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Modulation instabilities in equilateral three-core optical fibers for isosceles-triangle symmetric continuous waves

Pei Shi-Xin Xu Hui Sun Ting-Ting Li Jin-Hua

Modulation instabilities in equilateral three-core optical fibers for isosceles-triangle symmetric continuous waves

Pei Shi-Xin, Xu Hui, Sun Ting-Ting, Li Jin-Hua
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  • Modulation instability (MI) of the isosceles-triangle symmetric continuous wave in equilateral three-core fibers (ETCFs) is studied in detail. The so-called isosceles-triangle symmetric continuous wave state is the planar wave where the fields in its two cores are identical but different from the field in the third core, and the premise of its existence is that the total power (P) exceeds a minimum value (Pmin) that depends on the linear coupling coefficient and nonlinear coefficient of ETCFs. For a given total power P (P ≥ qslant Pmin), set the power in one core to be P1, and the powers in the other two cores to be P2 (P=P1 + 2P2), then two kinds of filed distributions will be found. The first kind is for P1 > P2 with P1 becoming more and more large as total power P increases. By the linear stability analysis method, the main characteristics of MI in ETCFs are found which are quite similar to those of the asymmetric continuous wave states in two core optical fibers (TCFs). The other kind is that P1 becomes more and more small and P2 becomes more and more large as total power P increases. Through the same method, the main characteristics of MI in ETCFs are found which are distinctively different from those of the asymmetric continuous wave states in TCFs. On the one hand, MI can be generated in both normal and anomalous dispersion regimes without perturbations. In addition, the zero-perturbation frequency corresponds to the largest gain of MI in the normal dispersion regime. On the other hand, the coupling coefficient dispersion, which can dramatically modify the spectra of MI in TCFs, plays a minor role in both normal and anomalous dispersion regimes in ETCFs. In practical application, the findings in this paper are of guiding significance for studying the nonlinear effects of mode-division multiplexing system based on the multimode or multicore optical fibers.
      Corresponding author: Li Jin-Hua, lijinhua@nuist.edu.cn
    • Funds: Project supported by the National Natural Science Foundation of China (Grant No. 11605090), the Special Funds for Theoretical Physics in the National Natural Science Foundation of China (Grant No. 11447113), and the Natural Science Foundation of Jiangsu Provincial Universities, China (Grant No. 14KJB140009).
    [1]

    Alves E O, Cardoso W B, Avelar A T 2016 JOSA B 33 1134

    [2]

    Copie F, Conforti M, Kudlinski A, Trillo S, Mussot A 2017 Opt. Express 25 11283

    [3]

    Armaroli A, Biancalana F 2014 Opt. Lett. 39 4804

    [4]

    Benjamin T B, Feir J E 1967 J. Fluid Mech. 27 417

    [5]

    Fang Y, Yakimenko V E, Babzien M, Fedurin M, Kusche K P, Malone R, Vieira J, Mori W B, Muggli P 2014 Phys. Rev. Lett. 112 045001

    [6]

    Mithun T, Porsezian K 2012 Phys. Rev. A 85 013616

    [7]

    Zhong X, Cheng K, Chiang K S 2014 JOSA B 31 1484

    [8]

    Canabarro A, Santos B, de Lima Bernardo B, Moura A L, Soares W C, de Lima E, Gleria I, Lyra M L 2016 Phys. Rev. A 93 023834

    [9]

    Kibler B, Amrani F, Morin P, Kudlinski A 2016 Phys. Rev. A 93 013857

    [10]

    Armaroli A, Trillo S 2014 JOSA B 31 551

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    Agrawal G P 1987 Phys. Rev. Lett. 59 880

    [12]

    Tanemura T, Ozeki Y, Kikuchi K 2004 Phys. Rev. Lett. 93 163902

    [13]

    Dinda P T, Porsezian K 2010 JOSA B 27 1143

    [14]

    Bale B G, Boscolo S, Hammani K, Finot C 2011 JOSA B 28 2059

    [15]

