阿秒光学进展及发展趋势 
下载： 4170次封底文章特邀综述
Significance Attosecond (1 as=10 -18 s) light pulses provide new approach to the basic mechanics in the quantum world in its natural time scale. A novel research area called attosecond science was opened up since the first observation of attosecond pulses in 2001. Owing to the advances of ultrafast laser techniques and the in-depth understanding of the attosecond pulse generation mechanism, a world record of 43 as light pulse has been demonstrated in 2017, which is shortest pulse ever obtained by human beings. Nowadays table-top attosecond sources based on high harmonic generation (HHG) have been routinely achieved by many groups worldwide. It is widely applied in the measurements of various ultrafast phenomena like photoionization time delay in atoms, molecules, and solids, electron correlation effects such as Fano resonance, Auger decay, and inner shell ionization, charge migration and dissociation in molecules, and manipulation of dielectrics. Attosecond pulses has achieved impressive progress in different fields such as atomic and molecular physics, condensed matter physics, chemistry, and biology in the past two decades.
Progress The limited photon flux of the attosecond pulses due to low conversion efficiency and phase mismatch of HHG process prevents the potential applications in multi-photon ionization, single shot coherent diffraction imaging, and attosecond pump-probe. HHG driven by TW or even PW high power laser is the straightforward way to generate intense attosecond pulses. Loose focusing geometry is proposed to overcome the over-ionized plasma that will destroy the phase matching process. Attosecond pulse with μJ pulse energy and 10 14W/cm 2power density is obtained using loose focusing geometry and adaptive optics. It serves as an alternative to free electron laser with shorter pulse duration and better stability to investigate ultrafast nonlinear phenomena.
Various gating technique is utilized to isolate singleattosecond burst from an attosecond pulse train. Few-cycle driving laser with stabilized carrier envelope phase (CEP) is typically required for isolated attosecond pulse (IAP) generation. Such driving laser with high pulse energy is still challenging even nowadays. The coherent synthesizer consisting of two-color or multi-color laser fields might produce “perfect” waveform to optimize the HHG conversion efficiency as well as relaxing the pulse duration limitation required for IAP gating. Sub-cycle light transients from waveform synthesizer which is ideal for IAP generation has also been demonstrated.
The so-called “water window” wavelength ranging from 2.3 nm to 4.4 nm between the K-edge of carbon and oxygen elements is very important in chemistry and biology. HHG in water window wavelength or even higher photon energy can be obtained using long wavelength driving laser combined with high gas density waveguide and transient phase matching to compensate the unfavorable scaling of HHG efficiency with driving laser wavelength. The world record of light pulse (43 as) is reported using mid-inferred driven HHG in 2017.
High repetition rate attosecond pulses are required to fulfill coincidence counting or to avoid space charge effect in precise photoelectron spectroscopy. According to the HHG scaling principle, tight focusing, and high pressure are needed to generate high harmonics using low pulse energy laser. The high repetition rate, high average power driving laser, and frequency up conversion technique make it an ideal source for high flux HHG.
HHG from solid phase material follows different mechanism with that from gas phase. The intraband HHG is due to the nonlinear radiation of the Bloch oscillation in the conduction band while the interband HHG is resulted from the transition between electron-hole pairs in different bands. It is not only a potential method to generate high efficiency harmonics, but also an important approach to the band structure and electron interaction of the material.
