Rep. 370, 63–235 (2002).
[Crossref]

Carter, J.D.

B. Deconinck, D.E. Pelinovsky, and J.D. Carter, “Transverse instabilities of deep-water solitary waves,” Proc. of the Royal Soc. A 462, 2039–2061 (2006).
[Crossref]

Cheskis, D.

D. Cheskis, S. Bar-Ad, R. Morandotti, J.S. Aitchison, H.S. Eisenberg, Y. Silberberg, and D. Ross, “Strong Spatiotemporal Localization in a Silica Nonlinear Waveguide Array,” Phys. Rev. Lett. 91, 223901 (2003).
[Crossref] [PubMed]

Christodoulides, D.

Christodoulides, D.N.

J. Meier, G.I. Stegeman, D.N. Christodoulides, Y. Silberberg, R. Morandotti, H. Yang, G. Salamo, M. Sorel, and J.S. Aitchison, “Experimental observation of discrete modulational instability,” Phys. Rev. Lett. 92163902 (2004).
[Crossref] [PubMed]

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

D.N. Christodoulides and R.I. Joseph, “Discrete self-focusing in nonlinear arrays of coupled waveguides,” Opt. Lett. 16, 446–448 (1991).
[Crossref] [PubMed]

Darmanyan, S.

S. Darmanyan, I. Relke, and F. Lederer, “Instability of continuous waves and rotating solitons in waveguide arrays,” Phys. Rev. E 55, 7662–7668 (1997).
[Crossref]

De Angelis, C.

Deconinck, B.

B. Deconinck, D.E. Pelinovsky, and J.D. Carter, “Transverse instabilities of deep-water solitary waves,” Proc. of the Royal Soc. A 462, 2039–2061 (2006).
[Crossref]

Di Trapani, P.

S.D. Jenkins, D. Salerno, S. Minardi, G. Tamosauskas, T.A.B. Kennedy, and P. Di Trapani, “Quantum-noise-initiated symmetry breaking of spatial solitons,” Phys. Rev. Lett. 95, 203902 (2005).
[Crossref] [PubMed]

S. Minardi, J. Yu, G. Blasi, A. Varanavicius, G. Valiulis, A. Berzanskis, A. Piskarskas, and P. Di Trapani “Red solitons: Evidence of spatiotemporal instability in χ(2) spatial soliton dynamics,” Phys. Rev. Lett. 91, 123901 (2003).
[Crossref] [PubMed]

A.V. Buryak, P. Di Trapani, D.V. Skryabin, and S. Trillo, “Optical solitons due to quadratic nonlinearities: from basic physics to futuristic applications,” Phys. Rep. 370, 63–235 (2002).
[Crossref]

F. Wise and P. Di Trapani, “The hunt for light bullets - Spatio-temporal solitons,” Opt. Phot. News (February, 2002), pages 29–32.

Droulias, S.

Dumon, P.

P. Dumon, G. Priem, L.R. Nunes, W. Bogaerts, D. van Thourhout, P. Bienstman, T.K. Liang, M. Tsuchiya, P. Jaenen, S. Beckx, J. Wouters, and R. Baets, “Linear and nonlinear nanophotonic devices based on silicon-oninsulator wire waveguides,” Jap. J. of Appl. Phys. 45, 6589–6602 (2006).
[Crossref]

Eisenberg, H.S.

D. Cheskis, S. Bar-Ad, R. Morandotti, J.S. Aitchison, H.S. Eisenberg, Y. Silberberg, and D. Ross, “Strong Spatiotemporal Localization in a Silica Nonlinear Waveguide Array,” Phys. Rev. Lett. 91, 223901 (2003).
[Crossref] [PubMed]

Emplit, P.

Fibich, G.

A.B. Aceves, G. Fibich, and B. Ilan, “Gap-soliton bullets in waveguide gratings,” Physica D 189, 277–286 (2004).
[Crossref]

Foster, M.A.

M.A. Foster, A.C. Turner, J.E. Sharping, B.S. Schmidt, M. Lipson, and A.L. Gaeta, “Broad-band optical parametric gain on a silicon photonic chip,” Nature 441, 960–963 (2006).
[Crossref] [PubMed]

Gaeta, A.L.