    Finot C, Wabnitz S 2015 JOSA B 32 892

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    Tang D Y, Guo J, Song Y F, Li L, Zhao L M, Shen D Y 2014 Opt. Fiber Technol. 20 610

    [17]

    Kennedy R E, Popov S V, Taylor J R 2006 Opt. Lett. 31 167

    [18]

    Pan N, Huang P, Huang L G, Lei M, Liu W J 2015 Acta Phys. Sin. 64 090504 (in Chinese) [潘楠, 黄平, 黄龙刚, 雷鸣, 刘文军 2015 物理学报 64 090504]

    [19]

    Gu B, Yuan W, Frosz M H, Zhang A P, He S L, Bang O 2012 Opt. Lett. 37 794

    [20]

    Bendahmane A, Mussotm A, Kudlinski A, Szriftgiser P, Conforti M, Wabnitz S, Trillo S 2015 Opt. Express 23 30861

    [21]

    Richardson D J, Fini J M, Nelson L E 2013 Nature Photon. 7 354

    [22]

    Saitoh K, Matsuo S 2016 J. Lightwave Technol. 34 55

    [23]

    Radosavljevic A, Danicic A, Petrovic J, Maluckov A, Haziewski L 2015 JOSA B 32 2520

    [24]

    Sillard P, Molin D, Bigot-Astruc M, Amezcua-Correa A, de Jongh K, Achten F 2016 J. Lightwave Technol. 34 1672

    [25]

    Wang L, Zhu Y J, Qi F H, Li M, Guo R 2015 Chaos 25 063111

    [26]

    Zhang J H, Wang L, Liu C 2017 Proc. R. Soc. A 473 20160681

    [27]

    Wang L, Zhang J H, Liu C, Li M, Qi F H 2016 Phys. Rev. E 93 062217

    [28]

    Cai L Y, Wang X, Wang L, Li M, Liu Y, Shi Y Y 2017 Nonlinear Dyn. 90 2221

    [29]

    Wang L, Jiang D Y, Qi F H, Shi Y Y, Zhao Y C 2017 Commun. Nonlinear Sci. Numer. Simulat. 42 502

    [30]

    Wang L, Wang Z Q, Sun W R, Shi Y Y, Li M, Xu M 2017 Commun. Nonlinear Sci. Numer. Simulat. 47 190

    [31]

    Ding W S, Xi L, Liu L H 2008 Acta Phys. Sin. 57 7705 (in Chinese) [丁万山, 席崚, 柳莲花 2008 物理学报 57 7705]

    [32]

    Trillo S, Wabnitz S, Stegeman G I, Wright E M 1989 JOSA B 6 889

    [33]

    Tasgal R S, Malomed B A 1999 Phys. Scr. 60 418

    [34]

    Xiang Y J, Wen S C, Dai X Y, Fan D Y 2010 Phys. Rev. E 82 056605

    [35]

    Li J H, Chiang K S, Chow K W 2011 JOSA B 28 1693

    [36]

    Li J H, Chiang K S, Malomed B A, Chow K W 2012 J. Phys. B 45 165404

    [37]

    Ding W, Staines O K, Hobbs G D, Gorbach A V, de Nobriga C, Wadsworth W J, Knight J C, Skryabin D V, Strain M J, Sorel M 2012 Opt. Lett. 37 668

    [38]

    Tatsing P H, Mohamadou A, Bouri C, Tiofack G L, Kofane T C 2012 JOSA B 29 3218

    [39]

    Nithyanandan K, Raja R V J, Porsezian K 2013 Phys. Rev. A 87 043805

    [40]

    Zhang J G, Dai X Y, Zhang L F, Xiang Y J, Li Y F 2015 JOSA B 32 1

    [41]

    Ali A K S, Porsezian K, Uthayakumar T 2014 Phys. Rev. E 90 042910

    [42]

    Mohamadou A, Tatsing P H, Tiofack L C G, Tabi C B, Kofane T C 2014 J. Mod. Opt. 61 1670

    [43]

    Li J H, Zhou H, Chiang K S, Xiao S R 2016 JOSA B 33 2357

  • [1]

