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本文中激光场E(t)可以分为单色、双色、三色和四色激光场,其形式为
$ \begin{gathered} E(t)=E_1 \exp \left[-4 \ln (2)\left(\frac{t}{\tau_1}\right)^2\right] \cos \left(\omega_1 t+c_1 t^2\right)+ \\ E_2 \exp \left[-4 \ln (2)\left(\frac{t}{\tau_2}\right)^2\right] \cos \left(\omega_2 t+c_2 t^2\right)+ \\ E_3 \exp \left[-4 \ln (2)\left(\frac{t}{\tau_3}\right)^2\right] \cos \left(\omega_3 t+c_3 t^2\right)+ \\ E_4 \exp \left[-4 \ln (2)\left(\frac{t}{\tau_4}\right)^2\right] \cos \left(\omega_4 t+c_4 t^2\right) \end{gathered} $
(1) 式中,t表示时间。激光波形可以通过调控激光振幅E1~4、激光频率ω1~4、激光脉宽τ1~4和啁啾参数c1~4来实现。
本文中采用1维He原子为计算模型,其中势能函数V(x)可以表示为: $ V(x)=-\frac{1}{\sqrt{x^2+0.484}}$,x表示电子坐标。当He原子在强激光场下时,其满足的外场下薛定谔方程可表示为[19-20]:
$ \mathrm{i} \frac{\partial \psi(x, t)}{\partial t}=\left[-\frac{1}{2} \frac{\partial^2}{\partial x^2}+V(x)+x E(t)\right] \psi(x, t) $
(2) 式中,ψ(x, t)为波函数。当最终波函数获得后,通过傅里叶变换可获得高次谐波光谱S(ω):
$ S(\omega)=\left|\frac{1}{\sqrt{2 {\rm{ \mathsf{ π} }}}} \int a(t) \exp (-\mathrm{i} \omega t) \mathrm{d} t\right|^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 $表示偶极加速度。
若无其它说明,本文中计算采用原子单位(atomic units, a.u.),高次谐波光谱强度采用任意单位(arbitrary units, arb.unit)。
固定光强下组合啁啾波形优化谐波光谱的研究
Optimization of harmonic spectra by combined chirp waveform under fixed laser intensity
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摘要: 为了输出具有高转化效率和高光子能量的谐波光谱, 采用求解薛定谔方程的方法, 理论研究了多色组合啁啾波形对谐波光谱的影响。结果表明, 在固定激光强度下, 最佳三色啁啾波形可以有效延伸谐波截止能量; 最佳四色啁啾波形可以增强谐波强度; 选择最佳三色和四色组合波形下的谐波光谱进行谐波叠加可获得42as的孤立阿秒脉冲。这一结果对超短阿秒脉冲的产生是有帮助。Abstract: To produce the harmonic spectra with high conversion efficiency and high photon energy, the effect of the multi-color chirp waveform on the harmonic spectra was theoretically studied by solving the Schrödinger equation. The results show that, under the fixed laser intensity, the harmonic cutoff energy can be effectively extended by the best 3-color chirp waveform. The harmonic intensity can be enhanced by the best 4-color chirp waveform. Finally, the isolated attosecond pulses of 42as can be obtained by superposition of the harmonic spectrum of the best 3-color and 4-color combined waveforms. The results are helpful for the generation of ultra-short attosecond pulses.
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