Conclusions and Prospects The frontier of attosecond science has been paved by the advances in the laser technique. 10 μJ attosecond pulse is obtained by loose focusing geometry of the intense driving laser and phase matching optimization. The mid-inferred driving laser enables the high photon energy HHG up to 1.6 keV and sub-50-as short attosecond pulse. The high repetition rate laser source allows >100 kHz attosecond pulse with photon flux as high as 1015 s-1 which is ideal for coincidence measurements. Last but not least, the recent progress of HHG in solid state material provides new approaches to both attosecond pulse generation and all optical measurement of laser-matter interaction. All these novel attosecond sources towards the true attosecond-pump-attosecond-probe measurements will give new insight into the microscopic mechanics in their natural time scale.
1 引言
激光与物质相互作用的研究是人们揭示科学规律、取得新发现的重要科学研究手段。1987年前后,美国和法国科学家各自独立地发现,当利用具有一定能量的皮秒激光脉冲与气体相互作用时,会产生驱动激光频率奇次倍的一系列谐波[1-2],这一现象被称为高次谐波 (HHG)。高次谐波现象被发现后不久,即被理论预言将可支持阿秒脉冲[3-4]。但由于驱动激光性能及测量技术的限制,直至2001年,人们才基于高次谐波分别在实验中测量得到阿秒脉冲串及独立的阿秒脉冲[5-6],脉冲宽度在百阿秒量级,是人类所能获得并操控的最短时间尺度。目前国际上已有多个研究组产生并实现了阿秒脉冲的测量,脉宽从数百阿秒到亚百阿秒,波长覆盖了从极紫外至软X射线辐射的范围,已被广泛应用于原子分子物理[7-10]及表面结构[11]的电离延时、Fano共振[12-13]、俄歇衰变[14]、内壳层电离[15]的电子关联效应、分子中的电荷迁移[16]、超快化学中的解离过程[17]、固体中的导体-绝缘体转变[18]等不同物质体系中超快时间分辨测量。2017年,美国及瑞士的研究小组采用1.8 μm波长的红外飞秒激光作为驱动光源,先后报道了53 as[19]及43 as[20]的最短脉冲世界纪录。国际上对阿秒脉冲的先驱性研究及其展现出的广阔的应用前景,也刺激了国内对阿秒脉冲相关研究的进展,在阿秒脉冲选通[21-23]、高次谐波产生[24-26]、瞬态吸收光谱学[27-28]、光电子能谱学[29-30]等领域取得了一系列重要的理论及实验成果。中国科学院物理研究所于2013年报道了160 as孤立阿秒脉冲的测量结果[31],并在2018报道了结合阿秒光源与多种测量终端,开展跨学科的超快时间分辨测量用户装置的建设计划[32]。2020年,华中科技大学[33]、国防科技大学[34]和中国科学院西安光学精密机械研究所[35]相继实现了孤立阿秒脉冲的测量。
HHG的很多重要性质可以用半经典的三步模型理论来解释[36-37],如
式中:IP为电离势。UP为有质动力势,即电子在光场中周期性振荡的平均动能,表示为
式中:e和m分别为电子的电荷量和质量;E为激光的电场强度;I为激光的光强;λ和ω分别为光子的波长和角频率。采用这一理论人们给出了与实验相吻合的结果,成功解释了高次谐波的截止频率与驱动激光强度和波长的平方成正比的基本规律。由于激光脉冲所支持的最短脉宽也取决于其载波的中心频率,中心波长越短,即对应中心频率越高的激光脉冲,所能产生的脉宽也越短,由此可以看出,强度越强、中心波长越长的驱动激光,其产生的高次谐波的截止频率也越高,对应的阿秒脉宽也就越短。
作为人类挑战最短脉冲宽度世界纪录极限的工作,目前阿秒脉冲不仅继续朝着脉宽越来越短的方向发展,而且也向对应更高强度(通量)的大脉冲能量、更高光子能量的极短波长、更高平均功率的高重复频率方向迈进。为此提高HHG的转换效率,发展基于超强飞秒激光、不同波长飞秒激光、高重复频率飞秒激光的驱动技术,成为阿秒光源的重要前沿内容。本文基于这样的发展趋势,将结合相位匹配技术及飞秒激光驱动技术,综述介绍阿秒脉冲通量增强、紫外扩展、脉宽压缩及重复频率提高等方面的进展,并对未来发展做了初步的预测和展望。
2 高通量阿秒脉冲的研究进展
2.1 常规单脉冲能量飞秒激光驱动下阿秒高次谐波产生的相位匹配
由于HHG的产生机制决定了其具有转换效率较低的特点,从而限制了阿秒脉冲在多光子电离[39-40]、相干衍射成像[41]、阿秒泵浦-阿秒探测[42]等对通量有一定要求的领域的应用,因此在常规能量的飞秒激光驱动下,如何实现HHG产生过程中的相位匹配,是获得高通量阿秒脉冲的重要手段。HHG的低光通量受到两个主要因素的限制:1)由上述三步模型解释的单原子效应可知,由于电子波包在空间中扩散导致的返回电子与母核复合的概率较低,因此突出表现为单原子效应。通常复合概率一方面取决于反应介质的散射截面,例如Ne气中的典型转换效率为10-7,而在Xe气中则可以达到10-4的水平[43]。另一方面则取决于电子在激光场中的运动轨迹。虽然长波长驱动激光可获得更高光子能量的HHG,但其经历的复合轨道更长,因此转换效率也随驱动波长的增加而降低;而短波长驱动则与之相反,在常规的mJ量级单脉冲能量的800 nm钛宝石驱动激光下,通常只能获得nJ乃至pJ量级的阿秒脉冲能量。2)宏观的相位匹配效应,由于基频光与高次谐波之间的相位失配而导致反应区域内不同位置产生的高次谐波无法完全相干叠加,导致效率的下降。对相位匹配的不同贡献可以写成如下形式
式中:kq和k1分别为第q阶高次谐波和基频光的波矢;Δkg主要来自激光聚焦的相位(Gouy相位);Δkn和Δkp分别是反应介质中的中性原子和电离后的等离子体引发的色散;而最后一项Δkd则为主要取决于电子轨道的偶极相位。我们可以定义相干长度Lcoh=π/Δk与吸收长度Labs来衡量HHG的相位匹配的好坏,其中Δk为各项失配量之和,Lcoh表示高次谐波可以相干相长的传播距离,Labs为高次谐波产生后在介质中被重吸收所经历的传播长度,主要决定于气体散射截面与气压。优化的相位匹配一般要求Lcoh>5Labs并且反应介质的长度Lmed>3
图 2. 光子通量与作用介质长度的关系(以吸收长度Labs为单位)[44]
Fig. 2. Relationship between photon flux and medium length (in unit of Labs) [44]
2.2 高能量飞秒激光驱动下聚焦长度与阿秒高次谐波通量
采用高能量的飞秒驱动激光,是获得高通量HHG最有效直观的手段,已有不少采用TW乃至PW峰值功率飞秒激光作为阿秒脉冲驱动光源的研究和建议。在常规产生阿秒HHG的实验中,由于驱动光单脉冲能量不高,因此需要采用紧聚焦的方式,但一方面由于Gouy相位引发的相位失配更加严重,另一方面如果聚焦强度过大,则在激光达到峰值强度前介质就可能饱和电离,从而降低了HHG所能达到的截止频率,同时产生的等离子体会引发激光的自散焦等效应,破坏相位匹配,降低产生HHG的效率。因此在使用强激光产生阿秒脉冲时,通常采用松聚焦的光路设计。理论研究与实验均表明,当驱动激光能量增大时,通过控制实验条件,相应增加焦距与反应长度并以平方倍率降低气压,HHG将可以达到同等的转换效率[47-48],这也就保证了通过提升驱动激光能量而产生高通量阿秒脉冲的可行性。松聚焦光路产生阿秒脉冲,其聚焦长度可以达到数米甚至数十米,以保证聚焦功率密度低于介质饱和电离的阈值(通常为1014 W/cm2 量级)。2002年,法国CEA-SACLAY的Hergott等[49]利用Xe气产生15阶高次谐波,获得了μJ量级的极紫外输出。同年日本理化学研究所的 Takahashi等[50]利用松聚焦的TW级驱动激光,分别在不同气体中实现了高通量的HHG输出,其中在Ar中产生了输出能量达0.3 μJ的29.6 nm波长,转换效率达到1.5×10-5; 在Xe气中产生了总能量11.5 μJ的HHG,其中72.7 nm阶次的输出能量达7 μJ,转换效率高达4×1
