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Attenuated solitons through some dispersion profiles in a tapered inhomogeneous fiber with erbium effect

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Abstract

In this work, we study the propagation of optical solitons in a tapered optical fiber with attenuating effects under the effect of erbium dopants. Through the constructed Lax pair, two soliton solutions are obtained with the aid of Darboux transformation. Using Mathematica tool, obtained two soliton solution is graphically represented as 2D and 3D plots. The generated two solitons are manipulated through some dispersion profiles with attenuating effects. Results are meaningful to understand the propagation of optical soliton in the concept of lossy optical medium. Moreover, the proposed approach can be used to control the soliton with lossy effects via dispersion management scheme. Our results reveals that the changes of the soliton width, amplitude, and phases are potentially influenced by the variable coefficients particularly dispersion parameter. The GVD profile mainly affects the intensity of optical solitons which leads to control the attenuation due to absorption of optical medium. These results will be helpful to understand the dynamics of attenuated soliton transmission in an inhomogeneous optical fiber medium.

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References

  • Agrawal, G.P.: Nonlinear fiber optics, 3rd edn. Academic Press, California (2002)

    Google Scholar 

  • Arun Prakash, S., Malathi, V., Mani Rajan, M.S.: Tailored dispersion profile in controlling optical solitons in a tapered parabolic index fiber. J. Mod. Opt. 63, 468–476 (2016)

    Article  ADS  Google Scholar 

  • Gromov, E.M., Malomed, B.A., Tyutin, V.V.: Vector solitons in coupled nonlinear Schrödinger equations with spatial stimulated scattering and inhomogeneous dispersion. Commun. Nonlinear Sci. Numer. Simulat. 54, 13–20 (2018)

    Article  ADS  Google Scholar 

  • Guan, W.Y., Li, B.Q.: New observation on the breather for a generalized nonlinear Schrödinger system with two higher order dispersion operators in inhomogeneous optical fiber. Optik 181, 853–861 (2019a)

    Article  ADS  Google Scholar 

  • Guan, W.Y., Li, B.Q.: Mixed structures of optical breather and rogue wave for a variable coefficient inhomogeneous fiber system. Opt. Quant. Electron. 51, 352 (2019b)

    Article  Google Scholar 

  • Gugan, S., Subramanian, K., Mani Rajan, M.S., Alagesan, T.: Four soliton propagation in a generalized nonautonomous Hirota equation using Darboux transformation. Opt. Quant. Electron. 55, 354 (2023)

    Article  Google Scholar 

  • Guo, R., Hao, H.Q.: Breathers and localized solitons for the Hirota–Maxwell–Bloch system on constant backgrounds in erbium doped fibers. Ann. Phys. 344, 10–16 (2014)

    Article  ADS  CAS  Google Scholar 

  • Hasegawa, A., Tappert, F.: Transmission of stationary nonlinear optical pulses in dispersive dielectric fibers1. Anomalous dispersion. Appl. Phys. Lett. 23, 142–144 (1973)

    Article  ADS  CAS  Google Scholar 

  • Karthikeyaraj, G., Mani Rajan, M.S., Tantawy, M., Subramanian, K.: Periodic oscillations and nonlinear tunneling of soliton for Hirota-MB equation in inhomogeneous fiber. Optik 181, 440–448 (2019)

    Article  ADS  Google Scholar 

  • Khalifa, S.B., Chebaane, S., Senthil Nayagam, V., Veni, S., Mani Rajan, M.S.: Periodic and nonperiodic amplifications of attosecond solitons in an inhomogeneous lossy optical fiber. Optik 252, 168498 (2022)

    Article  ADS  Google Scholar 

  • Kodama, Y., Hasegawa, A.: Nonlinear pulse propagation in a monomode dielectric guide. IEEE J. Quant. Electron. 23, 510–524 (1987)

    Article  ADS  Google Scholar 

  • Li, B.Q.: Loop-like kink breather and its transition phenomena for the Vakhnenko equation arising from high-frequency wave propagation in electromagnetic physics. Appl. Math. Lett. 112, 106822 (2021)

    Article  ADS  MathSciNet  Google Scholar 

  • Li, B.Q., Guan, W.Y.: Optical vector lattice breathers of a two-component Rabi-coupled Gross-Pitaevskii system with variable coefficients. Optik 194, 163030 (2019)

    Article  ADS  Google Scholar 

  • Li, B.Q., Ma, Y.L.: Multiple-lump waves for a (3+1)-dimensional Boiti-Leon-Manna-Pempinelli equation arising from incompressible fluid. Comput. Math. Appl. 76, 204–214 (2018)

