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中红外波段飞秒激光在超快光谱学、高分辨宽光谱光谱学、量子光学及中红外光学频率梳等方面都具有重要的应用价值[1-3]。Cr: ZnS/ZnSe增益介质的宽发射谱特性，使其成为中红外波段直接产生飞秒激光的优异材料。得益于成熟稳定的掺铒、掺铥光纤激光器，Cr:ZnS/ZnSe能够被便捷地泵浦[4-5]。宽的发射谱支持Cr:ZnS/ZnSe激光器能够实现少周期量级的飞秒脉冲输出[6-8]。Cr:ZnS/ZnSe飞秒激光能够用于产生中红外的光学频率梳和分子探测等方面[9]。同时其还可以作为优良的驱动光源，用于泵浦光参量振荡器[10]、高次谐波的产生[11]、差频产生宽光谱中红外激光[12-13]等。
可饱和吸收镜（SESAM）锁模和克尔透镜锁模（KLM）是Cr:ZnS/ZnSe中获得飞秒激光的两种主要方式[14-16]。最早在Cr:ZnS/ZnSe上实现飞秒脉冲的输出就是基于SESAM锁模的方法[14]。这种方法能够实现稳定的自启动锁模运转，但SESAM的带宽限制使得这种锁模激光器的平均功率较低，脉冲宽度很难达到少周期量级[17-18]。而克尔透镜锁模没有带宽限制，因此，基于克尔透镜锁模的Cr:ZnS/ZnSe激光器就成为了更好的选择，它的输出功率可以达到瓦级，脉冲宽度可以达到少周期量级[19-20]。表1中列举了在Cr:ZnS中实现SESAM锁模和克尔透镜锁模的国内外研究进展。
表 1 Cr:ZnS中SESAM和克尔透镜锁模输出脉冲参数
Table 1. Parameters of SESAM or Kerr-lens mode-locked output pulses in Cr:ZnS
Published year Mode-locking method Pulse width Average power Ref. 2006 SESAM 1.1 ps 125 mW [23] 2012 SESAM 130 fs 130 mW [17] 2013 KLM 68 fs 1 W [19] 2016 KLM 41 fs 1.9 W [24] 2017 KLM 125 fs 80 mW [25] 2019 KLM 45 fs 1 W [13] 2020 KLM 34 fs 0.8 W [26] 2021 KLM 23 fs 1.4 W [27] 2021 SESAM 79 fs 0.8 W [28] 2021 KLM + normal dispersion 37 fs 0.66 W This work 克尔透镜锁模系统根据腔内色散量情况，可以分为孤子锁模和全正色散锁模。孤子锁模是最为常见的一种运转方式，其相对容易实现，同时也具有很好的稳定性，但随着脉冲能量的增加，容易发生脉冲分裂，在腔内出现多脉冲的情况。相比之下，全正色散锁模由于脉冲在谐振腔内放大时为啁啾脉冲，能够获得更高的脉冲能量，输出后经过脉冲压缩得到更接近傅里叶变换极限的脉冲[9, 21-22]。
文中报道了一种Cr:ZnS的全正色散克尔透镜锁模激光器，这也是首次在Cr:ZnS激光器中实现了全正色散锁模。
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Cr:ZnS锁模激光器的实验装置如图1所示，泵浦源为中心波长在1 908 nm的掺铥光纤激光器，通过焦距为100 mm的聚焦透镜聚焦在Cr:ZnS晶体上。多晶Cr:ZnS尺寸为3 mm×2 mm×9 mm，在波长为1 908 nm处的透过率为15%，晶体两端均镀有1.5~3 μm的增透膜。晶体用铟箔包裹四个侧面并被固定在通水的紫铜热沉中，水冷温度设定为18 ℃。谐振腔由十个镜片和一个硬光阑组成。整个谐振腔的总长度为1.610 m，对应输出脉冲的重复频率为93 MHz。DM1，DM2为曲率半径为100 mm的双色镜，对1.91 μm波段高透，对2.05~3.0 μm高反。HR是对2.05~3.0 μm高反的平面反射镜。OC是输出镜，对1.7~2.7 μm透过率为30%，基底材料为红外熔融石英。6.35 mm厚的红外熔融石英，在2.4 μm处的材料色散为1352 fs2，会将输出的飞秒啁啾脉冲在输出时进行脉冲压缩。为补偿输出脉冲的剩余啁啾，在输出镜后加上3 mm厚镀有2~3 μm增透膜的多晶ZnS。H是硬光阑，它被放置在非对称腔的短臂一侧，来获得更加稳定的克尔透镜锁模脉冲激光。谐振腔一端的平面反射镜HR放在平移台上，通过推动平移台启动锁模。
图 1 实验装置图。DM：双色镜；CM：啁啾镜；TM：三阶色散镜；FL：平凸透镜；H：硬光阑
Figure 1. Experimental setup. DM: dichroic mirror; CM: chirped mirror; TM: third-order dispersion mirror; FL: focusing lens; H: hard aperture
