Two key frontier issues on picosecond pulses generated by mode-locked fiber lasers
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摘要: 窄带耗散孤子锁模光纤激光器可以产生接近变换限制的皮秒脉冲，但受非线性相移的限制，输出脉冲重复频率不能通过增加腔长来降低，脉冲能量仅在0.1 nJ以下，严重制约着这类皮秒脉冲的实际应用。提出一种通过耦合器抽取腔内脉冲能量、抑制腔内非线性相移积累，进而允许增加腔长来降低窄带耗散孤子皮秒光纤激光脉冲重复频率的方法。运用该方法，成功地将激光器重复频率由35.2 MHz降低到了1.77 MHz，且脉冲时频特性保持不变。提出了一种基于级间FBG陷波滤波的抑制皮秒脉冲光纤放大中光谱展宽的方法。通过简单地使用级间陷波滤波器，既可窄化第一级光纤放大器后的输出脉冲谱宽，允许采用第二级光纤放大器进一步提升脉冲能量，而且，还可将脉冲重塑为近高斯形，利用高斯脉冲光谱展宽斜率小的特点，允许第二级光纤放大器将脉冲能量提升得更高。利用该方法，在RMS（均方值）谱宽保持0.4 nm以内的前提下，10 ps脉冲经标准单模光纤放大器后，能量可由0.2 nJ可提升到10 nJ以上。Abstract: Narrowband dissipative soliton mode-locked fiber lasers can produce transform-limited picosecond pulses. Unfortunately, due to the limitation of allowable nonlinear phase shift for the intracavity pulse, the repetition rate of the pulses generated by such lasers cannot be reduced by increasing the cavity length; the pulse energy is only below 0.1 nJ. These seriously restrict the practical application of such picosecond pulsed fiber lasers. In this paper, we propose a method that allows the cavity length to be increased to reduce the repetition rate of the narrowband dissipative soliton picosecond fiber laser pulses by extracting the pulse energy out of the cavity with a coupler to suppress the accumulation of nonlinear phase shift of the intracavity pulses. Using this method, the laser repetition rate was successfully reduced from 35.2 MHz to 1.77 MHz, and the pulse time-frequency characteristics remained unchanged. We also propose a method to suppress spectral broadening in picosecond pulse fiber amplification based on inter-stage FBG notch filtering. By simply using the inter-stage notch filter, the output pulse spectrum width after the first-stage fiber amplifier can be narrowed, allowing the second-stage fiber amplifier to further increase the pulse energy, and also, the pulse can be reshaped to be nearly Gaussian-shaped, allowing the second-stage fiber amplifier to increase the pulse energy higher by using the Gaussian pulse characteristics of the smaller spectral broadening slope. Using this method, on the premise of keeping the RMS spectral width within 0.4 nm, after a 10 ps pulse passes through a standard single-mode fiber amplifier, the pulse energy can be increased from 0.2 nJ to more than 10 nJ.
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图 1 基于SESAM和窄带FBG滤波器的线性腔皮秒脉冲光纤激光器的结构及脉冲腔内往返传输示意图
Figure 1. Configuration of linear cavity picosecond pulsed fiber laser based on SESAM and narrowband FBG filter, equivalent schematic diagram of the round-trip transmission for the pulses in the cavity
图 2 输出脉冲的时域（a）和频域（b）电场包络
Figure 2. Electric field envelopes of output pulses in (a) time domain and (b) frequency domain
图 3 脉冲时域和频域电场包络在腔内各段光纤中的演化
Figure 3. Electric field envelope evolutions in time domain and frequency domain for pulse propagating along different fibers in the cavity
图 4 （a）输出脉冲的能量和NPS与增益之间的关系；（b）输出脉冲的脉宽和谱宽与增益之间的关系
Figure 4. (a) Output pulse energy and NPS experienced by the intra-cavity pulse as functions of the cavity gain； (b) temporal and spectral widths of the output pulses as functions of the cavity gain
图 5 输出脉宽和NPS上限与（a）窄带滤波器带宽以及（b）腔长之间的关系
Figure 5. Output pulse duration and the maximum allowable NPS as functions of (a) intra-cavity filter bandwidth，and (b) cavity length
图 6 输出脉冲平均功率及其相应激光器运转状态随泵浦功率的变化关系
Figure 6. Changes of output pulse average power and the corresponding operation state of the laser with the pump power
图 7 当输出脉冲能量为73 pJ时测得的强度自相关迹（a）和光谱（b）
Figure 7. Measured intensity autocorrelation trace (a) and spectrum (b) of output pulses when the pulse energy is 73 pJ
图 8 低重复频率被动锁模光纤激光器结构示意图
Figure 8. Configuration of the passively mode-locked fiber laser for picosecond pulses with reduced repetition rate
图 9 实测的输出脉冲光谱，其中的泵浦功率分别为：（a）98 mW；（b）116 mW；（c）130 mW
Figure 9. Measured output pulse spectra of the 35.2 MHz laser when the pump power is (a) 98 mW, (b) 116 mW，and (c) 130 mW，respectively
图 10 实测的输出脉冲强度自相关曲线（彩色）及其高斯拟合（黑色），其中泵浦功率分别为：（a）98 mW；（b）116 mW；（c）130 mW
