Contributions of the pre-ionized H$_2$ (PI-H$_2$) and ionized H$_2^+$ subsystems of the two-electron H$_2$ system to its high-order harmonic generation in 8-cycle $\sin^{2}$-like ultrafast intense laser pulses are calculated and analyzed based on the solution of the time-dependent Schrödinger equation (TDSE) for the one-dimensional two-electronic H$_2$ system with fixed nuclei. The laser pulses have $λ =\ 390\ \&\ 532$ nm wavelengths and $I=1\times 10^{14}$, 5$\times 10^{14}$, 1$\times 10^{15}$ \&\ 5$\times 10^{15}$ Wcm$^{-2}$ intensities. It is found that at the two lower intensities, the PI-H$_2$ subsystem dominantly produces the HHG spectra. While, at the two higher intensities, both PI-H$_2$ and ionized H$_2^+$ subsystems contribute comparably to the HHG spectra. In the H$_2^+$ subsystem, the symmetry of the populations of H$_2^+$(I) and H$_2^+$(II) regions (left and right regions of H$_2^+$ subsystem) is broken by increasing the laser intensity. Complex patterns and even harmonics also appear at these two higher intensities. For instance, at $1\times 10^{15}$ Wcm$^{-2}$ intensity and $λ$ = 532 nm, the even harmonics are appeared near cut-off region. Interestingly, at $5\times 10^{15}$ Wcm$^{-2}$ intensity and $λ$ = 390 nm, the even harmonics replaced by the odd harmonics with red shift. At $λ$ = 390 \&\ 532 nm and $I=1\times 10^{15}$ intensity, the two-electron cutoffs corresponding to nonsequential double-recombination (NSDR) with maximum return kinetic energy of 4.70$U_p$ are detected. The HHG spectra of the whole H$_2$ system obtained with and without nuclear dynamics treated classically are approximately similar. However, at $1\times 10^{15}$ Wcm$^{-2}$ intensity and $λ$ = 532 nm, if we take into account nuclear dynamics, the even harmonics which are appeared near cutoff region, replaced by the odd harmonics with blue shift.
We present an analysis of the appearance of the Cooper Minimum in singly ionized argon in both the photoionization cross-section (PICS) and high-harmonic generation (HHG) spectrum. We employ two computational approaches based on the same R-matrix technique to provide a coherent description of the atomic structure of the Ar+ system, finding that the PICS and HHG spectrum are affected differently by the inclusion of additional residual ion states and the improved description of correlation effects. Both the PICS and HHG spectrum possess a clear minimum for all atomic structure models used, with …
We present theoretical results on the high-harmonic generation (HHG) in bulk diamond induced by intense laser pulse of wavelength 800 nm and duration 15 fs. For laser intensity in the range $1 \le I \le 50 $ TW/cm$^2$ above bandgap harmonics are generated after the pulse peak. We find that the intensity of individual harmonics increases non-linearly with the peak laser intensity, following a non-perturbative trend. For moderate intensity the HHG spectrum exhibits a primary plateau with noisy odd order harmonic structure and a cutoff. For increased laser intensity a secondary plateau emerges wi…
The ongoing development of intense high-harmonic generation (HHG) sources has recently enabled highly nonlinear ionization of atoms by the absorption of at least 10 extreme-ultraviolet (XUV) photons within a single atom [Senfftleben \textit{et al.}, arXiv1911.01375]. Here we investigate the role that reshaping of the fundamental, few-cycle, near-infrared (NIR) driving laser within the 30-cm-long HHG Xe medium plays in the generation of the intense HHG pulses. Using an incident NIR intensity that is higher than what is required for phase-matched HHG, signatures of reshaping are found by measuri…
Intense extreme-ultraviolet (XUV) pulses enable the investigation of XUV-induced nonlinear processes and are a prerequisite for the development of attosecond pump - attosecond probe experiments. While highly nonlinear processes in the XUV range have been studied at free-electron lasers (FELs), high-harmonic generation (HHG) has allowed the investigation of low-order nonlinear processes. Here we suggest a concept to optimize the HHG intensity, which surprisingly requires a scaling of the experimental parameters that differs substantially from optimizing the HHG pulse energy. As a result, we are…
The underlying physics behind the molecular harmonic emission in relatively long sin$^2$-like laser pulses is investigated. We numerically solved the full-dimensional electronic time-dependent Schrödinger equation beyond the Born-Oppenheimer approximation for simple molecular ion H$_2^+$. The occurrence and the effect of electron localization, non-adiabatic redshift and spatially asymmetric emission are evaluated to understand better complex patterns appearing in the high-order harmonic generation (HHG) spectrum. Results show that the complex patterns in the HHG spectrum originate mainly from …
