Numerical Analysis of Stability for Temporal Bright Solitons in a PT-Symmetric NLDC

Document Type : Articles

Authors

• Lida Safaei ¹
• Mohsen Hatami ²
• mahmood Borhani Zarandi ¹

¹ Department of Physics, University of Yazd, Yazd, Iran

² Department of Physics, University of Shiraz Technology, Shiraz, Iran

Abstract

PT-Symmetry is one of the interesting topics in quantum mechanics and optics. One of the demonstration of PT-Symmetric effects in optics is appeared in the nonlinear directional coupler (NLDC). In the paper we numerically investigate the stability of temporal bright solitons propagate in a PT-Symmetric NLDC by considering gain in bar and loss in cross. By using the analytical solutions of perturbed eigenfunctions and corresponding eigenvalues the stability of temporal bright solitons is studied numerically. Three perturbed eigenfunctions corresponding to the two eigenvalues are examined for stability. The results show that the two degenerate eigenfunctions are unstable while other one is stable which have important result that the eigenfunctions are equilibrium function but not stable for all cases. Stability is tested by using energy of perturbed soliton that propagate thought the length of NLDC. In addition, the behavior of solitons under instable perturbation in a PT-Symmetric NLDC can be used to design integrated optics at Nano scales, for ultrafast all optical communication systems and logic gates.

Keywords

• Nano Couplers
• Fibers
• Nonlinear Optics
• Photonics
• Solitons
• PT-Symmetry

20.1001.1.24237361.2017.2.3.7.5

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References

[1]     R. Boyed, Nonlinear Optics , third edition. Academic Press,  2009, 336-383.

[2]     Y. Kivshar, G. P. Agrawal, Optical Solitons from fibers to photonic crystals, Academic Press, 2003.

[3]     L. Feng, Z. J. Wong, R. M. Ma, Y. Wang and X. Zhang, Single-mode laser by parity-time symmetry breaking, Science, 346 (2014) 972.

[4]     A. Zakeri and M. Hatami,  Design of an ultra-fast all-optical dark soliton switch in a nonlinear directional coupler (NLDC) made of chalcogenide glasses, Applied Physicd D. 12 (2007) 591.

[5]     G. P. Agrawal, Application of nonlinear fiber optics, Academic Press, 2001.

[6]     J. S. Russell, British association reports, John Murray, London, 1984.

[7]     T. Dauxois, M. Peyrard, Physics of Solitons, Cambridge University Press, 2006.

[8]     A.C. Newell, Solitons in Mathematics and Physics, SIAM, Philadelphia, 1985.

[9]     G. Agrawal, Nonlinear fiber optics, 4th Edition, Academic Press, 2007.

[10]  L. Safaei, M. Hatami and M. Borhani Zarandi, Pt-Symmetric Nonlinear Directional Fiber Couplers with Gain and Loss for Ultrashort Optical Pulses, J Laser Opt Photonics, 4 (2017)155.

[11]  J. C. Bender and S. Boettcher, Real spectra in non- Hermitian Hamiltonians having PT- symmetry, Phys. Rev. Lett. 80(1998) 5243.

[12]  E. Rueter, K. G. Makris, R. El-Ganainy, D. N. Christodoulides, M. Segev and D. Kip, “Observation of parity-time symmetry in optics”, Nat. Phys. 6 (2010)192.

[13]  S. Suchkov, A. Sukhorukov, J. Huang, S. Dmitriev, C. Lee andY. Kivshar, Nonlinear switching and solitons in PT-symmetric photonic systems, Laserand Photonics Rev. 10 (2015).

[14]  L. Safaei, M. Hatami and M. B. Zarndi, Stability of Temporal Dark Soliton in PT-Symmetric Nonlinear Fiber Couplers in Normal Dispersion Regime, J Laser Opt Photonics, 3 (2016) 141.

[15]  J. Yang, Nonlinear Wavesin Integrable and Nonintegrable Systems, SIAM Press, (2010) 119-162.

[16]  E. Gromov, B. Malomed and V. Tyutin, Vector solitons in coupled nonlinear Schrodinger equations with spatial stimulated scattering and inhomogeneous dispersion, Communications in Nonlinear Science and Numerical Simulation, 54(2017).

[17]  X. Chen and J. Yang, A direct perturbation theory for solitons of the derivative nonlinear Schrodinger equation and the modified nonlinear Schrodinger equation, Phys. Rev. E., 65 (2002) 066608.

[18]  M. Hatami, Sh. Gharibnavaz, A. Keshavarz, Coupling Coefficient and Nonlinear Characteristics of Nanowire Directional Coupler, International conference on nanotechnology, Tbilisi, Georgia, (2017).