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$ \begin{array}{l} {\rm{i }}\frac{{\partial \psi (z, R, t)}}{{\partial t}} = H\left( t \right)\psi \left( {z, R, t} \right) = \\ \left[ {} \right. - \frac{{1{\rm{ }}}}{{{m_{\rm{p}}}}}\frac{{{\partial ^2}}}{{\partial {R^2}}} - \frac{{2{m_{\rm{p}}} + 1}}{{4{m_{\rm{p}}}}}\frac{{{\partial ^2}}}{{\partial {z^2}}} + V\left( {z, R} \right) + \\ \left( {1 + \frac{1}{{2{m_{\rm{p}}} + 1}}} \right)zE\left( {z, t} \right)\left. {} \right]{\rm{ }}\psi (z, R, t){\rm{ }} \end{array} $
(1) $ \begin{array}{l} V\left( {z, R} \right) = \frac{1}{R} - \\ \frac{1}{{\sqrt {{{\left( {z - R/2} \right)}^2} + 1} }} - \frac{1}{{\sqrt {{{\left( {z + R/2} \right)}^2} + 1} }} \end{array} $
(2) 式中,H(t)为体系哈密顿量;ψ(z, R, t)为电子波函数;V(z, R)为势能项;mp,R,z分别为核质量、核间距离以及电子坐标;t表示时间。
E(z, t)为空间非均匀场,可以表示为:
$ \begin{array}{l} E\left( {z, t} \right) = \left[ {1 + g\left( z \right)} \right]{\rm{ }}\left\{ {} \right.{E_{800}}{\rm{exp}}\left[ { - 4{\rm{ln}}\left( 2 \right)\frac{{{t^2}}}{{{\tau _{800}}^2}}} \right] \times \\ {\rm{cos}}({\omega _{800}}t) + {E_{1600}}{\rm{exp}}\left[ { - 4{\rm{ln}}\left( 2 \right)\frac{{{{(t - {t_{\rm{d}}})}^2}}}{{{\tau _{1600}}^2}}} \right] \times \\ {\rm{cos}}\left[ {{\omega _{1600}}(t - {t_{\rm{d}}})} \right]\left. {} \right\} \end{array} $
(3) 其空间非均匀形式为:
$ \begin{array}{l} g\left( z \right) = - 5.2 \times {10^{8}}\left( {z + {z_0}} \right) + \\ 3.0 \times {10^{ - 5}}{(z + {z_0})^2} - 2.5 \times {10^{12}}{(z + {z_0})^3} - \\ 3.4 \times {10^{ - 10}}{(z + {z_0})^4} \end{array} $
(4) 式中,z0表示H2+在纳米结构中的空间位置;E800 (E1600),ω800 (ω1600),τ800 (τ1600)分别表示抽运以及探测激光场的振幅、频率和脉宽;td为两束激光场的延迟时间。
高次谐波频谱图可表示为:
$ S\left( \omega \right) = |\frac{1}{{\sqrt {2{\rm{ \mathsf{ π} }}} }}\int {} a(t){\rm{exp}}( - {\rm{i}}\omega t){\rm{d}}t|{^2} $
(5) 式中,$a\left( t \right) = - \left\langle {\psi \left( {z, R, t} \right)|\left[ {H\left( t \right), \left[ {H\left( t \right), z} \right]} \right]{\rm{ |}}\psi \left( {z, R, t} \right)} \right\rangle $为偶极加速度; ω为谐波频次。由于谐波辐射能E=hω(h为普朗克常量),因此在本文中,通过分析谐波阶次ω/ω1600来讨论谐波辐射频率。
阿秒脉冲瞬时强度ISAP(t)可由谐波光谱的傅里叶变换获得:
$ {I_{{\rm{SAP}}}}(t) = |\sum\limits_q {\left[ {a(t){\rm{exp}}( - {\rm{i}}q\omega t)} \right]{\rm{exp}}({\rm{i}}q\omega t)} |{^2} $
(6) 式中,q为叠加谐波次数。
利用非均匀抽运探测激光增强阿秒脉冲强度
Enhancement of attosecond pulse intensity based on inhomogeneous pump-probe laser field
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摘要: 为了增强高次谐波光谱及阿秒脉冲的强度,采用数值求解薛定谔方程的方法,理论研究了H2+在抽运探测激光驱动下高次谐波辐射特点。结果表明,在抽运激光驱动下,H2+首先被激发到多光子共振电离区间,进而增大电离几率; 随后在探测激光驱动下,谐波辐射强度得到增强; 当采用不对称非均匀激光场时,谐波截止频率可以进一步延伸,并且谐波平台区只由单一谐波辐射能量峰贡献; 最后通过叠加傅里叶变换后的谐波可获得脉宽在32as的脉冲。该研究对单个阿秒脉冲的产生是有帮助的。Abstract: In order to enhance intensity of high-order harmonic spectrum and attosecond pulse, characteristics of high-order harmonic radiation of H2+ driven by pump probe laser were studied by numerical solution of Schrodinger equation. The results show that H2+ is excited into the multi-photon resonance ionization region at first and then increases the ionization probability under the pump laser. The harmonic radiation intensity is enhanced under the detection laser. The cut-off frequency of the harmonic wave can be further extended when the asymmetric non-uniform laser field is used. The energy peak contribution of single harmonic radiation is obtained. Finally, the pulse width of 32as can be obtained by superposing the harmonics of Fourier transform. This study is helpful for the generation of single attosecond pulses.
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