M.A. Foster, A.C. Turner, J.E. Sharping, B.S. Schmidt, M. Lipson, and A.L. Gaeta, “Broad-band optical parametric gain on a silicon photonic chip,” Nature 441, 960–963 (2006).
[Crossref] [PubMed]

Gorza, S.P.

Hadzieski, L.

M. Stepic, L. Hadzieski, and M. Skoric, “Stability of one-dimensional array solitons,” Phys. Rev. E 65, 026604 (2002).
[Crossref]

Haelterman, M.

Hizanidis, K.

Ilan, B.

A.B. Aceves, G. Fibich, and B. Ilan, “Gap-soliton bullets in waveguide gratings,” Physica D 189, 277–286 (2004).
[Crossref]

Jaenen, P.

P. Dumon, G. Priem, L.R. Nunes, W. Bogaerts, D. van Thourhout, P. Bienstman, T.K. Liang, M. Tsuchiya, P. Jaenen, S. Beckx, J. Wouters, and R. Baets, “Linear and nonlinear nanophotonic devices based on silicon-oninsulator wire waveguides,” Jap. J. of Appl. Phys. 45, 6589–6602 (2006).
[Crossref]

Jenkins, S.D.

S.D. Jenkins, D. Salerno, S. Minardi, G. Tamosauskas, T.A.B. Kennedy, and P. Di Trapani, “Quantum-noise-initiated symmetry breaking of spatial solitons,” Phys. Rev. Lett. 95, 203902 (2005).
[Crossref] [PubMed]

Joseph, R.I.

Kartashov, Y.V.

Y.V. Kartashov and L. Torner, “Surface soliton arrays,” Eur. Opt. Soc. Topical Meeting on Nonlinear Optics, TOM 6 (Paris, 2006).

Kennedy, T.A.B.

S.D. Jenkins, D. Salerno, S. Minardi, G. Tamosauskas, T.A.B. Kennedy, and P. Di Trapani, “Quantum-noise-initiated symmetry breaking of spatial solitons,” Phys. Rev. Lett. 95, 203902 (2005).
[Crossref] [PubMed]

Kivshar, Y.S.

Y.S. Kivshar and D.E. Pelinovsky, “Self-focusing and transverse instabilities of solitary waves,” Phys. Rep. 331, 118–195 (2000).
[Crossref]

A.A. Sukhorukov and Y.S. Kivshar, “Slow-light optical bullets in arrays of nonlinear Bragg-grating waveguides,” http://xxx.lanl.gov/abs/physics/0605194.

Laedke, E.W.

E.W. Laedke, K.H. Spatschek, and S.K. Turitsyn, “Stability of Discrete Solitons and Quasicollapse to Intrinsically Localized Modes,” Phys. Rev. Lett. 73, 1055–1059 (1994).
[Crossref] [PubMed]

Lederer, F.

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

S. Darmanyan, I. Relke, and F. Lederer, “Instability of continuous waves and rotating solitons in waveguide arrays,” Phys. Rev. E 55, 7662–7668 (1997).
[Crossref]

Liang, T.K.

P. Dumon, G. Priem, L.R. Nunes, W. Bogaerts, D. van Thourhout, P. Bienstman, T.K. Liang, M. Tsuchiya, P. Jaenen, S. Beckx, J. Wouters, and R. Baets, “Linear and nonlinear nanophotonic devices based on silicon-oninsulator wire waveguides,” Jap. J. of Appl. Phys. 45, 6589–6602 (2006).
[Crossref]

Lipson, M.

M.A. Foster, A.C. Turner, J.E. Sharping, B.S. Schmidt, M. Lipson, and A.L. Gaeta, “Broad-band optical parametric gain on a silicon photonic chip,” Nature 441, 960–963 (2006).
[Crossref] [PubMed]

Malomed, B.A.

B.B. Baizakov, B.A. Malomed, and M. Salerno, “Multidimensional solitons in a low-dimensional periodic potential,” Phys. Rev. A 70053613 (2004).
[Crossref]

Meier, J.

