Coupled-generalized nonlinear Schrödinger equations solved by adaptive step-size methods in interaction picture

doi:10.1088/1674-1056/ac76a8

Abstract We extend two adaptive step-size methods for solving two-dimensional or multi-dimensional generalized nonlinear Schrödinger equation (GNLSE): one is the conservation quantity error adaptive step-control method (RK4IP-CQE), and the other is the local error adaptive step-control method (RK4IP-LEM). The methods are developed in the vector form of fourth-order Runge-Kutta iterative scheme in the interaction picture by converting a vector equation in frequency domain. By simulating the supercontinuum generated from the high birefringence photonic crystal fiber, the calculation accuracies and the efficiencies of the two adaptive step-size methods are discussed. The simulation results show that the two methods have the same global average error, while RK4IP-LEM spends more time than RK4IP-CQE. The decrease of huge calculation time is due to the differences in the convergences of the relative photon number error and the approximated local error between these two adaptive step-size algorithms.

Keywords: nonlinear optics, optical propagation in nonlinear media, coupled-generalized nonlinear Schrö dinger equations (C-GNLSE), adaptive step-size methods

Received: 23 March 2022
Revised: 26 May 2022
Accepted manuscript online: 08 June 2022

PACS:	42.65.Tg	(Optical solitons; nonlinear guided waves)
	42.25.Bs	(Wave propagation, transmission and absorption)

Fund: Project supported by the National Key Research and Development Program of China (Grant Nos. 2021YFC2201803 and 2020YFC2200104).

Corresponding Authors: Pan Li, Zi-Ren Luo
E-mail: lipan@imech.ac.cn;luoziren@imech.ac.cn

Cite this article:

Lei Chen(陈磊), Pan Li(李磐), He-Shan Liu(刘河山), Jin Yu(余锦), Chang-Jun Ke(柯常军), and Zi-Ren Luo(罗子人) Coupled-generalized nonlinear Schrödinger equations solved by adaptive step-size methods in interaction picture 2023 Chin. Phys. B 32 024213

