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详细分析了正三角型三芯光纤中等腰对称平面波的调制不稳定性.等腰对称平面波即两芯中场完全相同，第三芯中场入射功率与其他两芯中不同的平面波，其存在的前提是入射光总功率（P）必须大于某最小值（Pmin），该最小值取决于光纤的线性耦合系数和非线性系数.对一给定的总功率P ≥ qslant Pmin，令一芯中的入射功率为P1，其他两芯中入射功率均为P2，有两种形式的场分布：一种是P1始终大于P2，随着P的增加，P1越来越大，P2越来越小，依线性稳定性分析方法，该场分布对应的增益谱主要特征与双芯光纤非对称平面波的增益谱相似；另一种是随着P的增加，P1越来越小，P2越来越大，使用同样的分析方法，发现该场分布下增益谱与双芯光纤非对称平面波增益谱截然不同，其显著特征是无扰动下，在正常和反常色散区域均可产生不稳定性增益，且在正常色散区域，零扰动频率对应的增益最强；另一方面，耦合系数色散对增益谱的影响在正常和反常色散区域都非常弱，这与其在双芯光纤中的影响截然不同.该结果对基于多芯光纤的模分复用系统非线性效应的研究具有一定的指导意义.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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Keywords:
- modulation instability /
- equilateral three-core fiber /
- isosceles-triangle symmetric continuous wave state
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[2] Copie F, Conforti M, Kudlinski A, Trillo S, Mussot A 2017 Opt. Express 25 11283
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[25] Wang L, Zhu Y J, Qi F H, Li M, Guo R 2015 Chaos 25 063111
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[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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[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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