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$ \begin{array}{*{20}{c}} {{\rm{i}}\frac{{\partial \varphi (r, t)}}{{\partial t}} = H(t)\varphi (r, t) = }\\ {\left[ { - \frac{1}{2}{\nabla ^2} + V(r) - zE(t)} \right]\varphi (r, t)} \end{array} $
(1) 式中,V(r)=-1.535r-1是He原子的库仑势能,r为电子坐标; E(t)表示激光场; z表示激光偏振方向; t表示时间; H(t)为哈密顿量,$\nabla $为梯度算符; φ(r, t)为体系波函数, 可由球谐函数来展开(具体方法见参考文献[22]),随后其可通过2阶分裂算服方法进行传播并获得最终波函数[23]。激光场可描述为:
$ \begin{array}{*{20}{c}} {E(t) = {E_1}\exp \left[ { - 4\ln (2)\frac{{{t^2}}}{{\tau _1^2}}} \right]\cos \left( {{\omega _1}t + b{\omega _1}{t^2}} \right) + }\\ {{E_2}\exp \left[ { - 4\ln (2)\frac{{{{\left( {t - {t_{\rm{d}}}} \right)}^2}}}{{\tau _2^2}}} \right]\cos \left[ {{\omega _2}\left( {t - {t_{\rm{d}}}} \right)} \right]} \end{array} $
(2) 式中,Ei,ωi和τi(i=1, 2)为2束激光场振幅、频率和脉宽, td为2束激光场延迟时间。本文中采用非线性2阶啁啾形式(bω1t2)来调控激光波形[24],其中,b为啁啾参量。b>0和b < 0分别表示正向和负向啁啾。
高次谐波表示为:
$ S(\omega ) = {\left| {\frac{1}{{\sqrt {2{\rm{ \mathsf{ π} }}} }}\int a (t)\exp ( - {\rm{i}}\omega t){\rm{d}}t} \right|^2} $
(3) 式中,a(t)=-〈φ(r, t)|[H(t), [H(t), r]]|φ(r, t)〉为偶极加速度。
最后,通过叠加傅里叶变换后的平台区谐波可获得阿秒脉冲:
$ {I_{{\rm{AP}}}}(t) = {\left| {\sum\limits_q {\left[ {\int a (t)\exp ( - {\rm{i}}q\omega t){\rm{d}}t} \right]} \exp ({\rm{i}}q\omega t)} \right|^2} $
(4) 式中,IAP(t)表示阿秒脉冲强度,q表示叠加平台区的谐波级次。
紫外-啁啾激光束驱动He原子获得阿秒脉冲
Generation of attosecond pulses from He atom driven by UV-chirped laser beam
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摘要: 为了获得X射线范围内的阿秒脉冲, 采用紫外-啁啾组合激光束产生高强度谐波光谱和阿秒脉冲的方法, 进行了理论分析。结果表明, 当引入正向啁啾参量时, 虽然谐波截止能量有微小延伸, 但是谐波辐射效率明显下降; 当引入负向啁啾参量时, 不仅谐波截止能量得到延伸, 并且谐波辐射效率比正向啁啾条件下有所增强; 将一束125nm的紫外光源引入到啁啾激光下, 由于共振增强电离的影响, 谐波辐射效率有明显增强, 在紫外-正向啁啾驱动下, 不仅谐波辐射强度被增强25倍, 而且谐波截止能量得到延伸, 形成了一个382eV的平台区, 在紫外-负向啁啾驱动下, 虽然谐波截止能量没有明显变化, 但是谐波辐射效率有110倍的提高, 进而形成一个410eV的平台区; 通过叠加组合场下的谐波, 可获得一系列70as以内的单个阿秒脉冲。该研究对阿秒科学的发展是有帮助的。Abstract: In order to obtain attosecond pulses in X-ray range, the method of generating high intensity harmonic spectra and attosecond pulses by combining ultraviolet and chirped laser beams was introduced. The theoretical analysis was carried out. The results show that, when forward chirp parameter is introduced, harmonic cut-off energy has a slight extension and the efficiency of harmonic radiation decreases significantly. When negative chirp parameter is introduced, harmonic cut-off energy is extended and harmonic radiation efficiency is enhanced under the condition of forward chirp. When a 125nm ultraviolet light source is introduced into the chirped laser, the efficiency of harmonic radiation is obviously enhanced because of the effect of resonance-enhanced ionization. Driven by ultraviolet-forward chirp, harmonic radiation intensity is enhanced 25 times and harmonic cut-off energy is extended. A 382eV platform area is formed. Driven by ultraviolet-negative chirp, harmonic cut-off energy does not changed significantly but the efficiency of harmonic radiation is 110 times higher. A 410eV platform area is formed. By superposing the harmonics in the combined field, a series of single attosecond pulses within 70as can be obtained. This study is helpful for the development of attosecond science.
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Key words:
- laser optics /
- attosecond pulse /
- high-order harmonic generation /
- ultraviolet pulse /
- chirped pulse
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