Eigenvalue spectrum analysis for temporal signals of Kerr optical frequency combs based on nonlinear Fourier transform

doi:10.1088/1674-1056/ab683a

中国物理B ›› 2020, Vol. 29 ›› Issue (3): 34207-034207.doi: 10.1088/1674-1056/ab683a

• ELECTROMAGNETISM, OPTICS, ACOUSTICS, HEAT TRANSFER, CLASSICAL MECHANICS, AND FLUID DYNAMICS • 上一篇下一篇

Eigenvalue spectrum analysis for temporal signals of Kerr optical frequency combs based on nonlinear Fourier transform

Jia Wang(王佳), Ai-Guo Sheng(盛爱国), Xin Huang(黄鑫), Rong-Yu Li(李荣玉), Guang-Qiang He(何广强)

1 State Key Laboratory of Advanced Optical Communication Systems and Networks, Department of Electronic Engineering, Shanghai Jiao Tong University, Shanghai 200240, China;
2 State Key Laboratory of Precision Spectroscopy, East China Normal University, Shanghai 200062, China;
3 National Laboratory of Solid State Microstructures, Nanjing University, Nanjing 210093, China

收稿日期:2019-09-24 修回日期:2019-11-20 出版日期:2020-03-05 发布日期:2020-03-05
通讯作者: Guang-Qiang He E-mail:gqhe@sjtu.edu.cn
基金资助:
Project supported by the National Natural Science Foundation of China (Grant Nos. 61475099 and 61922040), Program of State Key Laboratory of Quantum Optics and Quantum Optics Devices, China (Grant No. KF201701), and the Key R&D Program of Guangdong Province, China (Grant No. 2018B030325002).

Eigenvalue spectrum analysis for temporal signals of Kerr optical frequency combs based on nonlinear Fourier transform

Jia Wang(王佳)¹, Ai-Guo Sheng(盛爱国)¹, Xin Huang(黄鑫)¹, Rong-Yu Li(李荣玉)¹, Guang-Qiang He(何广强)^1,2,3

1 State Key Laboratory of Advanced Optical Communication Systems and Networks, Department of Electronic Engineering, Shanghai Jiao Tong University, Shanghai 200240, China;
2 State Key Laboratory of Precision Spectroscopy, East China Normal University, Shanghai 200062, China;
3 National Laboratory of Solid State Microstructures, Nanjing University, Nanjing 210093, China

Received:2019-09-24 Revised:2019-11-20 Online:2020-03-05 Published:2020-03-05
Contact: Guang-Qiang He E-mail:gqhe@sjtu.edu.cn
Supported by:
Project supported by the National Natural Science Foundation of China (Grant Nos. 61475099 and 61922040), Program of State Key Laboratory of Quantum Optics and Quantum Optics Devices, China (Grant No. KF201701), and the Key R&D Program of Guangdong Province, China (Grant No. 2018B030325002).

摘要/Abstract

摘要： Based on the nonlinear Schrödinger equation (NLSE) with damping, detuning, and driving terms describing the evolution of signals in a Kerr microresonator, we apply periodic nonlinear Fourier transform (NFT) to the study of signals during the generation of the Kerr optical frequency combs (OFCs). We find that the signals in different states, including the Turing pattern, the chaos, the single soliton state, and the multi-solitons state, can be distinguished according to different distributions of the eigenvalue spectrum. Specially, the eigenvalue spectrum of the single soliton pulse is composed of a pair of conjugate symmetric discrete eigenvalues and the quasi-continuous eigenvalue spectrum with eye-like structure. Moreover, we have successfully demonstrated that the number of discrete eigenvalue pairs in the eigenvalue spectrum corresponds to the number of solitons formed in a round-trip time inside the Kerr microresonator. This work shows that some characteristics of the time-domain signal can be well reflected in the nonlinear domain.

关键词: nonlinear Fourier transform, Kerr optical frequency combs, nonlinear signal processing

Abstract: Based on the nonlinear Schrödinger equation (NLSE) with damping, detuning, and driving terms describing the evolution of signals in a Kerr microresonator, we apply periodic nonlinear Fourier transform (NFT) to the study of signals during the generation of the Kerr optical frequency combs (OFCs). We find that the signals in different states, including the Turing pattern, the chaos, the single soliton state, and the multi-solitons state, can be distinguished according to different distributions of the eigenvalue spectrum. Specially, the eigenvalue spectrum of the single soliton pulse is composed of a pair of conjugate symmetric discrete eigenvalues and the quasi-continuous eigenvalue spectrum with eye-like structure. Moreover, we have successfully demonstrated that the number of discrete eigenvalue pairs in the eigenvalue spectrum corresponds to the number of solitons formed in a round-trip time inside the Kerr microresonator. This work shows that some characteristics of the time-domain signal can be well reflected in the nonlinear domain.

Key words: nonlinear Fourier transform, Kerr optical frequency combs, nonlinear signal processing

中图分类号: (Dynamics of nonlinear optical systems; optical instabilities, optical chaos and complexity, and optical spatio-temporal dynamics)

42.65.Sf

42.65.Tg (Optical solitons; nonlinear guided waves)

王佳, 盛爱国, 黄鑫, 李荣玉, 何广强. Eigenvalue spectrum analysis for temporal signals of Kerr optical frequency combs based on nonlinear Fourier transform[J]. 中国物理B, 2020, 29(3): 34207-034207.

Jia Wang(王佳), Ai-Guo Sheng(盛爱国), Xin Huang(黄鑫), Rong-Yu Li(李荣玉), Guang-Qiang He(何广强). Eigenvalue spectrum analysis for temporal signals of Kerr optical frequency combs based on nonlinear Fourier transform[J]. Chin. Phys. B, 2020, 29(3): 34207-034207.

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Eigenvalue spectrum analysis for temporal signals of Kerr optical frequency combs based on nonlinear Fourier transform

Eigenvalue spectrum analysis for temporal signals of Kerr optical frequency combs based on nonlinear Fourier transform

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