在克尔透镜锁模脉冲激光中，腔内净色散的控制十分重要。CM1~CM4和TM1，TM2用于补偿腔内的材料色散，并使整个激光器运转在正色散区域。腔内色散元件的色散曲线如图2(a)所示。9 mm长Cr:ZnS的色散量为1080 fs2；CM1~CM4是啁啾镜，单片色散补偿量约为−200 fs2，四片啁啾镜腔内单程的总色散补偿量为−800 fs2；TM1，TM2为三阶色散镜，色散补偿量为−3000 fs3。整个谐振腔的净色散曲线如图2(b)所示，在输出脉冲的光谱范围内（2.0~2.7 μm），总色散量均为正色散。由于整个腔运转在全正色散区域，腔内的脉冲会带有较大的啁啾，输出镜（色散为1352 fs2）和3 mm厚ZnS（色散为354 fs2）恰好对输出脉冲的啁啾进行了色散补偿，实现对脉冲宽度的压缩。
图 2 群延迟色散曲线。(a) 1 mm Cr:ZnS、单片CM、单片TM的群延迟色散曲线；(b) 腔内单程净群延迟色散曲线
Figure 2. Curve of group delay dispersion. (a) Group delay dispersion curve of 1 mm Cr:ZnS, single CM and single TM; (b) Net round-trip group delay dispersion curve in the cavity
实现克尔透镜锁模，需要对谐振腔的参数进行精细的设计和调整。文中采用的是典型的非对称的“X”型复合腔。腔中凹面镜的位置会对锁模实现产生很大影响，在设计时引入克尔透镜灵敏度
$ \delta $ ，只有当$ \delta $ <0且$ \left|\delta \right| $ 越大，才越容易实现克尔透镜锁模。如图3(a)所示，固定腔的长短两臂和CM1，改变晶体和CM1之间的距离x和CM1与CM2之间的距离z，根据Vittorio.M和Cerullo.G等人给出的计算公式[29-30]，计算克尔透镜灵敏度（图3(b)），图中空白部分为非稳定部分，可以看到只在很短的一段范围内才能实现克尔透镜锁模，稳定区间分为前稳区（z<108 mm）和后稳区（z>110.5 mm）。在实验中，采用图3(b)所示的前稳区范围实现稳定的锁模脉冲输出。
图 3 (a) 谐振腔简化模型； (b) 增益晶体上的克尔透镜灵敏度计算
Figure 3. (a) Simplified mode of resonator cavity; (b) Calculation of Kerr lens sensitivity in gain crystal
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基于上述实验装置，在泵浦功率为5.1 W的情况下实现了660 mW稳定的脉冲输出，光光转化效率为13%。光谱测量使用B & W Tek公司1600~2700 nm量程的光谱仪（BTG 500E），其分辨率为1 nm，测得的输出脉冲的光谱如图4所示，光谱覆盖了从2 μm一直到2.7 μm的范围，光谱在2 050 nm处的小尖峰是由于在腔内在2 μm附近的色散量急剧变化导致的。
图 4 输出脉冲光谱
Figure 4. Spectrum of output pulse
基于二次谐波法频率分辨光学开关（SHG-FROG）装置测量经过3 mm ZnS色散补偿后的输出脉冲时频域信息，FROG的测量结果如图5所示。通过程序对脉冲信息的反演，笔者得到了脉冲时频域信息，利用FROG测量脉冲的还原误差小于0.4%。如图6所示，红色曲线为时域分布的归一化的强度信息，黑色曲线为时域电场的相位信息。从图中看到反演脉冲宽度为37 fs，全正色散条件运转下的锁模脉冲比较接近傅里叶变换极限脉宽(25 fs)。图7中红色曲线为反演后光谱的归一化强度曲线，黑色曲线为脉冲频域电场的相位信息。
图 5 输出脉冲的实测及反演SHG-FROG行迹图
Figure 5. Measurement and retrieved SHG-FROG traces of the output pulse
图 6 通过SHG-FROG反演的时域脉冲
Figure 6. Temporal profile retrieved from an SHG-FROG measurement
图 7 用SHG-FROG反演重建的光谱强度和相位分布
Figure 7. Reconstructed spectrum intensity and phase distribution retrieved from an SHG-FROG measurement
笔者对没有经过3 mm ZnS色散补偿前的脉冲宽度也进行了测量，脉冲宽度为70 fs。输出镜在2.4 μm处的材料色散为−1352 fs2，会将输出的飞秒啁啾脉冲在输出时进行脉冲压缩，经过反向推算在输出镜前腔内脉冲宽度为0.3 ps，因此，脉冲在谐振腔内为啁啾脉冲，锁模为全正色散锁模。
利用Thorlabs公司的探测器（DET05D2，带宽为20.6 MHz）对脉冲进行探测，采用带宽为500 MHz示波器观测脉冲，输出的脉冲在不同时间尺度下的波形图如图8(a)所示。可以看到在不同的时间尺度下都观测到了稳定的锁模脉冲，脉冲的重复频率为93 MHz，由于探测器的带宽较小，因此脉冲的锁模信号有失真的情况。图8(b)给出了锁模脉冲序列的频谱信号，可以看出频谱的中心频率与噪声强度比值>60 dB，说明锁模信号非常稳定。