[1] Dudley J M and Taylor J R 2010 Supercontinuum Generation in Optical Fibers (Cambridge: Cambridge University Press)
[2] Agrawal G P 2007 Nonlinear Fiber Optics, 4th edn. (San Diego, CA: Academic)
[3] Povazay B, Bizheva K, Unterhuber A, Hermann B, Sattmann H, Fercher A F, Drexler w, Apolonski A, Wadsworth W J, Knight J C, Russell P S J, Vetterlein M and Scherzer E 2002 Opt. Lett. 27 1800
[4] Paulsen H N, Hilligse K M, Thogersen J, Keiding S R and Larsen J J 2003 Opt. Lett. 28 1123
[5] Dudley J M, Genty G and Coen S 2006 Rev. Mod. Phys. 78 1135
[6] Zakharov V E and Shabat A B 1972 Sov. Phys. JETP. 34 62
[7] Fermann M E, Kruglov V I, Thomsen B C, Dudley J M and Harvey J D 2000 Phys. Rev. Lett. 84 6010
[8] Hohage T and Schmidt F 2002 Tech. Rep. ZIB-Report 2
[9] Reeves W H, Skyabin D V, Biancalana F, Knight J C, Omenetto F G, Efimov A and Taylor A J 2003 Nature 424 511
[10] Hillingsoe K M, Paulsen H N, Thogersen J, Keiding S R and Larsen J J 2003 J. Opt. Soc. Am. B. 20 1887
[11] Siederdissen T H Z, Nielsen N C, Kuhl J and Giessen H 2006 J. Opt. Soc. Am. B. 23 1360
[12] Cristiani I, Tediosi R, Tartara L and Degiorgio V 2004 Opt. Express. 12 124
[13] Ming L X and Byoungho L 2004 Jpn. J. Appl. Phys. 43 2492
[14] Blow K and Wood D 1989 IEEEJ. Quantum Electron. 25 2665
[15] Hult J 2008 J. Lightwave Technol. 25 3770
[16] Heidt A M 2009 J. Lightwave Technol. 27 3984
[17] Sinkin O V, Holzlöhner R, Zweck J and Menyuk C R 2003 J. Lightwave Technol. 21 61
[18] Rieznik A A, Heidt A M, König P G, Bettachini V A and Grosz D F 2012 IEEE. Photon. 4 552
[19] Torre A D, Sinobad M, Armand R, Davies B L, Madden P M S, Mitchell A, Moss D J, Hartmann J M, Reboud V, Fedeli J M, Monat C and Grillet C 2021 APL Photon. 6 016102
[20] Scheibinger R, Lüpken N M, Chemnitz M, Schaarschmidt K, Kobelke J, Fallnich C and Schmidt M 2021 Sci. Rep. 11 5270
[21] Saini T S, Tuan T H, Suzuki T and Ohishi Y 2020 Sci. Rep. 10 2236
[22] Zitelli M, Mangini F, Ferraro M, Niang A, Kharenko D and Wabnitz S 2020 Opt. Express 28 20473
[23] Eftekhar M A, Sanjabi-Eznaveh Z, Lopez-Aviles H E, Benis S, Antonio-Lopez J E, Kolesik M, Wise F, Amezcua-Correa R and Christodoulides D N 2019 Nat. Commun. 10 1638
[24] Niang A, Mansuryan T, Krupa K, Tonello A, Fabert M, Leproux P and Wabnitz S 2019 Opt. Express 27 24018
[25] Teǧin U and Ortaç B 2018 Sci. Rep. 8 12470
[26] Yuan J H, Kang Z, Li F, Zhang X T, Mei C, Zhou G Y, Sang X Z, Wu Q, Yan B B, Zhou X, Zhong K P, Wang K, Yu C X, Farrell G, Lu C, Tam H Y and Wai P K A 2017 Opt. Lett. 42 3537
[27] Wright L G, Christodoulides D N and Wise F W 2015 Nat. Photon. 9 306
[28] Wright L G, Ziegler Z M, Lushnikov P M, Zhu Z M, Eftekhar M A, Christodoulides D N and Wise F W 2017 IEEE. Trans. Industr. Inform. 24 1
[29] Dupiol R, Bendahmane A, Krupa K, Fatome J, Tonello A, Fabert M, Couderc V, Wabnitz S and Millot G 2017 Opt. Lett. 42 3419
[30] Lu F, Lin Q, Knox W H and Agrawal G P 2004 Phys. Rev. Lett. 93 183901
[31] Tu H, Liu Y, Liu X, Turchinovich D, Logsgaard J and Boppart S A 2012 Opt. Express 20 1113
[32] Nishizawa N, Ukai Y and Goto T 2005 Opt. Express 13 8128
[33] Aleksandr A V, Il'ya V F, Jens K, Matthias J, Kay S, Andrei B F, Hartmut B and Aleksei M Z 2012 Opt. Lett. 37 5163
[34] Shavrin I, Novotny S and Ludvigsen H 2013 Opt. Express 21 32141
[35] Khakimov R, Shavrin I, Novotny S, Kaivola M and Ludvigsen H 2013 Opt. Express 21 14388
[36] Li P, Shi L and Mao Q H 2013 Acta Phys. Sin. 62 154205 (in Chinese)
[37] Brehler M, Schirwon M, Göddeke D and Krummrich P M 2017 J. Lightw. Technol. 35 3622
[38] Trillo S and Wabnitz S 1992 J. Opt. Soc. Am. B 9 1061
[39] Martins E R, Spadoti D H, Romero M A and Borges B H V 2007 Opt. Express 15 14335
[40] Ghosh A, Meneghetti M, Petersen C, Bang O, Brilland L, Venck S, Troles J, Dudley J and Sylvestre T 2019 J Phys: Photonics 1 044003
[41] Lin Q and Agrawal G P 2006 Opt. Lett. 31 3086
[42] Menyuk C R, Islam M N and Gordon J P 1991 Opt. Lett. 16 566
[43] Chick B J and Chon J W and Gu M 2008 Opt. Express 16 20099
[44] Lægsgaard J 2007 Opt. Express 15 16110

