Plasma Mirror: An Effective System for High-order Harmonic Generation

Schematic of the experimental setup for high-order harmonic generation measurement. Top panel: One femtosecond laser beam is used to irradiate the polished fused silica surface at an incidence angle of 15°. The radiations at specular direction are measured by a flat-field spectrometer. Bottom panel: Raw image of the harmonic spectrum. Harmonics up to the 21st order are obtained from the glass target with a plasma mirror.

Generation of light pulses with shorter duration for diagnosing and controlling the ultrafast processes in microcosm has been a subject of strong scientific interest. Femtosecond laser pulses can be extensively produced by the self-mode locking technique, which make it achievable to make the “slow movie” of atoms in chemical reactions and to research the chemical bond breaking and forming processes at atomic level. To further investigate the electron movement inside atoms, a flash light in attosecond (10^-18 s) time scale becomes necessary. Since the light duration could not be shorter than an optical period, attosecond pulses can only be generated in the region of extreme ultraviolet or even X-ray. Up to now, the most successful method to produce attosecond pulses is based on the high-order harmonic generation (HOHG) through the interactions of ultrashort intense laser beams with gases, which has generated light pulses shorter than 100 as. However, limited by the gas ionization threshold, the intensities of driving laser cannot be above 10¹⁵ W/cm². On the other hand, recent theoretical and experimental researches have demonstrated that the HOHG from the plasma surfaces has no limitation on laser intensities, which makes it hopeful to generate more intense and shorter coherent pulses.

So far, two basic mechanisms of HOHG from plasma surfaces have been clearly identified by the laser intensities, coherent wake emission (CWE) and relativistically oscillating mirror (ROM). At moderate laser intensities (>10¹⁵ W/cm²), the CWE mechanism dominates the radiation. In this scenario, the surface electrons are first pulled out of plasma and gain energy by the laser electric field. When the sign of electric field reverses, these electrons will be re-injected into the plasma and excite plasma waves. If there is an electron density gradient in front of the target, high-order harmonics can be effectively generated by the linear mode conversion of plasma waves. When the laser reaches the relativistic intensities (>10¹⁸ W/cm²), the ROM mechanism becomes dominant. The plasma surface will oscillate periodically at nearly the speed of light driven by the laser. As the incident laser is reflected by the oscillating surface, high-order harmonics are generated by the Doppler frequency shift.

The HOHG is not only dependent on the laser intensities, but also influenced by the density profile of preplasma induced by the front of laser pulse. Using the 200 TW laser facility at Laboratory for Laser Plasmas at Shanghai Jiao Tong University, the research team led by Prof. Zhang Jie and Prof. Liu Feng has investigated the effect of laser temporal contrast on the HOHG from solid targets. To obtain a steep density gradient in front of targets, a single plasma mirror (PM) system had been set up to enhance the laser temporal contrast from 10^-8 to 10^-10 at 10 ps prior to the main peak. Harmonics up to the 21st order are generated by this scheme. This work is published in Chinese Optics Letters, Volume 15, No. 8, 2017 (Jian Gao, et al., Influence of laser contrast on high-order harmonic generation from solid-density plasma surface).

The femtosecond laser beam with peak intensity of 3.5×10¹⁹ W/cm² was used in the experiment to irradiate the polished fused silica surface at an incidence angle of 15°. The radiations at specular direction were measured by a flat-field spectrometer. CWE harmonics up to the 21st order are observed only when high contrast laser pulses are used by applying the PM. No harmonics but only plasma emission is obtained when PM is not used.

The density scale length of preplasma is crucial to the HOHG from the surface of solid target. 2D particle-in-cell (PIC) has been employed to simulate the dependence of high harmonic intensities on the density scale lengths. The team finds that there is an optimum length which corresponds to the maximum high harmonic intensity. The research on this effect is useful to understand the underlying physics and optimize the experimental conditions. The results will help to obtain coherent and ultrashort pulses with higher intensities in the future.

Only CWE harmonics have been observed in the experiment. ROM harmonics could generate radiations with shorter wavelength and narrower pulse duration，which is very important for many applications. Both the laser intensities and plasma density gradient in the experiment should be able to generate ROM harmonics. Following experiment will try to change the incidence angle of laser to investigate its impact on the HOHG and obtain ROM harmonics. In the future, it is possible to realize coherent diffraction imaging experiment by picking up a single harmonic pulse.