图 8 (a) 锁模脉冲波形图；(b) 锁模脉冲序列的频谱信号
Figure 8. (a) Oscilloscope pulse trace of mode-locking pulses; (b) RF spectrum of the mode-locking pulses sequence
使用Pyrocam Ⅲ HR camera (Ophir Optronics InC.) 测量了在不同位置下锁模激光的水平和竖直方向的光束直径，如图9所示，通过拟合计算得到锁模激光的光束质量因子Mx2=1.25, My2=1.07。由于凹面镜在水平方向引入像散造成水平方向光束质量略差于竖直方向。
图 9 锁模脉冲的光斑直径随距离变化示意图
Figure 9. Plot of the measured beam diameter of mode-locking pulses varied with distance
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文中首次报道了Cr:ZnS全正色散飞秒激光脉冲输出。利用啁啾镜和三阶色散镜使腔内色散保持在接近零的正色散区域，最终获得了平均功率为660 mW、光谱可覆盖2.0~2.7 μm、脉冲宽度为37 fs、重复频率为93 MHz及光束质量因子Mx2=1.25，My2=1.07的飞秒激光脉冲。这样的全正色散锁模脉冲由于腔内的正群延迟色散引起的啁啾会使腔内的激光脉冲宽度展宽，从而降低了在增益介质上的峰值功率密度，增加了锁模的难度。但相比于孤子锁模，在应用于飞秒啁啾脉冲放大器和飞秒啁啾光参量放大器时不必引入额外的色散元件进行脉冲展宽。并且经过对输出啁啾脉冲的色散补偿，能够获得峰值功率更高，更接近傅里叶变换极限的飞秒脉冲。文中2.0~2.7 μm的宽光谱全正色散锁模脉冲，其脉冲宽度（37 fs）已经非常接近光谱的傅里叶变换极限（25 fs），这说明全正色散锁模的飞秒激光器有巨大的发展潜力。相信这样2 μm波段高峰值功率、宽光谱的超短脉冲在高分辨的分子光谱学，高能量的中红外光频梳以及通过差频产生超宽光谱中红外激光等方面具有重要的应用价值。
Operation of femtosecond Kerr-lens mode-locked laser with all-normal dispersion at 2.4 μm (Invited)
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摘要: 2 μm波段的飞秒激光光源在高分辨分子光谱学、中红外光学频率梳产生和超宽光谱的中红外光源产生等方面都具有重要的应用价值。Cr: ZnS/ZnSe具有很宽的发射峰，使其成为该波段产生宽光谱短脉冲中红外飞秒激光的重要材料。全正色散锁模的飞秒激光由于更容易实现较短的脉冲宽度与较高的峰值功率而受到青睐。文中在Cr: ZnS上实现全正色散条件下的克尔透镜锁模运转。在5.1 W的泵浦功率下实现波长覆盖范围2.0~2.7 μm，平均功率660 mW，脉冲宽度37 fs的稳定锁模脉冲输出，这是首次在Cr: ZnS中实现全正色散锁模运转的固体激光器。Cr:ZnS 全正色散锁模的飞秒激光器在高分辨分子光谱学、宽光谱中红外光光源产生等方面具有广阔的应用前景。Abstract: Femtosecond laser sources operating at around 2 μm spectral range support a plethora of applications, especially in high-resolution molecule spectroscopy, synthesis of mid-infrared optical frequency combs, and broadband mid-infrared sources. Cr:ZnS/ZnSe with broad emission bands is an ideal material to support femtosecond pulse generation at around 2 μm spectral range. Femtosecond mode-locked lasers with all-normal dispersion have recently attracted great attention due to their short pulse duration and large output pulse peak power. An operation of femtosecond Kerr-lens mode-locked laser was demonstrated in Cr: ZnS with all-normal dispersion. The laser system delivered stable mode-locked pulses with pump power of 5.1 W, spectral range from 2.0 to 2.7 μm, average power of 660 mW, duration of 37 fs. It is the first time to realize the operation of femtosecond mode-locked solid laser with all-normal dispersion in Cr: ZnS, which have potential applications in high-resolution molecule spectroscopy and generation of broadband mid-infrared sources.
