The effect of relative phase on the stability of temporal dark soliton in \({{\mathcal {PT}}}\)-symmetric nonlinear directional fiber coupler

  • Lida Safaei
  • Mahmood Borhani Zarandi
  • Mohsen HatamiEmail author


In this paper, we numerically investigate the effect of relative phase on the stability of dark solitons in \({\mathcal {PT}}\)-Symmetric nonlinear directional coupler (NLDC), by considering gain in the bar and loss in the cross in the range of \(\theta =0^\circ\) to \(180^\circ\). The \({\mathcal {PT}}\)-Symmetric perturbed eigenfunctions are used to study the soliton stability. The results of simulations are shown that in the first half region of the relative phase the soliton is unstable while in the second one, is stable. In the stable region gain and loss cancel each other and also the perturbed eigenfunctions have no effect on solitons while in the unstable region solitons are amplified in the bar and attenuated in the cross except for some small intervals which the roles are changed. The behavior of such perturbation can be interpreted as self all-optical phase soliton switching and optical logic gates.


Fibers Nonlinear optics Directional coupler Photonic Ultrashort optical pulses \({\mathcal {PT}}\)-symmetry Dark soliton 


  1. Ablowitz, M.J., Biondini, G., Ostrovsky, L.A.: Optical solitons: perspectives and applications. Chaos 10(3), 471–474 (2000)ADSMathSciNetCrossRefGoogle Scholar
  2. Agrawal, G.: Nonlinear Fiber Optics, 4th edn. Academic Press, London (2007)zbMATHGoogle Scholar
  3. Alexeeva, N.V., Barashenkov, I.V., Sukhorukov, A.A., Kivshar, Y.S.: Optical solitons in PT-Symmetric nonlinear couplers with gain and loss. Phys. Rev. A 85, 063837 (2012)ADSCrossRefGoogle Scholar
  4. Barashenkov, I.V., Suchkov, S.V., Sukhorukov, A.A., Dimitriev, S.V., Kivshar, Y.S.: Breathers in PT-Symmetric nonlinear couplers. Phys. Rev. A. 86, 053809 (2012)ADSCrossRefGoogle Scholar
  5. Bludov, V.Y., Konotop, V.V., Malomed, B.A.: Stable dark solitons in PT-Symmetric dual-core waveguides. Phy. Rev. A 87, 013816 (2013)ADSCrossRefGoogle Scholar
  6. Dai, C.Q., Zhang, J.F.: Controllable dynamical behaviors for spatiotemporal bright solitons on continues wave background. Nonlinear Dyn. 73, 2049–2057 (2013)CrossRefGoogle Scholar
  7. Dai, C.Q., Wang, Y.Y., Fan, Y., Yu, D.G.: Reconstruction of stability for Gaussian spatial solitons in quintic-septimal nonlinear materials under PT-symmetric potentials. Nonlinear Dyn. 92, 1351–1358 (2018)CrossRefGoogle Scholar
  8. Ding, D., Jin, D., Dai, C.Q.: Analytical solutions of differential-difference Sine–Gordon Equation. Therm. Sci. 21(4), 1701–1705 (2017)CrossRefGoogle Scholar
  9. Fernandes, D.E., Silveirinha, M.G.: Bright and dark spatial solitons in metallic nanowire arrays. Photon. Nanostruct. Fundam. Appl. 12, 340–349 (2014)ADSCrossRefGoogle Scholar
  10. Hasegawa, A., Tappert, F.: Transmission of stationary nonlinear optical pulses in dispersive dielectric fibers. II. Normal dispersion. Appl. Phys. Lett. 23, 171–172 (1973)ADSCrossRefGoogle Scholar
  11. Kivshar, Y.S., Agrawal, G.P.: Optical Solitons from Fibers to Photonic Crystals. Academic Press, Sandiego (2003)Google Scholar
  12. Ruter, C.E., Mrkis, K.G., El-Gnainy, R., Christodoulides, D.N., Segev, M., Kip, D.: Observation of parity-time symmetry in optics. Nat. Phys. 6, 192–195 (2010)CrossRefGoogle Scholar
