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Effect of weak nonlocal nonlinearity on generalized sixth-order dispersion modulational instability in optical media

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Abstract

This paper analyzes the emergence of soliton trains in even higher-order dispersive media and explores the modulational instability phenomenon in optical media. The analysis considers quadratic, quartic, and sextic dispersions with weakly nonlocal Kerr nonlinearity. The results show that nonlocality enhances the MI gain and leads to soliton trains in response to different combinations of even dispersions and nonlocal nonlinearity. The study suggests that Kerr nonlocality can enhance the excitation of extreme events in even higher-order dispersive nonlinear media with potential applications in optical fibers and fiber lasers.

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The simulation data related to the current study are not publicly available due to but can be obtained from the corresponding author, CBT, on reasonable request.

References

  1. Benjamin, T.B., Feir, J.E.: The disintegration of wave trains on deep water Part 1. J. Fluid Mech. 27, 417 (1967)

    Google Scholar 

  2. Kraych, A.E., Suret, P., El, G., Randoux, S.: Nonlinear evolution of the locally induced modulational instability in fiber optics. Phys. Rev. Lett. 122, 054101 (2019)

    Google Scholar 

  3. Zanga, D., Fewo, S.I., Tabi, C.B., Kofané, T.C.: Generation of dissipative solitons in a doped optical fiber modeled by the higher-order dispersive cubic-quintic-septic complex Ginzburg–Landau equation. Phys. Rev. A 105, 023502 (2022)

    Google Scholar 

  4. Ndebele, K.K., Tabi, C.B., Latchio Tiofack, C.G., Kofané, T.C.: Higher-order dispersion and nonlinear effects of optical fibers under septic self-steepening and self-frequency shift. Phys. Rev. E 104, 044208 (2021)

    Google Scholar 

  5. Li, X.-X., Cheng, R.-J., Zhang, A.-X., Xue, J.-K.: Modulational instability of Bose–Einstein condensates with helicoidal spin-orbit coupling. Phys. Rev. E 100, 032220 (2019)

    Google Scholar 

  6. Tabi, C.B., Wamba, E., Nare, E., Kofané, T.C.: Interplay between spin-orbit couplings and residual interatomic interactions in the modulational instability of two-component Bose–Einstein condensates. Phys. Rev. E 107, 044206 (2023)

    Google Scholar 

  7. Sabari, S., TamilThiruvalluvar, R., Radha, R.: Modulational instability of spin-orbit coupled Bose–Einstein condensates in discrete media. Phys. Lett. A 418, 127696 (2021)

    Google Scholar 

  8. Madimabe, E.B., Tabi, C.B., Latchio Tiofack, C.G., Kofané, T.C.: Modulational instability in vector exciton-polariton condensates with photonic spin-orbit coupling. Phys. Rev. B 107, 184502 (2023)

    Google Scholar 

  9. Zaoro, N.R., Tabi, C.B., Etémé, A.S., Kofané, T.C.: Unstable cAMP wave patterns during aggregation of Dictyostelium discoideum cells. Phys. Lett. A 384, 126133 (2020)

    Google Scholar 

  10. Okaly, J.B., Mvogo, A., Tabi, C.B., Ekobena Fouda, H.P., Kofané, T.C.: Base pair opening in a damped helicoidal Joyeux–Buyukdagli model of DNA in an external force field. Phys. Rev. E 102, 062402 (2020)

    Google Scholar 

  11. Tankou, E., Tabi, C.B., Kofané, T.C.: Soliton-mediated ionic pulses and coupled ionic excitations in a dissipative electrical network model of microtubules. Chaos Solitons Fractals 162, 112446 (2022)

    MathSciNet  Google Scholar 

  12. Lazarides, N., Veldes, G.P., Javed, A., Kourakis, I.: Modulational electrostatic wave–wave interactions in plasma fluids modeled by asymmetric coupled nonlinear Schrödinger (CNLS) equations. Chaos Solitons Fractals 175, 113974 (2023)

    Google Scholar 

  13. Tabi, C.B., Panguetna, C.S., Kofané, T.C.: Electronegative (3 + 1)-dimensional modulated excitations in plasmas. Physica B 5C, 370 (2018)

    Google Scholar 

  14. Panguetna, C.S., Tabi, C.B., Kofané, T.C.: Electronegative nonlinear oscillating modes in plasmas. Commun. Nonlinear Sci. Numer. Simul. 55, 326 (2018)

    Google Scholar 

  15. Agrawal, G.P.: Nonlinear Fiber Optics. Academic, San Diego (1989)

    Google Scholar 

  16. Akhmediev, N., Ankiewicz, A., Soto-Crespo, J.M.: Rogue waves and rational solutions of the nonlinear Schrödinger equation. Phys. Rev. E 80, 026601 (2009)

    Google Scholar 

  17. Dudley, J.M., Dias, F., Erkintalo, M., Genty, G.: Instabilities, breathers and rogue waves in optics. Nat. Photon. 8, 755 (2014)

