Pulse width measurement of high-order harmonics by autocorrelation

Pulse widths of the 7th and 9th harmonics of a Ti:sapphire (TiS) laser have been measured by an autocorrelation technique using two-photon and three-photon ionization of He and Ar as nonlinear phenomena. The pulse widths of the 7th and 9th harmonics were 47 fs and 27 fs, respectively, where the pulse width of the fundamental pulse was 34 fs. The pulse width of the 9th harmonic depends strongly on the peak intensity of the fundamental pulse. These results can be explained by quantum theory by taking into account the temporal and spatial distribution of the fundamental beam. Received: 15 June 1999 / Revised version: 8 October 1999 / Published online: 2 February 2000     

Generation of a Super Strong Attosecond Pulse from an Atomic Superposition State Irradiated by a Shape-Optimized Short Pulse

Using a linearly polarized, phase-stabilized 3-fs driving pulse of 800 nm central wavelength shape-optimized on its＇ascending edge by its an amplitude-reduced pulse irradiating on a superposition state of the helium atom, we demonstrate theoretically the generation of a super strong isolated 176-attosecond pulse in the spectral region of 93-124 eV. The unusually high intensity of this attosecond pulse is marked by the Rabi-like oscillations emerging in the time-dependent populations of the ground state and the continuum during the occurrence of the electron recombination, which is for the first time observed in this work.     

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.     

A Theoretical Strategy to Generate an Isolated 80-Attosecond Pulse

Using a linearly polarized, phase-stabilized 2.66-femtosecond driving pulse of 400 nm central wavelength orthogonally combined with another linearly polarized long pulse of 800 nm central wavelength irradiating jointly on the helium atom, we demonstrate theoretically the generation of a clean isolated 80-attosecond pulse in the spectral region of 93-155 electron volts in a two-dimensional model.     

Single X-Ray Attosecond Pulse Generation by Using Combined Pulses Irradiating on a United Two-Atom System

A scheme of a single x-ray attosecond pulse generation from a two-atom system exposed to the combined laser pulses is proposed. Our numerical results show that a single x-ray attosecond pulse rather than a train one can be produced by modulation of ionization. Furthermore, when we change the peak intensity Ih of the high-frequency pulse and keep the intensity of the low-frequency pulse constant, we can find that a range of Ih where the intensity of the attosecond pulse is optimal is available, and a explanation by the stimulated property of the recombination is also presented.     

Harmonic Enhancement Mechanism of a Superposition State Atom Irradiated by Short Pulses

We investigate the high-order harmonic generation （HHG） of a model atom whose initial state is prepared in a superposition of its ground state and an excited state irradiated by different duration laser pulses. Compared to the HHG generated from an atom whose initial state is in its ground state, its conversion efficiency obtains some enhancement. The enhancement originates from the higher ionization rate （rather than the ionization yield） of the atom with superposition initial state.     

Enhancement of Bichromatic High-Order Harmonic Generation by a Strong Laser Field and Its Third Harmonic

We investigate high-order harmonic generation （HHG） in a linearly polarized bichromatic field composed of a fundamental laser field with frequency w and an additional laser field with frequency 3w. The numerical results show that it is possible to enhance the intensity of most high harmonics in orders of magnitude. A most striking feature in the enhancement is that the intensity of several special high harmonics is practically impaired as compared with that in the monochromatic case. The qualitative explanation to the great enhancement is that the additional high-frequency field can provide new transition paths for electrons to reach the continuum. The relative phase between the fundamental field and its third harmonic field also affects the intensity of high-order harmonics near the cutoff efficiently.     

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.     

Harmonic generation in an ionized gas medium with a 100-femtosecond, high repetition rate laser source at intermediate intensities

 We report the realization of a vacuum-ultraviolet radiation source based on high-order harmonic generation in noble-gas samples, operating at high repetition rate. In particular, we observed up to the 13th harmonic (λ=61 nm) of the fundamental frequency of a short pulse, high repetition rate titanium–sapphire laser after its interaction with a Xe gas jet. The effects of the propagation of the fundamental and harmonic beams through an ionized medium are studied by analysing the spectral profile of the 9th and 7th harmonics. Finally, we report a study of the dependence of the harmonic conversion efficiency on relative position of the focus and the gas target. Received: 29 March 1996/Revised version: 25 July 1996     

Tracking individual electron trajectories in a high harmonic spectrum

The harmonic spectrum generated by a few-cycle laser pulse propagating through a gas jet is calculated. Two complementary atomic response models are used, one based on the time-dependent Schrödinger equation and the other on quantum orbits in which only a single pair of electron trajectories are taken into account. The role played by individual electron trajectories in determining particular features of the spectrum are considered and phase-matching maps are used to help understand their structure. A method based on this connection is proposed for diagnosing the carrier-envelope phase and the pulse duration of the incident laser field.     

Approach to extreme ultraviolet supercontinuum in a two-color laser field

In recent years, it has been shown that an intense few-cycle driving pulse combined with a weak control pulse could efficiently extend the harmonic spectrum in the generation of high-order harmonics (HHG). In this paper, we adjust the intensities of the driving and control pulse to generate broader extreme ultraviolet (XUV) supercontinuum. We find that in some special situation when the intensity of the control pulse equals to that of the driving pulse, a clean supercontinuum as long as 80 eV can be realized and a 53-as pulse can be straightforwardly obtained.     