Figure 10. Measured intensity autocorrelation traces (color curves) and their Gaussian fitting (black curves) of output pulses for the 35.2 MHz laser when the pump power is (a) 98 mW，(b) 116 mW，and (c) 130 mW，respectively
图 11 （a）实测的13.1 MHz激光器输出脉冲自相关曲线（蓝色）及其高斯拟合（红色），插图为相应输出脉冲光谱；（b）实测的输出脉冲序列
Figure 11. (a) Measured intensity autocorrelation trace (red curve) and its Gaussian fitting (blue curve) of the output pulses for the 13.1 MHz laser， the inset shows the corresponding spectrum；(b) Measured pulse trains of the laser
图 12 （a）测得的7.7 MHz激光器强度自相关曲线（蓝色）及其高斯拟合（红色），插图为相应输出脉冲光谱；（b）测得的输出脉冲序列
Figure 12. (a) Measured intensity autocorrelation trace (blue curve) and its Gaussian fitting (red curve) of the output pulses for the 7.7 MHz laser， the inset shows the corresponding spectrum；(b) Measured pulse trains of the laser
图 13 插入50 m的PLMA光纤后激光器单脉冲锁模的输出特性。（a）高速示波器测得的单脉冲，插图为脉冲序列；（b）输出脉冲的频谱，测量分辨率为100 Hz，测量范围为1 MHz，插图为高次谐波频谱，测量分辨率为3 kHz；（c）输出脉冲光谱；（d）实测脉冲强度自相关曲线（蓝色）及其高斯拟合（红色）
Figure 13. Output pulse characteristics of the laser after inserting 50 m LMA fiber in position A：(a) measured pulse profile，the inset shows the pulse train；(b) measured RF spectrum of pulse train with resolution of 300 Hz，the inset shows the higher harmonics with resolution of 3 kHz；(c) measured optical spectrum；(d) measured intensity autocorrelation traces (blue) and Gaussian fitting traces (red) of output pulses
图 14 （a）基于级间FBG陷波滤波的皮秒脉冲光纤放大器结构示意图；（b）振荡器输出脉冲光谱；（c）振荡器输出脉冲强度自相关曲线及其洛伦兹拟合
Figure 14. (a) Schematic diagram of the high fidelity two-stage picosecond pulse fiber amplifier based on inter-stage FBG notch filter；(b) measured output pulse spectrum of the oscillator with the resolution of 0.02 nm；and (c) measured intensity autocorrelation trace and its Lorentz fitting for the output pulses. In the mark of 9.4 ps×2.42，2.42 is the Lorentz fitting constant，and 9.4 ps is regarded as the measured pulse width
图 15 （a）当YDFA-1输出脉冲能量不同时的光谱；（b）经不同控制温度的FBG陷波滤波后的脉冲光谱；（c）经不同控制温度的FBG陷波滤波后的脉冲强度自相关曲线及其拟合；（d）FBG陷波滤波控制温度为40 ℃下，YDFA-2输出不同脉冲能量时的脉冲光谱（标注的带宽为3 dB带宽）
Figure 15. (a) Measured spectra when the output pulse energies of YDFA-1 are different；(b) measured spectra for the pulses after the FBG notch filter under different controlling temperature；(c) measured intensity autocorrelation traces and their fitting curves for the pulses after the FBG notch filter under different controlling temperature；(d) measured spectra for different output pulse energies of YDFA-2 when the controlling temperature of the FBG notch filter is at 40 ℃，where the labeled bandwidths are 3-dB bandwidths
图 16 （a）高斯和洛伦兹形脉冲的光谱展宽斜率N与非线性相移
${\mathit{\Phi}} $ 之间的关系；（b）光谱展宽斜率与脉冲光谱波形系数m之间的关系；（c）不同FBG陷波滤波器控制温度下，YDFA-2输出脉冲RMS谱宽与能量之间的关系，其中绿色三角、红色圆形和黑色矩形分别对应于20，30和40 ℃的控制温度Figure 16. (a) Spectral broadening factor N as functions of nonlinear phase shift
${\mathit{\Phi}} $ for Gaussian and Lorentz-shaped pulses；(b) spectral broadening slope as a function of spectral profile coefficient m of the pulse；(c) RMS bandwidths for the output pulse of YDFA-2 as functions of the pulse energy when the controlling temperatures of the FBG notch filter are at 20 ℃ (green triangle)，30 ℃ (red circle) and 40 ℃ (black rectangle)，respectively
图 17 （a）FBG陷波滤波器控制温度分别为20和40 ℃时，YDFA-2输出脉冲的自相关迹及其拟合；（b）当FBG陷波滤波器控制温度为40 ℃时，基于不同芯径增益光纤的YDFA-2输出脉冲RMS谱宽和能量之间的关系，其中黑色矩形、洋红五边形和紫色六边形分别对应于6，11和15 μm芯径的增益光纤
Figure 17. (a) Measured intensity autocorrelation traces and their fitting curves for the output pulses of YDFA-2 when the controlling temperature of the FBG notch filter is at 20 and 40 ℃，respectively；(b) RMS bandwidths as functions of output pulse energy from YDFA-2 with 6 μm (black rectangle)， 11 μm (magenta pentagon) and 15 μm (purple hexagon) core-diameter gain fibers when the controlling temperature of the FBG notch filter is at 40 ℃
表 1 激光器模拟参数表
Table 1. Parameters used in simulations of the fiber laser
parameter value $\Delta \nu $，${v_0}$ and ${T_0}$ of NBF 0.3 nm，1064 nm，60% ${q_0}$，relaxation time and ${P_{{\rm{sat}}}}$ of SAM 18%，0.5 ps，6 W length，GVD and nonlinearity of SMF1 1 m，0.024 ps2/m，3.5×10−3 W−1·m−1 length，g and saturation energy of YDF 1 m，9.6 dB/m，1 nJ length，GVD and nonlinearity of SMF2 1 m，0.024 ps2/m，3.5×10−3 W−1·m−1 
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