We investigate the high harmonic generation (HHG) from solids by simulating the dynamics of a single active electron in periodic potentials. The corresponding time-dependent Schrödinger equations (TDSE) are solved numerically by using B-spline basis sets in coordinate space. The energy band structure and wave vectors can be directly retrived from the eigenfunctions. The harmonic spectra obtained agree well with the results simulated by TDSE in $k$ space using Bloch states and show a two-plateau structure. Both of the cutoff energies of the two plateaus in the harmonic spectrum scale linearly w…
Two different induced effects of a laser falling edge on high-order harmonic generation are resolved by solving numerically full-dimensional electronic time-dependent Schrödinger equation beyond the Born-Oppenheimer approximation. The harmonic spectrum of H$_2^+$ and T$_2^+$ isotopes are compared to see the effects of a 4-cycle falling edge of a 800 nm, 15-cycle trapezoidal laser pulse of $I=$3 $\times 10^{14}$ Wcm$^{-2}$ intensity on harmonic emission spectrum. The harmonic emission at the laser falling part is negligible for H$_2^+$ due to ionization suppression, but considerable for T$_2^+$…
We report on a compact and spectrally intense extreme-ultraviolet (XUV) source, which is based on high-harmonic generation (HHG) driven by 395 nm pulses. In order to minimize the XUV virtual source size and to maximize the XUV flux, HHG is performed several Rayleigh lengths away from the driving laser focal plane in a high-density gas jet. As a result, a high focused XUV intensity of $5 \times 10^{13}$ W/cm$^2$ is achieved, using a beamline with a length of only two meters and a modest driving laser pulse energy of 3 mJ. The high XUV intensity is demonstrated by performing a nonlinear ionizati…
The generation of high harmonics (HHG) in atomic systems by the highly non-linear response to an intense laser field is a prominent pathway to the synthesis of ever shorter laser pulses at increasingly higher photon energies. Extensions of this process to molecules add to the complexity but also offers novel opportunities as multi-center effects and the coupling to nuclear degrees of freedom can influence HHG. In this work we theoretically explore the impact of coherent vibronic excitations of diatomic molecules on the HHG spectrum within the framework of time-dependent density functional theo…
We theoretically study high-order harmonic generation (HHG) from solid-phase systems in spatially inhomogeneous strong laser fields originated by resonant plasmons within a metallic nanostructure. The intensity of the second plateau in HHG may be enhanced by two-three orders and be comparable with the intensity of the first plateau. This is due to bigger transition probabilities to higher conduction bands. It provides us a practical way to increase the yields of HHG with laser intensity below the damage threshold. It presents a promising way to triple the range of HHG spectra in experimental m…
High-intensity laser pulses covering the ultraviolet to terahertz spectral regions are nowadays routinely generated in a large number of laboratories. In contrast, intense extreme-ultraviolet (XUV) pulses have only been demonstrated using a small number of sources including free-electron laser facilities [1-3] and long high-harmonic generation (HHG) beamlines [4-9]. Here we demonstrate a concept for a compact intense XUV source based on HHG that is focused to an intensity of $2 \times 10^{14}$ W/cm$^2$, with a potential increase up to $10^{17}$ W/cm$^2$ in the future. Our approach uses tight f…
Medium propagation effects in high harmonic generation of Ar and N$_{2}$
本文报道了强红外激光在原子和分子靶中产生高次谐波（HHG）的理论计算，同时考虑了基波和谐波场的宏观传播。在Ar和N $_2$的例子中，我们证明了这些{ \it ab initio}计算能够准确地再现各向同性和对齐的目标介质的实验结果。我们进一步提出了详细的分析HHG的强度和相位，在各种实验条件下，特别是，作为驱动激光的波长的变化。最重要的是，我们的研究结果强烈支持因子分解的HHG在宏观水平的产品返回电子波包和光复合跃迁偶极子，在典型的实验条件下。这意味着单原子/分子的结构信息可以从实验测量的HHG光谱检索。
High harmonic generation (HHG) is a manifestation of the strongly nonlinear response of matter to intense laser fields and has, as the basis for coherent XUV sources a variety of applications. Recently, HHG from atoms in a phase and polarization structured laser was demonstrated and interpreted based on the transverse electric field component of the driving pulse. Here we point out that as dictated by Maxwell equations, such fields have a longitudinal component which in general has a fundamental influence on the charge dynamics. For instance, its interplay with the transversal field component …
We study high-order harmonic generation (HHG) driven by seeded plasmonic-enhanced fields. On one hand, plasmonic-enhanced fields have shown a great potential to extend the HHG cutoff, an instrumental pre-requisite for the generation of attosecond pulses. On another hand, the use of XUV seeds appears to have a considerable potential to improve the HHG conversion efficiency, which is typically modest when a unique fundamental laser pulse is employed. By mixing these two sources, we show it is possible to, simultaneously, boost the HHG cutoff and to increase the harmonic photon flux. The combinat…
