Two-center interference in high-harmonic generation of H_2~+ in a combination of a mid-infrared laser field and a terahertz field

We theoretically investigate the two-center interference in high-order harmonics generated from the H_2~+ in a combination of a mid-infrared laser and a terahertz field by numerically solving the time-dependent Schr ¨odinger equation(TDSE).The interference minima in high-order harmonic generation(HHG) are effectively suppressed when a THz field is added.The contribution to HHG from the two separate nuclei is used to demonstrate the locating order of the harmonic minima.Furthermore, we also investigate the emission time of harmonics. The results show that the intensity of the short path around 60 thorder after adding a THz field is stronger than that in the mid-infrared laser field, which further illustrates the suppression of the interference minima in HHG.     

Generation of elliptical isolated attosecond pulse from oriented H2+ in a linearly polarized laser field

We investigate the ellipticity of the high-order harmonic generation from the oriented H₂⁺ exposed to a linearly polarized laser field by numerically solving the two-dimensional time-dependent Schrödinger equation (2D TDSE). Numerical simulations show that the harmonic ellipticity is remarkably sensitive to the alignment angle. The harmonic spectrum is highly elliptically polarized at a specific alignment angle θ=30°, which is insensitive to the variation of the laser parameters. The position of the harmonic intensity minima indicates the high ellipticity, which can be attributed to the two-center interference effect. The high ellipticity can be explained by the phase difference of the harmonics. This result facilitates the synthesis of a highly elliptical isolated attosecond pulse with duration down to 65 as, which can be served as a powerful tool to explore the ultrafast dynamics of molecules and study chiral light-matter interaction.     

Chirp control on molecular harmonic generation and distribution in H2+

Chirp control on the molecular harmonic emission and distribution in H₂⁺ has been theoretically investigated. The results show that (i) with the introduction of the up-chirped pulse, the intensities of the higher harmonics are decreased; while with the introduction of the down-chirped pulse, the intensities of the higher harmonics can be enhanced. When E(t) < 0.0, the harmonic emission events (HEEs) from the positive-H are higher than those from the negative-H; while when E(t) > 0.0, the HEEs from the negative-H are higher than those from the positive-H. As a result, when the higher harmonics are produced from E(t) < 0.0 or E(t) > 0.0, the positive-H or the negative-H plays the main role in the harmonic spectra. (ii) The distribution of the higher harmonics from the two-H nuclei can be controlled with the introduction of the chirps and the carrier-envelope-phases of the laser field. (iii) Some minima on the harmonic spectra can be obtained, which is attributed to the coupling of the two-center interference and the electron-nuclear dynamics. (iv) By properly superposing the harmonics from the down-chirped pulse, an isolated attosecond pulse (IAP) with the duration of 45 as can be obtained, which is nearly 1 order of magnitude enhancement in pulse intensity compared with the chirp- free case.     

New results in above-threshold ionization and high-order harmonic generation of atomic and molecular systems

Numerical results obtained applying the strong-field approximation to atomic and molecular processes in intense laser fields are presented. In particular, the forward-backward asymmetry in high-order above-threshold ionization (HATI) of Ar atoms by a few-cycle laser pulse is considered. It is shown that the resonantlike enhancements observed in the focal-averaged spectra disappear with the decreasing laser pulse duration. For HATI and high-order harmonic generation (HHG) by molecular systems, we present new results for diatomic molecules. The choice of gauge and the problem of dressing of the initial bound state are discussed. The appearance of the interference minima in molecular HATI and HHG spectra and their role in the characterization of the molecular structure are considered using the example of the Ar₂ molecule.     

少周期XUV激光中氢分子离子单光子电离理论研究

通过数值求解二维含时薛定谔方程研究了氢分子离子在圆偏振XUV少周期激光电场中的单光子电离,结果观察到不同核间距的氢分子离子的光电子能谱的能移现象.分析表明,在少周期激光场宽频情况下,分子电离电子的双中心干涉改变了夫兰克-康登因子的单调递减趋势,使不同核间距氢分子离子的光电子能谱出现能量移动.     

Dynamic two-center interference in high-order harmonic generation from molecules with attosecond nuclear motion

We report a new dynamic two-center interference effect in high-harmonic generation from H2, in which the attosecond nuclear motion of H2+ initiated at ionization causes interference to be observed at lower harmonic orders than would be the case for static nuclei. To enable this measurement we utilize a recently developed technique for probing the attosecond nuclear dynamics of small molecules. The experimental results are reproduced by a theoretical analysis based upon the strong-field approximation which incorporates the temporally dependent two-center interference term.     

Molecular recollision interferometry in high harmonic generation

We use extreme-ultraviolet interferometry to measure the phase of high-order harmonic generation from transiently aligned CO(2) molecules. We unambiguously observe a reversal in phase of the high-order harmonic emission for higher harmonic orders with a sufficient degree of alignment. This results from molecular-scale quantum interferences between the molecular electronic wave function and the recolliding electron as it recombines with the molecule, and is consistent with a two-center model. Furthermore, using the combined harmonic intensity and phase information, we extract accurate information on the dispersion relation of the returning electron wave packet as a function of harmonic order. This analysis shows evidence of the effect of the molecular potential on the recolliding electron wave.     

