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.     

Theoretical Exploration of the Isotopic Effect on Molecular High-Order Harmonic Generation

The isotopic effect on the generation of the molecular high-order harmonics is studied by numerically solving the one-dimensional time-dependent Schrödinger equation when the model hydrogen molecule ions/hydrogen deuterium molecule ions are exposed to an intense laser pulse. To explain the effect more clearly, not only the ionization probabilities but also the electron–nuclear probability density distributions and time-frequency profiles are calculated. The results show that more intense harmonics are generated in the asymmetric diatomic molecule ions/hydrogen deuterium molecule ions than those of hydrogen molecule ions. Moreover, the interference minimum in the harmonic spectra is investigated by adjusting the laser intensity and the initial vibrational state. It is shown that the interference minimum is sensitive to the laser intensity and the initial vibrational level for hydrogen molecule ions; in contrast, it is only dependent on the initial vibrational level for hydrogen deuterium molecule ions.     

Near-threshold high-order harmonic spectroscopy with aligned molecules

We study high-order harmonic generation in aligned molecules close to the ionization threshold. Two distinct contributions to the harmonic signal are observed, which show very different responses to molecular alignment and ellipticity of the driving field. We perform a classical electron trajectory analysis, taking into account the significant influence of the Coulomb potential on the strong-field-driven electron dynamics. The two contributions are related to primary ionization and excitation processes, offering a deeper understanding of the origin of high harmonics near the ionization threshold. This Letter shows that high-harmonic spectroscopy can be extended to the near-threshold spectral range, which is in general spectroscopically rich.     

High-order harmonic generation with a two-color laser pulse

We theoretically investigate the electron dynamics of the high-order harmonics generation process by combining a near-infrared 800 nm driving pulse with a mid-infrared 2000 nm control field.We also investigate the emission time of harmonics using time-frequency analysis to illustrate the physical mechanisms of high-order harmonic generation.We calculate the ionization rate using the Ammosov-Delone-Krainov model and interpret the variations in harmonic intensity for different control field strengths and delays.We find that the width of the harmonic plateau can be extended when the control electric field is added,and a supercontinuum from 198 to 435 eV is generated,from which an isolated 61-as pulse can be directly obtained.     

High-order harmonic generation with a two-color laser pulse

We theoretically investigate the electron dynamics of the high-order harmonics generation process by combining a near-infrared 800 nm driving pulse with a mid-infrared 2000 nm control field. We also investigate the emission time of harmonics using time-frequency analysis to illustrate the physical mechanisms of high-order harmonic generation. We calculate the ionization rate using the Ammosov-Delone-Krainov model and interpret the variations in harmonic intensity for different control field strengths and delays. We find that the width of the harmonic plateau can be extended when the control electric field is added, and a supercontinuum from 198 to 435 eV is generated, from which an isolated 61-as pulse can be directly obtained.     

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.     

Ionization effects on field-free molecular alignment observed with high-order harmonic generation

In this paper, high-order harmonic generation (HHG) is demonstrated to provide a sensitive way for studying the dynamic process in the field-free molecular alignment. The dependence of the harmonic yield and the degree of alignment on the intensity of aligning pulse is observed in impulsively aligned CO₂ molecules. A good agreement is found between the experimental and calculated results. At low pump intensities, the harmonic yield increases monotonously until the ionization induced refractive index gradient and neutral molecule depletion are significant. The results show that the optimum intensity is around 8.95 × 10¹³ W/cm²; this value is related to the molecular ionization potential.     

