Carrier-Envelope-Phase Dependence of Emission Properties of High-Order Harmonic Generation

The carrler-envelope-phase （CEP） dependence of the emission properties of high-order harmonic generation （HHG） are quantitatively investigated. Calculation shows that a two-cycle laser with CEP of 15° can produce a single energy distribution pulse peaked at 0.94 radian （tad） and spanned 1.29 tad with the cutoff energy 2.9Up ＋ Ip and a bandwidth 0.86Up （where Up is the ponderomotive potential of the laser field and Ip is the atomic ionization potential）. The CEP dependence of the energy and temporal localizations of the single distribution pulse show interesting 180° periodic structures. These characteristics may be useful in optimizing attosecond x-ray sources and measurements.     

高次谐波辐射发射特性研究

报告由不同脉冲宽度(半高宽,FWHM)和不同载波-包络相位(CEP,Φ)的激光产生的高次谐波辐射能量输出时间特性即发射特性的研究结果. 计算表明,由宽度为几个周期的激光产生的高次谐波辐射的截止能量明显低于由无限长脉冲宽度激光产生的截止能量ω_max=3.17U_p+I_p(其中ω_max为光子角频率,U_p和I_p分别为激光有质动力势和原子的电离能). 例如,由两周期(FWHM),Φ＝15°的激光产生的高次谐波辐射的截止能量为ω_max=2.90U_p+I_p,此时发射特性单脉冲(即分布单脉冲)具有最大的能量带宽0.86U_p. 脉冲中心位置的载波相位和时间宽度分别为0.94rad(弧度)和1.29rad. 而该激光脉冲在Φ＝-75°时能产生截止能量为ω_max=2.70U_p+I_p,最大能量带宽为0.70U_p的双分布脉冲,其中心位置分别为-0.58rad和2.43rad,宽度分别为1.22rad和1.33rad. 随着激光脉冲宽度的增加,分布单脉冲的能量带宽比时间宽度下降得更快. 对于一定宽度的激光脉冲,所产生的分布单脉冲的能量带宽和时间宽度的CEP依赖性显示出180°的周期结构. 利用这个有趣的特点,在实验上可以通过调节CEP来选择分布脉冲的能量参数,也可用来定位和控制阿秒脉冲的时间参数. 理论分析指出,只要选择合适的阿秒X射线能量带宽,CEP不稳定性对于光电子谱和测量结果的影响将大为降低,甚至在最大程度上消除这种影响. 这些研究结果不仅有助于在物理上深入了解高次谐波辐射的动力学过程,而且对于进一步在实验上优化和选择阿秒单脉冲和双脉冲具有重要的参考和指导意义. 关键词： 高次谐波产生 鞍点方法 谐波发射特性 分布脉冲     

静电场对高次谐波时频特性的影响

通过数值求解含时薛定谔方程，发现在静电场的作用下，对原子高次谐波谱截止区附近的谐波进行叠加可以得到脉冲间隔为一个光周期的阿秒脉冲链. 利用这种性质，用12fs波长为800nm的激光附加强度为激光强度0.25%的静电场脉冲驱动He原子可以得到脉宽为220as的单个脉冲. 当静电场与激光场幅度之比达到0.39时，原子谐波谱的截止区可以被拓宽到I_p+9.1U_p，同时，次数高于I_p+0.7U_p的谐波的相位几乎是锁定的，因此可以得到谱宽大于40eV且相位锁定的谐波. 对这部分谐波进行叠加就可以得到脉宽小于100as的阿秒脉冲链.     

高次谐波辐射光子的能量-激光相位关系研究

原子在强激光电场中高次谐波辐射的理论与实验研究是当今科学前沿之一.利用量子力学理论和鞍点方法,细致地研究了高次谐波辐射光子的能量与激光相位的关系.对于时间宽度无限长激光,在一个激光周期内特定相位处产生的高阶辐射(X射线)有特定的能量.能量分布在7180°处成峰,有高斯形函数的对称形状.给出了这种分布的参数化公式.对于不同宽度的飞秒激光,能量分布的成峰位置、最大值和带宽等参数会发生变化.计算表明,三个振荡周期(半高宽)的飞秒激光,当载波-包络相位为175°和105°时,可以分别得到纯净的阿秒单脉冲和双脉 关键词： 超短脉冲激光 高次谐波产生 鞍点方法 能量相位关系     

High-order harmonics generation by few-cycle and multi-cycle femtosecond laser pulses