S. Droulias, K. Hizanidis, J. Meier, and D. Christodoulides, “X - waves in nonlinear normally dispersive waveguide arrays,” Opt. Express 13, 1827–1832 (2005).
[Crossref] [PubMed]

J. Meier, G.I. Stegeman, D.N. Christodoulides, Y. Silberberg, R. Morandotti, H. Yang, G. Salamo, M. Sorel, and J.S. Aitchison, “Experimental observation of discrete modulational instability,” Phys. Rev. Lett. 92163902 (2004).
[Crossref] [PubMed]

Minardi, S.

S.D. Jenkins, D. Salerno, S. Minardi, G. Tamosauskas, T.A.B. Kennedy, and P. Di Trapani, “Quantum-noise-initiated symmetry breaking of spatial solitons,” Phys. Rev. Lett. 95, 203902 (2005).
[Crossref] [PubMed]

S. Minardi, J. Yu, G. Blasi, A. Varanavicius, G. Valiulis, A. Berzanskis, A. Piskarskas, and P. Di Trapani “Red solitons: Evidence of spatiotemporal instability in χ(2) spatial soliton dynamics,” Phys. Rev. Lett. 91, 123901 (2003).
[Crossref] [PubMed]

Morandotti, R.

J. Meier, G.I. Stegeman, D.N. Christodoulides, Y. Silberberg, R. Morandotti, H. Yang, G. Salamo, M. Sorel, and J.S. Aitchison, “Experimental observation of discrete modulational instability,” Phys. Rev. Lett. 92163902 (2004).
[Crossref] [PubMed]

D. Cheskis, S. Bar-Ad, R. Morandotti, J.S. Aitchison, H.S. Eisenberg, Y. Silberberg, and D. Ross, “Strong Spatiotemporal Localization in a Silica Nonlinear Waveguide Array,” Phys. Rev. Lett. 91, 223901 (2003).
[Crossref] [PubMed]

Nunes, L.R.

P. Dumon, G. Priem, L.R. Nunes, W. Bogaerts, D. van Thourhout, P. Bienstman, T.K. Liang, M. Tsuchiya, P. Jaenen, S. Beckx, J. Wouters, and R. Baets, “Linear and nonlinear nanophotonic devices based on silicon-oninsulator wire waveguides,” Jap. J. of Appl. Phys. 45, 6589–6602 (2006).
[Crossref]

Pelinovsky, D.E.

B. Deconinck, D.E. Pelinovsky, and J.D. Carter, “Transverse instabilities of deep-water solitary waves,” Proc. of the Royal Soc. A 462, 2039–2061 (2006).
[Crossref]

Y.S. Kivshar and D.E. Pelinovsky, “Self-focusing and transverse instabilities of solitary waves,” Phys. Rep. 331, 118–195 (2000).
[Crossref]

Piskarskas, A.

S. Minardi, J. Yu, G. Blasi, A. Varanavicius, G. Valiulis, A. Berzanskis, A. Piskarskas, and P. Di Trapani “Red solitons: Evidence of spatiotemporal instability in χ(2) spatial soliton dynamics,” Phys. Rev. Lett. 91, 123901 (2003).
[Crossref] [PubMed]

Priem, G.

P. Dumon, G. Priem, L.R. Nunes, W. Bogaerts, D. van Thourhout, P. Bienstman, T.K. Liang, M. Tsuchiya, P. Jaenen, S. Beckx, J. Wouters, and R. Baets, “Linear and nonlinear nanophotonic devices based on silicon-oninsulator wire waveguides,” Jap. J. of Appl. Phys. 45, 6589–6602 (2006).
[Crossref]

Relke, I.

S. Darmanyan, I. Relke, and F. Lederer, “Instability of continuous waves and rotating solitons in waveguide arrays,” Phys. Rev. E 55, 7662–7668 (1997).
[Crossref]

Ross, D.

D. Cheskis, S. Bar-Ad, R. Morandotti, J.S. Aitchison, H.S. Eisenberg, Y. Silberberg, and D. Ross, “Strong Spatiotemporal Localization in a Silica Nonlinear Waveguide Array,” Phys. Rev. Lett. 91, 223901 (2003).
[Crossref] [PubMed]

Rubenchik, A. M.

