Abstract
We systematically explore the effects of Raman scattering (RS) on modulation instabilities (MIs) in nonlinear two-core optical fibers (TCFs) with the symmetric and antisymmetric continuous wave (CW) states. The main contribution of this paper is that the analytical gain spectra with RS effects are given explicitly for both anomalous and normal dispersion regimes. Our results show that the MI spectra with RS effects can be significantly changed. First of all, MI arises for any total power in both normal and anomalous dispersion regimes. Secondly, MI gain can be significantly enhanced especially at large values of perturbation frequencies. In addition, the modulation frequency generating MI expands from the finite frequency domain without RS effects to the infinite frequency domain. The MI analysis is finally verified numerically with wave propagation method.
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Abdelkrim, B., Katarzyna, K., Alessandro, T.: Seeded intermodal four-wave mixing in a highly multimode fiber. J. Opt. Soc. Am. B 35(2), 295–301 (2018)
Agrawal, G.P.: Nonlinear Fiber Optics. Academic Press, Burlington (2007)
Agrawal, G.P.: Applications of Nonlinear Fiber Optics. Academic Press, Burlington (2008)
Ali, A.K.S., Nithyanandan, K., Porsezian, K.: Theoretical investigation of modulation instability in a three-core coupler with negative index material channel. Phys. Lett. A 379(3), 223–229 (2015)
Ali, A.K.S., Nithyanandan, K., Porsezian, K., Maimistov, A.I.: Modulation instability in a triangular three-core coupler with a negative-index material channel. J. Opt. 18(3), 035102 (2016)
Alim, A., Youssoufa, M., Mohamadou, A.: Effects of higher-order nonlinear dispersions on modulational instability in a three-core coupler with negative index material channel and saturable nonlinearity. Optik 149, 5–21 (2017)
Alves, E.O., Cardoso, W.B., Avelar, A.T.: Modulation instability in a nonlinear oppositely directed coupler with saturable nonlinearities and high-order effects. J. Opt. Soc. Am. B 33(6), 1134–1142 (2016)
Balla, P., Buchand, S., Agrawal, G.P.: Effect of Raman scattering on soliton interactions in optical fibers. J. Opt. Soc. Am. B 34(6), 1247–1254 (2017)
Bendahmane, A., Mussot, A., Kudlinski, A., Szriftgiser, P., Conforti, M., Wabnitz, S., Trillo, S.: Optical frequency conversion in the nonlinear stage of modulation instability. Opt. Express 23(24), 30861–30871 (2015)
Buch, S., Agrawal, G.P.: Intermodal soliton interaction in nearly degenerate modes of a multimode fiber. J. Opt. Soc. Am. B 33(11), 2217–2224 (2016)
Canabarro, A.A., Santos, B., Gleria, I., Lyra, M.L., Sombra, A.S.B.: Interplay of XPM and nonlinear response time in the modulational instability of copropagating optical pulses. J. Opt. Soc. Am. B 27(9), 1878–1885 (2010)
Canabarro, A., Santos, B., de Lima Bernardo, B.: Modulation instability in noninstantaneous Kerr media with walk-off and cross-phase modulation for mixed group-velocity-dispersion regimes. Phys. Rev. A 93(2), 023834 (2016)
Chiang, K.S.: Intermodal dispersion in two-core optical fibers. Opt. Lett. 20(9), 997–999 (1995)
Chowdhury, N.A., Hasan, M.M., Mannan, A., Mamun, A.A.: Nucleus-acoustic envelope solitons and their modulational instability in a degenerate quantum plasma system. Vacuum 147, 31–37 (2018)
Conforti, M., Arabi, C.M., Mussot, A., Kudlinski, A.: Fast and accurate modeling of nonlinear pulse propagation in graded-index multimode fibers. Opt. Lett. 42(19), 4004–4007 (2017)
Djidna, D., Betchewe, G., Alim, A., Mohamadou, A.: Cross-phase modulation instability in an elliptical birefringent positive-negative index coupler with self-steepening and intrapulse Raman Scattering effects. Optik 185, 726–739 (2019)