This paper investigates experimentally high-order harmonic generation(HHG) of neon gas with 5-fs and 25-fs driving laser pulses.It has been demonstrated that the cutoff energy of the harmonic extreme ultraviolet photons is extended to 131 eV and the HHG spectrum near the cutoff region becomes continuum as the driving laser pulse duration is 5 fs;whereas much lower cutoff photon energy and discrete harmonic spectrum near the cutoff region are presented as the laser pulse duration is 25 fs.The results can be explained by the fact that neutral atoms can be exposed to more intense laser field before they are depleted by ionization because of the extremely short rising time of the few-cycle pulse.The 5-fs driving laser pulse paves the way of generation of coherent x-ray in the water window and single attosecond pulse.     

Pulse compression of a high-order harmonic

The fifth harmonic pulses of an intense femtosecond Ti:sapphire laser were experimentally shown to be negatively chirped by using an LiF plate as a positive dispersive medium. The chirp of the harmonic pulse originates from the intensity-dependent atomic dipole phase, which is estimated to be proportional to 25 U_p, where U_p is the ponderomotive energy. Consequently, we have succeeded in compressing the chirped pulses to 13 fs by compensating the intrinsic negative chirp. Chirp effects of the fundamental laser on the pulse width of the fifth harmonic were consistent with the negative chirp of the fifth harmonic.     

Time-energy properties of an attosecond extreme ultra-violet pulse

The time-energy properties of high-order harmonic generation (HHG) are calculated for a linearly polarized 7-fs laser pulse with different carrier-envelope phases (CEPs). The quantum trajectory paths that contribute to an as (1 as=10-18 s) pulse in HHG are identified. The laser-duration dependence and the CEP dependence of HHG energy property are investigated. The study shows that an as extreme ultra-violet (XUV) pulse can be selected from HHG spectrum near cut-off energy with a bandpass optical filter. The theoretical prediction of the pulse duration is proportional to bandwidth. Analysis suggests that a measured narrowband as XUV pulse may consist of instantaneous shorter pulses each dependent on laser pulse duration, intensity, and CEP. These information can be used as references for producing, selecting, improving and manipulating (timing) as pulses.     

Observation of Sub-femtosecond Polarization Beats Using Twin Noisy Driving Fields

We study the phase-conjugate polarization interference in a V-type three-level system and obtain an analytic closed form for the second-order stochastic correlation of sum-frequency polarization beat. In our Na vapour atomic system pumped by laser pulse of nano-second timescale duration, we experimentally demonstrate an ultrafast modulation of the four-wave mixing signal intensity with a sub-femtosecond timescale period, corre- sponding to the sum-frequency of the resonant transitions from 3S1/2 to 3Pl/2 and 3P3/2.     

激光驱动晶体发射高次谐波的特性研究

通过数值模拟激光驱动下电子在周期性势阱中的动力学行为, 研究了晶体在激光场中发射高次谐波的特性. 研究发现在一定的激光波长和光强驱动下, 晶体发射的谐波谱会呈现出双平台结构, 经分析后得知第一个平台主要来自于最低导带与价带间的电流(电子-空穴对复合), 第二个平台主要来源于较高导带与价带间的电流(电子-空穴对复合), 且两个平台的截止位置处的能量都与激光场的振幅呈线性关系. 在少周期激光驱动下, 晶体谐波第二平台的截止位置与激光的载波相位呈单调变化, 由此我们提出可以利用晶体谐波第二平台的截止位置来确定少周期激光的载波相位. 进一步研究发现, 在啁啾激光驱动下, 晶体发射谐波谱的第二平台有较大变化, 第二平台的发射效率会随啁啾参数而改变, 能够通过改变啁啾激光场来提高晶体谐波第二平台的发射效率.     

