Parametric instability in the pure-quartic nonlinear Schrödinger equation

doi:10.1088/1674-1056/ad11e7

中国物理B ›› 2024, Vol. 33 ›› Issue (3): 30506-030506.doi: 10.1088/1674-1056/ad11e7

Parametric instability in the pure-quartic nonlinear Schrödinger equation

Yun-Hong Zhang(张云红)^1,2 and Chong Liu(刘冲)^1,2,3,†

1 School of Physics, Northwest University, Xi'an 710127, China;
2 Shaanxi Key Laboratory for Theoretical Physics Frontiers, Xi'an 710127, China;
3 Peng Huanwu Center for Fundamental Theory, Xi'an 710127, China

收稿日期:2023-10-20 修回日期:2023-11-28 接受日期:2023-12-04 出版日期:2024-02-22 发布日期:2024-03-06
通讯作者: Chong Liu E-mail:chongliu@nwu.edu.cn
基金资助:
Project supported by the National Natural Science Foundation of China (Grant Nos. 12175178 and 12247103), the Natural Science Basic Research Program of Shaanxi Province, China (Grant No. 2022KJXX-71), and the Shaanxi Fundamental Science Research Project for Mathematics and Physics (Grant No. 22JSY016).

Parametric instability in the pure-quartic nonlinear Schrödinger equation

Yun-Hong Zhang(张云红)^1,2 and Chong Liu(刘冲)^1,2,3,†

1 School of Physics, Northwest University, Xi'an 710127, China;
2 Shaanxi Key Laboratory for Theoretical Physics Frontiers, Xi'an 710127, China;
3 Peng Huanwu Center for Fundamental Theory, Xi'an 710127, China

Received:2023-10-20 Revised:2023-11-28 Accepted:2023-12-04 Online:2024-02-22 Published:2024-03-06
Contact: Chong Liu E-mail:chongliu@nwu.edu.cn
Supported by:
Project supported by the National Natural Science Foundation of China (Grant Nos. 12175178 and 12247103), the Natural Science Basic Research Program of Shaanxi Province, China (Grant No. 2022KJXX-71), and the Shaanxi Fundamental Science Research Project for Mathematics and Physics (Grant No. 22JSY016).

摘要/Abstract

摘要： We study the nonlinear stage of modulation instability (MI) in the non-intergrable pure-quartic nonlinear Schrödinger equation where the fourth-order dispersion is modulated periodically. Using the three-mode truncation, we reveal the complex recurrence of parametric resonance (PR) breathers, where each recurrence is associated with two oscillation periods (PR period and internal oscillation period). The nonlinear stage of parametric instability admits the maximum energy exchange between the spectrum sidebands and central mode occurring outside the MI gain band.

关键词: modulation instability, parametric resonance breather, three-mode truncation, energy exchange

Abstract: We study the nonlinear stage of modulation instability (MI) in the non-intergrable pure-quartic nonlinear Schrödinger equation where the fourth-order dispersion is modulated periodically. Using the three-mode truncation, we reveal the complex recurrence of parametric resonance (PR) breathers, where each recurrence is associated with two oscillation periods (PR period and internal oscillation period). The nonlinear stage of parametric instability admits the maximum energy exchange between the spectrum sidebands and central mode occurring outside the MI gain band.

Key words: modulation instability, parametric resonance breather, three-mode truncation, energy exchange

中图分类号: (Nonlinear dynamics and chaos)

05.45.-a

05.10.-a (Computational methods in statistical physics and nonlinear dynamics)

Yun-Hong Zhang(张云红) and Chong Liu(刘冲). Parametric instability in the pure-quartic nonlinear Schrödinger equation[J]. 中国物理B, 2024, 33(3): 30506-030506.

Yun-Hong Zhang(张云红) and Chong Liu(刘冲). Parametric instability in the pure-quartic nonlinear Schrödinger equation[J]. Chin. Phys. B, 2024, 33(3): 30506-030506.