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Key words:
- all-normal dispersion /
- Kerr-lens mode-lock /
- Cr: ZnS /
- mid-infrared femtosecond laser
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图 1 实验装置图。DM：双色镜；CM：啁啾镜；TM：三阶色散镜；FL：平凸透镜；H：硬光阑
Figure 1. Experimental setup. DM: dichroic mirror; CM: chirped mirror; TM: third-order dispersion mirror; FL: focusing lens; H: hard aperture
图 2 群延迟色散曲线。(a) 1 mm Cr:ZnS、单片CM、单片TM的群延迟色散曲线；(b) 腔内单程净群延迟色散曲线
Figure 2. Curve of group delay dispersion. (a) Group delay dispersion curve of 1 mm Cr:ZnS, single CM and single TM; (b) Net round-trip group delay dispersion curve in the cavity
图 3 (a) 谐振腔简化模型； (b) 增益晶体上的克尔透镜灵敏度计算
Figure 3. (a) Simplified mode of resonator cavity; (b) Calculation of Kerr lens sensitivity in gain crystal
图 5 输出脉冲的实测及反演SHG-FROG行迹图
Figure 5. Measurement and retrieved SHG-FROG traces of the output pulse
图 6 通过SHG-FROG反演的时域脉冲
Figure 6. Temporal profile retrieved from an SHG-FROG measurement
图 7 用SHG-FROG反演重建的光谱强度和相位分布
Figure 7. Reconstructed spectrum intensity and phase distribution retrieved from an SHG-FROG measurement
图 8 (a) 锁模脉冲波形图；(b) 锁模脉冲序列的频谱信号
Figure 8. (a) Oscilloscope pulse trace of mode-locking pulses; (b) RF spectrum of the mode-locking pulses sequence
图 9 锁模脉冲的光斑直径随距离变化示意图
Figure 9. Plot of the measured beam diameter of mode-locking pulses varied with distance
表 1 Cr:ZnS中SESAM和克尔透镜锁模输出脉冲参数
Table 1. Parameters of SESAM or Kerr-lens mode-locked output pulses in Cr:ZnS
Published year Mode-locking method Pulse width Average power Ref. 2006 SESAM 1.1 ps 125 mW [23] 2012 SESAM 130 fs 130 mW [17] 2013 KLM 68 fs 1 W [19] 2016 KLM 41 fs 1.9 W [24] 2017 KLM 125 fs 80 mW [25] 2019 KLM 45 fs 1 W [13] 2020 KLM 34 fs 0.8 W [26] 2021 KLM 23 fs 1.4 W [27] 2021 SESAM 79 fs 0.8 W [28] 2021 KLM + normal dispersion 37 fs 0.66 W This work 
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