High-order harmonic generation from organic molecules in ultra-short pulses

We have studied high-order harmonic generation (HHG) from organic molecules irradiated with near-infrared high intensity laser pulses of 70 fs and 240 fs duration. The molecular systems studied were the aromatics benzene and naphthalene and the alkanes cyclopropane and cyclohexane (cyclic) and n-hexane (linear). Harmonic intensities were measured both as a function of laser intensity (in the range 5×10¹³-5×10¹⁵ W cm^-2) and as a function of ellipticity of the laser field polarisation. The results were compared with those from the xenon atom. For 70 fs pulses, harmonic generation from the organic systems was similar to that of xenon, revealing an atom-like behaviour for molecules when the laser pulse duration is shorter than the fragmentation timescale of the molecule. We note significant differences between molecules with respect to HHG efficiencies and the suppression of HHG in larger species. We discuss these differences in the context of the molecular properties, electronic structure and behaviour of ionisation and fragmentation that result in enhancement of field ionisation in larger systems. Study of the polarisation ellipticity dependence of HHG shows that the harmonic yield in molecules is less sensitive to the polarisation than for atoms (xenon). This is consistent with the expected behaviour given the larger recollision cross-section presented by the core in the molecular system compared to the atom. Our results suggest that study of HHG from molecules exposed to ultra-short pulses is potentially a powerful tool for understanding the electron dynamics of molecules exposed to an intense field. Received 14 September 2000 and Received in final form 6 December 2000     

Atomic high-order harmonic generation from a circularly polarized laser pulse

We demonstrate theoretically that the high-order harmonic of an atom can be generated by a circularly polarized laser pulse.The harmonic spectrum shows a clear cutoff with an energy Ip + 2Up.In particular,the high-order harmonic generation comes from the multiple recombination of the ionized electron with non-zero initial velocity.These results are verified by the classical model theory and the time-frequency analysis of a harmonic spectrum.     

啁啾激光与半周期脉冲形成的组合场驱动原子产生单个阿秒脉冲

提出了由波长为800 nm、脉冲宽度为5 fs的啁啾激光与半周期脉冲形成组合场,并利用这种组合场驱动一维模型氦原子获得单个阿秒脉冲. 通过数值求解一维氦原子的含时薛定谔方程,发现氦原子在组合场驱动下高次谐波谱的截止位置可以扩展到I_p+21.6U_p. 对第二平台区域不同范围内高次谐波的叠加都能得到单个阿秒脉冲,最短可达37 as,特别是对平台区域的前端进行叠加不仅能够得到较短的单个阿秒脉冲,而且与截止位置附近高次谐波构造的阿秒脉冲相比,强度提高了3个数量级. 关键词： 啁啾激光场 半周期脉冲 高次谐波 阿秒脉冲     

量子路径控制生成宽频软X射线连续辐射谱

数值研究了双色激光脉冲与一维氩原子相互作用的谐波发射功率谱.双色激光脉冲由800 nm和1600 nm的两束激光组成,脉冲持续时间为9.7 fs.计算结果表明,相对相位为π时,谐波截止频率从单色场情形的58 eV大幅度地展宽到316 eV,获得频宽为93 eV的软X射线连续辐射谱.此外,还采用短程的普薛耳－特勒势和长程的软化库仑势进行比对,数值结果表明该连续辐射谱的存在具有普适性.通过半经典的“三步”模型和时频分析小波变换方法对该连续辐射谱进行分析,发现其主要由单一的“短”量子路径生成,直接叠加频率从22 关键词： 红外双色激光脉冲 连续辐射谱 阿秒脉冲     

High-order harmonic generation of pulses with multiple timescales: selection rules,carrier envelope phase and cutoff energy

ABSTRACT

High harmonic generation (HHG) is sensitive to the carrier envelope phase (CEP) of its driving laser field if it is a sufficiently short pulse (several-cycle pulse). Here we show that strong CEP effects can also be found in HHG from long duration multi-cycle pulses (up to 200?fs at 800?nm central wavelength). We find that HHG from multi-cycle pulses may be CEP dependent when the driving pulse exhibits two distinct timescales (multi-timescale pulse): (i) a short timescale associated with the average frequency, and (ii) a long timescale associated with the pulse’s temporal periodicity. The interplay of these timescales results in significant changes to both the cutoff frequency, and the appearance of symmetry allowed harmonics in the spectrum as function of CEP, similar to HHG from several-cycle pulses. We relate this effect to the multi-timescale intensity variations in the driving pulse, and construct an analytical condition to access the phenomenon. Lastly, we numerically demonstrate reconstruction of the CEP through HHG from long duration multi-timescale pulses. Our work may be useful in several areas of strong-field physics and attosecond science, for example, allowing spectroscopy of multi-timescale processes (e.g. HHG from vibrationally active media), and paving the way towards CEP characterisation using long pulses.     

