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Optical and Quantum Electronics

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01.04.2023

Role of nonlinear saturation on modulational instability in Kundu–Eckhaus equation with the presence of inter modal, XPM and SPM

verfasst von: P. Mohanraj, R. Sivakumar, Jayaprakash Kaliyamurthy, Rajesh Kumar

Erschienen in: Optical and Quantum Electronics | Ausgabe 4/2023

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Abstract

With cross phase modulation (XPM), conventional saturable nonlinearity (CSNL), and self phase modulation (SPM) present, we analyze the effect of inter modal dispersion on the modulation instability (MI) of an optical rogue waves in the Kundu-Eckhaus (KE) equation. We take into account the two component KE model without the four wave mixing term and with intermodal dispersion along with CSNL. On the basis of the conventional linear stability analysis, the MI criterion for the KE equation is determined. Using the MI criterion, it is possible to determine how inter modal dispersion and CSNL affect the MI of an optical rogue waves in a birefringent fiber when XPM and SPM are present. Through a graphical illustration of MI gain, the effects of intermodal dispersion and CSNL on MI in optical fiber for the presence of SPM and XPM are explored.

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Nächster Artikel Dispersive optical soliton solutions of the -dimensional cascaded system governing by coupled nonlinear Schrödinger equation with Kerr law nonlinearity in plasma

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Arshed, A., Biswas, M., Abdelaty, Q., Zhou, S.P., Moshokoa, M.: Belic, Optical soliton perturbation with kundu–eckhaus equation by exp(ϕ(ξ))-expansion scheme and G′∕G2-expansion method. Optik 172, 79–85 (2018)ADS

Bayindir, C.: Rogue waves of the Kundu-Eckhaus equation in a chaotic wave field. Phys. Rev. E 93, 032201 (2016)ADSMathSciNet

Bayındır, C.: Rogue wave spectra of the Kundu-Eckhaus equation. Phys. Rev. E 93, 062215 (2016)ADSMathSciNet

Bayındır, C.: Self-localized solutions of the Kundu-Eckhaus equation in nonlinear waveguides. Res. Phys. 14, 102362 (2019)

Bayındır, C., Yurtbak, H.: A Split-step fourier scheme for the dissipative Kundu-Eckhaus equation and its rogue wave dynamics. Twms J. Appl. Eng. Math. 11, 56–65 (2021)

Biswas, A.: Soliton solutions of the perturbed resonant nonlinear Schrodinger’s equation with full nonlinearity by semi-inverse variational principle. Quantum Phys. Lett. 1(2), 79–89 (2012)

Biswas, A., Zhou, Q., Ullah, M.Z., Asma, M., Moshokoa, S.P., Belic, M.: Perturbation theory and optical soliton cooling with anti-cubic nonlinearity. Optik 142, 73–76 (2017)ADS

Biswas, A., Yildirim, Y., Yasar, E., Triki, H., Alshomrani, A.S., Ullah, M.Z., Zhou, Q., Moshokoa, S.P., Belic, M.: Optical soliton perturbation with full nonlinearity for Kundu-Eckhaus equation by modified simple equation method. Optik 157, 1376–1380 (2018)ADS

Biswas, A., Yıldırım, Y., Yaşar, E., Zhou, Q., Khan, S., Adesanya, S., Belic, M.: Optical soliton molecules in birefringent fibers having weak non-local nonlinearity and four-wave mixing with a couple of strategic integration architectures. Optik 179, 927–940 (2019)ADS

Biswas, A., Ekici, M., Sonmezoglu, A., Belic, M.R.: Highly dispersive optical solitons with cubic-quintic-septic law by F-expansion. Optik 182, 897–906 (2019a)ADS

Biswas, A., Arshed, S., Ekici, M., Zhou, Q., Moshokoa, S.P., Alfiras, M., Belic, M.: Optical solitons in birefringent fibers with Kundu-Eckhaus equation. Optik 178, 550–556 (2019b)ADS

Brainis, E., Amans, D., Massar, S.: Scalar and vector modulation instabilities induced by vacuum fluctuations in fibers: Numerical study. Phys. Rev. A 71, 023808 (2005)ADS

Chabchoub, A., Hoffmann, N., Tobisch, E., Waseda, T., Akhmediev, N.: Drifting breathers and Fermi-Pasta–Ulam paradox for water waves. Wave Motion 90, 168–174 (2019)MathSciNetMATH

Chai, X., Zhang, Y.: The dressing method and dynamics of soliton solutions for the Kundu-Eckhaus equation. Nonlinear Dyn. (2022). https://doi.org/10.1007/s11071-022-08106-xCrossRef

