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考虑最简单的H2+(或D2+)模型,即核运动、电子运动及激光偏振都在同一方向。此时,体系的薛定谔方程为[19]:
$ \begin{array}{*{20}{l}} {{\rm{i}}\frac{{\partial \psi \left( {z,R,t} \right)}}{{\partial t}} = \left[ { - \frac{1}{{{m_j}}}\frac{\partial }{{\partial {R^2}}}} \right. - \frac{{2{m_j} + 1}}{{4{m_j}}}\frac{{{\partial ^2}}}{{\partial {z^2}}} + }\\ {V\left( {z,R} \right) + \left( {1 + \frac{1}{{2{m_j} + 1}}} \right)zE\left. {\left( t \right)} \right]\psi \left( {z,R,t} \right)} \end{array} $
(1) $ \begin{array}{*{20}{l}} {V\left( {z, R} \right){\rm{ = }}\frac{1}{R} - \frac{1}{{\sqrt {{{\left( {z - \frac{R}{2}} \right)}^2}} + 1}} - }\\ {\;\;\;\;\;\;\;\;\;\;\;\;\;\frac{1}{{\sqrt {{{\left( {z + \frac{R}{2}} \right)}^2}} + 1}}} \end{array} $
(2) 式中, t为激光的作用时间,R和z为核与电子的坐标,V(z, R)为势能项,ψ(z, R, t)为体系波函数,mj=H和mj=D为H和D的核质量。激光场E(t)为:
$ E\left( t \right) = E\exp \left[ { - 4{\rm{ln}}\left( 2 \right){{\left( {\frac{t}{\tau }} \right)}^2}} \right]\cos \left( {{\omega _\lambda }t} \right) $
(3) 式中, E为激光振幅,ωλ为激光频率,λ表示对应波长,τ为激光半峰全宽且τ=20fs。高次谐波谱图可表示为:
$ S\left( \omega \right) = {\left| {\frac{1}{{\sqrt {2{\rm{ \mathit{ π} }}} }}\int {a\left( t \right)} \exp \left( { - {\rm{i}}{\omega _\lambda }t} \right){\rm{d}}t} \right|^2} $
(4) 式中, 。
本文中谐波辐射强度定义为谐波截止附近20阶谐波强度的平均值。
H2+和D2+谐波强度与波长的关系
The relation of harmonic intensity between H2+ and D2+ with wavelength
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摘要: 为了了解H2+及其同位素分子谐波光谱效率与激光波长之间的关系,采用求解2维薛定谔方程的方法,理论研究了600nm~1600nm激光波长下H2+和D2+谐波光谱强度随波长的变化关系。结果表明,光谱强度随波长增大而减小;在短波长区间,H2+光谱强度减小的倍率要大于D2+,在长波长区间,H2+光谱强度减小的倍率要小于D2+;此外,在弱光强下,H2+光谱强度总是大于D2+, 在强光强下,H2+光谱强度在短波长区间小于D2+, 而其在长波长区间大于D2+; 核间距延伸和电荷共振增强电离在H2+和D2+谐波光谱强度变化上起到主要作用。这一结果对分子谐波调控是有帮助的。Abstract: In order to understand the relation between the harmonic spectra efficiency of H2+ and its isotope molecule with laser wavelength, the relation between the harmonic intensity of H2+ and D2+ with the wavelength in the range of 600nm~1600nm was theoretically studied by solving 2-D time-dependent Schrdinger equation. It is shown that the intensity of harmonic spectrum is decreased as the wavelength increases. In shorter wavelength region, the decrease rate of harmonic intensity of H2+ is greater than that of D2+. In longer wavelength region, the decrease rate of harmonic intensity of H2+ is smaller than that of D2+. Furthermore, driven by lower laser intensity, the harmonic yield of H2+ is always higher than that of D2+. Driven by stronger laser intensity, the harmonic yield of H2+ is lower than that of D2+ in shorter wavelength region; while, it is higher than that of D2+ in longer wavelength region. Theoretical analyses show that the extension of nuclear distance and charge resonance enhanced ionization play the important role in the change of harmonic yield of H2+ and D2+. The results are helpful for molecular harmonic control.
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