除了提高输出阿秒脉冲的通量之外,优化其聚焦条件也是进一步获得高强度阿秒脉冲的重要途径。利用Hartmann波前探测装置及变形镜构成的自适应光学系统,通过对极紫外以及软X射线波段的阿秒脉冲波前进行探测与优化,可以获得具有高聚焦功率密度的阿秒脉冲,
图 3. 典型的实验光路及HHG输出结果[53]。(a)采用单发极紫外波前测量装置的自适应光学系统优化松聚焦高次谐波产生的典型光路图;(b)Ar气中的典型高次谐波;(c)Hartmann波前探测装置的原理
Fig. 3. Typical experimental optical path and HHG output results [53]. (a) Typical setup for loose focusing driven HHG using single shot XUV wave front sensor and adaptive optics; (b) HHG from Ar gas; (c) principle of Hartmann wave front sensor
2017年,欧盟投资建设的全世界最大的阿秒脉冲装置——位于匈牙利的ELI-ALPS(Extreme light Infrastructure Attosecond Light Pulse Source)装置报道了其建设计划[60],其中驱动激光器SYLOS将在第一阶段达到45 mJ/1 kHz/10 fs的输出,并计划在第二阶段达到200 mJ/5 fs的输出。GHHG SYLOS Compact束线将采用长至10 m的焦距,通过准相位匹配机制[61-62]优化谐波转换效率,结合偏振选通[63]技术产生孤立阿秒脉冲。GHHG SYLOS Long束线则计划采用长至55 m的焦距及长至6 m的气体介质产生高通量的高次谐波,并可利用电离选通[64]或双光选通[65]产生孤立阿秒脉冲。正是由于采用了较高单脉冲能量的飞秒驱动激光源,所以也采用了长焦距的松聚焦结构。
图 4. ELI-ALPS装置采用松聚焦光路设计方案的GHHG SYLOS Long束线[60]
Fig. 4. ELI-ALPS GHHG SYLOS Long beam line setup driven by loose focusing laser[60]
松聚焦设计虽然经过反复理论及实验验证,证明非常适合于高通量阿秒脉冲的产生,但采用高能量的驱动脉冲与多达数十米的焦距,无疑将会极大地增加实验成本。2020年,ELI-ALPS与德国MBI的Major等[66]提出了利用紧聚焦产生紧凑高强度阿秒光源的方案。该方案将产生介质置于数个焦点瑞利距离以外,采用紧凑聚焦的设计将设备整体控制在2 m以内,获得了单脉冲能量30 nJ、功率密度2×1014 W/cm2的阿秒脉冲。
2.3 相干合成光场产生高通量阿秒脉冲研究
尽管人们在实验中很早已经实现高通量的高次谐波,即阿秒脉冲序列,但是产生高通量的孤立阿秒脉冲依然存在挑战。常规的孤立阿秒脉冲选通技术[5,63]对于驱动激光的脉冲宽度以及载波包络相位(CEP)的稳定性通常有着很高的要求,产生CEP稳定的高强度周期量级驱动激光脉冲,迄今仍是技术难度复杂的工作,为此人们提出多种不同方案的选通技术[67]。利用合成的双色或多色超快光场,理论上能够产生优化的高次谐波[26]以及孤立阿秒脉冲[65,21-22],并已在实验中被应用于孤立阿秒脉冲的选通[68-69]。虽然采用双光选通方案,放宽了对脉冲宽度的要求,但依然受限于介质在长脉冲中饱和电离的问题。随着对双色及多色光场相干合成产生HHG认识的深入,人们发现相干合成的光场不仅可以克服对驱动激光脉宽的限制,还可以以控制电子轨道的方式提升阿秒脉冲的产生效率[70-73],从而证明其为产生高通量孤立阿秒脉冲的一种理想的方法。2010年,日本理化学研究所的Takahashi等[74-75]提出了利用多周期的双色场激光相干合成产生孤立阿秒脉冲的方案,显著降低了长脉冲的过度电离,2013年他们利用脉宽30 fs、中心波长800 nm的飞秒钛宝石激光及通过参量放大产生的脉宽35 fs、中心波长1300 nm的参量激光组合的双色光场作为驱动光源,获得了能量达1.3 μJ、脉宽约500 as、中心波长等效30 eV光子能量的孤立阿秒脉冲,正是由于具有较高的脉冲能量,使得他们能够通过自相关技术测量得到脉宽信息,
图 5. 利用N+离子信号对孤立阿秒脉冲进行自相关测量[75]
Fig. 5. Autocorrelation measurements of isolated attosecond pulse using N+ ion signal [75]
利用相干合成产生孤立阿秒脉冲的另一种思路是利用多路少周期的超短脉冲合成亚周期量级的瞬态光[79-80],这种光本身具有少于单个光周期的持续时间,并可能获取宽度在阿秒量级的光学振荡。同时这种光由于其超短的亚周期结构,无需采用复杂的选通技术即可获得孤立阿秒脉冲,也是利用高次谐波产生孤立阿秒脉冲的一种可行方案。
图 6. 相干光场合成的原理[81]。(a)不同波长的相干光源;(b)由光强和时延可控的光源相干和合成光场;(c)对合成波形进行时域测量的结果
Fig. 6. Principle of coherent light synthesizer[81]. (a) Coherent light source with different wavelengths; (b) synthesized light field from the coherent sum of light sources with controllable intensity and time delay; (c) results of time-domain measurement of synthesized waveform
3 长波长飞秒激光驱动阿秒脉冲激光产生的进展
波长在2.3~4.4 nm“水窗”波段的软X射线位于碳元素和氧元素K吸收边之间,因其对水透明而对构成生命的重要元素碳、氮等具有较强吸收,因而在生物、化学等领域受到很大的关注。另外一些重要的元素如Fe、Co、Cu、Ni等吸收边则在更高的1 keV附近,吸收边的位置对于环境与物质结构十分敏感,因此可用于对特定元素的氧化、自旋态等进行探测。根据(2)式,有质动力势与驱动激光的光强成正比,虽然可以通过增加激光强度来提高截止频率,但因受限于介质的饱和电离,这一强度无法无限制的增加。另一方面,由于有质动力势也与波长的平方成正比,因此采用长波长激光驱动产生高次谐波,无疑是提高截止频率的有效方案,此外根据傅里叶变化关系,中心波长越短,即载波振荡频率越高的激光脉冲,支持越短的激光脉冲,因此采用长波长的中红外飞秒激光作为驱动光源,便成了产生更高光子能量、更短阿秒脉冲非常重要的途径。2001年,美国密歇根大学的Shan等[82]利用1.51 μm参量放大激光(OPA)驱动气体HHG,将Ar气产生的HHG的截止能量从64 eV扩展到了160 eV,从而验证了中红外激光作为阿秒驱动源的重大潜力。随着OPA[83]以及OPCPA[84]光源的发展,目前利用2 μm左右的中红外激光,HHG的光谱范围已被扩展到了水窗波段。但同时因为电子在长波长光场中所经历的复合轨道更长,量子扩散效应导致高次谐波的产生效率通常随驱动激光波长的增长,而以λ-(5~7)的规律急剧下降[85]。2012年,Popmintchev等[86]将多种波长的驱动激光注入充有高密度气体的长空心波导管中,以弥补HHG转换效率的不足,其中3.9 μm激光产生了截止能量在1.6 keV,带宽大于0.7 keV,理论上可支持2.5 as转换极限的孤立阿秒脉冲。
图 7. 相位匹配条件下产生于不同波长驱动激光的高次谐波光谱[86]
Fig. 7. HHG spectra driven by lasers with different wavelengths under phase matching conditions[86]
利用长波长飞秒激光驱动HHG理论上可以产生支持极短脉宽孤立阿秒脉冲的宽带连续谱,由于影响阿秒脉冲脉宽的固有阿秒啁啾与驱动光波长成反比[89],因此长波长飞秒激光是驱动HHG产生孤立阿秒脉冲潜在的理想光源。2016年,东京大学Saito等[90]用基于OPCPA输出的1.7 μm中红外少周期光脉冲产生的HHG,在100 eV能量附近测量得到了宽度为(449±27) as的阿秒脉冲,为中红外飞秒激光驱动产生HHG的阿秒条纹相机首次测量与时间分辨电子能谱测量。2017年Cousin等[91]进一步利用阿秒条纹相机,对中心波长1850 nm的少周期CEP稳定激光脉冲驱动Ne气产生的高次谐波进行了测量,也是对284~350 eV水窗波段阿秒脉冲的第一次条纹相机测量,得到了脉宽上限为322 as的孤立阿秒脉冲。
特别值得一提的是,2017年美国中佛罗里达大学的常增虎及其研究组利用中心波长为1.8 μm的双周期飞秒放大激光与Ne相互作用,突破之前利用800 nm钛宝石飞秒激光作驱动得到的67 as的原世界纪录,得到了53 as的孤立阿秒脉冲,其光子能量达到碳K吸收边缘(284 eV)[19]。同年,瑞士苏黎世联邦理工学院(ETH)的研究人员同样利用OPA技术获得的长波长飞秒激光为驱动脉冲,进一步报道了脉宽为43 as的孤立阿秒脉冲(