Laser phase control of high-order harmonic generation at large internuclear distance: the H+ -H2+ system

Exact (Born-Oppenheimer) 3-D numerical solutions of the time-dependent Schr?dinger equation are obtained for the one electron linear H+-H2+ atom-molecule system at large internuclear distance R in interaction with two-cycles intense (I>10(14) W cm(-2)) 800 nm laser pulses. High-order harmonic generation (HHG) spectra are obtained with an energy cutoff larger than the atomic maximum of I(p)+3U(p), where I(p) is the ionization potential and U(p) is the ponderomotive energy. At large R, this extended cutoff is shown to be related to the nature of electron transfer, whose direction is shown to depend critically on the carrier-envelope phase (CEP) of the ultrashort pulse. Constructive and destructive interferences in the HHG spectrum resulting from coherent superpositions of electronic states in the H+-H2+ system are interpreted in terms of multiple electron trajectories extracted from a time profile analysis.     

Restraint of spatial distribution in high-order harmonic generation from a model of hydrogen molecular ion

The spatial distribution in high-order harmonic generation(HHG) is theoretically investigated by using a few-cycle laser pulse from a two-dimensional model of a hydrogen molecular ion. The spatial distribution in HHG demonstrates that the harmonic spectra are sensitive to the carrier envelope phase and the duration of the laser pulse. The HHG can be restrained by a pulse with the duration of 5 fs in the region from the 90 th to 320th order. This characteristic is illustrated by the probability density of electron wave packet distribution. The electron is mainly located near the nucleus along the positive-x direction from 3.0 o.c. to 3.2 o.c., which is an important time to generate the HHG in the plateau area. We also demonstrate the time-frequency distribution in the region of the positive-and negative-x direction to explain the physical mechanism.     

基于固体薄片超连续飞秒光源驱动的高次谐波产生实验

本文报道了采用基于熔石英薄片超连续的少周期飞秒光源驱动高次谐波产生的实验研究.实验中通过将重复频率1kHz的飞秒钛宝石激光放大器所输出的能量0.8mJ、脉宽30fs的脉冲聚焦到7片0.1mm厚的熔融石英片中,得到了覆盖带宽大于倍频程的展宽光谱.利用啁啾镜补偿色散后,经瞬态光栅频率分辨光学开关法测得脉宽为6.3fs,对应约2.3个光学周期.利用压缩后的激光脉冲聚焦作用于惰性气体,并通过调节尖劈插入量改变脉宽,分别测得了分立以及连续的高次谐波截止区信号,结果与6.3fs的脉冲宽度相符合.     

非均匀激光场中氢分子离子高次谐波的增强

通过数值求解非波恩-奥本海默近似下的一维含时薛定谔方程,研究了蝴蝶结型纳米结构基元中氢分子离子高次谐波的产生.研究表明,在蝴蝶结型纳米结构基元内部产生的非均匀场的空间位置对高次谐波的发射有较大影响.当非均匀场的空间位置从30 a.u.平移到-30 a.u.时,高次谐波的截止位置被延展且形成光滑的超连续的谐波谱,并应用时频分析方法、经典三步模型以及电离概率等解释了高次谐波发射的物理机理.研究了高次谐波谱对非均匀场空间位置的依赖性与载波包络值的关系,发现随着载波包络值的变化,非均匀场在不同空间位置处的高次谐波谱变化趋势相同.     

利用低频场控制轨道直接产生低于50阿秒的单个脉冲

提出一种直接得到脉宽小于50as的单个脉冲的新方法.利用波长为800nm脉宽为5fs的超短脉冲叠加上波长为10μm,强度为超短脉冲强度的10％且脉宽足够长的低频场脉冲驱动氦原子,谐波谱可以拓展到I_p+8.2U_p,同时,高于4.2U_p的谐波几乎是连续的.如果继续调节超短脉冲的载波包络相位,超连续谱可以继续拓宽,从而可以得到低于50as的单个脉冲. 关键词： 阿秒脉冲 超连续谱     

Experimental study of a broad-band XeCl double-pass amplifier with SBS mirror

An oscillator-amplifier XeCl laser system has been used to experimentally investigate the effectiveness of a liquid stimulated Brillouin scattering (SBS) mirror for correcting the spatial aberrations of broad-band laser radiation in a double-pass amplifier. It has been found that the SBS amplifier performance is strongly dependent on the intensity I _p exciting the Brillouin medium. A good beam reconstruction has been attained at I _p1GW/cm², whereas highly aberrated output beams have been delivered by the SBS amplifier for I _p>1 GW/cm². By comparing the broad-band SBS amplifier performance to that of the same amplifier with a dielectrically coated flat mirror at one end, it has been found that the use of a SBS mirror is advantageous to obtain lower divergence output beams only for low energy pump beams (<1 mJ).