多周期强激光场中高次谐波选择性增强Control of Enhanced High-Order Harmonic Generation in a Multi-Cycle Laser Field

Abstract: By using strong-field approximation, we theoretically investigate the selective enhancement of high-order harmonic generation in a small spectral range driven by a multi-cycle three-color laser field which is composed of an 800 nm laser pulse, a 1600 nm laser pulse and a 2400 nm laser pulse. The results show that a narrow-bandwidth spectrum can be selectively enhanced with the intensity increased by nearly one order of magnitude compared to the adjacent harmonics, which can be attributed to the modified electron trajectories in the three-color field. Furthermore, it is revealed that the central wavelength of the enhanced spectrum can be effectively tuned by changing the time delay between laser pulses of different colors.

1. 引言

2. 理论模型

$\begin{array}{l}x\left(t\right)=i{\int }_{0}^{\infty }\text{d}\tau \left(\frac{\pi }{\epsilon +i\tau /2}\right){d}_{x}^{*}\left({p}_{st}\left(t,\tau \right)-{A}_{x}\left(t\right)\right){d}_{x}\left({p}_{st}\left(t,\tau \right)-{A}_{x}\left(t-\tau \right)\right)\\ \text{}×E\left(t-\tau \right)\mathrm{exp}\left[-i{S}_{st}\left(t,\tau \right)\right]\mathrm{exp}\left(-{\int }_{-\infty }^{t}w\left({t}^{\prime }\right)\text{d}{t}^{\prime }\right)+c.c\end{array}$ (1)

${p}_{st}\left(t,\tau \right)={\int }_{t-\tau }^{t}\text{d}{t}^{\prime }A\left({t}^{\prime }\right)/\tau$ (2)

${S}_{st}\left(t,\tau \right)={I}_{p}-\frac{1}{2}{p}_{st}^{2}\left(t,\tau \right)+\frac{1}{2}{\int }_{t-\tau }^{t}\text{d}{t}^{\prime }{A}_{x}^{2}\left({t}^{\prime }\right)$ (3)

d为跃迁矩阵元，本文中采用类氢原子的跃迁矩阵元，表达式为

$d\left(p\right)=i\frac{{2}^{7/2}{\left(2{I}_{p}\right)}^{5/4}}{\pi }\frac{p}{{\left({p}^{2}+2{I}_{p}\right)}^{3}}$ (4)

${I}_{p}$ 为电离势。

3. 窄带高次谐波增强及分析

$\begin{array}{l}{E}_{s}={E}_{1}\mathrm{exp}\left[-2\mathrm{ln}\left(2\right)\cdot {t}^{2}/{\tau }_{1}^{2}\right]\cdot \mathrm{cos}\left({\omega }_{1}t\right)+{E}_{2}\mathrm{exp}\left[-2\mathrm{ln}\left(2\right)\cdot {t}^{2}/{\tau }_{2}^{2}\right]\cdot \mathrm{cos}\left({\omega }_{2}t\right)\\ \text{}+{E}_{3}\mathrm{exp}\left[-2\mathrm{ln}\left(2\right)\cdot {\left(t+{T}_{d}\right)}^{2}/{\tau }_{3}^{2}\right]\mathrm{cos}\left({\omega }_{3}\left(t+{T}_{d}\right)\right)\end{array}$ (5)

3.1. 延迟时间对增强谱段的影响

Figure 1. High-order harmonic spectrum driven by the laser field synthesized by a 16 fs, 800 nm pulse, a 32 fs, 1600 nm pulse and a 48 fs, 2400 nm laser pulse. Inset: The enhanced harmonic spectrum in a linear scale

Figure 2. The enhanced high-order harmonic spectra at different time delays: (a) 1.15 fs~1.95 fs and (b) 8.95 fs~9.75 fs

Figure 3. Time-frequency analyses corresponding to high-order harmonic spectrum in Figure 2 at the time delays of (a) 1.35 fs, (b) 1.55 fs, (c) 1.75 fs, (d) 9.15 fs, (e) 9.35 fs, (f) 9.55 fs.

3.2. 脉冲宽度对增强谱段的影响

Figure 4. High-order harmonic spectrum driven by three-color field of the different durations (R = 0.5~2.0)

4. 结论

NOTES

*通讯作者。

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