High-order harmonic generation (HHG) is combined with resonant x-ray excitation of a core electron into the transient valence vacancy that is created in the course of the HHG process. To describe this setting, I develop a two-active-electron quantum theory for a single atom assuming no Coulomb interaction among the electrons; one electron performs a typical HHG three-step process whereas another electron is excited (or even Rabi flops) by intense x rays from the core shell into the valence hole after the first electron has left the atom. Depending on the amplitude to find a vacancy in the vale…
The interplay between high-harmonic generation and photoluminescence in ZnO: Anisotropic spectral properties of harmonic emission and the role of excitons
We theoretically study multielectron effects in high-harmonic generation (HHG), using all-electron first-principles simulations for a one-dimensional (1D) model atom. In addition to usual plateau and cutoff (from a cation in the present case, since the neutral is immediately ionized), we find a prominent resonance peak far above the plateau and a second plateau extended beyond the first cutoff. These features originate from the dication response enhanced by orders of magnitude due to the action of the Coulomb force from the rescattering electron, and, hence, are a clear manifestation of electr…
We present the first demonstration of two-photon double ionization of neon using an intense extreme ultraviolet (XUV) attosecond pulse train (APT) in a photon energy regime where both direct and sequential mechanisms are allowed. For an APT generated through high-order harmonic generation (HHG) in argon we achieve a total pulse energy close to 1 $μ$J, a central energy of 35 eV and a total bandwidth of $\sim30$ eV. The APT is focused by broadband optics in a neon gas target to an intensity of $3\cdot10^{12} $W$\cdot$cm$^{-2}$. By tuning the photon energy across the threshold for the sequential …
Emission of high-order harmonics from solids provides a new avenue in attosecond science. On one hand, it allows to investigate fundamental processes of the non-linear response of electrons driven by a strong laser pulse in a periodic crystal lattice. On the other hand, it opens new paths toward efficient attosecond pulse generation, novel imaging of electronic wave functions, and enhancement of high-order harmonic generation (HHG) intensity. A key feature of HHG in a solid (as compared to the well-understood phenomena of HHG in an atomic gas) is the delocalization of the process, whereby an e…
Solid-state materials have recently emerged as a new stage of strong-field physics and attosecond science. The mechanism of the electron dynamics driven by an ultrashort intense laser pulse is under intensive discussion. Here we theoretically discuss momentum-space strong-field electron dynamics in graphene and crystalline dielectrics and semiconductors. First, within massless Dirac fermion and tight-binding models for graphene, we rigorously derive intraband displacement and interband transition, which form the basis for understanding solid-state strong-field physics including high-harmonic g…
The cut-off regime of high-order harmonic generation (HHG) by atoms in an intense laser field is studied numerically and analytically. We find that the cut-off regime is characterized by equal dephasing between the successive harmonics. The change of the harmonic phase-locking when HHG evolves from the cut-off to the plateau regime determines the optimal bandwidth of the spectral region which should be used for attosecond pulse generation via amplitude gating technique. The cut-off regime is also characterized by a linear dependence of the harmonic phase on the fundamental intensity. The propo…
Real-space picture of electron recollision with the parent ion guides our understanding of the highly nonlinear response of atoms and molecules to intense low-frequency laser fields. It is also among several leading contestants for the dominant mechanism of high harmonic generation (HHG) in solids, where it is typically viewed in the momentum space, as the recombination of the conduction band electron with the valence band hole, competing with another HHG mechanism, the strong-field driven Bloch oscillations. In this work, we use numerical simulations to directly test and confirm the real-spac…
Subcycle phase matching effects in short attosecond pulse trains
Universidad de Salamanca（萨拉曼卡大学）；Lund University（隆德大学）；Politecnico di Milano（米兰理工大学）；Institute for Photonics and Nanotechnologies, IFN-CNR（光子与纳米技术研究所，意大利国家研究委员会）
