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$ \begin{array}{l} {\rm{i}}\frac{{\partial \varphi \left( {r, t} \right)}}{{\partial t}} = H\left( t \right)\varphi \left( {r, t} \right) = \\ \left[ { - \frac{1}{2}{\nabla ^2} - \frac{{1.55}}{r} + zE\left( t \right)} \right]\varphi \left( {r, t} \right) \end{array} $
(1) 式中,H(t)为体系哈密顿量,▽为拉普拉斯算符,t表示时间,r为电子坐标,z表示激光偏振方向, 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]、参考文献[23])。E(t)表示激光场, 可描述为:
$ \begin{array}{l} E\left( t \right) = {E_1}\exp \left[ { - 4\ln \left( 2 \right)\frac{{{t^2}}}{{\tau _1^2}}} \right]\cos \left( {{\omega _1}t + {c_1}{\omega _1}{t^2}} \right) + \\ \;\;\;{E_2}\exp \left[ { - 4\ln \left( 2 \right)\frac{{{t^2}}}{{\tau _2^2}}} \right]\cos \left( {{\omega _2}t + {c_2}{\omega _2}{t^2}} \right) \end{array} $
(2) 式中,Ei,ωi,τi和ci(i=1, 2)分别为2束激光场振幅、频率、脉宽和啁啾参量。
高次谐波表示为:
$ S\left( \omega \right) = {\left| {\frac{1}{{\sqrt {2{\rm{ \mathsf{ π} }}} }}\int {a\left( t \right)\exp \left( { - {\rm{i}}\omega t} \right){\rm{d}}t} } \right|^2} $
(3) 式中,a(t)=-〈φ(r, t)[H(t), [H(t), z]φ(r, t)〉为偶极加速度,ω为谐波阶次。
通过调控激光波形获得波长可调的单阶谐波
Generation of wavelength-tunable single-order harmonic through controlling laser waveform
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摘要: 为了获得波长可调的单阶谐波, 采用调控双色场激光波形的方法, 对谐波辐射进行了理论分析, 并取得了单阶谐波增强的范围在182阶谐波到328阶谐波的数据。结果表明, 单阶谐波的增强来源于谐波辐射短量子路径中的折叠区域; 第2束调控场的脉宽对谐波辐射折叠区域有较大影响。该研究为获得单阶谐波脉冲提供了一种新的方案, 对激光光源的发展有帮助。Abstract: In order to obtain single-order harmonics with adjustable wavelength, the method of adjusting and controlling the waveform of two-color field laser was used. Harmonic radiation was analyzed theoretically. The data of single-order harmonic enhancement ranging from the 182nd to 328th were obtained. The results show that, the enhancement of single-order harmonics comes from the folded region in short quantum path of harmonic radiation. Pulse width of the second control field has great influence on the folding region of harmonic radiation. This study provides new scheme for obtaining single-order harmonic pulses. It is helpful for the development of laser source.
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