激光强度依赖的阈下谐波产生机制

利用广义伪谱方法精确数值求解了氢原子在强激光场中的三维含时薛定谔方程,获得了强激光中氢原子的含时波函数,利用时间依赖的偶极矩的傅里叶变换得到了高次谐波谱,研究了氢原子在强激光场中发射低于电离阈值的谐波谱对激光强度的依赖性.研究发现,激光强度在低于电离阈值的谐波产生的通道选择的过程中扮演着重要角色,主要有两种量子通道对阈下谐波的产生有贡献,即广义的短轨道和长轨道,其中长轨道对激光场强度比较敏感.结合小波时频变换、经典轨道分析、以及强度依赖的量子通道选择分析,本文阐明了其背后的物理机制.     

不同取向角下CO2分子波长依赖的垂直谐波效率

通过数值计算, 研究了强激光场中CO₂ 分子在不同波长和取向角下产生的高次谐波辐射的效率. 发现CO₂ 分子的垂直谐波效率在较小的和中间的取向角时倾向于与平行谐波效率可比或更高, 而在较大的取向角时, 垂直谐波效率远低于平行谐波效率. 进一步的分析表明, CO₂ 分子的结构对其垂直谐波效率有重要的影响, 且该影响与波长有关. 建议对于较复杂的分子, 应该在分子的轨道成像实验中考虑垂直谐波的贡献.     

Influence of the initial electronic state on minima of high-order harmonic spectrum radiated from hydrogen molecular ion

We theoretically investigate the high-order harmonic generation of the one-dimensional hydrogen molecular ion at fixed intermediate internuclear distance, driven by a multicycle laser field. Our results show that the initial electronic state of the hydrogen molecular ion affects the modulation of the high-order harmonic spectrum, especially the positions of the minima. Based on the two-state model, the underlying physical mechanism of the minimum is analyzed and discussed.Further analysis shows that the different positions of the minima in the different initial electronic states can be understood via the different interferences of the two phase-adiabatic states at the ionization times.     

Role of the intramolecular phase in high-harmonic generation

We study numerically the generation of high-order harmonics by two-center molecules for arbitrary angles between the molecular axis and the laser polarization axis. For fixed angle, the harmonic spectrum exhibits a minimum at a frequency which is independent of the laser parameters. The amplitude of each harmonic is strongly angle dependent, and a pronounced minimum is found at the same angle where a sudden jump in the harmonic phase occurs. By calculating the spatial dependence of the harmonic amplitudes and phases, we are able to explain these effects in terms of interfering contributions from various regions within the molecule.     

Interferences in Photodetachment of a Negative Molecular Ion Model

By employing a two-center model, the total and differential cross sections in the photodetachment of ``a negative molecular ion" are studied theoretically and obtained for the case of light polarization parallel to the molecular axis. We find that in contrast to the smooth behavior of the total cross section for perpendicular polarized light, the cross section for parallel polarized light shows an interesting oscillatory structure. The oscillations in the total cross section may provide a method to determine the distance between the two centers. We explain the oscillation in the total cross section as an interference effect using closed-orbit theory. We also calculated the detached-electron flux distributions on a screen placed at a large distance from the negative molecular ion. The distributions display multiple-ring-like interference patterns. Such interference patterns are similar to those in the photodetachment microscopy experiments.     

Molecular above-threshold ionization with a circularly polarized laser field

Molecular above-threshold ionization by a circularly polarized laser field is investigated. Our theoretical approach is based on the modified molecular strong-field approximation. Various gauge-dependent versions of this approximation are considered and homonuclear and heteronuclear molecular species characterized by different symmetries are used as targets. As in the case of a linearly polarized field, the imprint of the molecular multicenter structure can be observed in the above-threshold ionization spectra. It manifests itself as minima in the rate of the ionized electrons as a function of their energy. The locations of these minima are strongly influenced by the symmetry of the corresponding highest occupied molecular orbital as well as the internuclear separation. Analyzing the interference structures of the electron spectra one can obtain information about the molecular symmetry.     

Electron Flux Distributions in the Photodetachment of H2- in an Electric Field

The electron flux distributions in the photdetachment of a negative hydrogen molecular ion in an electric field have been studied by using the two-center model and the dosed orbit theory. An analytic formula is presented for the electron flux of H2 in the presence of an electric field. The results show that the interference between the two orbits passing through the given spatial point leads to the oscillation in the electron flux distribution. Besides, the interference between the two centers of the H2^- is also very important. The comparison between the electron flux of H2^- in electric field with the result of H^- shows that at the equilibrium distance of two centers in the H2^-, the interference of the two nuclei on the detached electron＇s flux distribution is very strong, while at larger distance of the two centers, the interference effect of the two centers is decreased.     