    Google Scholar 

  18. Liu, C., Yang, Z.Y., Zhao, L.C., Yang, W.L.: State transition induced by higher-order effects and background frequency. Phys. Rev. E 91, 022904 (2015)

    Google Scholar 

  19. Liu, C., Yang, Z.Y., Zhao, L.C., Duan, L., Yang, G., Yang, W.L.: Symmetric and asymmetric optical multipeak solitons on a continuous wave background in the femtosecond regime. Phys. Rev. E 94, 042221 (2016)

    MathSciNet  Google Scholar 

  20. Liu, L., Tian, B., Chai, H.P., Yuan, Y.Q.: Certain bright soliton interactions of the Sasa–Satsuma equation in a monomode optical fiber. Phys. Rev. E 95, 032202 (2017)

    Google Scholar 

  21. Uzunov, I.M., Pulov, V.I.: Vector solitary waves in strongly birefringent fibers with Raman scattering. Phys. Lett. A 372, 2730 (2008)

    Google Scholar 

  22. Blanco-Redondo, A., Martijn de Sterke, C., Sipe, J.E., Krauss, T.F., Eggleton, B.J., Husko, C.: Pure-quartic solitons. Nat. Commun. 7, 10427 (2016)

    Google Scholar 

  23. Tam, K.K.K., Alexander, T.J., Blanco-Redondo, A., Martijn de Sterke, C.: Stationary and dynamical properties of pure-quartic solitons. Opt. Lett. 44, 3306 (2019)

    Google Scholar 

  24. Runge, A.F.J., Hudson, D.D., Tam, K.K.K., Martijn de Sterke, C., Blanco-Redondo, A.: The pure-quartic soliton laser. Nat. Photon. 14, 492 (2020)

    Google Scholar 

  25. Runge, A.F.J., Qiang, Y.L., Alexander, T.J., Rafat, M.Z., Hudson, D.D., Blanco-Redondo, A., Martijn de Sterke, C.: Infinite hierarchy of solitons: interaction of Kerr nonlinearity with even orders of dispersion. Phys. Rev. Res. 3, 013166 (2021)

    Google Scholar 

  26. Martijn de Sterke, C., Runge, A.F.J., Hudson, D.D., Blanco-Redondo, A.: Pure-quartic solitons and their generalizations? Theory and experiments. APL Photon. 6, 091101 (2021)

    Google Scholar 

  27. Lo, C.-W., Stefani, A., Martijn de Sterke, C., Blanco-Redondo, A.: Analysis and design of fibers for pure-quartic solitons. Opt. Express 26, 7786 (2018)

    Google Scholar 

  28. Taheri, H., Matsko, A.B.: Quartic dissipative solitons in optical Kerr cavities. Opt. Lett. 44, 3086 (2019)

    Google Scholar 

  29. Kruglov, V.I., Harvey, J.D.: Solitary waves in optical fibers governed by higher-order dispersion. Phys. Rev. A 98, 063811 (2018)

    Google Scholar 

  30. Gao, P., Liu, C., Zhao, L.-C., Yang, Z.-Y., Yang, W.-L.: Modified linear stability analysis for quantitative dynamics of a perturbed plane wave. Phys. Rev. E 102, 022207 (2020)

    MathSciNet  Google Scholar 

  31. Tam, K.K.K., Alexander, T.J.: Generalized dispersion Kerr solitons. Phys. Rev. A 101, 043822 (2020)

    MathSciNet  Google Scholar 

  32. Parker, R., Aceves, A.: Multi-pulse solitary waves in a fourth-order nonlinear Schrödinger equation. Physica D 422, 132890 (2021)

    Google Scholar 

  33. Bandara, R.I., Giraldo, A., Broderick, N.G.R., Krauskopf, B.: Infinitely many multipulse solitons of different symmetry types in the nonlinear Schrödinger equation with quartic dispersion. Phys. Rev. A 103, 063514 (2021)

    Google Scholar 

  34. Zhao, K., Gao, C., Xiao, X., Yang, C.: Vector quartic solitons in birefringent fibers. Opt. Lett. 46, 761 (2021)

    Google Scholar 

  35. Zhang, Z.-X., Luo, M., Chen, J.-X., Chen, L.-H., Liu, M., Luo, A.-P., Xu, W.-C., Luo, Z.-C.: Pulsating dynamics in a pure-quartic soliton fiber laser. Opt. Lett. 47, 1750 (2022)

    Google Scholar 

  36. Qian, Z.-C., Liu, M., Luo, A.-P., Luo, Z.-C., Xu, W.-C.: Dissipative pure-quartic soliton fiber laser. Opt. Express 30, 22066 (2022)

    Google Scholar 

  37. Yao, X., Liu, C., Yang, Z.-Y., Yang, W.-L.: Heteroclinic-structure transition of the pure quartic modulation instability. Phys. Rev. Res. 4, 013246 (2022)