[1]	All-optical switches based on three-soliton inelastic interaction and its application in optical communication systems Shubin Wang(王树斌), Xin Zhang(张鑫), Guoli Ma(马国利), and Daiyin Zhu(朱岱寅). Chin. Phys. B, 2023, 32(3): 030506.
[2]	Modulational instability of a resonantly polariton condensate in discrete lattices Wei Qi(漆伟), Xiao-Gang Guo(郭晓刚), Liang-Wei Dong(董亮伟), and Xiao-Fei Zhang(张晓斐). Chin. Phys. B, 2023, 32(3): 030502.
[3]	Quantitative analysis of soliton interactions based on the exact solutions of the nonlinear Schrödinger equation Xuefeng Zhang(张雪峰), Tao Xu(许韬), Min Li(李敏), and Yue Meng(孟悦). Chin. Phys. B, 2023, 32(1): 010505.
[4]	Oscillation properties of matter-wave bright solitons in harmonic potentials Shu-Wen Guan(关淑文), Ling-Zheng Meng(孟令正), and Li-Chen Zhao(赵立臣). Chin. Phys. B, 2022, 31(8): 080506.
[5]	Spatio-spectral dynamics of soliton pulsation with breathing behavior in the anomalous dispersion fiber laser Ying Han(韩颖), Bo Gao(高博), Jiayu Huo(霍佳雨), Chunyang Ma(马春阳), Ge Wu(吴戈),Yingying Li(李莹莹), Bingkun Chen(陈炳焜), Yubin Guo(郭玉彬), and Lie Liu(刘列). Chin. Phys. B, 2022, 31(7): 074208.
[6]	Sequential generation of self-starting diverse operations in all-fiber laser based on thulium-doped fiber saturable absorber Pei Zhang(张沛), Kaharudin Dimyati, Bilal Nizamani, Mustafa M. Najm, and S. W. Harun. Chin. Phys. B, 2022, 31(6): 064204.
[7]	Soliton fusion and fission for the high-order coupled nonlinear Schrödinger system in fiber lasers Tian-Yi Wang(王天一), Qin Zhou(周勤), and Wen-Jun Liu(刘文军). Chin. Phys. B, 2022, 31(2): 020501.
[8]	Propagation dynamics of dipole breathing wave in lossy nonlocal nonlinear media Jian-Li Guo(郭建丽), Zhen-Jun Yang(杨振军), Xing-Liang Li(李星亮), and Shu-Min Zhang(张书敏). Chin. Phys. B, 2022, 31(1): 014203.
[9]	Optical solitons supported by finite waveguide lattices with diffusive nonlocal nonlinearity Changming Huang(黄长明), Hanying Deng(邓寒英), Liangwei Dong(董亮伟), Ce Shang(尚策), Bo Zhao(赵波), Qiangbo Suo(索强波), and Xiaofang Zhou(周小芳). Chin. Phys. B, 2021, 30(12): 124204.
[10]	Generation of domain-wall solitons in an anomalous dispersion fiber ring laser Wen-Yan Zhang(张文艳), Kun Yang(杨坤), Li-Jie Geng(耿利杰), Nan-Nan Liu(刘楠楠), Yun-Qi Hao(郝蕴琦), Tian-Hao Xian(贤天浩), and Li Zhan(詹黎). Chin. Phys. B, 2021, 30(11): 114212.
[11]	Collapse arrest in the space-fractional Schrödinger equation with an optical lattice Manna Chen(陈曼娜), Hongcheng Wang(王红成), Hai Ye(叶海), Xiaoyuan Huang(黄晓园), Ye Liu(刘晔), Sumei Hu(胡素梅), and Wei Hu(胡巍). Chin. Phys. B, 2021, 30(10): 104206.
[12]	Analysis of dark soliton generation in the microcavity with mode-interaction Xin Xu(徐昕), Xueying Jin(金雪莹), Jie Cheng(程杰), Haoran Gao(高浩然), Yang Lu(陆洋), and Liandong Yu(于连栋). Chin. Phys. B, 2021, 30(2): 024210.
[13]	Generation and manipulation of bright spatial bound-soliton pairs under the diffusion effect in photovoltaic photorefractive crystals Ze-Xian Zhang(张泽贤), Xiao-Yang Zhao(赵晓阳), Ye Li(李烨), Hu Cui(崔虎)†, Zhi-Chao Luo(罗智超), Wen-Cheng Xu(徐文成), and Ai-Ping Luo(罗爱平). Chin. Phys. B, 2020, 29(10): 104208.
[14]	Stable soliton propagation in a coupled (2+1) dimensional Ginzburg-Landau system Li-Li Wang(王丽丽), Wen-Jun Liu(刘文军). Chin. Phys. B, 2020, 29(7): 070502.
[15]	Four-soliton solution and soliton interactions of the generalized coupled nonlinear Schrödinger equation Li-Jun Song(宋丽军), Xiao-Ya Xu(徐晓雅), Yan Wang(王艳). Chin. Phys. B, 2020, 29(6): 064211.

No Suggested Reading articles found!

Viewed

Full text

Abstract

Cited

Metrics
Related Articles

Coupled-generalized nonlinear Schrödinger equations solved by adaptive step-size methods in interaction picture

Cite this article:

Online attention