Transmission, reflection, scattering, and trapping of traveling discrete solitons by $\mathcal{C}$ and $\mathcal{V}$ point defects

Abstract

We study the interactions of moving discrete solitons in waveguide arrays with two types of point defects that are constructed by varying either the local linear coupling or local waveguide propagation constant at the center of the waveguide array. A broad discrete soliton is kicked toward the defect and interacts with it. Transmission, reflection, scattering, and trapping during the interaction between the soliton and the defect occur depending on the parameters. The detailed behavior of the soliton dynamics is analyzed numerically. A transmission window in the parameter domain is found and the behavior of this window for different parameters is studied. The dynamics of the soliton in the transmission window is found to have chaotic features under certain circumstances and the causes of these phenomena are identified and discussed.

Graphical abstract

Keywords

traveling discrete soliton / waveguide arrays / -defect and -defect

References

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

[2] D. N. Christodoulides, F. Lederer, and Y. Silberberg, Discretizing light behaviour in linear and nonlinear waveguide lattices, Nature424(6950), 817 (2003)

[3] I. L. Garanovich, S. Longhi, A. A. Sukhorukova, and Y. S. Kivshar, Light propagation and localization in modulated photonic lattices and waveguides, Phys. Rep.518(1-2), 1 (2012)

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

[5] C. Lou, L. Tang, D. Song, X. Wang, J. Xu, and Z. Chen, Novel spatial solitons in light-induced photonic bandgap structures, Front. Phys.3(1), 1 (2008)

[6] D. N. Christodoulides and E. D. Eugenieva, Blocking and routing discrete solitons in two-dimensional networks of nonlinear waveguide arrays., Phys. Rev. Lett.87(23), 233901 (2001)

[7] V. Ahufinger, A. Sanpera, P. Pedri, L. Santos, and M. Lewenstein, Creation and mobility of discrete solitons in Bose-Einstein condensates, Phys. Rev. A69(5), 053604 (2004)

[8] R. A. Vicencio and M. Johansson, Discrete soliton mobility in two-dimensional waveguide arrays with saturable nonlinearity, Phys. Rev. E73(4), 046602 (2006)

[9] Y. V. Kartashov, V. A. Vysloukh, and L. Torner, Soliton shape and mobility control in optical lattices, Progress in Optics52, 63 (2009)

[10] Y. S. Kivshar and B. A. Malomed, Dynamics of solitons in nearly integrable systems, Rev. Mod. Phys.61(4), 763 (1989)

[11] V. V. Konotop, O. A. Chubykalo, and L. Vázquez, Dynamics and interaction of solitons on an integrable inhomogeneous lattice, Phys. Rev. E48(1), 563 (1993)

[12] D. Cai, A. R. Bishop, N. Grøbech-Jensen, and B. A. Malomed, Moving solitons in the damped Ablowitz-Ladik model driven by a standing wave, Phys. Rev. E50(2), R694 (1994)

[13] U. Peschel, R. Morandotti, J. S. Aitchison, H. S. Eisenberg, and Y. Silberberg, Nonlinearly induced escape from a defect state in waveguide arrays, Appl. Phys. Lett.75(10), 1348 (1999)

[14] R. Morandotti, H. S. Eisenberg, D. Mandelik, Y. Silberberg, D. Modotto, M. Sorel, C. R. Stanley, and J. S. Aitchison, Interactions of discrete solitons with structural defects, Opt. Lett.28(10), 834 (2003)

[15] L. Morales-Molina and R. A. Vicencio, Trapping of discrete solitons by defects in nonlinear waveguide arrays, Opt. Lett.31(7), 966 (2006)

[16] M. I. Molina, I. L. Garanovich, A. A. Sukhorukov, and Y. S. Kivshar, Discrete surface solitons in semiinfinite binary waveguide arrays, Opt. Lett.33(15), 2332 (2006)

[17] M. I. Molina and Y. S. Kivshar, Nonlinear localized modes at phase-slip defects in waveguide arrays, Opt. Lett.33(9), 917 (2008)

[18] Y. Li, W. Pang, Y. Chen, Z. Yu, J. Zhou, and H. Zhang, Defect-mediated discrete solitons in optically induced photorefractive lattices, Phys. Rev. A80(4), 043824 (2009)

[19] X. Zhang, J. Chai, J. Huang, Z. Chen, Y. Li, and B. A. Malomed, Discrete solitons and scatttering of lattice waves in guiding arrays with a nonlinear PT-symmetricdefect, Opt. Exp.22(11), 13927 (2014)

[20] X. Zhang, J. Chai, D. Ou, and Y. Li, Antisymmetry breaking of discrete dipole gap solitons induced by a phase-slip defect, Mod. Phys. Lett. B28(12), 1450097 (2014)

[21] S. V. Dmitriev, S. V. Suchkov, A. A. Sukhorukov, and Y. S. Kivshar, Scattering of linear and nonlinear waves in a waveguide array with a PT-symmetric defect, Phys. Rev. A84(1), 013833 (2011)

[22] S. V. Suchkov, A. A. Sukhorukov, S. V. Dmitriev, and Y. S. Kivshar, Scattering of the discrete solitons on the Ptsymmetric defects, Eur. Phys. Lett.100(5), 54003 (2012)

[23] A. Regensburger, M. A. Miri, C. Bersch, J. Nager, G. Onishchukov, D. N. Christodoulides, and U. Peschel, Observation of defect states in PT-symmetric optical lattices, Phys. Rev. Lett.110(22), 223902 (2013)

[24] M. L. Chiofalo, S. Succi, and M. P. Tosi, Ground state of trapped interacting Bose-Einstein condensates by an explicit imaginary-time algorithm, Phys. Rev. E62(5), 7438 (2000)

[25] J. Yang, Newton-conjugate gradient methods for solitary wave computations, J. Comput. Phys.228(18), 7007 (2009)

[26] O. Morsch and M. Oberthaler, Dynamics of Bose-Einstein condensates in optical lattices, Rev. Mod. Phys.78(1), 179 (2006)

[27] Y. Li, J. Liu, W. Pang, and B. A. Malomed, Lattice solitons with quadrupolar intersite interactions, Phys. Rev. A88(6), 063635 (2013)

[28] S. W. Song, L. Wen, C. F. Liu, S. C. Gou, and W. M. Liu, Ground states, solitons and spin textures in spin-1 Bose- Einstein condensates, Front. Phys.8(3), 302 (2013)

[29] C. Lee, J. Huang, H. Deng, H. Dai, and J. Xu, Nonlinear quantum interferometry with Bose condensed atoms, Front. Phys.7(1), 109 (2012)

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2014 Higher Education Press and Springer-Verlag Berlin Heidelberg