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

doi:10.1088/1674-1056/ac76a8

中国物理B ›› 2023, Vol. 32 ›› Issue (2): 24213-024213.doi: 10.1088/1674-1056/ac76a8

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

Lei Chen(陈磊)^1,3, Pan Li(李磐)^2,3,†, He-Shan Liu(刘河山)^2,3, Jin Yu(余锦)^1,3, Chang-Jun Ke(柯常军)^1,3, and Zi-Ren Luo(罗子人)^2,3,‡

1 Aerospace Information Research Institute, Chinese Academy of Sciences, Beijing 100094, China;
2 National Microgravity Laboratory, Institute of Mechanics, Chinese Academy of Sciences, Beijing 100190, China;
3 University of Chinese Academy of Sciences, Beijing 100049, China

收稿日期:2022-03-23 修回日期:2022-05-26 接受日期:2022-06-08 出版日期:2023-01-10 发布日期:2023-02-07
通讯作者: Pan Li, Zi-Ren Luo E-mail:lipan@imech.ac.cn;luoziren@imech.ac.cn
基金资助:
Project supported by the National Key Research and Development Program of China (Grant Nos. 2021YFC2201803 and 2020YFC2200104).

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

Lei Chen(陈磊)^1,3, Pan Li(李磐)^2,3,†, He-Shan Liu(刘河山)^2,3, Jin Yu(余锦)^1,3, Chang-Jun Ke(柯常军)^1,3, and Zi-Ren Luo(罗子人)^2,3,‡

1 Aerospace Information Research Institute, Chinese Academy of Sciences, Beijing 100094, China;
2 National Microgravity Laboratory, Institute of Mechanics, Chinese Academy of Sciences, Beijing 100190, China;
3 University of Chinese Academy of Sciences, Beijing 100049, China

Received:2022-03-23 Revised:2022-05-26 Accepted:2022-06-08 Online:2023-01-10 Published:2023-02-07
Contact: Pan Li, Zi-Ren Luo E-mail:lipan@imech.ac.cn;luoziren@imech.ac.cn
Supported by:
Project supported by the National Key Research and Development Program of China (Grant Nos. 2021YFC2201803 and 2020YFC2200104).

摘要/Abstract

摘要： 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.

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

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.

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

中图分类号: (Optical solitons; nonlinear guided waves)

42.65.Tg

42.25.Bs (Wave propagation, transmission and absorption)

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[J]. 中国物理B, 2023, 32(2): 24213-024213.

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

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

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