    Article  MathSciNet  Google Scholar 

  • Li, B.Q., Ma, Y.L.: Darboux transformation and Nth-order rogue wave solutions for a (2+ 1)-dimensional Heisenberg ferromagnetic spin chain equation. Comput. Math. Appl. 77(2), 514–524 (2019)

    Article  MathSciNet  Google Scholar 

  • Li, B.Q., Ma, Y.L.: Extended generalized Darboux transformation to hybrid rogue wave and breather solutions for a nonlinear Schrödinger equation. Appl. Math. Comput. 386, 125469 (2020a)

    MathSciNet  Google Scholar 

  • Li, B.Q., Ma, Y.L.: Interaction dynamics of hybrid solitons and breathers for extended generalization of Vakhnenko equation. Nonlinear Dyn. 102, 1787–1799 (2020b)

    Article  Google Scholar 

  • Li, B.Q., Ma, Y.L.: Soliton resonances and soliton molecules of pump wave and Stokes wave for a transient stimulated Raman scattering system in optics. Eur. Phys. J. plus 137, 1227 (2022)

    Article  Google Scholar 

  • Li, B.Q., Ma, Y.L.: Optical soliton resonances and soliton molecules for the Lakshmanan-Porsezian-Daniel system in nonlinear optics. Nonlinear Dyn. 111, 6689–6699 (2023a)

    Article  Google Scholar 

  • Li, B.Q., Ma, Y.L.: Hybrid soliton and breather waves, solution molecules and breather molecules of a (3+ 1)-dimensional Geng equation in shallow water waves. Phys. Lett. A 463, 128672 (2023b)

    Article  MathSciNet  CAS  Google Scholar 

  • Li, M., Tian, B., Liu, W.J., Zhang, H.Q., Meng, X.H., Xu, T.: Soliton-like solutions of a derivative nonlinear Schrödinger equation with variable coefficients in inhomogeneous optical fibers. Nonlinear Dyn. 62, 919–929 (2010)

    Article  Google Scholar 

  • Liu, W.J., Tian, B., Jian, Y., Sun, K., Qu, Q.X., Li, M., Wang, P.: Bright and dark solitons in the normal dispersion regime of inhomogeneous optical fibers. J. Mod. Opt. 57, 1498–1503 (2010)

    Article  ADS  CAS  Google Scholar 

  • Liu, W.J., Lin, X.C., Lei, M.: Soliton amplification in inhomogeneous optical waveguides. J. Mod. Opt. 60, 932–935 (2013)

    Article  ADS  MathSciNet  CAS  Google Scholar 

  • Liu, W.J., Zhang, Y., Pang, L., Yan, H., Ma, G., Lei, M.: Study on the control technology of optical solitons in optical fibers. Nonlinear Dyn. 86, 1069–1073 (2016a)

    Article  Google Scholar 

  • Liu, W.J., Pang, L., Yan, H., Lei, M.: Optical soliton shaping in dispersion decreasing fibers. Nonlinear Dyn. 84, 2205–2209 (2016b)

    Article  MathSciNet  Google Scholar 

  • Liu, X., Triki, H., Zhou, Q., Liu, W.J., Biswas, A.: Analytic study on interactions between periodic solitons with controllable parameters. Nonlinear Dyn. 94, 703–709 (2018)

    Article  Google Scholar 

  • Liu, X.Y., Liu, W.J., Triki, H., Zhou, Q., Biswas, A.: Periodic attenuating oscillation between soliton interactions for higher-order variable coefficient nonlinear Schrödinger equation. Nonlinear Dyn. 96, 801–809 (2019a)

    Article  Google Scholar 

  • Liu, W.J., Zhang, Y., Triki, H., Mirzazadeh, M., Ekici, M., Zhou, Q., Biswas, A., Belic, M.: Interaction properties of solitonics in inhomogeneous optical fibers. Nonlinear Dyn. 95, 557–563 (2019b)

    Article  Google Scholar 

  • Ma, Y.L., Li, B.Q.: Rogue wave solutions, soliton and rogue wave mixed solution for a generalized (3+1)-dimensional Kadomtsev-Petviashvili equation in fluids. Mod. Phys. Lett. B 32, 1850358 (2018)

    Article  ADS  MathSciNet  CAS  Google Scholar 

  • Ma, Y.L., Li, B.Q.: Analytic rogue wave solutions for a generalized fourth-order Boussinesq equation in fluid mechanics. Math. Methods Appl. Sci. 42, 39–48 (2019a)