图 8. 基于中红外飞秒激光作驱动测量得到的43 as孤立阿秒脉冲[20]。(a)利用Xe气测得的阿秒条纹能谱;(b)使用ML-VTGPA算法反演重建的阿秒条纹能谱;(c)以ML-VTGPA算法重建孤立阿秒脉冲的时域振幅与相位,光谱所支持的傅里叶转换极限脉冲如虚线所示;(d)由ML-VTGPA算法重建的中红外脉冲与傅里叶转换极限脉冲和TG-FROG测量结果的比较
Fig. 8. Characterization of the 43 as isolated pulse generated by mid-inferred femtosecond laser[20]. (a) Measured attosecond streaking spectrogram in Xe gas; (b) retrieved attosecond streaking spectrogram using ML-VTGPA algorithm; (c) temporal amplitude and phase of the reconstructed isolated attosecond pulse using ML-VTGPA algorithm, Fourier transform limit pulse is shown in dashed line; (d) reconstructed mid-inferred pulse using ML-VTGPA algorithm com
4 高重复频率阿秒脉冲的进展
目前人们探测物质电子结构的主要手段,如光电子能谱仪[92],需要对特定位置激发出的电子进行高精度探测,因此不仅对材料本身有很高的要求,还需要探测设备能够在短时间内就采集到足够强的信号。为了实现采用符合测量的统计要求,并抑制对电子的探测精度产生影响的空间电荷效应,例如采用冷靶反冲离子动量谱仪(COLTRIMS)[93]或角分辨光电子能谱仪(ARPES)[94]等设备的光电子能谱实验,要在限制单个脉冲激发电子数目的同时维持光通量。为满足这类光电子能谱实验的需求,需要发展高重复频率光源驱动的高次谐波及阿秒脉冲。2003年,德国马克斯-普朗克量子光学研究所的Lindner等首次报道了使用高重复频率(100 kHz)和低脉冲能量(7 μJ)的钛宝石再生放大驱动光源产生的HHG。此类高重复频率HHG面临的最大问题之一是光子转换效率[95]。由于高重复频率驱动光源的脉冲能量很低,因此需要紧聚焦以达到足够的场强[96],由此出现极小反应体积与紧聚焦带来的相位失配,导致其光子转换效率很低。在早期的实验中,往往只能实现重复频率为MHz激光[97]到百kHz激光[98-99]的量级,远低于低重复频率高次谐波的正常水平。
对紧聚焦HHG的理论及实验探索表明,同步调节实验参数(气压、介质长度和激光焦距)优化相位匹配,在紧聚焦下可以通过提升气压达到与其他聚焦条件近似的转换效率(
图 9. HHG相位匹配气压与光束半径的关系[100]
Fig. 9. Relationship between HHG phase matching pressure and beam radius[100]
2020年,德国耶拿大学Klas等[107]利用1030 nm波长的 Yb光纤激光倍频后输出的重复频率为1 MHz、平均功率为89W的515 nm波段飞秒激光作为驱动,在26.5 eV光子能量处得到了约3×1015光子每秒(12.9 mW)的HHG输出。
在利用高重复频率HHG产生阿秒脉冲方面,已有多个研究组的成功报道。2014年,瑞士ETH的Sabbar等[108]利用偏振选单实现了10 kHz重复频率的280 as孤立阿秒脉冲的条纹相机测量结果。近两年,匈牙利ELI-ALPS设施相继报道了重复频率100 kHz、脉宽分别为420 as[109]和395 as[110]的阿秒脉冲序列测量结果。2020年,德国MBI使用非共线参量放大啁啾脉冲(OPCPA)获得的CEP锁定的脉宽7 fs、单脉冲能量190 μJ、重复频率100 kHz、中心波长800 nm的光源,产生并测量得到了160 as的孤立阿秒脉冲实验结果[111]。
对于更高重复频率的HHG装置,使用提升气压的方法满足相位匹配非常困难。对于这类系统可行的方案就是增强作用区域内驱动光源的场强。一个是等离子体场增强方法[112],一般是利用特殊设计的纳米结构材料,利用等离子表面激元使得局域内电场强度得到数个量级的提升;另一个方向是使用共振增强腔的手段,使高次谐波产生的源位于一个谐振腔的内部,通过驱动光源在腔内的振荡实现腔内电场强度的提升,可以实现极紫外波段的频率梳(
5 固体高次谐波的研究进展
近年来关于固体介质产生HHG的研究,让我们看到了使用该技术高效率产生阿秒脉冲的希望。固体HHG的设计与气体相比更加简单,同时通过研究固体HHG的微观机理,人们能够获得原始材料的电子结构以及其中电子之间的相互作用信息。1997年,Faisal 等[115]通过计算提出在半导体中可以产生较强的HHG,其需要的功率密度在1012 W/cm2量级,此后对固体HHG的研究进展较为缓慢,主要是由于人们对材料的选择以及对信号的观测存在困难。2008年,Golde 等[116]提出了固体中带内布洛赫振荡产生HHG的模型与带间电子-空穴复合产生HHG的模型。直到2010年,人们才第一次从块状材料中得到HHG信号[117],使用的材料为500 μm的ZnO 晶体,驱动激光参数为中心波长3.25 μm、脉宽100 fs、重复频率1 kHz,聚焦后的功率密度约为5×1012 W/cm2,如
图 11. 实验结果[117]。(a)固体HHG强度随阶次变化情况;(b)固体HHG截止阶次随驱动光功率变化情况
Fig. 11. Experimental results[117]. (a) Intensity of HHG from solid state varies with order; (b) cut off order of HHG from solid state varies with driving laser power
由于固体HHG来源于材料中电子在能带间跃迁以及能带上的振荡,因此通过探测固体HHG这一光信号我们可以得到材料本身的能带性质,2015年,Vampa等[119]使用中心波长3.76 μm、单脉冲能量19 μJ、脉宽95 fs的驱动激光,通过聚焦到0.25 V/Å的电场强度(对应0.85×1012 W/cm2的激光强度),在500 nm 厚度的ZnO单晶中产生HHG的基础上,使用仅有驱动光强10-5的二倍频激光对偶次HHG产生过程进行调制,并从偶次谐波信号中提取出产生过程中电子-空穴对积累的相位,通过反演算法得到了ZnO晶体中的带隙信息,从而在实验上第一次实现了能带结构的全光学测量(
图 12. 测量结果[120]。(a)固体HHG不同阶次的强度随基频光和二倍频微扰光之间延时的变化情况;(b)电子-空穴对积累的相位;(c)相位反演得到晶体带隙色散关系图
Fig. 12. Measurement result[120]. (a) Intensity of different orders of HHG varies with time delay between fundamental frequency light and double-frequency perturbing field; (b) accumulated phase retrieved from electron-hole pairs; (c) bandgap dispersion relationship retrieved from phase inversion
2017年,Lanin等[121]使用低于带隙的带内HHG获取了ZnSe的能带色散关系,实验中只采用单色光驱动产生的HHG数据就获取了能带色散关系。之前人们对能带结构的测量主要使用ARPES,该方法作为ARPES的一种补充,可以应用在无法测量光电子的条件下重建能带结构,例如在块状材料中或高压、强磁场中的材料等,因此在高温超导、拓扑绝缘体等领域有着潜在的应用。2020年,德国Goulielmakis研究组和中国科学院物理研究所孟胜等合作,通过分析MgF2晶体中产生的固体高次谐波[122],反演得到了材料中价电子势能与电子密度信息,并实现了26 pm的分辨率,为精确观测材料中价电子波包形貌奠定了基础。
6 结束语