参考文献

[1] Benjamin T B and Feir J 1967 J. Fluid Mech. 27 417
[2] Zakharov V and Ostrovsky L 2009 Physica D 238 540
[3] Whitham G B 1965 Physical and Engineering Sciences 283 238
[4] Taniuti T and Washimi H 1968 Phys. Rev. Lett. 21 209
[5] Abdullaev F Kh, Baizakov B B, Darmanyan S A, Konotop V V and Salerno M 2001 Phys. Rev. A 64 043606
[6] Andrade D and Stuhlmeier R 2023 J. Fluid Mech. 958 1103
[7] Cappellini G and Trillo S 1991 J. Opt. Soc. Am. 8 824
[8] Lake B M, Yuen H C, Rungaldier H and Ferguson W E 1977 J. Fluid Mech. 83 49
[9] Simaeys G V, Emplit P and Haelterman M 2001 Phys. Rev. Lett. 87 033902.
[10] Akhmediev N 2007 Nature 413 267
[11] Kimmoun O, Hsu H C, Branger H, Li M S, Chen Y Y, Kharif C, Onorato M, Kelleher E J R, Kibler B, Akhmediev N and Chabchoub A 2016 Sci. Rep. 6 28516
[12] Pierangeli D, Flammini M, Zhang L, Marcucci G, Agranat A J, Grinevich P G, Santini P M, Conti C and DelRe E 2018 Phys. Rev. X 8 041017
[13] Akhmediev N and Korneev V 1986 Theoret. Math. Phys. 69 1089
[14] Dudley J M, Genty G, Dias F, Kibler B and Akhmediev N 2009 Opt. Express 24 21497
[15] Liu C, Wu Y H, Chen S C, Yao X K and Akhmediev N 2021 Phys. Rev. Lett. 127 094102
[16] Chen S C, Liu C, Yao X K, Zhao L C and Akhmediev N 2021 Phys. Rev. E 104 024215
[17] Chen S C and Liu C 2022 Physica D 438 133364
[18] Trillo S and Wabnitz S 1991 Opt. Lett. 16 986
[19] Mussot A, Naveau C, Conforti M, Kudlinski A, Copie F, Szriftgiser P and Trillo S 2018 Nat. Photon. 12 303
[20] Conforti M, Mussot A, Kudlinski A, Rota Nodari S, Dujardin G, De Biévre S, Armaroli A and Trillo S 2016 Phys. Rev. Lett. 117 013901
[21] Zhu C X, Yi W, Guo G C and Zhou Z W 2019 Phys. Rev. A 99 023619
[22] Conforti M, Copie F, Mussot A, Kudlinski A and Trillo S 2016 Opt. Lett. 41 5027
[23] Staliunas K, Hang C and Konotop V V 2013 Phys. Rev. A 88 023846
[24] Blanco-Redondo A, de Sterke C M, Sipe J E, Krauss T F, Eggleton B J and Husko C 2016 Nat. Commun. 7 10427
[25] Blanco-Redondo A, de Sterke C M, Husko C and Eggleton B 2017 Opt. Lett. 47 3800
[26] Lo C W, Stefani A, de Sterke C M and Blanco-Redondo A 2018 Opt. Express 26 7786
[27] Taheri H and Matsko A B 2019 Opt. Lett. 44 3086
[28] Zhang Z X, Luo M, Chen J X, Chen L H, Liu M, Luo A P, Xu W C and Luo Z C 2022 Opt. Lett. 47 1750
[29] Qian Z C, Liu M, Luo A P, Luo Z C and Xu W C 2022 Opt. Express 30 22066
[30] Runge F A, Hudson D D, Tam K K K, de Sterke C M and Blanco-Redondo A 2020 Nat. Photon. 14 492
[31] Zeng J L, Dai J X, Hu W and Lu D Q 2022 Appl. Math. Lett. 129 107923
[32] Tam K K K, Alexander T J, Blanco-Redondo A and de Sterke C M 2019 Opt. Lett. 44 3306
[33] Zhao K, Gao C, Xiao X and Yang C 2021 Opt. Lett. 46 761
[34] de Sterke C M, Runge A F J, Hudson D D and Blanco-Redondo A 2021 APL Photon. 6 091101
[35] Yao X K, Liu C, Yang Z Y and Yang W L 2022 Phys. Rev. Res. 4 013246
[36] Tabi C B, Tagwo H, Tiofack C G L and Kofané T C 2022 Opt. Lett. 47 5557
[37] Li Y H, Dai J X, Liu J S, Weng Z W, Hu W and Lu D Q, 2022 Opt. Commun. 524 128790
[38] Wang Z T, Luo C Y, Wang Y W, Ling X H and Zhang L F 2022 Opt. Lett. 47 3800
[39] Dai J X, Zeng J L, Hu W and Lu D Q 2022 Chaos, Solitons and Fractals 165 112867
[40] Zhu Z W, Yang S, He C J and Lin X C 2023 Chaos, Solitons and Fractals 175 113978
[41] Tiofack C G L, Tabi C B, Tagwo H and Kofané T C 2023 Phys. Lett. A 480 128982