等离子体镜助力产生固体高次谐波

图片说明：上图为实验装置示意图：一束强飞秒激光脉冲以15°入射角照射抛光的熔融石英玻璃靶表面，在其反射方向测量产生的高次谐波光谱；下图为实验获得的高次谐波原始图像，利用等离子体镜系统可以获得阶次为21阶的高次谐波。

获得持续时间更短的脉冲光源用于微观世界超快过程的诊断与控制，一直是人们追求的目标。自锁模技术可以产生飞秒激光脉冲，使得人们可以记录下化学反应过程中原子运动的“慢动作”，在原子的层面研究化学键的断裂与形成过程。如果想更进一步深入原子内部捕捉电子的运动过程，则需要时间尺度在阿秒（10^-18 s）量级的“闪光灯”。由于光脉冲宽度不可能小于一个光振荡周期，产生阿秒脉冲必须使用波长比可见光更短的极紫外光甚至ｘ射线才有可能。目前最成功的阿秒脉冲产生方法是基于超短超强激光与气体相互作用的高次谐波机制，已经可以产生脉宽小于100 as的超短脉冲。由于气体电离阈值的限制，驱动激光强度不能超过10¹⁵ W/cm²。最近的理论和实验研究表明，相对论强激光与固体靶相互作用产生的高次谐波辐射可以突破对驱动激光强度的限制，有望产生能量更高、时间更短的相干脉冲辐射。

从等离子体表面产生高次谐波主要有两种机制，即相干尾场辐射机制 (coherent wake emission, CWE) 和相对论振荡镜机制 (relativistically oscillating mirror, ROM)。当激光强度较低时，主导机制是CWE。靶表面的电子会被激光电场加速并拉出等离子体表面，而后当激光电场的方向改变时，这些电子会被重新注入到等离子体中激发等离子体波。如果靶面电子有一定的密度梯度分布，等离子体波可以通过线性模式转换产生高次谐波辐射。当激光强度达到相对论光强（10¹⁸ W/cm²）时，主导机制是ROM。靶表面在激光的驱动下，以接近光速的速度做周期振荡。激光被这一高速运动的表面反射后，由于多普勒频移产生高次谐波。

高次谐波产生过程不但依赖于激光强度，并且激光脉冲前沿产生的预等离子体密度分布对其也有很大影响。张杰院士、刘峰特别副研究员带领的团队利用上海交通大学的200 TW飞秒激光装置，研究了激光对比度对固体靶表面高次谐波产生的影响。为了在靶表面获得陡峭的密度梯度，该团队利用等离子体镜系统把激光主脉冲10 ps以前的对比度从10^-8提高至10^-10，成功获得阶次为21阶的高次谐波。相关工作发表在Chinese Optics Letters 2017年第8期上（Jian Gao, et al., Influence of laser contrast on high-order harmonic generation from solid-density plasma surface）。

实验中一束强度为3.5×10¹⁹ W/cm²的飞秒激光脉冲以15°入射角照射抛光的熔融石英玻璃靶表面，在其反射方向测量产生的高次谐波光谱。实验结果表明：利用等离子体镜系统可以获得阶次为21阶CWE机制的高次谐波。当不使用等离子体镜系统时，只能获得非相干的等离子体辐射。

预等离子体密度标长对固体靶表面高次谐波产生有非常重要的作用，该研究团队还利用2D particle-in-cell （PIC）方法模拟了密度标长对高次谐波强度的影响，发现存在最佳的密度标长使得高次谐波强度达到最大化。这一结果有助于深刻理解相互作用过程，优化实验条件，为将来获得更大能量的相干短波长超短脉冲提供实验基础和重要技术手段。

目前实验中只获得了CWE机制的高次谐波。ROM机制可以产生比CWE机制波长更短脉宽更窄的辐射，这对于很多应用都非常重要。实验中激光强度和等离子体密度梯度都满足获得ROM机制高次谐波的条件。后续的工作将通过改变激光入射角来探究其对高次谐波产生的影响，尝试获得ROM高次谐波。将来还计划选择出单阶谐波做相干衍射成像演示实验。