随着人们对HHG与阿秒脉冲机理认识的不断深入,基于快速发展的激光技术并结合时间分辨光电子能谱等探测手段,不仅最短激光脉宽已突破了50 as,而且利用相位匹配技术、高能量驱动技术及多色光场相干合成的超快激光,人们所能得到的阿秒脉冲能量也已超过了10 mJ;利用中红外波长激光作为驱动,产生了截止光子能量高达1.6 keV的高次谐波,理论上支持短至2.5 as的超短脉冲。此外利用高平均功率飞秒钛宝石激光驱动光源,已产生重复频率大于100 kHz、脉宽仅160 as的阿秒脉冲,并且还有多个研究组采用波长1030 nm的高平均功率光纤及全固态驱动激光,得到了重复频率大于1 MHz的HHG。这些不同参数性能的阿秒脉冲及高次谐波的出现,使得人们能够全面表征认知原子、分子以及纳米结构中阿秒时间尺度上的超快过程,并将阿秒科学进一步扩展到了化学、生物以及凝聚态物理等诸多领域。特别值得指出的是,随着近年固体高次谐波研究的出现和兴起,不仅为阿秒科学的未来发展提供了新的思路,也为人们研究激光与材料相互作用提供了新的光学研究方法。可以预见,随着驱动激光的峰值功率越来越高,中红外波段飞秒激光的更加完善和重复频率的进一步提升,在不久的未来有望得到脉宽更短、光子能量更高的高通量阿秒脉冲,从而能够方便地利用阿秒泵浦-阿秒探测实验等超快光谱技术,将人们对于微观世界的认知带入电子运动自然的阿秒时间尺度之中。
[1] McPherson A, Gibson G, Jara H, et al. Studies of multiphoton production of vacuum-ultraviolet radiation in the rare gases[J]. Journal of the Optical Society of America B, 1987, 4(4): 595-601.
[2] Ferray M, L'Huillier A, Li X F, et al. Multiple-harmonic conversion of 1064 nm radiation in rare gases[J]. Journal of Physics B: Atomic, Molecular and Optical Physics, 1988, 21(3): L31-L35.
[3] Farkas G, Tóth C. Proposal for attosecond light pulse generation using laser induced multiple-harmonic conversion processes in rare gases[J]. Physics Letters A, 1992, 168(5/6): 447-450.
[4] Harris S E, Macklin J J, Hänsch T W. Atomic scale temporal structure inherent to high-order harmonic generation[J]. Optics Communications, 1993, 100(5/6): 487-490.
[5] Hentschel M, Kienberger R, Spielmann C, et al. Attosecond metrology[J]. Nature, 2001, 414(6863): 509-513.
[6] Paul P M, Toma E S, Breger P, et al. Observation of atrain of attosecond pulses from high harmonic generation[J]. Science, 2001, 292(5522): 1689-1692.
[7] Schultze M, Fiess M, Karpowicz N, et al. Delay in photoemission[J]. Science, 2010, 328(5986): 1658-1662.
[8] Klünder K, Dahlström J M, Gisselbrecht M, et al. Probing single-photon ionization on the attosecond time scale[J]. Physical Review Letters, 2011, 106(16): 169904.
[9] Nandi S, Plésiat E, Zhong S, et al. Attosecond timing of electron emission from a molecular shape resonance[J]. Science Advances, 2020, 6(31): eaba7762.
[10] Cavalieri A L, Müller N, Uphues T, et al. Attosecond spectroscopy in condensed matter[J]. Nature, 2007, 449(7165): 1029-1032.
[11] Locher R, Castiglioni L, Lucchini M, et al. Energy-dependent photoemission delays from noble metal surfaces by attosecond interferometry[J]. Optica, 2015, 2(5): 405-410.
[12] Gruson V, Barreau L, et al. Attosecond dynamics through a Fano resonance: monitoring the birth of a photoelectron[J]. Science, 2016, 354(6313): 734-738.
[13] Cirelli C, Marante C, Heuser S, et al. Anisotropic photoemission time delays close to a Fano resonance[J]. Nature Communications, 2018, 9(1): 955.
[14] Drescher M, Hentschel M, Kienberger R, et al. Time-resolved atomic inner-shell spectroscopy[J]. Nature, 2002, 419(6909): 803-807.
[15] Zhong S Y, Vinbladh J, Busto D, et al. Attosecond electron-spin dynamics in Xe 4d photoionization[J]. Nature Communications, 2020, 11(1): 5042.
[16] Calegari F, Ayuso D, Trabattoni A, et al. Ultrafast electron dynamics in phenylalanine initiated by attosecond pulses[J]. Science, 2014, 346(6207): 336-339.
[17] Burt M, Boll R. Lee J W L, et al. Coulomb-explosion imaging of concurrent CH2BrI photodissociation dynamics[J]. Physical Review A, 2017, 96(4): 043415.
[18] Schultze M, Bothschafter E M, Sommer A, et al. Controlling dielectrics with the electric field of light[J]. Nature, 2013, 493(7430): 75-78.
[19] Li J, Ren X, Yin Y, et al. Erratum: 53-attosecond X-ray pulses reach the carbon K-edge[J]. Nature Communications, 2017, 8(1): 186.
[20] Gaumnitz T, Jain A, Pertot Y, et al. Streaking of 43-attosecond soft-X-ray pulses generated by a passively CEP-stable mid-infrared driver[J]. Optics Express, 2017, 25(22): 27506-27518.
[21] Lan P F, Lu P X, Cao W, et al. Isolated sub-100-as pulse generation via controlling electron dynamics[J]. Physical Review A, 2007, 76: 011402.
[22] Zeng Z N, Cheng Y, Song X H, et al. Generation of an extreme ultraviolet supercontinuum in a two-color laser field[J]. Physical Review Letters, 2007, 98(20): 203901.
[23] Zhong S Y, He X K, Jiang Y J, et al. Noncollinear gating for high-flux isolated-attosecond-pulse generation[J]. Physical Review A, 2016, 93(3): 033854.