    Google Scholar 

  38. Alexander, T.J., Tsolias, G.A., Demirkaya, A., Decker, R.J., Martijn de Stecrke, C., Kevrekidis, P.G.: Dark solitons under higher-order dispersion. Opt. Lett. 47, 1174 (2022)

    Google Scholar 

  39. Li, Y., Dai, J., Liu, J., Weng, Z., Hu, W., Lu, D.: Evolution of pure-quartic solitons studied by the variational approach. Opt. Commun. 524, 128790 (2022)

    Google Scholar 

  40. Qiang, Y.L., Alexander, T.J., Martijn de Stecrke, C.: Generalized sixth-order dispersion solitons. Phys. Rev. A 105, 023501 (2022)

    MathSciNet  Google Scholar 

  41. Tabi, C.B., Tagwo, H., Tiofack, C.G.L., Kofané, T.C.: Pure quartic modulational instability in weakly nonlocal birefringent fibers. Opt. Lett. 47, 5557 (2022)

    Google Scholar 

  42. Tiofack, C.G.L., Tabi, C.B., Tagwo, H., Kofané, T.C.: Nonlocal cubic and quintic nonlinear wave patterns in pure-quartic media. J. Opt. 25, 054001 (2023)

    Google Scholar 

  43. Tiofack, C.G.L., Tabi, C.B., Tagwo, H., Kofané, T.C.: Pure quartic wave modulation in optical fiber with the presence of self-steepening and intrapulse Raman scattering response. Phys. Lett. A 480, 128982 (2023)

    Google Scholar 

  44. Soltani, M., Triki, H., Azzouzi, F., Sun, Y., Biswas, A., Yildirim, Y., Alshehri, H.M., Zhou, Q.: Pure-quartic optical solitons and modulational instability analysis with cubic-quintic nonlinearity. Chaos Solitons Fractals 169, 113212 (2023)

    MathSciNet  Google Scholar 

  45. Salerno, M., Baizakov, B.: Normal mode oscillations of a nonlocal composite matter-wave soliton. Phys. Rev. E 98, 062220 (2018)

    MathSciNet  Google Scholar 

  46. Zanga, D., Fewo, S.I., Tabi, C.B., Kofané, T.C.: Modulational instability in weak nonlocal nonlinear media with competing Kerr and non-Kerr nonlinearities. Commun. Nonlinear Sci. Numer. Simul. 80, 104993 (2020)

    MathSciNet  Google Scholar 

  47. Crosignani, B., Degasperis, A., DelRe, E., Di Porto, P., Agranat, A.J.: Nonlinear optical diffraction effects and solitons due to anisotropic charge-diffusion-based self-interaction. Phys. Rev. Lett. 82, 1664 (1999)

  48. Gatz, S., Herrmann, J.: Anisotropy, nonlocality, and space-charge field displacement in (2 + 1)-dimensional self-trapping in biased photorefractive crystals. Opt. Lett. 23, 1176 (1998)

    Google Scholar 

  49. Rotschild, C., Alfassi, B., Cohen, O., Segev, M.: Long-range interactions between optical solitons. Nat. Phys. 2, 769 (2006)

    Google Scholar 

  50. Rasmussen, P.D., Bang, O., Krolikowski, W.: Theory of nonlocal soliton interaction in nematic liquid crystals. Phys. Rev. E 72, 066611 (2005)

  51. Krolikowski, W., Bang, O., Rasmussen, J.J., Wyller, J.: Modulational instability in nonlocal nonlinear Kerr media. Phys. Rev. E 64, 016612 (2001)

    Google Scholar 

  52. Bang, O., Krolikowski, W., Wyller, J., Rasmussen, J.J.: Collapse arrest and soliton stabilization in nonlocal nonlinear media. Phys. Rev. E 66, 046619 (2002)

    MathSciNet  Google Scholar 

  53. Lourdesamy, J.P., Runge, A.F.J., Alexander, T.J., Hudson, D.D., Blanco-Redondo, A., Martijn de Stecrke, C.: Spectrally periodic pulses for enhancement of optical nonlinear effects. Nat. Phys. 18, 59 (2021)

    Google Scholar 

  54. Karlsson, M., Höök, A.: Soliton-like pulses governed by fourth-order dispersion in optical fibers. Opt. Commun. 104, 303 (1994)

    Google Scholar 

  55. Triki, H., Pan, A., Zhou, Q.: Pure-quartic solitons in presence of weak nonlocality. Phys. Lett. A 459, 128608 (2023)

    MathSciNet  Google Scholar 

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Tabi, C.B., Latchio Tiofack, C.G., Tagwo, H. et al. Effect of weak nonlocal nonlinearity on generalized sixth-order dispersion modulational instability in optical media. Nonlinear Dyn 112, 10341–10354 (2024). https://doi.org/10.1007/s11071-024-09622-8

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