  13. Safaei, L., Hatami, M., Zarandi, M.B.: Stability of temporal dark soliton in PT-symmetric nonlinear fiber couplers in normal dispersion regime. Laser Opt. Photon. 3, 141–146 (2016)Google Scholar
  14. Safaei, L., Hatami, M., Borhani Zarandi, M.: Numerical analysis of stability for temporal Bright solitons in a PT-symmetric NLDC. J. Optoelectron. Nanostruct. 2(2), 69–78 (2017a)Google Scholar
  15. Safaei, L., Hatami, M., Borhani Zarandi, M.: PT-symmetric nonlinear directional fiber couplers with gain and loss for ultrashort optical pulses. J. Laser Opt. Photon. 4, 155–158 (2017b)Google Scholar
  16. Shakeri, S., Hatami, M.: Self-tunable chalcogenide Raman laser. J. Opt. Soc. Am. B 27, 679–684 (2010)ADSCrossRefGoogle Scholar
  17. Simovski, C.R., Belov, P.A., Atrashchenko, A.V., Kivshar, Y.S.: Wire metamaterials: physics and applications. Adv. Mater. 24, 4229–4248 (2012)CrossRefGoogle Scholar
  18. Suchkov, S.V., Molomed, B.A., Dimitriev, S.V., Kivshar, Y.S.: Solitons in a chain of parity-time invariant dimer. Phys. Rev. E 84, 046609 (2011)ADSCrossRefGoogle Scholar
  19. Suchkov, S.V., Sukhorukov, A.A., Huang, J., Dmitriev, S.V., Lee, C., Kivshar, Y.S.: Nonlinear switching and solitons in PT-Symmetric photonic systems. Laser Photon. Rev. 10, 177–213 (2015)ADSCrossRefGoogle Scholar
  20. Sukhorukov, A.A., Dimitriev, S.V., Kivshar, Y.S.: Nonlocality in PT-Symmetric waveguide array with gain and loss. Opt. Lett. 37, 2148–2150 (2012)ADSCrossRefGoogle Scholar
  21. Tahmasebi, Z., Hatami, M.: Study of the gain saturation effect on the propagation of dark solitonin Er+3-doped, Ga5Ge20Sb10S65 chalcogenide fiber amplifier. Opt. Commun. 284(2), 656–659 (2010)ADSCrossRefGoogle Scholar
  22. Wang, Y.Y., Zhang, Y.P., Dai, C.Q.: Re-study on localized structures based on variable separation solutions from the modified tanh-function method. Nonlinear Dyn. 83, 1331–1339 (2016). MathSciNetCrossRefGoogle Scholar
  23. Wang, Y.Y., Chen, L., Dai, C.Q., Zheng, J., Fan, Y.: Exact vector multipole and vortex solitons in the media with spatially modulated cubic-quintic nonlinearity. Nonlinear Dyn. 90, 1269–1275 (2017a)MathSciNetCrossRefGoogle Scholar
  24. Wang, Y.Y., Dai, C.Q., Zhou, G.Q.: Rogue wave and combined breather with repeatedly excited behaviors in the dispersion/diffraction decreasing medium. Nonlinear Dyn. 87, 67–73 (2017b). CrossRefGoogle Scholar
  25. Wang, Y.Y., Dai, C.Q., Xu, Y.Q., Zheng, J., Fan, Y.: Dynamics of nonlocal and localized spatiotemporal solitons for a partially nonlocal nonlinear Schrodinger equation. Nonlinear Dyn. 92, 1261–1269 (2018)CrossRefGoogle Scholar
  26. Zakeri, A., Hatami, M.: Design of an ultra-fast all-optical dark soliton switch in a nonlinear directional coupler (NLDC) made of chalcogenide glasses. Appl. Phys. D 12, 1010–1017 (2007)ADSCrossRefGoogle Scholar
  27. Zakeri, A., Hatami, M.: Nonlinear optical properties of pulsed-laser-deposited GeAsSe films and simulation of a nonlinear directional coupler switch. J. Opt. Soc. Am. B 22, 591–597 (2005). p. 192 (2010)ADSCrossRefGoogle Scholar
  28. Zhu, Y., Qin, W., Li, J.: Recurrence behavior for controllable excitation of rogue waves in a two-dimensional PT-Symmetric couple. Nonlinear Dyn. 88, 1883–1889 (2017)CrossRefGoogle Scholar

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Authors and Affiliations

  1. 1.Department of Physics, Faculty of ScienceYazd UniversityYazdIran
  2. 2.Department of PhysicsShiraz University of TechnologyShirazIran

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