    Article  ADS  MathSciNet  Google Scholar 

  • Ma, Y.L., Li, B.Q.: Interactions between rogue wave and soliton for a (2+1)-dimensional generalized breaking soliton system: hidden rogue wave and hidden soliton. Comput. Math. Appl. 78, 827–839 (2019b)

    Article  MathSciNet  Google Scholar 

  • Ma, Y.L., Wazwaz, A.M., Li, B.Q.: A new (3+1)-dimensional Sakovich equation in nonlinear wave motion: Painlev´e integrability, multiple solitons and soliton molecules. Qual. Theor. Dyn. Syst. 21, 158 (2022)

    Article  Google Scholar 

  • Mahalingam, A., Mani Rajan, M.S.: Influence of generalized external potentials on nonlinear tunneling of nonautonomous solitons: Soliton management. Opt. Fiber Technol. 25, 44–50 (2015)

    Article  ADS  Google Scholar 

  • Mahalingam, A., Porsezian, K., Mani Rajan, M.S., Uthayakumar, A.: Propagation of dispersion–nonlinearity-managed solitons in an inhomogeneous erbium-doped fiber system. J. Phys. a: Math. Theor. 42, 165101 (2009)

    Article  ADS  MathSciNet  Google Scholar 

  • Mallenuer, L.F., Stolen, R.H., Gorden, J.P.: Experimental observation of picosecond pulse narrowing and soliton in optical fiber. Phys. Rev. Lett. 45, 1095 (1980)

    Article  ADS  Google Scholar 

  • Mani Rajan, M.S.: Dynamics of optical soliton in a tapered erbium doped fiber under periodic distributed amplification system. Nonlinear Dyn. 85, 599–606 (2016a)

    Article  Google Scholar 

  • Mani Rajan, M.S.: Unexpected behavior on nonlinear tunneling of chirped ultrashort soliton pulse in non-Kerr media with Raman effect. Z. Für Nat. A 71, 751 (2016b)

    Article  Google Scholar 

  • Mani Rajan, M.S.: Transition from bird to butterfly shaped nonautonomous soliton and soliton switching in erbium doped resonant fiber. Phys. Scr. 95, 105203 (2020)

    Article  ADS  CAS  Google Scholar 

  • Mani Rajan, M.S., Mahalingam, A.: Multi-soliton propagation in a generalized inhomogeneous nonlinear Schrödinger-Maxwell-Bloch system with loss/gain driven by an external potential. J. Math. Phys. 54, 043514 (2013)

    Article  ADS  MathSciNet  Google Scholar 

  • Mani Rajan, M.S., Mahalingam, A.: Nonautonomous solitons in modified inhomogeneous Hirota equation: soliton control and soliton interaction. Nonlinear Dyn. 79, 2469–2484 (2015)

    Article  MathSciNet  Google Scholar 

  • Mani Rajan, M.S., Mahalingam, A., Uthayakumar, A.: Nonlinear tunneling of nonautonomous optical solitons in combined nonlinear Schrödinger and Maxwell-Bloch systems. J. Opt. 14, 105204 (2012)

    Article  ADS  Google Scholar 

  • Mani Rajan, M.S., Mahalingam, A., Uthayakumar, A., Porsezian, K.: Observation of two soliton propagation in an erbium doped inhomogeneous lossy fiber with phase modulation. Commun. Nonlinear Sci. Numer. Simul. 18, 1410–1432 (2013a)

    Article  ADS  MathSciNet  Google Scholar 

  • Mani Rajan, M.S., Hakkim, J., Mahalingam, A., Uthayakumar, A.: Dispersion management and cascade compression of femtosecond nonautonomous soliton in birefringent fiber. Eur. Phys. J. D 67, 1–8 (2013b)

    Article  Google Scholar 

  • Mani Rajan, M.S., Mahalingam, A., Uthayakumar, A.: Nonlinear tunneling of optical soliton in 3 coupled NLS equation with symbolic computation. Ann. Phys. 346, 1–13 (2014)

    Article  ADS  MathSciNet  CAS  Google Scholar 

  • McCall, S.L., Hahn, E.L.: Self-induced transparency by pulsed coherent light. Phys. Rev. Lett. 18, 908 (1967)

    Article  ADS  CAS  Google Scholar 

  • Mollenauer, L.F., Gordon, J.P., Islam, M.N.: Soliton propagation in long fibers with periodically compensated loss. IEEE J. Quant. Electron. 22, 157–173 (1986)

