中国物理B ›› 2000, Vol. 9 ›› Issue (10): 753-756.doi: 10.1088/1009-1963/9/10/007

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THE NONLINEAR SCHR?DINGER EQUATION AND THE CROSS-PHASE MODULATION IN ERBIUM-DOPED FIBER AMPLIFIERS

刘宁, 刘颂豪, 廖常俊, 郭旗, 徐文成   

  1. Institute of Quantum Electronics, South China Normal University, Guangzhou 510631, China
  • 收稿日期:2000-02-24 修回日期:2000-06-03 出版日期:2000-12-25 发布日期:2005-06-10
  • 基金资助:
    Project supported by the Outstanding Young Scholar Foundation of Guangdong Province, China.

THE NONLINEAR SCHR?DINGER EQUATION AND THE CROSS-PHASE MODULATION IN ERBIUM-DOPED FIBER AMPLIFIERS

Liu Ning (刘宁), Liu Song-hao (刘颂豪), Liao Chang-jun (廖常俊), Guo Qi (郭旗), Xu Wen-cheng (徐文成)   

  1. Institute of Quantum Electronics, South China Normal University, Guangzhou 510631, China
  • Received:2000-02-24 Revised:2000-06-03 Online:2000-12-25 Published:2005-06-10
  • Supported by:
    Project supported by the Outstanding Young Scholar Foundation of Guangdong Province, China.

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摘要： The nonlinear Schr$\ddot{o}$dinger equation(NLSE) in erbium-doped fiber(EDF) was obtained. The cross-phase modulation (XPM) in the erbium-doped fiber amplifiers (EDFA) was studied based on this NLSE and the rate equations. A more generalized form of the propagation equation in EDFA was obtained which included the phase shifts the EDFA induced. An analytical expression was given to the XPM in the EDFA. It was found that the XPM in the EDFA dose not change very much with the wavelength except at the neighboring wavelengths (around 1531 nm) where the absorption and emission cross-sections of the erbium ions reach their maxima, and the XPMs have opposite signs on the two sides around 1531 nm. Furthermore, it was found that the XPM increases with the increase of the length of EDF.

Abstract: The nonlinear Schr$\ddot{o}$dinger equation(NLSE) in erbium-doped fiber(EDF) was obtained. The cross-phase modulation (XPM) in the erbium-doped fiber amplifiers (EDFA) was studied based on this NLSE and the rate equations. A more generalized form of the propagation equation in EDFA was obtained which included the phase shifts the EDFA induced. An analytical expression was given to the XPM in the EDFA. It was found that the XPM in the EDFA dose not change very much with the wavelength except at the neighboring wavelengths (around 1531 nm) where the absorption and emission cross-sections of the erbium ions reach their maxima, and the XPMs have opposite signs on the two sides around 1531 nm. Furthermore, it was found that the XPM increases with the increase of the length of EDF.

Key words: cross-phase modulation, erbium-doped fiber amplifier, optical fiber communication, wavelength-division multiplexing.

中图分类号:  (Partial differential equations)

  • 02.30.Jr
42.55.Wd (Fiber lasers) 42.60.By (Design of specific laser systems) 42.60.Fc (Modulation, tuning, and mode locking) 42.79.Sz (Optical communication systems, multiplexers, and demultiplexers?)