Enhancement of high harmonics generated by field steering of electrons in a two-color orthogonally polarized laser field

We demonstrate enhancement by 1 order of magnitude of the high-order harmonics generated in argon by combining a fundamental field at 1300 nm (10(14) W cm(-2)) and its orthogonally polarized second harmonic at 650 nm (2 × 10(13) W cm(-2)) and by controlling the relative phase between them. This extends earlier work by ensuring that the main effect is the combined field steering the electron trajectory with negligible contribution from multiphoton effects compared to the previous schemes with 800/400 nm fields. We access a broad energy range of harmonics (from 20 eV to 80 eV) at a low laser intensity (far below the ionization saturation limit) and observe deep modulation of the harmonic yield with a period of π in the relative phase. Strong field theoretical analysis reveals that this is principally due to the steering of the recolliding electron wave packet by the two-color field. Our modeling also shows that the atto chirp can be controlled, leading to production of shorter pulses.     

Spatial control of recollision wave packets with attosecond precision

We propose orthogonally polarized two-color laser pulses to steer tunneling electrons with attosecond precision around the ion core. We numerically demonstrate that the angles of birth and recollision, the recollision energy, and the temporal structure of the recolliding wave packet can be controlled without stabilization of the carrier-envelope phase of the laser, and that the wave packet's properties can be described by classical relations for a point charge. This establishes unique mapping between parameters of the laser field and attributes of the recolliding wave packet. The method is capable of probing ionic wave packet dynamics with attosecond resolution from an adjustable direction and might be used as an alternative to aligning molecules. Shaping the properties of the recollision wave packet by controlling the laser field may also provide new routes for improvement of attosecond pulse generation via high harmonic radiation.     

Control the revisit time of the electron wave packet

Ionization of molecules by strong laser fields launches an electron wave packet. This electron wave packet, which can be driven back by the field to recollide with the parent ion, has been widely explored to probe the ultrafast nuclear dynamics. We numerically demonstrate the precise control of the temporal characteristic of the recolliding electron wave packet (REWP) by orthogonally polarized two-color fields. Through changing the relative phase of the two fields, the revisit time of REWP can be manipulated with a resolution of less than 200 attos, thus significantly improving the resolution of the well known molecular clock. This provides an efficient method for real-time observation of the ultrafast molecular dynamics with attosecond resolution.     

High-order harmonic generation from solid surfaces in intense laser fields

We give a Floquet analysis of high-order harmonic generation from a solid surface interacting with intense laser fields. A general theoretical algorithm, within a three-dimensional quasi-free electron model, is presented. It takes account of the effective masses of the electron both within and outside the solid and treats both reflected and refracted laser fields. The high-order harmonic spectrum is obtained from the off-diagonal photon components of the expectation value of the time-dependent current operator. We present the formation of a plateau, well known in the atomic case, in the spectrum of the high-order harmonic radiation, which arises from the evanescent part of the electron wave function at the surface.     

High-order harmonic transient grating spectroscopy in a molecular jet

We study high-order harmonic generation in excited media using a four-wave-mixing-like configuration. We analyze the spatial profile of high harmonics emitted by a grating of rotationally excited molecules as a function of the pump-probe delay. We demonstrate a dramatic improvement in the contrast of the diffracted signal relative to the total high harmonic signal. This allows us to observe subtle effects in the rotational wave packet excitation such as the pump-intensity dependence of the wave packet dynamics. High harmonic transient grating spectroscopy can be extended to all forms of molecular excitation and to weak resonant excitation.     

Molecular imaging using high-order harmonic generation and above-threshold ionization

Accurate molecular imaging via high-order harmonic generation relies on comparing harmonic emission from a laser-irradiated molecule and an adequate reference system. However, an ideal reference atom with the same ionization properties as the molecule is not always available. We show that for suitably designed, very short laser pulses, a one-to-one mapping from high-order harmonic frequencies to electron momenta in above-threshold ionization exists. Comparing molecular and atomic momentum distributions then provides the electron recollision amplitude in the molecule for enhanced molecular imaging. The method retrieves the molecular recombination transition moments highly accurately, even with suboptimal reference atoms.     

High harmonic generation and molecular orbital tomography in multielectron systems: beyond the single active electron approximation

It was recently shown that the highest molecular orbital of N2 could be reconstructed from a series of high harmonic measurements. Existing theories of high harmonic generation and orbital tomographic imaging are based on the single active electron approximation that ignores essential quantum mechanical properties such as the indistinguishability of identical particles and the Pauli exclusion principle. We show that, when fully antisymmetrized multielectron wave functions and electronic relaxation in the cation are considered, molecular orbital tomography records the image of the Dyson orbital plus exchange contributions from inner shells. The mixing of contributions from more than one molecular orbital gives access to additional wave function information. By utilizing the exchange term, harmonic emission from a closed-shell 4-electron system can be interpreted as a complete Hartree-Fock wave function.     

High harmonic generation via continuum wave-packet interference

High-order harmonic generation (HHG) is investigated theoretically in the over-the-barrier ionization regime revealing the strong signature of interference between two separately ionized and separately propagating free wave packets of a single electron. The interference leads to the emission of coherent light at a photon energy corresponding to the kinetic-energy difference of the two recolliding electron quantum paths, thus complementary to the well-known classical three-step picture of HHG. As will be shown by time-frequency analysis of the emitted radiation, the process entirely dominates the coherent HHG emission after the atomic ground state has been depleted by a strong field. Moreover, it can be isolated from the continuum-bound harmonics via phase matching.     