Effects of laser pulsewidth on higher-order harmonic generation in the barrier-suppression-ionization intensity regime

We studied the highest harmonic photon energies of high-order harmonic generation (HHG) for He, Ne, Ar, Kr, Xe, and N₂. This research employed 65-fs and 150-fs Ti:sapphire laser pulses, of which the peak intensities in a vacuum are higher than the barrier-suppression-ionization (BSI) intensities. We fitted two analytical formulae to the experimental results of HHG. One formula, which was obtained by fitting an analytical formula to the results by a quantum mechanical simulation of HHG, expresses the highest interaction intensity by a function of the BSI intensity and the Keldysh γ-parameter. The other formula is derived by introducing the saturation intensity of HHG, which was proposed by Chang et al. [Phys. Rev. Lett. 79, 2967 (1997)]. We discuss the highest interaction intensity for the condition when the peak laser intensities are higher than the BSI intensities. Received: 19 March 1999 / Revised version: 13 August 1999 / Published online: 27 October 1999     

Strengthened Hyper-Raman Lines with the Coherent Superposition State

High-order harmonic generations from a one-dimensional Coulomb potential atom are calculated with the initial state prepared as a coherent superposition between its ground and first excited states. When the energy difference of the two states is small, we can choose proper laser pulse such that the first excited state can be excited only to other bound states instead of being ionized. We show that only the hyper-Raman lines are observable instead of the harmonics. The energy difference of the ground and the first excited state can be deduced from the highest peak of the hyper-Raman lines. We further show that the similar results can be obtained by using a combination of two laser pulses with different frequencies interacting with the atom initially at the ground state.     

Characteristics of high-order harmonic spectrum by using laser-ablated two targets combination

We demonstrated a high-order harmonic generation from lowly charged ions in laser-ablation two-compound plumes (Ag-In, Ag-Mn, and Cr-Te). The high-order harmonic spectra from two-compound plumes were composed of those obtained from each target. Our results show that the control of cutoff energy and intensity of single high-order harmonics can be achieved by using the appropriate target combination.     

Laser-Duration Dependence of Emission Properties of High-Order Harmonic Generation

Quantitative investigations are made for the laser-duration dependence of the emission properties of high-order harmonic generation （HHG）. HHG emission properties produced by few-cycle lasers show some useful characteristics. The cutoff energy is less than that by laser for infinite duration. The single energy distribution pulse decreases much faster than its duration as the laser duration grows. A two-cycle laser with carrier-envelope phase of 0° can produce a single distribution pulse peaked at the laser carrier phase 1.22 rad and spanned 1.18 rad with the cutoff energy 2.9Up ＋ Ip and a bandwidth 0.63Up, where Up is the ponderomotive potential of the laser field and Ip is the atomic ionization potential.     

Study on Non-Sequential Double Ionization of Aligned Diatomic Molecules in Strong Laser Fields

We develop a semiclassical model to describe the non-sequential double ionization of aligned diatomic molecules in an intense linearly polarized field. It is found that in the tunnelling regime, the oriented molecule shows geometric effects on double ionization process when aligned parallel and perpendicular to the external field. Our results are qualitatively consistent with the recent experimental observations.     

Kilohertz extreme-ultraviolet light source based on femtosecond high-order harmonic generation from noble gases

A compact, versatile table-top kilohertz source of coherent extreme-ultraviolet (XUV) radiation in the wavelength region 18–100 nm, based on high-order harmonic generation from noble gases induced by a 40-femtosecond Ti:sapphire laser system, is presented. The XUV beamline delivers at its output 10⁸ photons/s at a wavelength of 23 nm. The monochromatized XUV radiation is directly focused onto a 10^-2-mm² spot by a toroidal grating, allowing one to reach intensities higher than 10⁶ W/cm². Optimization results are presented for a new XUV-generating geometry, utilizing a ‘semi-infinite’ quasi-static gas cell and strong focusing. In those conditions, we observe an anomalous inversion between the cutoffs of argon and krypton, with the krypton spectrum extending to much higher orders than expected in an adiabatic limit. Received: 9 July 2001 / Revised version: 1 August 2001 / Published online: 7 November 2001     

Measurement of Carrier-Envelope Phase and Field Strength of a Few-Cycle Pulse by Non-sequential Double Ionization

We propose a method to measure the carrier-envelop phase （CEP） and the intensity of a few-cycle pulse by controlling the non-sequentiai double ionization （NSDI） process. By using an additional static electric field, we can change the momentum distribution of the double-charged ions parallel to the laser polarization from an asymmetrical double-hump structure to a nearly symmetrical one. It is found that the ratio between the strength of the static electric field and that of the laser field is sensitive to the CEP but robust against the intensity fluctuation. Therefore we can determine the OEP of a few-cycle pulse precisely by measuring the static electric field. Fhrthermore, if the CEP of the few-cycle pulse is fixed at a certain value, we can also calibrate the intensity of the laser pulse by the static electric field.     

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.     

Polarization effects in resonance-enhanced frequency tripling and multiphoton ionization in xenon under excitation by crossed laser beams

Generation of resonance-enhanced third harmonic and multiphoton ionization in xenon have been studied for different polarizations of crossed laser beams. Polarization control over the harmonic generation and resonant ionization processes in crossed beams is analyzed and discussed.