The photoelectron energy spectra （PESs） excited by monochromatic femtosecond x-ray pulses in the presence of a femtosecond laser are investigated. APES is composed of a set of separate peaks, showing interesting comb-like structures. These structures result from the quantum interferences between photoelectron wave packets generated at different times. The width and the localization of each peak as well as the number of peaks are determined by all the laser and x-ray parameters. Most of peak heights of the PES are higher than the classical predictions.
The time-energy properties of high-order harmonic generation （HHG） are calculated for a linearly polarized 7- fs laser pulse with different carrier-envelope phases （CEPs）. The quantum trajectory paths that contribute to an as （1 as=10^-18 s） pulse in HHG are identified. The laser-duration dependence and the CEP dependence of HHG energy property are investigated. The study shows that an as extreme ultra-violet （XUV） pulse can be selected from HHG spectrum near cut-off energy with a bandpass optical filter. The theoretical prediction of the pulse duration is proportional to bandwidth. Analysis suggests that a measured narrowband as XUV pulse may consist of instantaneous shorter pulses each dependent on laser pulse duration, intensity, and CEP. These information can be used as references for producing, selecting, improving and manipulating （timing） as pulses.
To study the time evolution of a molecular state in an ultra-fast chemical reaction,the use of shorter pulses with higher photon energy and narrower bandwidth for both pump and probe is necessary.However,quick and precise measurement of their detailed time structures is a challenge.Over the last decade,great efforts have been made to measure an attosecond extreme ultraviolet (XUV) pulse.To date,several methods have been developed to measure the pulse duration and completely reconstruct it.The attosecond spectral phase interferometry for direct electric field reconstruction (SPIDER) and attosecond frequency-resolved optical gating (FROG) techniques are often used.However,these methods use state-of-the-art experimental set-ups and complicated data analysis procedures.To develop attosecond metrology for practical use (e.g.timing,measurement,evaluation,calibration,optimization,pumping,probing),we propose a quick and analytical method to precisely observe an attosecond XUV pulse with laser-assisted photo-ionization.The method is based on determining the laser-related phase of each streaked electron and using a transfer equation for one-step pulse reconstruction without any time-resolved measurements,iterative calculations,or data fitting procedures.Temporal errors of the pulse reconstruction are calculated from the XUV bandwidth.Because the transfer equation establishes a direct connection between the XUV pulse properties,the crucial laser parameters (peak intensity,phase,carrier envelope phase),the atomic ionization potential,and the measured photoelectron energy spectrum,we can use it to study any one of these properties from other known information and probe the dynamic processes of an ultra-fast reaction.
The photoelectron energy spectra （PESs） excited by narrow bandwidth attosecond x-ray pulses in the presence of a few-cycle laser are quantum-mechanically calculated. Transfer equations are used to reconstruct the detailed temporal structure of an attosecond x-ray pulse directly from a measured PES. Theoretical analysis shows that the temporal uncertainties of the pulse reconstruction depend on the x-ray bandwidth. The procedure of pulse reconstruction is direct and simple without making any previous pulse assumption, data fitting analysis and time-resolved measurement of PESs. The temporal measurement range is half of a laser optical cycle.
Radiation properties of high-order harmonic generation(HHG) are calculated for atoms in a strong laser field.The laser-duration dependence and the carrier-envelope-phase(CEP) dependence of HHG radiation properties are presented.The CEP dependence of the pure single distribution pulse of HHG radiation properties shows interesting 180° periodic structures.The quantum enhancement of the laser-assisted photo-ionization by femtosecond(1 fs=10-15 s) and attosecond(1 as=10-18 s) X-ray pulses and the interference patterns of photo-electron energy spectra are theoretically investigated.Transfer equations are presented for pulse reconstructions.The theoretical root-mean-square time(energy) differences of attosecond pulse reconstructions with different durations are less than 2 as(0.8 eV).These methods may be developed as basic techniques to access ultra-fast measurements and molecular movie.
The ways to produce and measure atto-and femtosecond soft X-ray pulses are reported. The laser phase relation of high-order harmonic generation(HHG) shows two different radiation energy distribu-tions in time(or laser phase) domain. These energy-phase relations are helpful for realizing the dy-namic processes of HHG. Two presented parameterized formulas can be used to calculate the durations of the energy distributions with a bandwidth of the pulse. These formulas are useful in calculating and simulating pulses transports and interactions with mediums. The time structures of atto-and femto-second soft X-ray pulses can be directly measured with photoelectron spectrum transfer equations and the related laser phase determination methods without any previous pulse shape and the instantane-ous frequency assumptions. These equations and methods can be used to evaluate and improve the technical parameters of the ultra-short X-ray sources. They have wide measurement ranges and high time resolutions,which may enable ultra-fast measurements to reach metrological precisions,and lead to a new tide of scientific researches in physics,chemistry,biochemistry,etc. The application of atto-and femtosecond X-rays as well as the theoretical and technical problems in measurements are briefly discussed.