拉伸分子高次谐波产生的阿秒控制

通过数值求解一维含时薛定谔方程,本文研究了高频阿秒脉冲对拉伸双原子分子模型与低频飞秒激光脉冲相互作用产生高次谐波谱的影响.研究表明,若阿秒脉冲在低频脉冲的第二个光学周期截止处注入时,只第二个平台截止位置IP 5.6UP(IP为电离势,UP为有质动力能)附近谐波的效率得到显著提高;若阿秒脉冲的包络峰值处于低频脉冲第三个光学周期T/4(为飞秒激光脉冲的光学周期)附近时,则谐波谱出现了明显的整体抬高现象.对此,本文根据拉伸分子谐波谱的四种产生机制及阿秒脉冲在飞秒激光不同相位注入时的电子电离曲线,对这些谐波谱的结构给出了合理解释.     

High-order harmonic generation in nitrogen molecules with subpicosecond visible dye-laser pulses

An experimental study of high-order harmonic generation in nitrogen molecules (N₂) has been made using intense visible (616 nm) dye-laser pulses, where the harmonic radiation up to the 21st order is observed. The harmonic distribution represents a plateau that is preceded by an intensity minimum at the 7th order. The harmonic generation characteristics were atomic-like. It has been found that there are some similarities in the high-order harmonic generation characteristics for N₂ and Ar, including the highest-order harmonics, harmonic distributions, and the influence of the multiphoton ionization on the high-order harmonic generation. These similarities are reasonably attributed to the energetic correspondence of excited levels and ionization potentials. It is pointed out that the ac Stark shift of excited levels and ionization potentials plays an important role also in the high-order harmonic generation in N₂.     

Retrieving angular distributions of high-order harmonic generation from a single molecule

We present a novel method to retrieve angular distributions of high-order harmonic generation from a single molecule. This technique uses an iterative procedure based only on experimental results of time and angle-dependent harmonic signals, and no actual shape of molecular orbital is assumed. The molecular axis distribution in a target gas can simultaneously be deduced in this procedure. The angle-dependent signal retrieved for a single N2 and O2 molecule is demonstrated to reflect the highest occupied molecular orbital, excluding the ambiguity due to the imperfect alignment.     

Ionization and Harmonic Generation of Diatomic Molecular Ion

l.IntroductionRecentexPerimentshavcdemonstratedthehigh-orderharmonicgenerationinraregasandmoleculargas[1~'j.TherearemanytheoreticalpaPersdealingwithharmonicgen-erationofatom[6~8j,comparativelysPeaking,theoreticalworksabouttheharmonicgen-erationofmolecuIeareless[9j,esPeciallyabouttheevolutionofionizationandharmonicgenerationwiththeinternuclearseparation,andtherelationbetweenionizationandhar-monicgeneration.InthispaPerwegivesomenumericalresultsofdiatomicmolecularionirradiatedbyalinearlyPOlari…     

双色高频激光作用下原子低阶次谐波的理论研究

通过数值求解含时薛定谔方程,研究了高频双色激光脉冲与原子相互作用产生的光辐射.研究表明,光辐射谱中既有基频光的谐波,又可观测到谐波能量附近的多个频率的光辐射产生,且辐射的峰值强度随着入射激光强度的提高呈指数增强,相邻辐射频率差值为入射的两束激光脉冲频率差.     

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.     

Controlling continuum harmonic generation with attosecond pulses

Photo-ionization and high-order harmonic generation (HOHG) in molecular systems under the combined action of infrared femtosecond (fs) and UV attosecond (as) intense laser pulses are investigated numerically for a one-dimensional non-Born–Oppenheimer H⁺ ₂ ion. It is shown that such a coherent control scheme of fs–as ionization leads to significant enhancement of HOHG, with efficiencies exceeding the one obtained from a single fs pulse by several orders of magnitude. The basic mechanism for this enhancement is established as enhanced ionization and control of the recollision of a high-energy non-zero-velocity ionized electron, as compared to tunneling ionization models where the ionized electron has initial zero velocity. The combined superposition of fs–as pulses results in broad HOHG spectra with a large continuum near the cutoff, thus providing a new source for synthesizing new X-ray (vacuum ultraviolet) as pulses. PACS 33.60.-q; 33.80.-b     