Minimum structure of high-harmonic spectrafrom aligned O2 and N2 molecules

We experimentally investigated the high-order harmonic generation (HHG) from aligned O₂ and N₂ molecules in a linearly polarized laser field, and presented the dependence of the harmonic spectrum on the driving laser intensity and molecular alignment angle. The minimum position of HHG of O₂ varies with changing the laser intensity, which is caused by multi-orbital interference. However, the location of the observed minimum structure in N₂ harmonic spectrum remained unchanged upon changing the laser intensity. The mechanism of the spectral minimum for N₂ case is regarded as a Cooper-like minimum in HHG associated with the molecular electronic structure. This work indicates that harmonic spectroscopy can effectively uncover information about molecular structure and electron dynamics.     

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.     

Laser phase effect on asymmetric harmonic distribution in H_2~+

The laser phase effect on the spatial distribution of the molecular high-order harmonic generation(MHHG) spectrum from H_2~+ is theoretically investigated through solving the Non-Bohn-Oppenheimer(NBO) time-dependent Schrodinger equation(TDSE).The results are shown as follows,(i) The generated harmonics from the two nuclei each present an asymmetric distribution.Particularly,when the laser phases are chosen from 0.0π to 0.6π and from 1.7π to 2.0π,the contribution from the negative-H plays a main role in harmonic generation.When the laser phases are chosen from 0.7πto 1.6k,the contribution from the positive-H to the harmonic generation is remarkably enhanced and becomes greater than that from the negative-H.The electron localization,the time-frequency analyses of the harmonic spectrum and the time-dependent wave function are shown to explain the asymmetric harmonic distribution in H_2~+,which provides us with a method to control the electron motion in molecules,(ⅱ) As the pulse duration increases,the asymmetric distributions of the MHHG in two H nuclei decrease,(ⅲ) Isotope investigation shows that the asymmetric harmonic distribution can be reduced by introducing the heavy nucleus(i.e.,D_2~+).     

Direct XUV probing of attosecond electron recollision

We demonstrate that the recolliding electron wave packet, fundamental to many strong field phenomena, can be directly imaged with sub-A spatial and attosecond temporal resolution using attosecond extreme ultraviolet (XUV) pulses. When the recolliding electron revisits the parent ion, it can absorb an XUV photon yielding high energy electron and thereby providing a measurement of the electron energy at the moment of recollision. The full temporal evolution of the recollision wave packet can be reconstructed by measuring the photoelectron spectra for different time delays between the driving laser and the attosecond XUV probe. The strength of the photoelectron signal can be used to characterize the spatial distribution of the electron density in the longitudinal direction. Elliptical polarization can be used to characterize the electron probability in transversal direction.     

Controlling two-center interference in molecular high harmonic generation

We experimentally investigate the process of intramolecular quantum interference in high-order harmonic generation in impulsively aligned CO2 molecules. The recombination interference effect is clearly seen through the order dependence of the harmonic yield in an aligned sample. The experimental results can be well modeled assuming that the effective de Broglie wavelength of the returning electron wave is not significantly altered by the Coulomb field of the molecular ion. We demonstrate that such interference effects can be effectively controlled by changing the ellipticity of the driving laser field.     

少周期激光脉冲附加太赫兹场对高次谐波发射的影响

本文通过数值求解非伯恩奥本海默近似下电子一维核一维的含时薛定谔方程,研究了少周期线偏振激光与氢分子离子相互作用下,太赫兹场的加入对高次谐波的发射影响.我们发现,在短周期线偏振激光脉冲的y方向上附加一个强度较弱的太赫兹场可以有效地扩展谐波的截止位置,并对量子轨道实现调控.通过时频分析、电子波包随时间变化以及半经典三步模型研究了高次谐波发射的物理机制,并对获得的物理现象给出合理的解释.     

Extracting continuum electron dynamics from high harmonic emission from molecules

We show that high harmonic generation is the most sensitive probe of rotational wave packet revivals, revealing very high-order rotational revivals for the first time using any probe. By fitting high-quality experimental data to an exact theory of high harmonic generation from aligned molecules, we can extract the underlying electronic dipole elements for high harmonic emission and uncover that the electron gains angular momentum from the photon field.     

Ultrahigh Harmonic Generation from an Atom with Superposition of Ground State and Highly Excited States

We investigate the high-order harmonic generation from an atom prepared in a superposition of ground state and highly excited state. When the atom is irradiated by an ultrashort pulse, the cutoff position of the plateau in the harmonic spectrum is largely extended compared with the case that the atom is initially in the ground state. The physics of the extension of the high-order harmonic plateau can be interpreted by the spatial structure of the atomic initial wave packet. We can optimize the generation of high-order harmonics by substituting the excited state for a particular coherent superposition of some highly excited states to form a spatially localized excited wave packet.     

Frequency dependence of quantum path interference in non-collinear high-order harmonic generation

High-order harmonic generation(HHG) driven by two non-collinear beams including a fundamental and its weak second harmonic is numerically studied. The interference of harmonics from adjacent electron quantum paths is found to be dependent on the relative delay of the driving pulse, and the dependences are different for different harmonic orders.This frequency dependence of the interference is attributed to the spatial frequency chirp in the HHG beam resulting from the harmonic dipole phase, which in turn provides a potential way to gain an insight into the generation of high-order harmonics. As an example, the intensity dependent dipole phase coefficient α is retrieved from the interference fringe.     

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.     

Influence of surface waves on plasma high-order harmonic generation

The influence of surface plasma waves on high-order harmonic generation from the interaction of intense lasers with overdense plasma is analyzed. It is shown that the surface waves lead to the emission of harmonics away from the optical axis, whereas the high-order on-axis harmonics are lowered in intensity. Our simulation results indicate that surface plasma wave generation plays a crucial role in surface high-order harmonic generation experiments. Furthermore, a novel surface plasma wave generation process different from the well-known two-surface wave decay is observed in the highly relativistic regime.