Dalt, N.D., Angelis, C.D., Nalesso, G.F., Santagiustina, M.: Dynamics of induced modulational instability in waveguides with saturable nonlinearity. Opt. Commun. 121, 69–72 (1995)ADS

Drummond, P.D., Kennedy, T.A.B., Dudley, J.M., Leonhardt, R., Harvey, J.D.: Cross-phase modulation instability in high-birefringence fibers. Opt. Commun. 78, 137–142 (1990)ADS

Ebadi, G., Yildirim, A., Biswas, A.: Chiral solitons with Bohm potential using G′G method and exp-function method. Rom. Rep. Phys. 64, 357–366 (2012)

Ekici, M., Mirzazadeh, M., Sonmezoglu, A., Zhou, Q., Triki, H., Zaka Ullah, M., Moshokoa, S.P., Biswas, A.: Optical solitons in birefringent fibers with Kerr nonlinearity by Exp-function method. Optik 131, 964–976 (2017)ADS

Ekici, M., Sonmezoglu, A., Biswas, A., Belic, M.R.: Optical solitons in (2+1)–Dimensions with Kundu-Mukherjee-Naskar equation by extended trial function scheme, Chinese. J. Phys. 57, 72–77 (2019)

Ganapathy, R., Malomed, B.A., Porsezian, K.: Modulational instability and generation of pulse trains in asymmetric dual-core nonlinear optical fibers. Phys. Lett. A 354(5–6), 366–372 (2006)ADS

Jaradat, M.M.M., Batool, A., Butt, A.R., Raza, N.: New solitary Wave and computational solitons for Kundu-Eckhaus equation. Res. Phys. 43, 106084 (2022)

Kennedy, R.E., Popov, S.V., Taylor, J.R.: Ytterbium gain band self-induced modulation instability laser. Opt. Lett. 31(2), 167–168 (2006)ADS

Kostylev, M., Ustinov, A.B., Drozdovskii, A.V., Kaliniko, B.A., Ivanov, E.: To words experimental observation of parametrically squeezed states of microwave magnons in yttrium iron garnet flms. Phys. Rev. B 100(2), 020401 (2019)ADS

Liu, X.M., Zhang, X.G., Lin, N., Zhang, T., Yang, B.J.: Modulation instability in non-Kerr-like optical fibers near the zero dispersion point. Chin. J. Lasers B 9, 79–84 (2000)ADS

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

Liu, W.J., Liu, M.L., Liu, B., Quhe, R.G., Lei, M., Fang, S.B., Teng, H., Wei, Z.Y.: Nonlinear optical properties of MoS2-WS2 hetero structure in fiber lasers. Opt. Exp. 27, 6689 (2019b)

Liu, M., Ouyang, Y., Hou, H., Liu, W., Wei, Z.: Q-switched fiber laser operating at 1.5 μm based on WTe 2. Chin. Opt. Lett. 17(2), 020006 (2019)ADS

Liu, M., Liu, W., Wei, Z.: MoTe2 saturable absorber with high modulation depth for erbium-doped fiber laser. J. Lightw. Technol. 37(13), 3100 (2019d)ADS

Liu, W.J., Liu, M.L., Lin, S., Liu, J.C., Lei, M., Wu, H., Dai, C.Q., Wei, Z.Y.: Synthesis of high quality silver nanowires and their applications in ultrafast photonics. Opt. Express 27, 16440 (2019e)ADS

Lyra, M.L., Gouveia-Neto, A.S.: Saturation effects on modulation instability in non-Kerr-like monomode optical fibers. Opt. Commun. 108, 117–120 (1994)ADS

Mamyshev, P.V., Bosshard, C., Stegeman, G.I.: Generation of a periodic array of dark spatial solitons in the regime of effective amplification. J. Opt. Soc. Amer. B 11(7), 1254–1260 (1994)ADS

Mirzazadeh, M., Yıldırım, Y., Yaar, E., Triki, H., Zhou, Q., Moshokoa, S.P., Ullah, M.Z., Seadawy, A.R., Biswas, A., Belic, M.: Optical solitons and conservation law of Kundu-Eckhaus equation. Optik 154, 551–557 (2018)ADS

Mohanraj, P., Sivakumar, R.: Saturation effects on modulational instability in birefringent media with the help of Kundu-Ekchaus equation. Optik 245, 167687 (2021a)ADS

Mohanraj, P., Sivakumar, R.: Saturable higher nonlinearity effects on the modulational instabilities in three-core triangular configuration couplers. J. Opt. 23, 045502 (2021b)ADS

Mohanraj, P., Sivakumar, R.: Investigation of modulational instability in a coupled Kundu-Ekchaus equation in the presence of modified form of saturable nonlinearity. Optik 248, 168111 (2021c)ADS