Rubenchik, A.M.

V.E. Zakharov and A.M. Rubenchik, “Instability of waveguides and solitons in nonlinear media,” Zh. Eksp. Teor. Fiz.65, 997–1011 (1973) [Sov. Phys. JETP 38, 494 (1974).

Russell, P. St.J.

P. St.J. Russell, “Photonic crystal fibers,” Science 299, 358–362 (2003).
[Crossref] [PubMed]

Salamo, G.

J. Meier, G.I. Stegeman, D.N. Christodoulides, Y. Silberberg, R. Morandotti, H. Yang, G. Salamo, M. Sorel, and J.S. Aitchison, “Experimental observation of discrete modulational instability,” Phys. Rev. Lett. 92163902 (2004).
[Crossref] [PubMed]

Salerno, D.

S.D. Jenkins, D. Salerno, S. Minardi, G. Tamosauskas, T.A.B. Kennedy, and P. Di Trapani, “Quantum-noise-initiated symmetry breaking of spatial solitons,” Phys. Rev. Lett. 95, 203902 (2005).
[Crossref] [PubMed]

Salerno, M.

B.B. Baizakov, B.A. Malomed, and M. Salerno, “Multidimensional solitons in a low-dimensional periodic potential,” Phys. Rev. A 70053613 (2004).
[Crossref]

Schmidt, B.S.

M.A. Foster, A.C. Turner, J.E. Sharping, B.S. Schmidt, M. Lipson, and A.L. Gaeta, “Broad-band optical parametric gain on a silicon photonic chip,” Nature 441, 960–963 (2006).
[Crossref] [PubMed]

Sekaric, L.

Sharping, J.E.

M.A. Foster, A.C. Turner, J.E. Sharping, B.S. Schmidt, M. Lipson, and A.L. Gaeta, “Broad-band optical parametric gain on a silicon photonic chip,” Nature 441, 960–963 (2006).
[Crossref] [PubMed]

Silberberg, Y.

J. Meier, G.I. Stegeman, D.N. Christodoulides, Y. Silberberg, R. Morandotti, H. Yang, G. Salamo, M. Sorel, and J.S. Aitchison, “Experimental observation of discrete modulational instability,” Phys. Rev. Lett. 92163902 (2004).
[Crossref] [PubMed]

D. Cheskis, S. Bar-Ad, R. Morandotti, J.S. Aitchison, H.S. Eisenberg, Y. Silberberg, and D. Ross, “Strong Spatiotemporal Localization in a Silica Nonlinear Waveguide Array,” Phys. Rev. Lett. 91, 223901 (2003).
[Crossref] [PubMed]

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

Skoric, M.

M. Stepic, L. Hadzieski, and M. Skoric, “Stability of one-dimensional array solitons,” Phys. Rev. E 65, 026604 (2002).
[Crossref]

Skryabin, D.V.

A.V. Buryak, P. Di Trapani, D.V. Skryabin, and S. Trillo, “Optical solitons due to quadratic nonlinearities: from basic physics to futuristic applications,” Phys. Rep. 370, 63–235 (2002).
[Crossref]

Sorel, M.

J. Meier, G.I. Stegeman, D.N. Christodoulides, Y. Silberberg, R. Morandotti, H. Yang, G. Salamo, M. Sorel, and J.S. Aitchison, “Experimental observation of discrete modulational instability,” Phys. Rev. Lett. 92163902 (2004).
[Crossref] [PubMed]

Soto-Crespo, J.M.

N. Akhmediev and J.M. Soto-Crespo, “Generation of a train of three-dimensional optical solitons in a selffocusing medium,” Phys. Rev. A 47, 1358–1364 (1993).
[Crossref] [PubMed]

Spatschek, K.H.

E.W. Laedke, K.H. Spatschek, and S.K. Turitsyn, “Stability of Discrete Solitons and Quasicollapse to Intrinsically Localized Modes,” Phys. Rev. Lett. 73, 1055–1059 (1994).
[Crossref] [PubMed]

Stegeman, G.I.

