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外场下He原子的薛定谔可描述为[18]:
$ \begin{array}{*{20}{c}} {{\rm{i}}\frac{{\partial \psi (x, t)}}{{\partial t}} = \left[ { - \frac{1}{2}\frac{{{{\rm{d}}^2}}}{{{\rm{d}}{x^2}}} + V(x) + } \right.}\\ {\left. {xE(t)} \right]\psi (x, t)} \end{array} $
(1) 式中,x为电子坐标, t表示时间, ψ(x, t)为体系波函数, $V(x) = - 1/\sqrt {0.484 + {x^2}} $表示He原子库仑势能, E(t)表示激光场, 可描述为:
$ \begin{array}{*{20}{c}} {E(t) = {E_1}\exp \left[ { - 4(\ln 2){t^2}/\tau _1^2} \right]\cos \left( {{\omega _1}t + } \right.}\\ {\left. {\beta {\omega _1}{t^2}} \right) + {E_2}\exp \left[ { - 4(\ln 2){{\left( {t - {t_{\rm{d}}}} \right)}^2}/\tau _2^2} \right] \times }\\ {\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, β为啁啾参量, td为2束激光场延迟时间。
高次谐波S(ω)表示为:
$ S(\omega ) = \mid \frac{1}{{\sqrt {2\pi } }}\int a (t)\exp ( - {\rm{i}}\omega t){\rm{d}}t{|^2} $
(3) 式中,$a(t) = \left\langle {\psi (x, t)\left| { - \frac{{\partial V(x)}}{{\partial x}} + E(t)} \right|\psi (x, t)} \right\rangle $为偶极加速度,ω为谐波阶数。
利用啁啾组合场获得单一谐波辐射能量峰
Generation of single harmonic emission peak by using chirped combined field
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摘要: 为了获得由单一谐波能量峰贡献产生的谐波平台区,采用负向啁啾场与紫外场组合调控谐波光谱的方法,进行了理论分析和数值模拟。结果表明,在负向啁啾场调控下,谐波截止能量可以达到选取的参考值,谐波平台区由单一谐波能量峰贡献产生; 适当引入一束紫外光源,在紫外共振电离的影响下,谐波平台区强度可以得到增强,并且达到参考值范围;选取平台区谐波进行叠加可以获得一个36as的超短脉冲。该研究提出了一种利用低强度组合激光场获得阿秒脉冲的新方案,对激光光源的发展有帮助。Abstract: In order to obtain the harmonic plateau, contributed by single harmonic emission peak, an effective method to control the harmonic spectrum by using the negative chirped pulse combined with an ultraviolet pulse has been proposed. It is shown that with the control of the negative chirped pulse, not only the harmonic cutoff can achieve the referenced value, but also the harmonic plateau is coming from the single harmonic emission peak. Further, with the proper introduction of an ultraviolet pulse, the intensity of harmonic plateau can be enhanced and reach the referenced value due to the ultraviolet-resonance-ionization. Finally, an ultra-short 36as pulse can be obtained by superposing the harmonics on the plateau. The present investigation provides a new method to obtain the attosecond pulse by using the low-intensity combined field, which is helpful to the development of the laser source.
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