图 1. 太赫兹场调制准相位匹配高次谐波产生原理(一束中心波长为λ₁的高强度飞秒泵浦激光从正向聚焦进气体靶中,用于产生高次谐波;另一束中心波长为λ₂的强度相对较弱的准连续太赫兹波场在气体靶中逆向传播,它与泵浦光发生干涉,导致泵浦光强产生周期性正弦调制。气体靶置于泵浦激光焦点前方0.5 mm处,以利于增加相干长度,并获得更高的谐波转换效率^[42])

Fig. 1. Principle of terahertz field modulated quasi-phase-matched high-order harmonic generation (an intense femtosecond pump laser with a central wavelength of λ₁ is focused into the gas target from the forward direction to generate high-order harmonics; another relatively weak quasi-CW terahertz field with a wavelength of λ₂ counter propagates in the gas target, which interferes with the pump laser and causes the pump intensity to produce a periodic sinusoidal modu

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图 2. 截止区附近的氩气高次谐波光谱,其中模拟所采用的太赫兹调制场的波长λ₂=100 μm,调制场比r=0.05,图中黑色实线表示未引入调制时的高次谐波光谱EHHG0(ω),红色实线表示在偶极相位周期性调制下获得的谐波光谱E_HHG(ω

Fig. 2. High-order harmonic spectra of argon near the cutoff region. The terahertz modulation field with a wavelength of λ₂=100 μm and with a modulation field ratio of r=0.05 is used in the simulation. In the figure, the black solid line represents the harmonic spectrum E

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图 3. 不同太赫兹调制波长λ₂下的准相位匹配高次谐波光谱E_HHG(ω,λ₂),模拟所采用的调制场比r=0.07,对应的太赫兹光场强度为2.45×10¹² W/cm²,其中黑色实线表示将准相位匹配的光子能量E_q随太赫兹光场波长λ₂的变化关系用反比例函数拟合得到的结果

Fig. 3. Quasi-phase-matched high-order harmonic spectra E_HHG(ω,λ₂) with different terahertz modulation wavelengths λ₂ under a modulation field ratio r=0.07, corresponding to a terahertz field intensity of 2.45×10¹² W/cm². The black solid line is the result of fitting the quasi-phase-matched photon energies E_q with the wavelengths of the terahertz light field λ₂ by inverse

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图 4. 不同太赫兹调制场比r下的准相位匹配高次谐波光谱E_HHG(ω,r),模拟所采用的调制场波长λ₂=100 μm,图中所对应的太赫兹光场强度变化范围为4.5×10¹¹~5.0×10¹² W/cm²,其中黑色实线表示准相位匹配的光子能量E_q随调制场比r的变化关系 用线性函数拟合得到的结果,其斜率值为0.0018

Fig. 4. Quasi-phase-matched high-order harmonic spectra E_HHG(ω,r) with different terahertz modulation field ratios r under a modulation wavelength λ₂=100 μm. The range of terahertz field intensity in the figure is from 4.5×10¹¹ to 5.0×10¹² W/cm². The black solid line with a slope of 0.0018 is obtained by linearly fitting the quasi-phase-matched photon energies E_q and the modulation field ratios

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