J. Meier, G.I. Stegeman, D.N. Christodoulides, Y. Silberberg, R. Morandotti, H. Yang, G. Salamo, M. Sorel, and J.S. Aitchison, “Experimental observation of discrete modulational instability,” Phys. Rev. Lett. 92163902 (2004).
[Crossref] [PubMed]

Stepic, M.

M. Stepic, L. Hadzieski, and M. Skoric, “Stability of one-dimensional array solitons,” Phys. Rev. E 65, 026604 (2002).
[Crossref]

Sukhorukov, A.A.

A.A. Sukhorukov and Y.S. Kivshar, “Slow-light optical bullets in arrays of nonlinear Bragg-grating waveguides,” http://xxx.lanl.gov/abs/physics/0605194.

Tamosauskas, G.

S.D. Jenkins, D. Salerno, S. Minardi, G. Tamosauskas, T.A.B. Kennedy, and P. Di Trapani, “Quantum-noise-initiated symmetry breaking of spatial solitons,” Phys. Rev. Lett. 95, 203902 (2005).
[Crossref] [PubMed]

Torner, L.

Y.V. Kartashov and L. Torner, “Surface soliton arrays,” Eur. Opt. Soc. Topical Meeting on Nonlinear Optics, TOM 6 (Paris, 2006).

Trillo, S.

A.V. Buryak, P. Di Trapani, D.V. Skryabin, and S. Trillo, “Optical solitons due to quadratic nonlinearities: from basic physics to futuristic applications,” Phys. Rep. 370, 63–235 (2002).
[Crossref]

Tsuchiya, M.

P. Dumon, G. Priem, L.R. Nunes, W. Bogaerts, D. van Thourhout, P. Bienstman, T.K. Liang, M. Tsuchiya, P. Jaenen, S. Beckx, J. Wouters, and R. Baets, “Linear and nonlinear nanophotonic devices based on silicon-oninsulator wire waveguides,” Jap. J. of Appl. Phys. 45, 6589–6602 (2006).
[Crossref]

Turitsyn, S. K.

Turitsyn, S.K.

E.W. Laedke, K.H. Spatschek, and S.K. Turitsyn, “Stability of Discrete Solitons and Quasicollapse to Intrinsically Localized Modes,” Phys. Rev. Lett. 73, 1055–1059 (1994).
[Crossref] [PubMed]

Turner, A.C.

M.A. Foster, A.C. Turner, J.E. Sharping, B.S. Schmidt, M. Lipson, and A.L. Gaeta, “Broad-band optical parametric gain on a silicon photonic chip,” Nature 441, 960–963 (2006).
[Crossref] [PubMed]

Valiulis, G.

S. Minardi, J. Yu, G. Blasi, A. Varanavicius, G. Valiulis, A. Berzanskis, A. Piskarskas, and P. Di Trapani “Red solitons: Evidence of spatiotemporal instability in χ(2) spatial soliton dynamics,” Phys. Rev. Lett. 91, 123901 (2003).
[Crossref] [PubMed]

van Thourhout, D.

P. Dumon, G. Priem, L.R. Nunes, W. Bogaerts, D. van Thourhout, P. Bienstman, T.K. Liang, M. Tsuchiya, P. Jaenen, S. Beckx, J. Wouters, and R. Baets, “Linear and nonlinear nanophotonic devices based on silicon-oninsulator wire waveguides,” Jap. J. of Appl. Phys. 45, 6589–6602 (2006).
[Crossref]

Varanavicius, A.

S. Minardi, J. Yu, G. Blasi, A. Varanavicius, G. Valiulis, A. Berzanskis, A. Piskarskas, and P. Di Trapani “Red solitons: Evidence of spatiotemporal instability in χ(2) spatial soliton dynamics,” Phys. Rev. Lett. 91, 123901 (2003).
[Crossref] [PubMed]

Vlasov, Y.A.

Wise, F.

F. Wise and P. Di Trapani, “The hunt for light bullets - Spatio-temporal solitons,” Opt. Phot. News (February, 2002), pages 29–32.

Wouters, J.

