1.Key Laboratory of All Optical Network and Advanced Telecommunication Network, Ministry of Education, Institute of Lightwave Technology, Beijing Jiaotong University, Beijing 100044, China 2.College of Physics and Electrical Engineering, Anyang Normal University, Anyang 455000, China 3.Beijing Institute of Astronautical System Engineering, Beijing 100076, China
Fund Project:Project supported by the National Natural Science Foundation of China (Grant Nos. 61775015, 61475015, 61605003) and the Fundamental Research Funds for the Central Universities, China (Grant No. 2018JBZ109).
Received Date:21 January 2019
Accepted Date:17 April 2019
Available Online:01 June 2019
Published Online:05 June 2019
Abstract:Supercontinuum generated in normal dispersion region of highly nonlinear fiber (HNLF) is widely used in signal processing and communication benefiting from its good flatness and high coherence. Because of the normal dispersion, optical wave breaking (OWB) occurs when non-frequency shift components and frequency shift components caused by self-phase modulation (SPM) overlap in time domain, and ends when non-frequency shift components disappear. The evolution of non-frequency shift components at the front and rear edge of optical pulse play an essential role in the supercontinuum generation process. In this paper, the evolution of non-frequency shift components in normal dispersion region is numerically calculated and analyzed based on generalized nonlinear Schr?dinger equation. The results demonstrate that non-frequency shift components shrink gradually as the pulse propagates in the normal dispersion region. Cross-phase modulation (XPM) and stimulated Raman scattering (SRS) play a major role in this process, while the third-order dispersion imposes little effect on it. Because of XPM, non-frequency shift components at the front and rear edge shrink gradually, and keep red shifting and blue-shifting respectively. The influence of XPM on the non-frequency shift components at both edges is symmetrical. However, the influence of SRS on the evolution of non-frequency-shift components at both edges is asymmetric. At the front edge, SRS transfers the energy from non-frequency shift component to frequency shift component, which is opposite to that at the rear edge. At the front edge, SRS accelerates the shrinking process of the non-frequency shift component, while it slows down the shrinking process at the rear edge. And this asymmetric effect is more obvious when the peak power of the pulse is higher and SRS is more efficient. The evolution of the non-frequency shift components of chirped pulses propagating in the normal dispersion region is studied. Comparing with the unchirped pulse, the non-frequency shift components at the front and rear edge of the chirped pulse have different wavelengths. For the negative chirped pulse, the wavelength spacing between the overlapped frequency-shift components and non-frequency shift components is larger, which is easier to satisfy the SRS gain range. Therefore, the evolution of non-frequency-shift components at the front and rear edge of the negative chirped pulse are more asymmetric due to the higher SRS efficiency. For positive chirped pulses, the wavelength spacing between the overlapped components is difficult to satisfy the SRS gain range. The evolution of non-frequency-shift components in the positive chirped pulses is more symmetrical due to the lower SRS efficiency. Keywords:supercontinuum/ nonlinear fiber optics/ stimulated Raman scattering/ cross-phase modulation
与无啁啾脉冲不同, 啁啾脉冲在HNLF正常色散区光谱展宽过程中前后沿非频移分量具有不同波长. 基于对脉冲尾部非频移分量演化的分析, 对啁啾脉冲非频移分量演化以及其对脉冲和光谱的影响进行分析讨论. 图5为啁啾参数C分别为3, 0和–3的脉冲在HNLF中不同位置的时谱图, 图6为对应的脉冲波形和光谱图. 仿真中采用的脉冲宽度和峰值功率为1.5 ps和50 W, 光纤参数为$\gamma = 11$ km–1·W–1, ${\beta _2} = 0.34$ ps2/km, ${\beta _3} =$0.0022 ps3/km. 图 5 不同初始啁啾脉冲在HNLF中0, 100, 400和600 m处的时谱图 Figure5. Spectrograms at the length of 0 m, 100 m, 400 m, 600 m of HNLF with different C.
图 6 不同初始啁啾脉冲在HNLF中100, 600 m处的波形和光谱 Figure6. Waveforms and spectra with different C, at l00 and 600 m of HNLF.