Elliptic dichroism, ellipticity and the offset angle of high harmonics generated by arbitrary homonuclear diatomic molecules

The nth harmonic emission rate has contributions of the components of the T-matrix element in the direction of the laser-field polarization and in the direction perpendicular to it. Using both components of the T-matrix element we present a theoretical approach for calculation of the ellipticity and the offset angle of high harmonics. The molecular bound state is represented by HOMO or by HOMO-1. We show that high harmonics, generated by molecules oriented by an angle ??_L with respect to the major semiaxis of the laserfield polarization ellipse, are elliptically polarized even if the applied field is linearly polarized. Using examples of N₂ and O₂ molecules we show the existence of extrema and sudden changes of the harmonic ellipticity and the offset angle for particular molecular alignment. The interference between different contributions to the T-matrix element depends on the molecular symmetry. Presenting partial or total parameters of elliptic dichroism in the (??_L, n) plane clear interference minima are observed. Therefore, the measurement of the elliptic dichroism may reveal information about the molecular structure and symmetry.     

High-order above-threshold ionization of heteronuclear diatomic molecules by a strong laser field with arbitrary polarization

The molecular strong-field approximation is applied to calculate angle-resolved photoelectron spectra in the process of high-order above-threshold ionization of carbon-monoxide molecules by an elliptically polarized laser field. The theory is formulated to include the Stark shift of the initial bound state of the valence electron. It is shown that the angle-resolved photoelectron spectra of aligned CO molecules exhibit pronounced minima which can be explained by destructive interference of two partial T-matrix contributions. The dependence of contributing partial amplitudes on the laser field ellipticity is analyzed in detail.     

线偏振激光场中分子高次谐波椭偏率的调控

高次谐波椭偏率的调控为人们研究磁性材料和手性介质中的超快动力学过程提供了有效途径.本文理论研究了线偏振激光脉冲驱动下,H₂~+和H₃²⁺分子高次谐波的偏振特性及阿秒脉冲产生.结果表明当取向角为0~o时,H₂~+分子谐波的椭偏率几乎为0,而H₃²⁺分子谐波具有较大椭偏率,这是由于分子轨道对称性决定的.通过改变取向角的大小,可以调控高次谐波强度以及谐波椭偏率大小,为产生椭偏XUV脉冲提供了手段.同时,发现椭偏率较大的谐波阶次对应的谐波强度较小,分析表明分子的双中心干涉效应对椭偏率有很大的影响.对于H₂~+和H₃²⁺分子,分别合成了椭偏率为0.75和0.55的椭圆偏振阿秒脉冲.这种大椭偏XUV脉冲的产生为高次谐波在材料与生物科学领域提供了重要应用.     

Ellipticity dependence of high-order above-threshold ionization from aligned diatomic molecules

We investigate high-order above-threshold ionization of the Ar₂ molecule by an elliptically polarized laser field. In order to describe this process we use the modified molecular strong-field approximation. We have found that the differential ionization rate is a very sensitive function of the ellipticity of the laser field and of the molecular orientation. For parallel orientation the rate has the maximum value for linear polarization, independently of the laser intensity. On the other hand, for perpendicular orientation the rate is maximal for a particular value of the ellipticity which is different from zero. Such a behavior can be related to the molecular symmetry. We consider the differential ionization rate of high-energy electrons as a function of the ellipticity for different internuclear distances. We also present, in the electron energy-emission angle plane, our new results for the focal-averaged spectra of electrons ionized by an elliptically polarized laser field. We have found that, in this case, the two-source two-rescattering-centers interference minima are blurred.     

Interferences in Photodetachment of a Negative Molecular Ion Model

By employing a two-center model, the total and differential cross sections in the photodetachment of ＂a negative molecular ion＂ are studied theoreticedly and obtained for the case of light polarization paredlel to the molecular axis. We find that in contrast to the smooth behavior of the total cross section for perpendicular polarized light, the cross section for parallel polarized light shows an interesting oscillatory structure. The oscillations in the toted cross section may provide a method to determine the distance between the two centers. We explain the oscillation in the toted cross section as an interference effect using closed-orbit theory. We also cedculated the detached-electron flux distributions on a screen placed at a large distance from the negative molecular ion. The distributions display multiple-ring-like interference patterns. Such interference patterns are similar to those in the photodetachment microscopy experiments.     

用强场近似方法研究强激光场中H原子的电离

利用传统的强场近似方法和考虑Coulomb修正的强场近似方法,计算了H原子在激光场中的总电离几率及H原子在不同波长激光场中电离的能量谱,并将得到的能量谱与直接数值求解含时Schrödinger方程的结果进行了比较,结果发现：当激光波长较长时,考虑Coulomb 修正的强场近似方法得到的结果与数值求解含时Schrödinger方程的结果符合得较好。