Highly Dispersive Optical Solitons in Fiber Bragg Gratings with Kerr Law of Nonlinear Refractive Index
Abstract
:1. Introduction
Governing Model
2. Mathematical Analysis
3. Generalized Kudryashov’s Method
- (I)
- The combo bright-singular soliton solutions:
- (II)
- The singular soliton solutions:
- (III)
- The dark soliton solutions:
4. Enhanced Kudryashov’s Method
5. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
- Ahmed, T.; Atai, J. Bragg solitons in systems with separated nonuniform Bragg grating and nonlinearity. Phys. Rev. E 2017, 96, 032222. [Google Scholar] [CrossRef] [PubMed]
- Ahmed, T.; Atai, J. Soliton–soliton dynamics in a dual-core system with separated nonlinearity and nonuniform Bragg grating. Nonlinear Dyn. 2019, 97, 1515–1523. [Google Scholar] [CrossRef]
- Akter, A.; Islam, M.J.; Atai, J. Effect of dispersive reflectivity on the stability of gap solitons in dual–core Bragg gratings with cubic–quintic nonlinearity. In Proceedings of the 7th International Conference on Photonics, Optics and Laser Technology (Photoptics 2019), 19–23, Prague, Czech Republic, 25–27 February 2019. [Google Scholar]
- Akter, A.; Islam, M.; Atai, J. Quiescent gap solitons in coupled nonuniform Bragg gratings with cubic–quintic nonlinearity. Appl. Sci. 2021, 11, 4833. [Google Scholar] [CrossRef]
- Anam, N.; Ahmed, T.; Atai, J. Bragg grating solitons in a dual–core system with separated Bragg grating and cubic–quintic nonlinearity. In Proceedings of the 7th International Conference on Photonics, Optics and Laser Technology (Photoptics 2019), 24–28, Prague, Czech Republic, 25–27 February 2019. [Google Scholar]
- Atai, J.; Malomed, B.A. Families of Bragg-grating solitons in a cubic–quintic medium. Phys. Lett. A 2001, 284, 247–252. [Google Scholar] [CrossRef]
- Atai, J.; Malomed, B.A. Solitary waves in systems with separated Bragg grating and nonlinearity. Phys. Rev. E 2001, 64, 066617. [Google Scholar] [CrossRef]
- Biswas, A.; Konar, S. Introduction to Non-Kerr Law Optical Solitons; CRC Press: Boca Raton, FL, USA, 2006. [Google Scholar]
- Kan, K.V.; Kudryashov, N.A. Solitary waves for the sixth order nonlinear differential equation in optical fiber Bragg grating. AIP Conf. Proc. 2022, 2425, 340008. [Google Scholar]
- Kan, K.V.; Kudryashov, N.A. Solitary waves described by a high-order system in optical fiber Bragg gratings with arbitrary refractive index. Math. Methods Appl. Sci. 2022, 45, 1072–1079. [Google Scholar] [CrossRef]
- Kudryashov, N.A. Periodic and solitary waves in optical fiber Bragg gratings with dispersive reflectivity. Chin. J. Phys. 2020, 66, 401–405. [Google Scholar] [CrossRef]
- Zayed, E.M.E.; Alngar, M.E.M.; Biswas, A.; Asma, M.; Ekici, M.; Alzahrani, A.K.; Belic, M.R. Optical soliton and conservation laws with generalized Kudryashov’s law of refractive index. Chaos Soliton Fract. 2020, 139, 110284. [Google Scholar] [CrossRef]
- Zayed, E.M.E.; Alngar, M.E.M. Optical soliton solutions for the generalized Kudryashov equation of propagation pulse in optical fiber with power nonlinearities by three integration algorithms. Math. Methods Appl. Sci. 2021, 44, 315–324. [Google Scholar] [CrossRef]
- Zayed, E.M.E.; Alngar, M.E.M.; Biswas, A.; Kara, A.H.; Ekici, M.; Alzahrani, A.K.; Belic, M.R. Cubic–quartic optical solitons and conservation law with Kudryashov’s sextic power law of refractive index. Optik 2021, 227, 166059. [Google Scholar] [CrossRef]
- Zayed, E.M.E.; Alngar, M.E.M.; El–Horbaty, M.M.; Biswas, A.; Ekici, M.; Zhou, Q.; Khan, S.; Mallawi, F.; Belic, M.R. Highly dispersive optical solitons in the nonlinear Schrodinger’s equation having polynomial law of the refractive index change. Indian J. Phys. 2021, 95, 109–119. [Google Scholar] [CrossRef]
- Zayed, E.M.E.; Al–Nowehy, A.; Alngar, M.E.M.; Biswas, A.; Asma, M.; Ekici, M.; Alzahrani, A.K. Highly dispersive optical solitons in birefringent fibers with four nonlinear forms using Kudryashov’s approach. J. Opt. 2021, 50, 120–131. [Google Scholar] [CrossRef]
- Zhao, Y.; Lei, Y.B.; Xu, Y.X.; Xu, S.; Triki, H.; Biswas, A.; Zhou, Q. Vector spatiotemporal solitons and their memory features in cold Rydberg gases. Chin. Phys. Lett. 2022, 39, 034202. [Google Scholar] [CrossRef]