[24] Wei P, Miao J, Zeng Z, et al. Selective enhancement of a single harmonic emission[J]. Bulletin of the Chinese Academy of Sciences, 2013, 27(4): 201.
[25] 汪丽, 薛金星, 曾志男, 等. 共振增强单色高次谐波产生[J]. 中国激光, 2019, 46(10): 1001003.
[26] Ye P, He X K, Teng H, et al. Full quantum trajectories resolved high-order harmonic generation[J]. Physical Review Letters, 2014, 113(7): 073601.
[27] Du M W, Liu C D, Zheng Y H, et al. Attosecond transient-absorption spectroscopy in one-dimensional periodic crystals[J]. Physical Review A, 2019, 100(4): 043840.
[28] 张煜, 杨帆, 刘灿东, 等. H2+阿秒瞬态吸收中的量子路径干涉[J]. 中国激光, 2020, 47(8): 0801004.
[29] Xu M H, Peng L Y, Zhang Z, et al. Attosecond streaking in the low-energy region as a probe of rescattering[J]. Physical Review Letters, 2011, 107(18): 183001.
[30] Ning Q C, Peng L Y, Song S N, et al. Attosecond streaking of Cohen-Fano interferences in the photoionizationof H2+[J]. Physical Review A, 2014, 90: 013423.
[31] Zhan M J, Ye P, Teng H, et al. Generation and measurement of isolated 160-attosecond XUV laser pulses at 82 eV[J]. Chinese Physics Letters, 2013, 30(9): 093201.
[32] Teng H, He X K, Zhao K, et al. Attosecond laser station[J]. Chinese Physics B, 2018, 27(7): 074203.
[33] Yang Z, Cao W, Chen X, et al. All-optical frequency-resolved optical gating for isolated attosecond pulse reconstruction[J]. Optics Letters, 2020, 45(2): 567-570.
[34] Wang X W, Wang L, Xiao F, et al. Generation of 88 as isolated attosecond pulses with double optical gating[J]. Chinese Physics Letters, 2020, 37(2): 023201.
[35] 王向林, 徐鹏, 李捷, 等. 利用自研阿秒条纹相机测得159 as孤立阿秒脉冲[J]. 中国激光, 2020, 47(4): 0415002.
[36] Corkum P B. Plasma perspective on strong field multiphoton ionization[J]. Physical Review Letters, 1993, 71(13): 1994.
[37] Schafer K J, Yang B R. DiMauro L F, et al. Above threshold ionization beyond the high harmonic cutoff[J]. Physical Review Letters, 1993, 70(11): 1599-1602.
[38] Arnold C L, Isinger M, Busto D, et al. How can attosecond pulse train interferometry interrogate electron dynamics?[J]. Photoniques, 2018: 28-35.
[39] Sekikawa T, Kosuge A, Kanai T, et al. Nonlinear optics in the extreme ultraviolet[J]. Nature, 2004, 432(7017): 605-608.
[40] Manschwetus B, Rading L, Campi F, et al. Two-photon double ionization of neon using an intense attosecond pulse train[J]. Physical Review A, 2016, 93(6): 061402.
[41] Ravasio A, Gauthier D, Maia F R, et al. Single-shot diffractive imaging with a table-top femtosecond soft X-ray laser-harmonics source[J]. Physical Review Letters, 2009, 103(2): 028104.
[42] Tzallas P, Skantzakis E. Nikolopoulos L A A, et al. Extreme-ultraviolet pump-probe studies of one-femtosecond-scale electron dynamics[J]. Nature Physics, 2011, 7(10): 781-784.
[43] Rudawski P, Heyl C M, Brizuela F, et al. A high-flux high-order harmonic source[J]. Review of Scientific Instruments, 2013, 84(7): 073103.
[44] Constant E, Garzella D, Breger P, et al. Optimizing high harmonic generation in absorbing gases: model and experiment[J]. Physical Review Letters, 1999, 82(8): 1668-1671.
[45] Balcou P. Sali`eres P, L'Huillier A, et al. Generalized phase-matching conditions for high harmonics: the role of field-gradient forces[J]. Physical Review A, 1997, 55(4): 3204-3210.
[46] Gaarde M B, Tate J L, Schafer K J. Macroscopic aspects of attosecond pulse generation[J]. Journal of Physics B: Atomic, Molecular and Optical Physics, 2008, 41(13): 132001.
[47] Heyl C M, Coudert-Alteirac H, Miranda M, et al. Scale-invariant nonlinear optics in gases[J]. Optica, 2016, 3(1): 75-81.
[48] Heyl C M, Arnold C L, Couairon A, et al. Introduction to macroscopic power scaling principles for high-order harmonic generation[J]. Journal of Physics B: Atomic, Molecular and Optical Physics, 2017, 50(1): 013001.
[49] Hergott J F, Kovacev M, Merdji H, et al. Extreme-ultraviolet high-order harmonic pulses in the microjoule range[J]. Physical Review A, 2002, 66(2): 021801.
[50] Takahashi E, Nabekawa Y, Otsuka T, et al. Generation of highly coherent submicrojoule soft x rays by high-order harmonics[J]. Physical Review A, 2002, 66(2): 021802.
[51] Takahashi E, Nabekawa Y, Midorikawa K. Generation of 10-μJ coherent extreme-ultraviolet light by use of high-order harmonics[J]. Optics Letters, 2002, 27(21): 1920-1922.
[52] Tzallas P, Charalambidis D, Papadogiannis N A, et al. Direct observation of attosecond light bunching[J]. Nature, 2003, 426(6964): 267-271.
[53] Dacasa H, Coudert-Alteirac H, Guo C, et al. Single-shot extreme-ultraviolet wavefront measurements of high-order harmonics[J]. Optics Express, 2019, 27(3): 2656-2670.
[54] Yoshitomi D, Nees J, Miyamoto N, et al. Phase-matched enhancements of high-harmonic soft X-rays by adaptive wave-front control with a genetic algorithm[J]. Applied Physics B, 2004, 78(3/4): 275-280.
[55] Takahashi E J, Nabekawa Y, Mashiko H, et al. Generation of strong optical field in soft X-ray region by using high-order harmonics[J]. IEEE Journal of Selected Topics in Quantum Electronics, 2004, 10(6): 1315-1328.
[56] Wang Y, Guo T Y, Li J L, et al. Enhanced high-order harmonic generation driven by a wavefront corrected high-energy laser[J]. Journal of Physics B: Atomic, Molecular and Optical Physics, 2018, 51(13): 134005.
[57] Nayak A, Orfanos I, Makos I, et al. Multiple ionization of argon via multi-XUV-photon absorption induced by 20-GW high-order harmonic laser pulses[J]. Physical Review A, 2018, 98(2): 023426.
