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Break Up of N-Soliton Bound State in a Gradient Refractive Index Waveguide with Nonlocal Nonlinearity

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DOI: 10.4236/opj.2012.23027    2,776 Downloads   4,760 Views  


We study the propagation of N-soliton bound state in a triangular gradient refractive index waveguide with nonlocal nonlinearity. The study is based on the direct numerical solutions of the model and subsequent eigenvalues evolution of the corresponding Zakharov-Shabat spectral problem. In the waveguide with local nonlinearity, the velocity of a single soliton is found to be symmetric around zero and therefore the soliton oscillates periodically inside the waveguide. If the nonlocality is presence in the medium, the periodic motion of soliton is destroyed due to the soliton experiences additional positive acceleration induced by the nonlocality. In the waveguide with the same strength of nonlocality, a higher amplitude soliton experiences higher nonlocality effects, i.e. larger acceleration. Based on this soliton behavior we predict the break up of N-soliton bound state into their single-soliton constituents. We notice that the splitting process does not affect the amplitude of each soliton component.

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I. Darti, S. Suhariningsih, M. Marjono and A. Suryanto, "Break Up of N-Soliton Bound State in a Gradient Refractive Index Waveguide with Nonlocal Nonlinearity," Optics and Photonics Journal, Vol. 2 No. 3, 2012, pp. 178-184. doi: 10.4236/opj.2012.23027.


