Effect of Relative Phase on the Stability of Temporal Bright Solitons in a PT- Symmetric NLDC

الموضوعات : فصلنامه نانوساختارهای اپتوالکترونیکی

Lida Safaei ¹ , mahmood Borhani Zarandi ² , Mohsen Hatami ³

1 - Department of Physics, Yazd University, Yazd, Iran
2 - Department of Physics, Yazd University, Yazd, Iran
3 - Department of Physics, University of Shiraz Technology, Shiraz, Iran

تاريخ الإرسال : 18 الإثنين , شوال, 1439 تاريخ التأكيد : 06 الأحد , محرم, 1440 تاريخ الإصدار : 21 السبت , ذو الحجة, 1439

الکلمات المفتاحية: Nonlinear Optics, Photonics, Solitons, PT-Symmetry, Fiber Couplers, Nano structures,

ملخص المقالة :

In this paper we numerically investigate the effect of relative phase on the
stability of temporal bright solitons in a Nano PT- Symmetric nonlinear directional
coupler (NLDC) by considering gain in bar and loss in cross. We also study the effect of
relative phase on the output perturbed bright solitons energies, in the range of   0 to
 180 . By using perturbation theory three eigenfunctions and corresponding
eigenvalues were derived analytically. These eigenvalues behave like equilibrium points
and are not stable in all cases. Stability of these perturbed solitons under the effect of
relative phase are examined and show that temporal bright solitons are almost unstable in
the range of   0 to  90 , but they keep their solitary shapes in the range of   90
to  180 . In addition the evolution of normalized energies in these ranges are
investigated.
Output pulse energy at bar and cross strongly depend on the relative phase. This effect
in a PT-Symmetric NLDC can be used for designing all-optical ultrafast self-switches
and logic gates and Nano structures.

المصادر:

[1] C. M., Bender and S. Boettcher, Real spectra in non- Hermitian Hamiltonians having PT- symmetry, Phys. Rev. Lett. 80 (1998) 5243.
[2] C. M., Bender; D. C., Brody, and H. F., Jones, Complex extension of quantum mechanics, Phys. Rev. Lett. 89 (2002) 270401–240404.
[3] C. M., Bender, Making sense of non-Hermitian hamiltonians, Rep. Prog. Phys. 70 (2007) 947–1018.
[4] Y. Kivshar, G. P. Agrawal, Optical Solitons from fibers to photonic crystals, Academic Press, (2003).
[5] 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.
[6] R. El., Ganainy, K. G., Makris, D. N., Christodoulides, and Z. H., Musslimani, Theory of coupled optical PT-symmetric structures, Opt. Lett. 32 (2007) 2632–2634.
[7] A., Ruschhaupt, F., Delgado and J. G., Muga, Physical realization of PT-symmetric potential scattering in a planar slab waveguide, J. Phys. A., 38 (2005) L171–L176.
[8] A. A., Zyablovsky, A. P., Vinogradov, A. A., Pukhov, A. V., Dorofeenko and A. A., Lisyansky, “PT-symmetry in optics”, Phys. Usp. 57 (2014) 1063–1082.
[9] 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.
[10] A. A., Sukhorukov, Z. Y., Xu, and Y. S., Kivshar, Nonlinear suppression of time reversals in PT-symmetric optical couplers, Phys. Rev. A. 82 (2010) 043815–043818.
[11] L. Safaei, M. Hatami and M. Borhani Zarndi, Numerical analysis of stability for temporal Bright solitons in a PT-symmetric NLDC, J. Optoelectronical Nanostructures, 2. 2 (2017) 69-78.
[12] L. Safaei, M. Hatami and M. Borhani Zarndi, Stability of Temporal Dark Soliton in PT-Symmetric Nonlinear Fiber Couplers in Normal Dispersion Regime, J Laser Opt Photonics, 3 (2016) 141.
[13] I. V., Barashenkov and M., Gianfreda, An exactly solvable PT-symmetric dimer from a hamiltonian system of nonlinear oscillators with gain and loss, J. Phys. A. 47 (2014) 282001–282018.
[14] L. Safaei, M. Hatami and M. Borhani Zarndi, PT-Symmetric Nonlinear Directional Fiber Couplers with Gain and Loss for Ultrashort Optical Pulses, J. Laser Opt. Photonics, 4 (2017) 155.
[15] 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.
[16] X., Lü and W. X., Ma, Study of lump dynamics based on a dimensionally reduced Hirota bilinear equation, Nonlinear Dyn. 85 (2016) 1217.
[17] A., Lupu, H., Benisty and A. Degiron, Using optical PT-symmetry for switching applications, Photonics Nanostruct, Fundam. Appl. 12 (2014) 305–311.
[18] S. Suchkov, A. Sukhorukov, J. Huang, S. Dmitriev, C. Lee and Y. Kivshar, Nonlinear switching and solitons in PT-symmetric photonic systems, Laserand Photonics Rev. 10 (2015).
[19] N. V., Alexeeva, I. V., Barashenkov, A. A., Sukhorukov and Y. S., Kivshar, Optical solitons in PT-symmetric nonlinear couplers with gain and loss, Phys. Rev. A. 85 (2012) 063837–13.
[20] C. Q., Dai, and J. F. Zhang., Controllable dynamical behaviors for spatiotemporal bright solitons on continues wave background, Nonlinear Dyn., (2013).
[21] Y., Zhu, W. Qin, J. Li, and et al., Recurrence behavior for controllable excitation of rogue waves in a two-dimensional pt-symmetric couple. Nonlinear Dyn. 88 (2017) 1883.
[22] R., Driben and B. A., Malomed, Stability of solitons in parity-time-symmetric couplers, Opt. Lett. 36 (2011) 4323-4325.