Impact of fractional effects on modulational instability and bright soliton in fractional optical metamaterials

References

• Pendry JB. Metamaterials and the control of electromagnetic fields. In Conference on coherence and quantum optics. Optical Society of America. 2007; p. CMB2.
   Google Scholar
• Veselago V, Braginsky L, Shklover V, et al. Negative index materials. J Comput Theor Nanosci. 2006;3:1–3.
   Web of Science ®Google Scholar
• Naqvi QA, Abbas M. Fractional duality and metamaterials in negative permittivity and permeability. Opt Commun. 2003;227:143–146.
   Web of Science ®Google Scholar
• Stockman MI. Criterion for negative refraction with low optical losses from a fundamental principle of causality. Phys Rev Lett PRL. 2007;98:177404.
   Google Scholar
• Xiang Y, Wu J, Dai X, et al. Manipulating dispersive wave generation by anomalous self-steepening effect in metamaterials. Opt Express. 2012;20(24):26828–26836.
   PubMed Web of Science ®Google Scholar
• Ruppin R. Electromagnetic energy density in a dispersive and absorptive material. Phys Lett A. 2002;299:309–312.
   Web of Science ®Google Scholar
• Shelby RA, Smith DR, Nemat-Nasser SC, et al. Microwave transmission through a two-dimensional, isotropic, left-handed metamaterial. Appl Phys Lett. 2001;78(4):489.
   Web of Science ®Google Scholar
• Smith DR, Padilla WJ, Vier DC, et al. Composite medium with simultaneously negative permeability and permittivity. Phys Rev Lett. 2000;84(18).
   Web of Science ®Google Scholar
• Sarma AK, Saha M. Modulational instability of coupled nonlinear field equations for pulse propagation in a negative index materials embedded into a kerr medium. J Opt Soc Am B. 2011;28(4):944.
   Web of Science ®Google Scholar
• Vroumsia D, Justin M, Betchewe G, et al. solitons in two attractive semiconductor nanowires. Superlattices Microstruct. 2018;114:37–52.
   Web of Science ®Google Scholar
• Zakharov VE, Ostrovsky LA. Modulation instability: the beginning. Physica D: Nonlinear Phenomena. 2009;238:540–548.
   Web of Science ®Google Scholar
• Ndzana II F, Mohamadou A, Kofane TC. Modulational instability in the cubicquintic nonlinear Schrödinger equation through the variational approach. Opt Commun. 2007;275:421–428.
   Web of Science ®Google Scholar
• Djidna D, Betchewe G, Aboukar A, et al. Cross-phase modulation instability in an elliptical birefringent positive-negative index coupler with self-steepening and intrapulse raman scattering effects. Optik – Int J Light Electron Opt. 2019;185:726–739.
   Google Scholar
• Sarma AK. Modulational instability of few cycle pulses in optical fibers. J Opt Soc Am B. 2011;28(4):944.
   Web of Science ®Google Scholar
• Wen S, Xiang Y, Su W, et al. Role of anomalous self-steepening effect in modulational instability in negative-index material. Opt Express. 2006;14(4):1568–1575.
   Google Scholar
• Saha M, Sarma AK. Modulation instability in nonlinear metamaterials induced by cubic-quintic nonlinearities and higher order dispersion effects. Opt Commun. 2013;291:321–325.
   Web of Science ®Google Scholar
• Wen S, Wang Y, Su W, et al. Modulation instability in nonlinear negative-index material. Phys Rev E. 2006;73:036617.
   Web of Science ®Google Scholar
• Kumar P, Rajasthan P, Chaudhary SK. Analysis of fractional order control system with performance and stability. Int J Eng Sci Technol. 2017; 9: 408–416.
   Google Scholar
• Herrmann R. Fractional calculus: an introduction for physicists. Germany: World Scientific, GigaHedron; 2014.
   Google Scholar
• Ekici M, Mirzazadeh M, Zhou Q, et al. Solitons in optical metamaterials with fractional temporal evolution. Optik. 2016;127:10879–10897.
   Web of Science ®Google Scholar
• Zhang L, He Z, Conti C, et al. Modulational instability in fractional nonlinear Schrödinger equation. Commun Nonlinear Sci Numer Simulat. 2017;48:531–540.
   Web of Science ®Google Scholar
• Jumarie G. Modified Riemann-Liouville derivative and fractional Taylor series of nondifferentiable functions further results. Comput Math Appl. 2006;51:1367–1376.
   Web of Science ®Google Scholar
• Gomez-Aguilar JF. Fractional space waves in conductors. Progr Fract Differ Appl. 2015;1(4):259–267.
   Google Scholar
• Tarasov VE. Fractional integro-differential equations for electromagnetic waves in dielectric media. Theor Math Phys. 2009;158(3):355–359.
   Web of Science ®Google Scholar
• Rosales JJ, Gmez JF, Gua M, et al. Fractional electromagnetic waves. In International Conference on Laser and Optical Network Modeling. IEEE. 2011; p.1–3.
   Google Scholar
• Hongbo Z, Zhongshu Y. Research on electromagnetic wave propagation in fractional space. In 3rd International Conference on Material, Mechanical and Manifacturing Engineering (IC3ME). Atlantis Press. 2015; p.1–6.
   Google Scholar
• Agrawal GP. Applications of nonlinear fiber optics. San Diego: Academic Press; 2001.
   Google Scholar
• Sarma AK, Biswas A. Solitary wave solution to the nonlinear evolution equation in cascaded quadratic media beyond the slowly varying enveloppe approximations. Opt. Appl. 2014;XLIV(2).
   Google Scholar
• Mohamad AJ. Optical solitons with Schrödinger-Hirota equation with Kerr law nonlinearity. Baghdad-00964: IRAD; 2017.
   Google Scholar
• Darvishi MT, Najafi M, Seadawy AR. Dispersive bright, dark and singular optical soliton solution in conformable fractional optical fiber Schrödinger models and its applications. Opt Quant Electron. 2018;50:181.
   Web of Science ®Google Scholar
• Korkmaz A, Hepson OE, Hosseini K, et al. Sine-gordon expansion method for exact solutions to conformable time fractional equations in RLW-Class. J King Saud Univ Sci. 2020;32:567–574.
   Web of Science ®Google Scholar
• Amadou Y, Justin M, Hubert MB, et al. Fractional effects on soliton in a 1D array of rectangular ferroelectric nanoparticles. Waves Random Complex Media. 2020; 30(3): 581–592.
   Google Scholar