P. Dumon, G. Priem, L.R. Nunes, W. Bogaerts, D. van Thourhout, P. Bienstman, T.K. Liang, M. Tsuchiya, P. Jaenen, S. Beckx, J. Wouters, and R. Baets, “Linear and nonlinear nanophotonic devices based on silicon-oninsulator wire waveguides,” Jap. J. of Appl. Phys. 45, 6589–6602 (2006).
[Crossref]

Xia, F.N.

Yang, H.

J. Meier, G.I. Stegeman, D.N. Christodoulides, Y. Silberberg, R. Morandotti, H. Yang, G. Salamo, M. Sorel, and J.S. Aitchison, “Experimental observation of discrete modulational instability,” Phys. Rev. Lett. 92163902 (2004).
[Crossref] [PubMed]

Yu, J.

S. Minardi, J. Yu, G. Blasi, A. Varanavicius, G. Valiulis, A. Berzanskis, A. Piskarskas, and P. Di Trapani “Red solitons: Evidence of spatiotemporal instability in χ(2) spatial soliton dynamics,” Phys. Rev. Lett. 91, 123901 (2003).
[Crossref] [PubMed]

Zakharov, V.E.

V.E. Zakharov and A.M. Rubenchik, “Instability of waveguides and solitons in nonlinear media,” Zh. Eksp. Teor. Fiz.65, 997–1011 (1973) [Sov. Phys. JETP 38, 494 (1974).

Jap. J. of Appl. Phys. (1)

P. Dumon, G. Priem, L.R. Nunes, W. Bogaerts, D. van Thourhout, P. Bienstman, T.K. Liang, M. Tsuchiya, P. Jaenen, S. Beckx, J. Wouters, and R. Baets, “Linear and nonlinear nanophotonic devices based on silicon-oninsulator wire waveguides,” Jap. J. of Appl. Phys. 45, 6589–6602 (2006).
[Crossref]

Nature (2)

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

M.A. Foster, A.C. Turner, J.E. Sharping, B.S. Schmidt, M. Lipson, and A.L. Gaeta, “Broad-band optical parametric gain on a silicon photonic chip,” Nature 441, 960–963 (2006).
[Crossref] [PubMed]

Opt. Express (2)

Opt. Lett. (3)

Phys. Rep. (2)

Y.S. Kivshar and D.E. Pelinovsky, “Self-focusing and transverse instabilities of solitary waves,” Phys. Rep. 331, 118–195 (2000).
[Crossref]

A.V. Buryak, P. Di Trapani, D.V. Skryabin, and S. Trillo, “Optical solitons due to quadratic nonlinearities: from basic physics to futuristic applications,” Phys. Rep. 370, 63–235 (2002).
[Crossref]

Phys. Rev. A (2)

B.B. Baizakov, B.A. Malomed, and M. Salerno, “Multidimensional solitons in a low-dimensional periodic potential,” Phys. Rev. A 70053613 (2004).
[Crossref]

N. Akhmediev and J.M. Soto-Crespo, “Generation of a train of three-dimensional optical solitons in a selffocusing medium,” Phys. Rev. A 47, 1358–1364 (1993).
[Crossref] [PubMed]

Phys. Rev. E (2)

S. Darmanyan, I. Relke, and F. Lederer, “Instability of continuous waves and rotating solitons in waveguide arrays,” Phys. Rev. E 55, 7662–7668 (1997).
[Crossref]

M. Stepic, L. Hadzieski, and M. Skoric, “Stability of one-dimensional array solitons,” Phys. Rev. E 65, 026604 (2002).
[Crossref]

Phys. Rev. Lett. (5)

J. Meier, G.I. Stegeman, D.N. Christodoulides, Y. Silberberg, R. Morandotti, H. Yang, G. Salamo, M. Sorel, and J.S. Aitchison, “Experimental observation of discrete modulational instability,” Phys. Rev. Lett. 92163902 (2004).
[Crossref] [PubMed]

E.W. Laedke, K.H. Spatschek, and S.K. Turitsyn, “Stability of Discrete Solitons and Quasicollapse to Intrinsically Localized Modes,” Phys. Rev. Lett. 73, 1055–1059 (1994).
[Crossref] [PubMed]