强激光场中模型氢原子和真实氢原子的高次谐波与电离特性研究

利用数值方法求解含时薛定谔方程，研究了一维、二维模型氢原子和真实的三维氢原子在强激光场中产生的高次谐波和电离特性.结果表明，在多光子电离区域和过垒电离区域，模型氢原子与真实的氢原子产生的高次谐波和电离概率差别很小；在隧道电离区域，它们产生的高次谐波的平台特征和截止位置相似，电离概率随时间变化的趋势相近，但其数值有明显的差异.对产生这种差异的原因进行了分析. 关键词： 强激光场 高次谐波 电离概率     

Interplay of polarization geometry and rotational dynamics in high-order harmonic generation from coherently rotating linear molecules

Recent reports on intense-field pump-probe experiments for high-order harmonic generation (HHG) from coherently rotating linear molecules have revealed remarkable characteristic effects of the simultaneous variation of the polarization geometry and the time delay on the high-order harmonic signals. We analyze the effects and give a unified theoretical account of the experimental observations. Furthermore, characteristic behavior at critical polarization angles are found that can help to identify the molecular orbital symmetry in connection with the problem of molecular imaging from the HHG data.     

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.     

High-order harmonic generation of the cyclo[18]carbon molecule irradiated by circularly polarized laser pulse

High-order harmonic generation of the cyclo[18]carbon (C₁₈) molecule under few-cycle circularly polarized laser pulse is studied by time-dependent density functional theory. Compared with the harmonic emission of the ring molecule C₆ H₆ having similar ionization potential, the C₁₈ molecule has higher efficiency and cutoff energy than C₆ H₆ with the same laser field parameters. Further researches indicate that the harmonic efficiency and cutoff energy of the C₁₈ molecule increase gradually with the increase of the laser intensity of the driving laser or decrease of the wavelength, both are larger than those of the C₆ H₆ molecule. Through the analysis of the time-dependent evolution of the electronic wave packets, it is also found that the higher efficiency of harmonic generation can be attributed to the larger spatial scale of the C₁₈ molecule, which leads to a greater chance for the ionized electrons from one atom to recombine with others of the parent molecule. Selecting the suitable driving laser pulse, it is demonstrated that high-order harmonic generation in the C₁₈ molecule has a wide range of applications in producing circularly polarized isolated attosecond pulse.     

High-Order Above-Threshold Ionization of H2+ in Intense Laser Field

The nonperturbative quantum electrodynamies method proposed by Fu et al. [Phys. Rev. A 75 （2007） 063419] is employed to study the high-order above-threshold ionization （ATI） of a diatomic molecule. Based on this frequency-domain theory, the high-order ATI process can be regarded as ATI followed by laser-assisted collision, where the total transition amplitude is the coherent summation of the contributions from each ATI channel. The angular-resolved ATI spectrum, which agrees with the results by Becket et al. based on the time-domain method, is obtained by this frequency domain theory. Furthermore, it is demonstrated that the interference characteristics representing the molecular structure in the ATI spectrum originates from the recollision of the electron with two-centre ion in each ATI channel.     

Isolated attosecond pulse generation from atom radiated by a three-color laser pulse

We theoretically investigate high-order harmonic and attosecond pulse generation from helium atom in a three-color laser field, which is synthesized by 10 fs/800 nm Ti-sapphire laser and a two-color field consisting of 30 fs/532 nm and30 fs/1330 nm pulses. Compared with harmonic spectrum generated by a monochromatic field, the harmonics generated from the synthesized three-color field show a supercontinuum spectrum with a bandwidth of 235 eV, ranging from the 154 th to the 306 th order harmonic. This phenomenon can be attributed to the fact that the ionization of atoms as well as motion of ionized electron can be effectively controlled in the three-color field. Therefore, an isolated 46-as pulse can be generated by superposing supercontinuum from the 160 th to the 210 th order harmonics.