[58] Senfftleben B, Kretschmar M, Hoffmann A, et al. Highly non-linear ionization of atoms induced by intense high-harmonic pulses[J]. Journal of Physics: Photonics, 2020, 2(3): 034001.
[59] Maclot S, Lahl J, Peschel J, et al. Dissociation dynamics of the diamondoid adamantane upon photoionization by XUV femtosecond pulses[J]. Scientific Reports, 2020, 10(1): 1-12.
[60] Kühn S, Dumergue M, Kahaly S, et al. The ELI-ALPS facility: the next generation of attosecond sources[J]. Journal of Physics B: Atomic, Molecular and Optical Physics, 2017, 50(13): 132002.
[61] Seres J, Yakovlev V S, Seres E, et al. Coherent superposition of laser-driven soft-X-ray harmonics from successive sources[J]. Nature Physics, 2007, 3(12): 878-883.
[62] Willner A, Tavella F, Yeung M, et al. Coherent control of high harmonic generation via dual-gas multijet arrays[J]. Physical Review Letters, 2011, 107(17): 175002.
[63] Sola I J, Mével E, Elouga L, et al. Controlling attosecond electron dynamics by phase-stabilized polarization gating[J]. Nature Physics, 2006, 2(5): 319-322.
[64] Ferrari F, Calegari F, Lucchini M, et al. High-energy isolated attosecond pulses generated by above-saturation few-cycle fields[J]. Nature Photonics, 2010, 4(12): 875-879.
[65] Chang Z H. Controlling attosecond pulse generation with a double optical gating[J]. Physical Review A, 2007, 76(5): 051403.
[67] 魏志义, 许思源, 江昱佼, 等. 阿秒脉冲产生的技术原理及进展[J]. 科学通报, 2021, 66: 1-1.
Wei Z Y, Xu S Y, Jiang Y J, et al. Progress on technology and principle of attosecond laser pulse generation[J]. Chinese Science Bulletin, 2021, 66: 1-1.
[68] Kaku M, Oishi Y, Suda A, et al. Generation of extreme ultraviolet continuum radiation driven by a sub-10-fs two-color field[J]. Optics Express, 2006, 14(16): 7230-7237.
[69] Mashiko H, Gilbertson S, Li C Q, et al. Double optical gating of high-order harmonic generation with carrier-envelope phase stabilized lasers[J]. Physical Review Letters, 2008, 100(10): 103906.
[70] HaesslerS, BalčiŭnasT, FanG, et al. Optimization of quantum trajectories driven by strong-field waveforms[C] //Ultrafast Phenomena XIX, 2015: 72- 77.
[71] Jin C, Wang G, Wei H, et al. Waveforms for optimal sub-keV high-order harmonics with synthesized two-or three-colour laser fields[J]. Nature Communications, 2014, 5: 4003.
[72] Jin C, Hong K H, Lin C D. Optimal generation of spatially coherent soft X-ray isolated attosecond pulses in a gas-filled waveguide using two-color synthesized laser pulses[J]. Scientific Reports, 2016, 6: 38165.
[73] Lan P F, Takahashi E J, Midorikawa K. Optimization of infrared two-color multicycle field synthesis for intense-isolated-attosecond-pulse generation[J]. Physical Review A, 2010, 82(5): 053413.
[74] Takahashi E J, Lan P F, Mücke O D, et al. Infrared two-color multicycle laser field synthesis for generating an intense attosecond pulse[J]. Physical Review Letters, 2010, 104(23): 233901.
[75] Takahashi E J, Lan P, Mücke O D, et al. Attosecond nonlinear optics using gigawatt-scale isolated attosecond pulses[J]. Nature Communications, 2013, 4(1): 2691.
[76] Xue B, Tamaru Y, Fu Y X, et al. Fully stabilized multi-TW optical waveform synthesizer: toward gigawatt isolated attosecond pulses[J]. Science Advances, 2020, 6(16): eaay2802.
[77] Matía-Hernando P, Witting T, Walke D J, et al. Enhanced attosecond pulse generation in the vacuum ultraviolet using a two-colour driving field for high harmonic generation[J]. Journal of Modern Optics, 2018, 65(5/6): 737-744.
[78] Greening D, Weaver B, Pettipher A J, et al. Generation and measurement of isolated attosecond pulses with enhanced flux using a two colour synthesized laser field[J]. Optics Express, 2020, 28(16): 23329-23337.
[79] Wirth A, Hassan M T, Grguras I, et al. Synthesized light transients[J]. Science, 2011, 334(6053): 195-200.
[80] Rossi G M, Mainz R E, Yang Y D, et al. Sub-cycle millijoule-level parametric waveform synthesizer for attosecond science[J]. Nature Photonics, 2020, 14(10): 629-635.
[81] Hassan M T, Wirth A, Grguraš I, et al. Attosecond photonics: synthesis and control of light transients[J]. The Review of Scientific Instruments, 2012, 83(11): 111301.
[82] Shan B, Chang Z H. Dramatic extension of the high-order harmonic cutoff by using a long-wavelength driving field[J]. Physical Review A, 2001, 65(1): 011804.
[83] Chen M C, Arpin P, Popmintchev T, et al. Bright, coherent, ultrafast soft X-ray harmonics spanning the water window from a tabletop light source[J]. Physical Review Letters, 2010, 105(17): 173901.
[84] Hong K H, Huang S W, Moses J, et al. High-energy, phase-stable, ultrabroadband kHz OPCPA at 21 μm pumped by a picosecond cryogenic Yb: YAG laser[J]. Optics Express, 2011, 19(16): 15538.
[85] Shiner A D, Trallero-Herrero C, Kajumba N, et al. Wavelength scaling of high harmonic generation efficiency[J]. Physical Review Letters, 2009, 103(7): 073902.
[86] Popmintchev T, Chen M C, Popmintchev D, et al. Bright coherent ultrahigh harmonics in the keV X-ray regime from mid-infrared femtosecond lasers[J]. Science, 2012, 336(6086): 1287-1291.
[87] Teichmann S M, Silva F, Cousin S L, et al. 0. 5 keV soft X-ray attosecond continua[J]. Nature Communications, 2016, 7: 11493.
[88] Johnson A S, Austin D R, Wood D A, et al. High-flux soft X-ray harmonic generation from ionization-shaped few-cycle laser pulses[J]. Science Advances, 2018, 4(5): eaar3761.
[89] Colosimo P, Doumy G, Blaga C I, et al. Scaling strong-field interactions towards the classical limit[J]. Nature Physics, 2008, 4(5): 386-389.
[90] Saito N, Ishii N, Kanai T, et al. Attosecond streaking measurement of extreme ultraviolet pulses using a long-wavelength electric field[J]. Scientific Reports, 2016, 6(1): 35594.
[91] Cousin S L, di Palo N, Buades B, et al. Attosecond streaking in the water window: a new regime of attosecond pulse characterization[J]. Physical Review X, 2017, 7(4): 041030.