    Alves E O, Cardoso W B, Avelar A T 2016 JOSA B 33 1134

    [2]

    Copie F, Conforti M, Kudlinski A, Trillo S, Mussot A 2017 Opt. Express 25 11283

    [3]

    Armaroli A, Biancalana F 2014 Opt. Lett. 39 4804

    [4]

    Benjamin T B, Feir J E 1967 J. Fluid Mech. 27 417

    [5]

    Fang Y, Yakimenko V E, Babzien M, Fedurin M, Kusche K P, Malone R, Vieira J, Mori W B, Muggli P 2014 Phys. Rev. Lett. 112 045001

    [6]

    Mithun T, Porsezian K 2012 Phys. Rev. A 85 013616

    [7]

    Zhong X, Cheng K, Chiang K S 2014 JOSA B 31 1484

    [8]

    Canabarro A, Santos B, de Lima Bernardo B, Moura A L, Soares W C, de Lima E, Gleria I, Lyra M L 2016 Phys. Rev. A 93 023834

    [9]

    Kibler B, Amrani F, Morin P, Kudlinski A 2016 Phys. Rev. A 93 013857

    [10]

    Armaroli A, Trillo S 2014 JOSA B 31 551

    [11]

    Agrawal G P 1987 Phys. Rev. Lett. 59 880

    [12]

    Tanemura T, Ozeki Y, Kikuchi K 2004 Phys. Rev. Lett. 93 163902

    [13]

    Dinda P T, Porsezian K 2010 JOSA B 27 1143

    [14]

    Bale B G, Boscolo S, Hammani K, Finot C 2011 JOSA B 28 2059

    [15]

    Finot C, Wabnitz S 2015 JOSA B 32 892

    [16]

    Tang D Y, Guo J, Song Y F, Li L, Zhao L M, Shen D Y 2014 Opt. Fiber Technol. 20 610

    [17]

    Kennedy R E, Popov S V, Taylor J R 2006 Opt. Lett. 31 167

    [18]

    Pan N, Huang P, Huang L G, Lei M, Liu W J 2015 Acta Phys. Sin. 64 090504 (in Chinese) [潘楠, 黄平, 黄龙刚, 雷鸣, 刘文军 2015 物理学报 64 090504]

    [19]

    Gu B, Yuan W, Frosz M H, Zhang A P, He S L, Bang O 2012 Opt. Lett. 37 794

    [20]

    Bendahmane A, Mussotm A, Kudlinski A, Szriftgiser P, Conforti M, Wabnitz S, Trillo S 2015 Opt. Express 23 30861

    [21]

    Richardson D J, Fini J M, Nelson L E 2013 Nature Photon. 7 354

    [22]

    Saitoh K, Matsuo S 2016 J. Lightwave Technol. 34 55

    [23]

    Radosavljevic A, Danicic A, Petrovic J, Maluckov A, Haziewski L 2015 JOSA B 32 2520

    [24]

    Sillard P, Molin D, Bigot-Astruc M, Amezcua-Correa A, de Jongh K, Achten F 2016 J. Lightwave Technol. 34 1672

    [25]

    Wang L, Zhu Y J, Qi F H, Li M, Guo R 2015 Chaos 25 063111

    [26]

    Zhang J H, Wang L, Liu C 2017 Proc. R. Soc. A 473 20160681

    [27]

    Wang L, Zhang J H, Liu C, Li M, Qi F H 2016 Phys. Rev. E 93 062217

    [28]

    Cai L Y, Wang X, Wang L, Li M, Liu Y, Shi Y Y 2017 Nonlinear Dyn. 90 2221

    [29]

    Wang L, Jiang D Y, Qi F H, Shi Y Y, Zhao Y C 2017 Commun. Nonlinear Sci. Numer. Simulat. 42 502

    [30]

    Wang L, Wang Z Q, Sun W R, Shi Y Y, Li M, Xu M 2017 Commun. Nonlinear Sci. Numer. Simulat. 47 190

    [31]

    Ding W S, Xi L, Liu L H 2008 Acta Phys. Sin. 57 7705 (in Chinese) [丁万山, 席崚, 柳莲花 2008 物理学报 57 7705]