S. Minardi, J. Yu, G. Blasi, A. Varanavicius, G. Valiulis, A. Berzanskis, A. Piskarskas, and P. Di Trapani “Red solitons: Evidence of spatiotemporal instability in χ(2) spatial soliton dynamics,” Phys. Rev. Lett. 91, 123901 (2003).
[Crossref] [PubMed]

S.D. Jenkins, D. Salerno, S. Minardi, G. Tamosauskas, T.A.B. Kennedy, and P. Di Trapani, “Quantum-noise-initiated symmetry breaking of spatial solitons,” Phys. Rev. Lett. 95, 203902 (2005).
[Crossref] [PubMed]

D. Cheskis, S. Bar-Ad, R. Morandotti, J.S. Aitchison, H.S. Eisenberg, Y. Silberberg, and D. Ross, “Strong Spatiotemporal Localization in a Silica Nonlinear Waveguide Array,” Phys. Rev. Lett. 91, 223901 (2003).
[Crossref] [PubMed]

Physica D (1)

A.B. Aceves, G. Fibich, and B. Ilan, “Gap-soliton bullets in waveguide gratings,” Physica D 189, 277–286 (2004).
[Crossref]

Proc. of the Royal Soc. A (1)

B. Deconinck, D.E. Pelinovsky, and J.D. Carter, “Transverse instabilities of deep-water solitary waves,” Proc. of the Royal Soc. A 462, 2039–2061 (2006).
[Crossref]

Science (1)

P. St.J. Russell, “Photonic crystal fibers,” Science 299, 358–362 (2003).
[Crossref] [PubMed]

Other (4)

F. Wise and P. Di Trapani, “The hunt for light bullets - Spatio-temporal solitons,” Opt. Phot. News (February, 2002), pages 29–32.

A.A. Sukhorukov and Y.S. Kivshar, “Slow-light optical bullets in arrays of nonlinear Bragg-grating waveguides,” http://xxx.lanl.gov/abs/physics/0605194.

V.E. Zakharov and A.M. Rubenchik, “Instability of waveguides and solitons in nonlinear media,” Zh. Eksp. Teor. Fiz.65, 997–1011 (1973) [Sov. Phys. JETP 38, 494 (1974).

Y.V. Kartashov and L. Torner, “Surface soliton arrays,” Eur. Opt. Soc. Topical Meeting on Nonlinear Optics, TOM 6 (Paris, 2006).

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Figures (2)

Fig. 1.
Fig. 1.

MI of discrete solitons. The first row corresponds to C=7, the second to C=15 and the third one to C=30, respectively. q=10 and N=51 for all the panels. The right column shows transverse profiles of the discrete solitons. The middle column presents the frequency dependence of the MI growth rate (Iml>0) in the anomalous GVD regime (s<0). The right column shows all the unstable eigenvalues in the case of the normal GVD (s>0). Letters ‘N’ and ‘S’ mark the ‘neck’ and ‘snake’ instabilities, respectively.

Fig. 2.
Fig. 2.

The left column shows patterns of the ‘neck’ instability for anomalous GVD (s< 0) for 3 consequential values of the propagation distance z: C=7. The middle column shows patterns of the ‘neck’ instability for normal GVD (s>0): C=7. The right column shows patterns of the ‘snake’ instability for normal GVD (s>0): C=30. q=10 and N=51 for all the panels.

Equations (4)

Equations on this page are rendered with MathJax. Learn more.

i ζ U n 1 2 β 2 τ 2 U n + κ ( U n + 1 + U n 1 2 U n ) + γ U n 2 U n = 0 , n = 1 , 2 N ,
A n = [ a n + ε n , + e i ω t i λ z + ε n , * e i λ * z i ω t ] e iqz .
λ ε = L ̂ 0 ε + 1 2 s ω 2 L ̂ 1 ε ,
[ q ~ 2 γ a 1 2 γ a 1 2 C 0 C 0 γ a 1 2 q ~ + 2 γ a 1 2 0 C 0 C C 0 q ~ 2 γ a 2 2 γ a 2 2 0 0 0 C γ a 2 2 q ~ + 2 γ a 2 2 0 0 C 0 0 0 q ~ 2 γ a N 2 γ a N 2 0 C 0 0 γ a N 2 q ~ + 2 γ a N 2 ] ,

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