    Article  ADS  Google Scholar 

  • Nakazawa, M., Yamada, E., Kubota, H.: Coexistence of self-induced transparency soliton and nonlinear Schrödinger soliton. Phys. Rev. Lett. 66, 2625–2628 (1991)

    Article  ADS  CAS  PubMed  Google Scholar 

  • Nakkeeran, K.: Optical solitons in erbium-doped fibers with higher-order effects and pumping. J. Phys. a: Math. Gen. 33, 4377 (2000)

    Article  ADS  MathSciNet  CAS  Google Scholar 

  • Prathap, N., Arunprakash, S., Mani Rajan, M.S., Tantawy, M.: Optical solitons and their shaping in a monomode optical fiber with some inhomogeneous dispersion profiles. Optik 192, 162906 (2019)

    Article  ADS  Google Scholar 

  • Raghuraman, P.J., Bhagya Shree, S., Mani Rajan, M.S.: Soliton control with inhomogeneous dispersion under the influence of tunable external harmonic potential. Waves Random Complex Media 31, 474–485 (2021)

    Article  ADS  MathSciNet  Google Scholar 

  • Saravana Veni, S., Mani Rajan, M.S., Vithya, A.: Controllable Phase shift of optical soliton through nonlinear tunneling in a dual mode optical fiber. Optik 242, 167094 (2021)

    Article  ADS  Google Scholar 

  • Saravana Veni, S., Vijayalekshmi, S., Surekha, R., Mani Rajan, M.S.: Non-collisional dynamics of nonautonomous three solitons through tailoring of modulated coefficients and modulation instability gain spectra. Optik 279, 170737 (2023)

    Article  Google Scholar 

  • Serkin, V.N., Hasegawa, A.: Exactly integrable onlinear Schrödinger equation models with varying dispersion, nonlinearity and gain: application for soliton dispersion management. J. Sel. Top. Quant. Electron. 8, 418–431 (2002)

    Article  CAS  Google Scholar 

  • Subramanian, K., Alagesan, T., Mahalingam, A., Mani Rajan, M.S.: Propagation properties of optical soliton in an erbium doped tapered parabolic index nonlinear fiber: soliton control. Nonlinear Dyn. 87, 1575–1587 (2017)

    Article  Google Scholar 

  • Vithya, A., Mani Rajan, M.S.: Attosecond soliton shaping through dispersion tailoring technique in a monomode optical fiber. Optik 167, 196–203 (2018)

    Article  ADS  Google Scholar 

  • Vithya, A., Mani Rajan, M.S.: Impact of fifth order dispersion on soliton solution for higher order NLS equation with variable coefficients. J. Ocean Eng. Sci. 5, 205–213 (2020)

    Article  Google Scholar 

  • Vithya, A., Mani Rajan, M.S., Arun Prakash, S.: Combined effects of frequency and higher-order effects on soliton conversion in an erbium fiber with inhomogeneous broadening. Nonlinear Dyn. 91, 687–696 (2018)

    Article  Google Scholar 

  • Yang, C.Y., Liu, W.J., Zhou, Q., Mihalache, D., Malomed, B.A.: One-soliton shaping and two-soliton interaction in the fifth-order variable-coefficient nonlinear Schrödinger equation. Nonlinear Dyn. 95, 369–380 (2019)

    Article  Google Scholar 

  • Yang, G., Wu, F.O., Lopez Aviles, H.E., Christodoulides, D.N.: Optical amplification and transmission of attenuated multi-soliton based on spectral characteristics of Akhmediev breather. Opt. Commun. 473, 125899 (2020)

    Article  CAS  Google Scholar 

  • Yu, W., Zhou, Q., Mirzazadeh, M., Liu, W.J., Biswas, A.: Phase shift, amplification, oscillation and attenuation of solitons in nonlinear optics. J. Adv. Res. 15, 69–76 (2019)

    Article  PubMed  Google Scholar 

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Acknowledgements

The authors of this work extend their appreciation for funding to the Deanship of Research through supporting project number (RSPD2023R1034), King Saud University, Riyadh 12373, Saudi Arab.

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Deanship of Scientific Research, King Saud University, RSPD2023R1034, RSPD2023R1034.

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NP wrote main text of manuscript and author MI contribute for mathematical calculations. Authors AS and ST are support to editing and graphs plotting.

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Correspondence to N. Prathap.

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Prathap, N., Ahamed, M.I., Alqahtani, A.S. et al. Attenuated solitons through some dispersion profiles in a tapered inhomogeneous fiber with erbium effect. Opt Quant Electron 56, 407 (2024). https://doi.org/10.1007/s11082-023-05948-6

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