[1] S. H. Crutcher, A. J. Osei and M. E. Edwards, “Optical Spatial Solitons, the Power Law, and the Swing Effect,” Proceedings of SPIE, Vol. 7056, 2008, p. 70560Q. HUdoi:10.1117/12.792007U
[2] M. Ebnali-Heidari, M. K. Moravvej-Farshi and A. Zarifkar, “Swing Effect of Spatial Solitons Propagating through Gaussian and Triangular Waveguides,” Applied Optics, Vol. 48, No. 26, 2009, pp. 5005-5014. HUdoi:10.1364/AO.48.005005U
[3] W. Krolikowski and O. Bang, “Solitons in Nonlocal Nonlinear Media: Exact Solutions,” Physical Review E, Vol. 63, No. 1, 2000, p. 016610. HUdoi:10.1103/PhysRevE.63.016610U
[4] V. Aleshkevich, Y. Kartashov and V. Vysloukh, “SelfBending of the Coupled Spatial Soliton Pairs in a Photorefractive Medium with Drift and Diffusion Nonlinearity,” Physical Review E, Vol. 63, No. 1, 2000, p. 016603. Hdoi:10.1103/PhysRevE.63.016603U
[5] J. Petter, C. Weilnau, C. Denz, A. Stepken and F. Kaiser, “Self-Bending of Photorefractive Solitons,” Optics Communications, Vol. 170, No. 4, 1999, pp. 291-297. HUdoi:10.1016/S0030-4018(99)00485-XU
[6] Y. V. Izdebskaya, V. G. Shvedov, A. S. Desyatnikov, W. Krolikowski and Y. S. Kivshar, “Soliton Bending and Routing Induced by Interaction with Curved Surfaces in Nematic Liquid Crystals,” Optics Letters, Vol. 35, No. 10, 2010, pp. 1692-1694. HUdoi:10.1364/OL.35.001692U
[7] A. Suryanto and I. Darti, “Soliton Steering in a Ramp Waveguide with Nonlocal Nonlinearity,” Journal Nonlinear Optical Physics and Materials, Vol. 20, No. 1, 2011, pp. 33-41. HUdoi:10.1142/S0218863511005826U
[8] A. Suryanto and I. Darti, “Dynamics of Spatial Soliton in a Gradient Refractive Index Waveguide with Nonlocal Nonlinearity,” International Journal of Applied Mathematics and Statistics, Vol. 28, No. 4, 2012, pp. 23-30.
[9] S. V. Manakov, S. P. Novikov, L. P. Pitaevskii and V. E. Zakharov, “Theory of Solitons,” Consultants Bureu, New York, 1984.
[10] V. A. Aleshkevich, Y. V. Kartashov, A. S. Zelenina, V. A. Vysloukh, J. P. Torres and L. Torner, “Eigenvalue Control and Switching by Fission of Multisoliton Bound States in Planar Waveguides,” Optics Letters, Vol. 29, No. 5, 2004, pp. 483-485. HUdoi:10.1364/OL.29.000483U
[11] A. Suryanto and E. van Groesen, “Break up of Bound-NSpatial-Soliton in a Ramp Waveguide,” Optical Quantum Electronics, Vol. 34, No. 5, 2002, pp. 597-606. HUdoi:10.1023/A:1015685122513U
[12] A. Suryanto and E. van Groesen, “Self-Splitting of Multisoliton Bound States in Planar Waveguides,” Optics Communications, Vol. 258, No. 2, 2006, pp. 264-274. HUdoi:10.1016/j.optcom.2005.07.063U
[13] K. Zhou, Z. Guo and S. Liu, “Position Dependent Splitting of Bound States in Periodic Photonic Lattices,” Journal of the Optical Society of America B, Vol. 27, No. 5, 2010, pp. 1099-1103. HUdoi:10.1364/JOSAB.27.001099U
[14] Y. V. Kartashov, L. C. Crasovan, A. S. Zelenina, V. A. Vysloukh, A. Sanpera, M. Lewenstein and L. Torner, “Soliton Eigenvalue Control in Optical Lattices,” Physical Review Letters, Vol. 93, No. 14, 2004, p. 143902. HUdoi:10.1103/PhysRevLett.93.143902U
[15] O. Katz, Y. Lahini and Y. Silberberg, “Multiple Break up of High-Order Spatial Soliton,” Optics Letters, Vol. 33, No. 23, 2008, pp. 2830-2832. HUdoi:10.1364/OL.33.002830U
[16] J. E. Prilepsky and S. A. Derevyanko, “Breakup of a Multisoliton State of the Linearly Damped Nonlinear Schrodinger Equation,” Physical Review E, Vol. 75, No. 3, 2007, p. 036616. HUdoi:10.1103/PhysRevE.75.036616U
[17] S. Pu, C. Hou, K. Zhan, C. Yuan and Y. Du, “Spatial Solitons in Nonlocal Materials with Defocusing Effects,” Optics Communications, Vol. 285, No. 6, 2012, pp. 14561460. HUdoi:10.1016/j.optcom.2011.11.037U
[18] Y. V. Kartashov, V. A. Vysloukh and L. Torner, “Tunable Soliton Self-Bending in Optical Lattices with Nonlocal Nonlinearity,” Physical Review Letter, Vol. 93, No. 15, 2004, p. 153903. HUdoi:10.1103/PhysRevLett.93.153903U
[19] V. E. Zakharov and A. B. Shabat, “Exact Theory of TwoDimensional Self-Focusing and One-Dimensional Self-Modulation of Waves in Nonlinear Media,” Journal of Experimental and Theoretical Physics, Vol. 34, No. 1, 1972, pp. 62-69.
[20] A. Hasegawa and Y. Kodama, “Solitons in Optical Communications,” Clarendon Press, Oxford, 1995.
[21] J. Satsuma and N. Yajima, “Initial Value Problems of One-Dimensional Self-Modulation of Nonlinear Waves in Dispersive Media,” Progress of Theoretical Physics Supplement, No. 55, 1974, pp. 284-306.
[22] P. Chamorro-Posada, G. S. McDonald, G. H. C. New and F. J. Fraile-Pelaez, “Fast Algorithm for the Evolution of Optical Solitons under Perturbations,” IEEE Transactions on Magnetics, Vol. 35, No. 3, 1999, pp. 1558-1561. HUdoi:10.1109/20.767268U
[23] I. Darti, Suhariningsih, Marjono and A. Suryanto, “A Conservative Finite Difference Scheme for Simulation of Soliton in Inhomogeneous Medium with Nonlocal Nonlinearity,” International Journal of Mathematics and Computation, Vol. 13. No. D11, 2011, pp. 69-77.

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