Ionization by relativistically intense laser pulses of finite duration is considered in the framework of strong-field quantum electrodynamics. Our main focus is on the formation of ionization supercontinua. More specifically, when studying the energy distributions of photoelectrons ionized by circularly polarized pulses, we observe the appearance of broad structures lacking the interference patterns. These supercontinua extend over hundreds of driving photon energies, thus corresponding to high-order nonlinear processes. The corresponding polar-angle distributions show asymmetries which are at…
High-order harmonic generation (HHG) in simultaneous intense near-infrared (NIR) laser light and brilliant x rays above an inner-shell absorption edge is examined. A tightly bound inner-shell electron is transferred into the continuum. Then, NIR light takes over and drives the liberated electron through the continuum until it eventually returns to the cation leading in some cases to recombination and emission of a high-order harmonic (HH) photon that is upshifted by the x-ray photon energy. We develop a theory of this scenario and apply it to $1s$ electrons of neon atoms. The boosted HH light …
We report on the design and performance of a velocity map imaging (VMI) spectrometer optimized for experiments using high-intensity extreme ultraviolet (XUV) sources such as laser-driven high-order harmonic generation (HHG) sources and free-electron lasers (FELs). Typically exhibiting low repetition rates and high single-shot count rates, such~experiments do not easily lend themselves to coincident detection of photo-electrons and -ions. In order to obtain molecular frame or reaction channel-specific information, one has to rely on other correlation techniques, such as covariant detection sche…
In this work we demonstrate the generation of two intense, ultrafast laser pulses that allow a controlled interferometric measurement of higher harmonic generation pulses with 12.8 attoseconds in resolution (half the atomic unit of time) and a precision as low as 680 zeptoseconds ($10^{-21}$ seconds). We create two replicas of a driving femtosecond pulse which share the same optical path except at the focus where they converge to two foci. An attosecond pulse train emerges from each focus through the process of HHG. The two attosecond pulse trains from each focus interfere in the far field pro…
We investigate the polarization properties of high harmonics generated with the bichromatic counterrotating circularly polarized (BCCP) laser fields by numerically solving time-dependent Schrödinger equation (TDSE). It is found that, the helicity of the elliptically polarized harmonic emission is reversed at particular harmonic orders. Based on the time-frequency analysis and the classical three-step model, the correspondence between the positions of helicity reversions and the classical trajectories of continuum electrons is established. It is shown that, the electrons ionized at one lobe of …
We analytically describe the strong-field light-electron interaction using a quantized coherent laser state with arbitrary photon number. We obtain a light-electron wave function which is a closed-form solution of the time-dependent Schrodinger equation (TDSE). This wave function provides information about the quantum optical features of the interaction not accessible by semi-classical theories. With this approach we can reveal the quantum optical properties of high harmonic generation (HHG) process in gases by measuring the photon statistics of the transmitted infrared (IR) laser radiation. T…
We theoretically investigate high-order harmonic generation (HHG) in Rydberg atoms driven by spatially inhomogeneous laser fields, induced, for instance, by plasmonic enhancement. It is well known that the laser intensity should to exceed certain threshold in order to generate HHG, when noble gas atoms in their ground state are used as an active medium. One way to enhance the coherent light coming from a conventional laser oscillator is to take advantage of the amplification obtained by the so-called surface plasmon polaritons, created when a low intensity laser field is focused onto a metalli…
Strong light fields coax intramolecular reactions on femtosecond time scales
高能H $_2^+$离子的形成是由于线性醇（甲醇，乙醇，丙醇，己醇和十二烷醇）的裂解过程中分子内重排的结果，所述裂解由100 fs长的红外激光脉冲产生的峰值强度为8 $\times10^{15}$ W cm $^{-2}$的强光场诱导。偏振相关的测量表明，违反直觉，重排是由一个单一的激光脉冲内的强光场引起的，并且它发生在库仑爆炸的场电离的多电荷醇。
Photoionization of hydrogen atom by coherent intense high-frequency short laser pulses: Direct propagation of electron wave packets on large spatial grids
通过传播单电子波包，数值精确求解了氢原子与相干强高频短脉冲相互作用的含时薛定谔方程。因此，在比脉冲持续时间长的时间内在空间和时间上跟随波函数。结果明确显示为3和10 fs的脉冲。特别注意识别在[ \emph{Ph.V. Demekhin and L.S. Cederbaum}，Phys.Rev.Lett.]中预测的脉冲的上升侧和下降侧期间在不同时间以相同动能发射的光电子的动态干扰的效果。\textbf{108}，253001（2012）]。为了能够在计算的电子谱中看到动态干涉图案，光电子波包必须传播很长的距离。显然，通常用于计算发射粒子光谱的复吸收势不能用于检测动态干扰。对于所考虑的3和10 fs持续时间的高频脉冲，这需要非常大的空间网格。目前计算的光电离和阈上电离光谱被发现表现出明显的动态干涉图案。在可用的情况下，图案是在非常好的协议与先前公布的结果已经计算使用完全不同的方法的光电离光谱，从而支持了先前作出的假设，即上述阈值电离过程是非常弱的脉冲强度和高载波频率。本文还数值研究了强激光脉冲中自由电子的时空运动。最后讨论了强脉冲电离原子的速度。