Parametric instability in the pure-quartic nonlinear Schrödinger equation

Parametric instability in the pure-quartic nonlinear Schrödinger equation

RichHTML

PDF (PC)

赞

可视化

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 15

Metrics

本文评价

推荐阅读 0

[1]	Qian Zhang(张倩), Xiankun Yao(姚献坤), and Heng Dong(董恒). Dual-wavelength pumped latticed Fermi-Pasta-Ulam recurrences in nonlinear Schrödinger equation[J]. 中国物理B, 2024, 33(3): 30502-030502.
[2]	王河林, 杨爱军, 王肖隆, 吴彬, 阮乂. Pressure dependent modulation instability in photonic crystal fiber filled with argon gas[J]. 中国物理B, 2018, 27(9): 94221-094221.
[3]	任杨, 杨战营, 刘冲, 杨文力. Controllable optical superregular breathers in the femtosecond regime[J]. 中国物理B, 2018, 27(1): 10504-010504.
[4]	陈伟, 张学亮, 胡晓阳, 宋章启, 孟洲. Optical pulse evolution in the presence of a probe light in CW-pumped nonlinear fiber[J]. 中国物理B, 2017, 26(6): 64206-064206.
[5]	王河林, 吴彬, 王肖隆. Ultra-broadband modulation instability gain characteristics in As₂S₃ and As₂Se₃ chalcogenide glass photonic crystal fiber[J]. 中国物理B, 2016, 25(6): 64207-064207.
[6]	李金花, 任海东, 裴世鑫, 曹兆楼, 咸冯林. Modulation instabilities in randomly birefringent two-mode optical fibers[J]. 中国物理B, 2016, 25(12): 124208-124208.
[7]	李荧, 侯静, 冷进勇, 王文亮, 姜宗福. Picosecond supercontinuum generation seeded by a weak continuous wave[J]. 中国物理B, 2013, 22(7): 74205-074205.
[8]	王河林, 杨爱军, 冷雨欣. Broadband tunable optical amplification based on modulation instability characteristic of high-birefringence photonic crystal fibers[J]. 中国物理B, 2013, 22(7): 74208-074208.
[9]	钟先琼, 程科, 向安平. Impacts of higher-order dispersions and saturable nonlinearities on modulation instability in negative-refractive metamaterials[J]. 中国物理B, 2013, 22(3): 34205-034205.
[10]	陈伟, 孟洲, 周会娟. Phase-matching analysis of four-wave mixing induced by modulation instability in a single-mode fiber[J]. 中国物理B, 2012, 21(9): 94215-094215.
[11]	张秋菊, 余玮, 栾仕霞, 马光金. Motion and acceleration of electrons in high-intensity laser standing waves[J]. 中国物理B, 2012, 21(1): 13403-013403.
[12]	魏益焕. Energy and first law of thermodynamics for Born–Infeld–anti-de-Sitter black hole[J]. 中国物理B, 2010, 19(9): 90404-090404.
[13]	钟先琼, 向安平. Cross-phase modulation instability in optical fibres with exponential saturable nonlinearity and high-order dispersion[J]. 中国物理B, 2010, 19(6): 64212-064212.
[14]	王河林, 冷雨欣, 徐至展. Optimization control of modulation-instability gain in photonic crystal fibres with two-zero dispersion wavelengths[J]. 中国物理B, 2009, 18(12): 5375-5384.
[15]	胡涛平, 罗青, 李晓卿. Density cavities generated by plasma--field interactions in the far wake region of a space vehicle[J]. 中国物理B, 2007, 16(8): 2449-2454.