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Experimental observation for multi-mode dynamic output of fiber ring laser based on modulation condition
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摘要
针对光纤环形激光器输出所表现出的复杂多纵模振荡现象，在实验研究中，采用光学外差并结合射频频谱仪的探测方法，对两种外加调制工作状态下光纤环形激光器的模式动态输出进行了实时测量与时频分析。通过对光纤环形激光器系统输出的总光强信息与探测范围内获取到的多纵模动态特性进行同步提取与时频分析，将光纤环形激光器输出动态特性的研究范畴从总光强表现出的低维混沌特性扩展到多纵模具有的高维混沌信息。根据实验结果分析多纵模强度随时间的演化行为与总光强输出的内在关联，以及掺铒光纤环形激光器输出在外部调制状态下的内在动力学特性。
Abstract
In order to detect and analyze the complex multi-mode dynamics of fiber ring laser (FRL), in this experiment, based on the heterodyne detection method together with radio-frequency spectrum, the output of FRL intensities on two kinds of modulation condition are synchronously detected and analyzed. From the low dimension to high dimension chaos, the total intensity and multi-mode characters can be synchronously acquired. These experimental results show the relationships between real-time intensity and frequency evolution behaviors about single mode and total mode. Moreover, according to experimental results, the chaotic characteristics and inner relationships of erbium-doped fiber ring laser (EDFRL) output mode dynamic can be analyzed.
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Overview
Overview: Aiming at the phenomena of complex multimode dynamics occurring in practical applications of fiber ring laser (FRLs), this thesis has put forward an improved real-time multichannel frequency-domain monitoring method, which breaks up frequency-domain limitations of traditional measuring tools for laser dynamics. This breakthrough promotes the understanding and analysis on nonlinear dynamics of FRLs from a low dimension to higher, also revealing the complicated correlation between the individual behavior and the collective behavior of dense longitudinal modes and corresponding inherent physics.
The frequency-domain dynamics of laser is a hard problem in the field of optical complex systems. Actually, FRLs belong to a type of optical complex system with large degree of freedom, exhibiting such nonlinear mode dynamics as complex mode hopping, high-dimensional chaos. This thesis adopts erbium doped fiber ring laser (EDFRL) as the research object.
Based on both optical heterodyne and joint time-frequency analysis, a novel frequency-domain method for monitoring multimode dynamics of fiber lasers is proposed. This method has a frequency resolution of kHz-magnitude, and can be used to extract simultaneously the nonlinear time series of multi parameters, i.e., frequency and intensity for dense modes of EDFRL. Experimentally, the frequency-domain dynamics of modulated EDFRL is measured and analyzed, which reveals the complex interaction and evolutional law between the individual behavior and the clustering behavior of modes. The EDFRL with a FBG as wavelength selector is usually considered as a typical single-wavelength laser. However, hundreds of intrinsic modes coexist within the reflective band of FBG and present unsteady multi-longitudinal-mode (MLM) oscillations under autonomous conditions. With the help of optical heterodyne and joint time-frequency analysis method, the fruitful local dynamical phenomenon of the dense modes generated by this kind of EDFRLs are clearly obtained for the first time, which demonstrates that the individual mode shows a typical chaotic behavior whereas the total modes clustering behaves steadily.
A modulated chaotic EDFRL is a typically low-dimensional dynamical system, into which an additional freedom is introduced to realize chaos output. Similarly, this system contains a large number of dense longitudinal modes. Moreover, the dynamics and evolution of these modes in frequency domain are still unclear when the total output of the system is chaotic. By improving the frequency resolution of optical heterodyne and joint time-frequency analysis, the temporal evolution of the frequency, spectrum and intensity of a single mode in chaotic EDFRL are extracted respectively. It is found that when the total intensity exhibits low-dimensional chaos, the frequency modulation and spectral broadening phenomena occur for a single mode in frequency domain, and the mode intensity is characterized by high-dimensional chaos or random fluctuation.
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图 1 激光器模式动态测量实验装置图
Figure 1. Schematic of the experimental setup for laser mode dynamics
图 3 斜率效率图。(a) EDFRL1; (b) 980 nm LD
Figure 3. Slope efficiency figure. (a) EDFRL1; (b) 980 nm LD
图 4 输出总光强随调制频率变化的分岔图。(a) 1 kHz~40 kHz; (b) 4 kHz~16 kHz
Figure 4. Bifurcation of total intensity with frequency modulation. (a) 1 kHz~40 kHz; (b) 4 kHz~16 kHz
图 5 频率调制总光强与相对强度噪声谱。(a)三倍周期态；(b)阵发态；(c)混沌态
Figure 5. Total intensity and relative intensity noise (RIN) spectrum. (a) Triple periodic state; (b) Popping state; (c) Chaotic state
图 6 输出总光强随调制强度变化的分岔图
Figure 6. Bifurcation of total intensity with intensity modulation
图 7 频率调制总光强与相对强度噪声谱。 (a) 三 倍周期； (b) 混沌态
Figure 7. Total intensity and relative intensity noise (RIN) spectrum. (a) Triple periodic state; (b) Chaotic state
图 8 频率调制混沌态部分多模时频瀑布图与时域强度信息图。(a)模式时频瀑布图；(b)强度二维图
Figure 8. Multi-mode oscillation with frequency modulation and mode intensity time series. (a) Mode time-frequency fall graph; (b) Mode intensity two dimension graph
图 9 强度调制混沌态部分多模时频瀑布图与时域强度信息图。(a)模式时频瀑布图；(b)强度三维图
Figure 9. Multi-mode oscillation with intensity modulation and mode intensity time series. (a) Mode time-frequency fall graph; (b) Mode intensity three dimension graph
表 1 调频实验混沌态下多纵模相空间重构参数
Table 1. Multi-mode phase space reconstruction parameters with frequency modulation
Mode1 Mode2 Mode3 Mode4 Mode5 Mode6 Mode7 Total mode T 8 8 9 11 10 9 8 9 D 6 8 7 6 5 7 8 4 Dtakens 3.6±0.2 3.7±0.1 3.2±0.2 Not convergent Not convergent Not convergent 4.6±0.1 2.8±0.1 
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表 2 调幅实验混沌态下多纵模相空间重构参数
Table 2. Multi-mode phase space reconstruction parameters with intensity modulation
Mode1 Mode2 Mode3 Mode4 Mode5 Mode6 Total mode T 19 14 11 8 15 16 8 D 9 10 8 9 10 10 6 Dtakens Not convergent 2.5±0.1 3.3±0.2 Not convergent 2.6±0.2 Not convergent 2.1±0.1
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