- Zhou, Q.; Wang, T.; Biswas, A.; Liu, W. Nonlinear control of logic structure of all–optical logic devices using soliton interactions. Nonlinear Dyn. 2022, 107, 1215–1222. [Google Scholar] [CrossRef]
- Zhou, Q.; Zhong, Y.; Triki, H.; Sun, Y.; Xu, S.; Liu, W.; Biswas, A. Chirped bright and kink solitons in nonlinear optical fibers with weak nonlocality and cubic-quintic–septic nonlinearity. Chin. Phys. Lett. 2022, 39, 044202. [Google Scholar] [CrossRef]
- Zhou, Q. Influence of parameters of optical fibers on optical soliton interactions. Chin. Phys. Lett. 2022, 39, 010501. [Google Scholar] [CrossRef]
- Biswas, A.; Topkara, E.; Johnson, S.; Zerrad, E.; Konar, S. Quasi—stationary optical solitons with non—Kerr law media with full nonlinearity. J. Nonlinear Opt. Phys. Mater. 2011, 20, 309–325. [Google Scholar] [CrossRef]
- Islam, M.J.; Atai, J. Stability of moving Bragg solitons in a semilinear coupled system with cubic–quintic nonlinearity. J. Mod. Opt. 2021, 68, 365–373. [Google Scholar] [CrossRef]
- Islam, M.; Atai, J. Stability of moving gap solitons in linearly coupled Bragg gratings with cubic–quintic nonlinearity. Nonlinear Dyn. 2018, 91, 2725–2733. [Google Scholar] [CrossRef]
- Chowdhury, S.S.; Atai, J. Interaction dynamics of Bragg grating solitons in a semilinear dual-core system with dispersive reflectivity. J. Mod. Opt. 2016, 63, 2238–2245. [Google Scholar] [CrossRef]
- Islam, M.J.; Atai, J. Stability of gap solitons in dual-core Bragg gratings with cubic-quintic nonlinearity. Laser Phys. Lett. 2014, 12, 015401. [Google Scholar] [CrossRef]
- Dasanayaka, S.; Atai, J. Moving Bragg grating solitons in a cubic-quintic nonlinear medium with dispersive reflectivity. Phys. Rev. E 2013, 88, 022921. [Google Scholar] [CrossRef] [PubMed]
- Dasanayaka, S.; Atai, J. Interactions of solitons in Bragg gratings with dispersive reflectivity in a cubic-quintic medium. Phys. Rev. E 2011, 84, 026613. [Google Scholar] [CrossRef] [PubMed]
- Dasanayaka, S.; Atai, J. Stability of Bragg grating solitons in a cubic–quintic nonlinear medium with dispersive reflectivity. Phys. Lett. A 2010, 375, 225–229. [Google Scholar] [CrossRef]
- Neill, D.R.; Atai, J.; Malomed, B.A. Dynamics and collisions of moving solitons in Bragg gratings with dispersive reflectivity. J. Opt. A Pure Appl. Opt. 2008, 10, 085105. [Google Scholar] [CrossRef]
- Atai, J. Interaction of Bragg grating solitons in a cubic–quintic medium. J. Opt. B Quantum Semiclassical Opt. 2004, 6, S177. [Google Scholar] [CrossRef]
- Cao, H.; Atai, J.; Zuo, J.; Yu, Y.; Gbadebo, A.; Xiong, B.; Hou, J.; Liang, P.; Gao, Y.; Shu, X. Simultaneous multichannel carrier-suppressed return-to-zero to non-return-to-zero format conversion using a fiber Bragg grating. Appl. Opt. 2015, 54, 6344–6350. [Google Scholar] [CrossRef]
- Islam, J.; Atai, J. Stability of Bragg grating solitons in a semilinear dual-core system with cubic–quintic nonlinearity. Nonlinear Dyn. 2017, 87, 1693–1701. [Google Scholar] [CrossRef]
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Zayed, E.M.E.; Alngar, M.E.M.; Shohib, R.M.A.; Biswas, A.; Yıldırım, Y.; Khan, S.; Moraru, L.; Moldovanu, S.; Iticescu, C. Highly Dispersive Optical Solitons in Fiber Bragg Gratings with Kerr Law of Nonlinear Refractive Index. Mathematics 2022, 10, 2968. https://doi.org/10.3390/math10162968
Zayed EME, Alngar MEM, Shohib RMA, Biswas A, Yıldırım Y, Khan S, Moraru L, Moldovanu S, Iticescu C. Highly Dispersive Optical Solitons in Fiber Bragg Gratings with Kerr Law of Nonlinear Refractive Index. Mathematics. 2022; 10(16):2968. https://doi.org/10.3390/math10162968
Chicago/Turabian StyleZayed, Elsayed M. E., Mohamed E. M. Alngar, Reham M. A. Shohib, Anjan Biswas, Yakup Yıldırım, Salam Khan, Luminita Moraru, Simona Moldovanu, and Catalina Iticescu. 2022. "Highly Dispersive Optical Solitons in Fiber Bragg Gratings with Kerr Law of Nonlinear Refractive Index" Mathematics 10, no. 16: 2968. https://doi.org/10.3390/math10162968
APA StyleZayed, E. M. E., Alngar, M. E. M., Shohib, R. M. A., Biswas, A., Yıldırım, Y., Khan, S., Moraru, L., Moldovanu, S., & Iticescu, C. (2022). Highly Dispersive Optical Solitons in Fiber Bragg Gratings with Kerr Law of Nonlinear Refractive Index. Mathematics, 10(16), 2968. https://doi.org/10.3390/math10162968