Mumtaz, S., Essiambre, R.J., Agrawal, G.P.: Nonlinear propagation in multimode and multicore fibers: generalization of the manakov equations. J. Lightwave Technol. 31(3), 398–406 (2012)ADS

Nielsen, A.U., Garbin, B., Coen, S., Murdoch, S.G., Erkintalo, M.: Coexistence and interactions between nonlinear states with different polarizations in a monochromatically driven passive Kerr resonator. Phys. Rev. Lett. 123(1), 013902 (2019)ADS

Nithyanandan, K., Raja, R.V.J., Porsezian, K., Uthayakumar, T.: A colloquium on the influence of versatile class of saturable nonlinear responses in the instability induced supercontinuum generation. Opt. Fib. Technol. 19(4), 348–358 (2013)ADS

Nithyanandan, K., Raja, R.V.J., Porsezian, K.: Modulational instability in a twin-core fiber with the effect of saturable nonlinear response and coupling coefficient dispersion. Phys. Rev. A 87(4), 043805 (2013)ADS

Parasuraman, E.: Modulational instability criterion for optical wave propagation in birefringent fiber of Kundu-Eckhaus equation. Optik 243, 167429 (2021)ADS

Parasuraman, E.: Effect of inter modal dispersion on modulational instability of optical soliton in Kundu-Eckhaus equation with the presence of SPM and XPM. Optik 270, 170020 (2022)ADS

Qiu, D., He, J., Zhang, Y., Porsezian, K.: The Darboux transformation of the Kundu-Eckhaus equation. Proc. R. Soc. A Math. Phys. Eng. Sci. 471(2180), 20150236 (2015)ADSMathSciNetMATH

Savescu, M., Khan, K.R., Naruka, P., Jafari, H., Moraru, L., Biswas, A.: Optical solitons in photonic nano wave guides with an improved nonlinear Schrödinger’s equation. J. Comput. Theor. Nanosci. 10, 1182–1191 (2013)

Tai, K., Hasegawa, A., Tomita, A.: Observation of modulational instability in optical fibers. Phys. Rev. Lett. 56, 135 (1986)ADS

Tasgal, R.S., Malomed, B.A.: Modulational instabilities in the dual-core nonlinear optical fiber. Phys. Scr. 60, 418 (1999)ADS

Tatsing, P.H., Mohamadou, A., Tiofack, C.G.L.: Modified Kerr-type saturable nonlinearity effect on the modulational instability of nonlinear coupler with a negative-index metamaterial channel. Optik 127(8), 4150–4155 (2016)ADS

Vega-Guzmana, J., Biswas, A., Mahmood, M.F., Zhouf, Q., Khan, S., Moshokoa, S.P.: Dark and singular optical solitons in birefringent fibers with Kundu-Eckhaus equation by undetermined coefficients. Optik 181, 499–502 (2019)ADS

Wang, X., Yang, Bo., Chen, Y., Yang, Y.: Higher-order rogue wave solutions of the Kundu-Eckhaus equation. Phys. Scr. 89, 095210 (2014)ADS

Xie, X.Y., Tian, B., Sun, W.R.: Rogue-wave solutions for the Kundu-Eckhaus equation with variable coefficients in an optical fiber. Nonlinear Dyn. 81, 1349–1354 (2015)MathSciNetMATH

Yildirim, Y.: Optical solitons to Kundu-Eckhaus equation in the context of birefringent fibers by using of trial equation methodology. Optik 182, 105–109 (2019)ADS

Yıldırım, Y., Biswas, A., Jawad, A.J.A.M., Ekici, M., Zhou, Q., Khan, S., Belic, M.R.: Cubic-quartic optical solitons in birefringent fibers with four forms of nonlinear refractive index by exp-function expansion. Res. Phys. 16, 102913 (2020)

Zhong, X., Cheng, K.: Modulation instability in metamaterials with fourth-order linear dispersion, second-order nonlinear dispersion, and three kinds of saturable nonlinearites. Optik 125(22), 6733–6738 (2014)ADS

Zhou, Q., Zhu, Q., Savescu, M., Bhrawy, A., Biswas, A.: Optical solitons with nonlinear dispersion in parabolic law medium. Proc. Rom. Acad. 16, 152–159 (2015)MathSciNet

Titel: Role of nonlinear saturation on modulational instability in Kundu–Eckhaus equation with the presence of inter modal, XPM and SPM
verfasst von: P. Mohanraj
R. Sivakumar
Jayaprakash Kaliyamurthy
Rajesh Kumar
Publikationsdatum: 01.04.2023
Verlag: Springer US
Erschienen in: Optical and Quantum Electronics / Ausgabe 4/2023
Print ISSN: 0306-8919
Elektronische ISSN: 1572-817X
DOI: https://doi.org/10.1007/s11082-023-04588-0

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