Dupiol, R., Bendahmane, A., Krupa, K., Fatome, J., Tonello, A., Fabert, M., Couderc, V., Wabnitz, S., Millot, G.: Intermodal modulational instability in graded-index multimode optical fibers. Opt. Lett. 42(17), 3419–3422 (2017)
Fatome, J., Pitois, S., Millot, G.: Measurement of nonlinear and chromatic dispersion parameters of optical fibers using modulation instability. Opt. Fiber Technol. 12(3), 243–250 (2006)
Fazea, Y., Mezhuyev, V.: Selective mode excitation techniques for mode-division multiplexing: a critical review. Opt. Fiber Technol. 45, 280–288 (2018)
Ferrier-Barbut, I., Wenzel, M., Schmitt, M., Bottcher, F., Pfau, T.: Onset of a modulational instability in trapped dipolar Bose-Einstein condensates. Phys. Rev. A 97(1), 011604 (2018)
Guasoni, M.: Generalized modulational instability in multimode fibers: wideband multimode parametric amplification. Phys. Rev. A 92(3), 033849 (2015)
Han, X., Xiao, H.F., Liu, Z.L., Zhao, T., Jia, H., Yang, J.H., Eggleton, B.J., Tian, Y.H.: Reconfigurable on-chip mode exchange for mode-division multiplexing optical networks. J. Lightwave Technol. 37(3), 1008–1013 (2019)
Islam, M.N., Dijaili, S.P., Gordon, J.P.: Modulation-instability-based fiber interferometer switch near 1.5 μm. Opt. Lett. 13(6), 518–520 (1988)
Kibler, B., Amrani, F., Morin, P., Kudlinski, A.: Cross-phase-modulation-instability band gap in a birefringence-engineered photonic-crystal fiber. Phys. Rev. A 93(1), 013857 (2016)
Kimmoun, O., Hsu, H.C., Kibler, B., Chabchoub, A.: Nonconservative higher-order hydrodynamics modulation instability. Phys. Rev. E 96(2), 022219 (2019)
Kraych, A.E., Suret, P., EI, G., Randoux, S.: Nonlinear evolution of the locally induced modulational instability in fiber optics. Phys. Rev. Lett. 122(5), 054101 (2019)
Lei, C., Jin, A., Song, R., Chen, Z., Hou, J.: Theoretical and experimental research of supercontinuum generation in an ytterbium-doped fiber amplifier. Opt. Express 24(9), 9237–9250 (2016)
Li, J.H., Chiang, K.S., Chow, K.W.: Modulation instabilities in two-core optical fibers. J. Opt. Soc. Am. B 28(7), 1693–1701 (2011)
Li, J.H., Chiang, K.S., Malomed, B.A., Chow, K.W.: Modulation instabilities in birefringent two-core optical fibers. J. Phys. B At. Mol. Opt. Phys. 45, 165404 (2012)
Li, J.H., Zhou, H., Chiang, K.S., Xiao, S.R.: Modulation instabilities in equilateral three-core optical fibers. J. Opt. Soc. Am. B 33(11), 2357–2367 (2016)
Li, J.H., Chiang, K.S., Li, C.R.: Modulation instability in collinear three-core optical fibers. J. Opt. Soc. Am. B 34(12), 2467–2477 (2017)
Li, J.X., Cai, C.K., Du, J.B., Jiang, S.L., Ma, L., Wang, L.L., Zhu, L., Wang, A.D., Li, M.J., Chen, H.: Ultra-low-noise mode-division multiplexed WDM transmission over 100-km FMF based on a second-order few-mode Raman amplifier. J. Lightwave Technol. 36(16), 3254–3260 (2018)
Liu, X.M.: Broad and tunable multiwavelength fiber laser at the assistance of modulation-instability-assisted four-wave mixing. Laser Phys. 20(4), 842–846 (2010)
Liu, X., Haus, J.W., Shahriar, S.M.: Modulation instability for a relaxational Kerr medium. Opt. Commun. 281(10), 2907–2912 (2008)
Mohamadou, A., Tatsing, P.H., Tiofack, C.G.L., Tabi, C.B., Kofane, T.C.: Effects of higher order nonlinearities on modulational instability in nonlinear oppositely directed coupler. J. Mod. Opt. 61(20), 1670–1678 (2014)
Nithyanandan, K., Porsezian, K.: Interplay between relaxation of nonlinear response and coupling coefficient dispersion in the instability spectra of dual core optical fiber. Opt. Commun. 303, 46–55 (2013)
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)