    [32]

    Trillo S, Wabnitz S, Stegeman G I, Wright E M 1989 JOSA B 6 889

    [33]

    Tasgal R S, Malomed B A 1999 Phys. Scr. 60 418

    [34]

    Xiang Y J, Wen S C, Dai X Y, Fan D Y 2010 Phys. Rev. E 82 056605

    [35]

    Li J H, Chiang K S, Chow K W 2011 JOSA B 28 1693

    [36]

    Li J H, Chiang K S, Malomed B A, Chow K W 2012 J. Phys. B 45 165404

    [37]

    Ding W, Staines O K, Hobbs G D, Gorbach A V, de Nobriga C, Wadsworth W J, Knight J C, Skryabin D V, Strain M J, Sorel M 2012 Opt. Lett. 37 668

    [38]

    Tatsing P H, Mohamadou A, Bouri C, Tiofack G L, Kofane T C 2012 JOSA B 29 3218

    [39]

    Nithyanandan K, Raja R V J, Porsezian K 2013 Phys. Rev. A 87 043805

    [40]

    Zhang J G, Dai X Y, Zhang L F, Xiang Y J, Li Y F 2015 JOSA B 32 1

    [41]

    Ali A K S, Porsezian K, Uthayakumar T 2014 Phys. Rev. E 90 042910

    [42]

    Mohamadou A, Tatsing P H, Tiofack L C G, Tabi C B, Kofane T C 2014 J. Mod. Opt. 61 1670

    [43]

    Li J H, Zhou H, Chiang K S, Xiao S R 2016 JOSA B 33 2357

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  • Received Date:  18 July 2017
  • Accepted Date:  25 November 2017
  • Published Online:  05 March 2018

Modulation instabilities in equilateral three-core optical fibers for isosceles-triangle symmetric continuous waves

    Corresponding author: Li Jin-Hua, lijinhua@nuist.edu.cn
  • 1. School of Physics and Optoelectronic Engineering, Nanjing University of Information Science and Technology, Jiangsu Key Laboratory for Optoelectronic Detection of Atmosphere and Ocean, Nanjing 210044, China
Fund Project:  Project supported by the National Natural Science Foundation of China (Grant No. 11605090), the Special Funds for Theoretical Physics in the National Natural Science Foundation of China (Grant No. 11447113), and the Natural Science Foundation of Jiangsu Provincial Universities, China (Grant No. 14KJB140009).

Abstract: Modulation instability (MI) of the isosceles-triangle symmetric continuous wave in equilateral three-core fibers (ETCFs) is studied in detail. The so-called isosceles-triangle symmetric continuous wave state is the planar wave where the fields in its two cores are identical but different from the field in the third core, and the premise of its existence is that the total power (P) exceeds a minimum value (Pmin) that depends on the linear coupling coefficient and nonlinear coefficient of ETCFs. For a given total power P (P ≥ qslant Pmin), set the power in one core to be P1, and the powers in the other two cores to be P2 (P=P1 + 2P2), then two kinds of filed distributions will be found. The first kind is for P1 > P2 with P1 becoming more and more large as total power P increases. By the linear stability analysis method, the main characteristics of MI in ETCFs are found which are quite similar to those of the asymmetric continuous wave states in two core optical fibers (TCFs). The other kind is that P1 becomes more and more small and P2 becomes more and more large as total power P increases. Through the same method, the main characteristics of MI in ETCFs are found which are distinctively different from those of the asymmetric continuous wave states in TCFs. On the one hand, MI can be generated in both normal and anomalous dispersion regimes without perturbations. In addition, the zero-perturbation frequency corresponds to the largest gain of MI in the normal dispersion regime. On the other hand, the coupling coefficient dispersion, which can dramatically modify the spectra of MI in TCFs, plays a minor role in both normal and anomalous dispersion regimes in ETCFs. In practical application, the findings in this paper are of guiding significance for studying the nonlinear effects of mode-division multiplexing system based on the multimode or multicore optical fibers.

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