Abstract
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.
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References
Ablowitz, M.J., Biondini, G., Ostrovsky, L.A.: Optical solitons: perspectives and applications. Chaos 10(3), 471–474 (2000)
Agrawal, G.: Nonlinear Fiber Optics, 4th edn. Academic Press, London (2007)
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)
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)
Bludov, V.Y., Konotop, V.V., Malomed, B.A.: Stable dark solitons in PT-Symmetric dual-core waveguides. Phy. Rev. A 87, 013816 (2013)
Dai, C.Q., Zhang, J.F.: Controllable dynamical behaviors for spatiotemporal bright solitons on continues wave background. Nonlinear Dyn. 73, 2049–2057 (2013)
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)
Ding, D., Jin, D., Dai, C.Q.: Analytical solutions of differential-difference Sine–Gordon Equation. Therm. Sci. 21(4), 1701–1705 (2017)
Fernandes, D.E., Silveirinha, M.G.: Bright and dark spatial solitons in metallic nanowire arrays. Photon. Nanostruct. Fundam. Appl. 12, 340–349 (2014)
Hasegawa, A., Tappert, F.: Transmission of stationary nonlinear optical pulses in dispersive dielectric fibers. II. Normal dispersion. Appl. Phys. Lett. 23, 171–172 (1973)
Kivshar, Y.S., Agrawal, G.P.: Optical Solitons from Fibers to Photonic Crystals. Academic Press, Sandiego (2003)
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)
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)
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)
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)
Shakeri, S., Hatami, M.: Self-tunable chalcogenide Raman laser. J. Opt. Soc. Am. B 27, 679–684 (2010)
Simovski, C.R., Belov, P.A., Atrashchenko, A.V., Kivshar, Y.S.: Wire metamaterials: physics and applications. Adv. Mater. 24, 4229–4248 (2012)
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)
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)
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)
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)
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). https://doi.org/10.1007/s11071-015-2406-5
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)
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). https://doi.org/10.1007/s11071-016-3025-5
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)
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)
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)
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)
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Safaei, L., Borhani Zarandi, M. & Hatami, M. The effect of relative phase on the stability of temporal dark soliton in \({{\mathcal {PT}}}\)-symmetric nonlinear directional fiber coupler. Opt Quant Electron 50, 382 (2018). https://doi.org/10.1007/s11082-018-1646-2
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DOI: https://doi.org/10.1007/s11082-018-1646-2