Ott, J.R., Heuck, M., Agger, C., Rasmussen, P.D., Bang, O.: Label-free and selective nonlinear fiber-optical biosensing. Opt. Express 16(25), 20834–20847 (2008)
Perret, S., Fanjoux, G., Bigot, L., Millot, G., Dudley, J.M., Sylvestre, T.: Supercontinuum generation by intermodal four-wave mixing in a step-index few-mode fibre. Apl. Photonics 49(2), 022905 (2018)
Porsezian, K., Ali, A.K.S., Nithyanandan, K.: A theoretical study on threshold conditions of modulation instability in oppositely directly couplers. J. Opt. 18(12), 125502 (2016)
Shafeeque Ali, A.K., Porsezian, K., Uthayakumar, T.: Influence of self-steepening and intrapulse Raman scattering on modulation instability in oppositely directed coupler. Phys. Rev. E 90(4), 042910 (2014)
Shao, G.D., Hu, X., Guo, J., Song, Y.F., Zhao, L.M., Shen, D.Y., Tang, D.Y.: Cavity-assisted modulation instability lasing of a fiber ring laser. Appl. Phys. B-Lasers O. 125(1), 5 (2019)
Tang, D.Y., Guo, J., Song, Y.F., Li, L., Zhao, L.M., Shen, D.Y.: GHz pulse train generation in fiber lasers by cavity induced modulation instability. Opt. Fiber Technol. 20(6), 610–614 (2014)
Tatsing, P.H., Mohamadou, A., Bouri, C., Tiofack, C.G.L., Kofane, T.C.: Modulation instability in nonlinear positive-negative index couplers with saturable nonlinearity. J. Opt. Soc. Am. B 29(12), 3218–3225 (2012)
Tchio, M.R.S., Abdoulkary, S., Mohamadou, A.: Modulation instability induced by high-order dispersion to a coupled nonlinear Schrödinger equation in a single-mode optical fiber with Kerr nonlinearity. Phys. Scr. 94(3), 035207 (2019)
Tegin, U., Ortac, B.: Spatialtemporal instability of femtosecond pulses in graded-index multimode fibers. IEEE Photonics Technol. Lett. 29(24), 2195–2198 (2017)
Trillo, S., Wabnitz, S.: Parametric amplification and modulational instabilities in dispesion nonlinear directional couplers with relaxing nonlinearity. J. Opt. Soc. Am. B 6(5), 889–900 (1989)
Umezawa, T., Sakamoto, T., Kanno, A., Yamamoto, N., Kawanishi, T.: High speed 2-D photodetector array for space and mode-division multiplexing fiber communications. J. Lightwave Technol. 36(17), 3684–3692 (2018)
Wright, L.G., Christodoulides, D.N., Wise, F.W.: Controllable spatiotemporal nonlinear effects in multimode fibres. Nat. Photonics 9(5), 306–310 (2015)
Wright, L.G., Ziegler, Z.M., Lushnikov, P.M.Z.M., Zhu, Z., Eftekhar, M.A.: Multimode nonlinear fiber optics: massively parallel numerical solver, tutorial, and outlook. IEEE J. Sel. Top. Quant. 24(3), 5100516 (2018)
Xiang, Y.J., Wen, S.C., Dai, X.Y., Fan, D.Y.: Modulation instability in nonlinear oppositely directed coupler with a negative-index metamaterial channel. Phys. Rev. E 82(5), 056605 (2010)
Zhang, J.G., Dai, X.Y., Zhang, L.F., Xiang, Y.J., Li, Y.F.: Modulation instability in the oppositely directed coupler with a quadratic nonlinearity. J. Opt. Soc. Am. B 32(1), 1–8 (2015)
Zhong, X., Cheng, K., Chiang, K.S.: Modulation instability with arbitrarily high perturbation frequencies in metamaterials with nonlinear dispersion and saturable nonlinearity. J. Opt. Soc. Am. B 31(7), 1484–1493 (2014)
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Partial financial support has been provided by the National Natural Science Foundation of China under Grant Nos. 11605090 and 11447113, and the Innovation and Entrepreneurship Training Program for College Students in NUIST under Grant No. 1214071701133.
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Sun, T., Li, J., Pei, S. et al. The effects of raman scattering on modulation instabilities in two-core optical fibers. Opt Quant Electron 53, 231 (2021). https://doi.org/10.1007/s11082-021-02824-z
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DOI: https://doi.org/10.1007/s11082-021-02824-z