[92] Koralek J D, Douglas J F, Plumb N C, et al. Laser based angle-resolved photoemission, the sudden approximation, and quasiparticle-like spectral peaks in Bi2Sr2CaCu2O8+δ[J]. Physical Review Letters, 2006, 96(1): 017005.
[93] Dörner R, Mergel V, Jagutzki O, et al. Cold target recoil ion momentum spectroscopy: a ‘momentum microscope’ to view atomic collision dynamics[J]. Physics Reports, 2000, 330(2/3): 95-192.
[94] Damascelli A, Hussain Z, Shen Z X. Angle-resolved photoemission studies of the cuprate superconductors[J]. Reviews of Modern Physics, 2003, 75(2): 473-541.
[95] Wernet P, Gaudin J, Godehusen K, et al. Femtosecond time-resolved photoelectron spectroscopy with a vacuum-ultraviolet photon source based on laser high-order harmonic generation[J]. The Review of Scientific Instruments, 2011, 82(6): 063114.
[96] Niu Y, Liu F Y, Liu Y, et al. Pressure-dependent phase matching for high harmonic generation of Ar and N2 in the tight focusing regime[J]. Optics Communications, 2017, 397: 118-121.
[97] Heyl C M, Güdde J, L’Huillier A, et al. High-order harmonic generation with μJ laser pulses at high repetition rates[J]. Journal of Physics B: Atomic, Molecular and Optical Physics, 2012, 45(7): 074020.
[98] Hädrich S, Krebs M, Rothhardt J, et al. Generation of μW level plateau harmonics at high repetition rate[J]. Optics Express, 2011, 19(20): 19374-19383.
[99] Vernaleken A, Weitenberg J, Sartorius T, et al. Single-pass high-harmonic generation at 20. 8 MHz repetition rate[J]. Optics Letters, 2011, 36(17): 3428-3430.
[100] Rothhardt J, Krebs M, Hädrich S, et al. Absorption-limited and phase-matched high harmonic generation in the tight focusing regime[J]. New Journal of Physics, 2014, 16(3): 033022.
[101] Cirmi G, Lai C J, Huang S W, et al. Tunable high harmonic generation driven by a visible optical parametric amplifier[J]. EPJ Web of Conferences, 2013, 41: 01002.
[102] Russbueldt P, Mans T, Rotarius G, et al. 400 W Yb∶YAG innoslab fs-amplifier[J]. Optics Express, 2009, 17(15): 12230-12245.
[103] Eidam T, Hanf S, Seise E, et al. Femtosecond fiber CPA system emitting 830 W average output power[J]. Optics Letters, 2010, 35(2): 94-96.
[104] Saraceno C, Schriber C, Emaury F, et al. Cutting-edge high-power ultrafast thin disk oscillators[J]. Applied Sciences, 2013, 3(2): 355-395.
[105] Wang H, Xu Y, Ulonska S, et al. Bright high-repetition-rate source of narrowband extreme-ultraviolet harmonics beyond 22 eV[J]. Nature Communications, 2015, 6(1): 7459.
[106] Comby A, Descamps D, Beauvarlet S, et al. Cascaded harmonic generation from a fiber laser: a milliwatt XUV source[J]. Optics Express, 2019, 27(15): 20383-20396.
[107] KlasR, KirscheA, GebhardtM, et al. Ultra-short-pulse high-average-power Megahertz-repetition-rate coherent extreme-ultraviolet light source[EB/OL]. (2020-12-21)[2021-01-20]. https: //arxiv. org/abs/2012. 11244.
[108] Sabbar M, Heuser S, Boge R, et al. Combining attosecond XUV pulses with coincidence spectroscopy[J]. The Review of Scientific Instruments, 2014, 85(10): 103113.
[109] HammerlandD, ZhangP, KühnS, et al., Molecular and OpticalPhysics, 2019, 52(23): 23LT01.
[110] Ye P, Csizmadia T, Oldal L G, et al. Attosecond pulse generation at ELI-ALPS 100 kHz repetition rate beamline[J]. Journal of Physics B: Atomic, Molecular and Optical Physics, 2020, 53(15): 154004.
[111] Witting T, Furch F, Osolodkov M, et al. Generation and characterization of isolated attosecond pulses for coincidence spectroscopy at 100 kHz repetition rate[J]. Journal of Physics: Conference Series, 2020, 1412: 072031.
[112] Kern C, Zürch M, Spielmann C. Limitations of extreme nonlinear ultrafast nanophotonics[J]. Nanophotonics, 2015, 4(3): 303-323.
[113] Mills A K, Hammond T J. Lam M H C, et al. XUV frequency combs via femtosecond enhancement cavities[J]. Journal of Physics B: Atomic, Molecular and Optical Physics, 2012, 45(14): 142001.
[114] Porat G, Heyl C M, Schoun S B, et al. Phase-matched extreme-ultraviolet frequency-comb generation[J]. Nature Photonics, 2018, 12(7): 387-391.
[115] Faisal F H M, Kamiński J Z. Floquet-Bloch theory of high-harmonic generation in periodic structures[J]. Physical Review A, 1997, 56(1): 748-762.
[116] Golde D, Meier T, Koch S W. High harmonics generated in semiconductor nanostructures by the coupled dynamics of optical inter- and intraband excitations[J]. Physical Review B, 2008, 77(7): 075330.
[117] Ghimire S, DiChiara A D, Sistrunk E, et al. Observation of high-order harmonic generation in a bulk crystal[J]. Nature Physics, 2011, 7(2): 138-141.
[118] Vampa G, McDonald C R, Orlando G, et al. Theoretical analysis of high-harmonic generation in solids[J]. Physical Review Letters, 2014, 113(7): 073901.
[119] Vampa G, Hammond T J, Thiré N, et al. Linking high harmonics from gases and solids[J]. Nature, 2015, 522(7557): 462-464.
[120] Vampa G, Hammond T J, Thiré N, et al. All-optical reconstruction of crystal band structure[J]. Physical Review Letters, 2015, 115(19): 193603.
[121] Lanin A, Stepanov E A, Fedotov A B, et al. Mapping the electron band structure by intraband high-harmonic generation in solids[J]. Optica, 2017, 4(5): 516-519.
[122] Lakhotia H, Kim H Y, Zhan M, et al. Laser picoscopy of valence electrons in solids[J]. Nature, 2020, 583(7814): 55-59.
Article Outline
魏志义, 钟诗阳, 贺新奎, 赵昆, 滕浩, 王帅, 梁玥瑛, 王佶, 喻苏玉, 陈云琳, 朱江峰. 阿秒光学进展及发展趋势[J]. 中国激光, 2021, 48(5): 0501001. Zhiyi Wei, Shiyang Zhong, Xinkui He, Kun Zhao, Hao Teng, Shuai Wang, Yueying Liang, Ji Wang, Suyu Yu, Yunlin Chen, Jiangfeng Zhu. Progresses and Trends in Attosecond Optics[J]. Chinese Journal of Lasers, 2021, 48(5): 0501001.
PDF全文
