Attosecond pulses provide higher measurement precision for analyzing ultrafast dynamics in atoms, molecules, and electrons, laying the foundation for studying electronic motion in atomic and molecular systems. The most important method currently is to generate attosecond pulse trains and isolated attosecond pulses through the interaction of femtosecond lasers with gases. The temporal information of attosecond pulses and the dynamic information of electrons can be extracted from spectrograms by using attosecond streak camera or the reconstruction of attosecond beating by interference of two-photon transitions (RABBITT) method based on two-photon transition interference. Although the differences in phase among different high-order harmonics can be directly extracted from the oscillation frequencies of sidebands, the iterative algorithm of attosecond streak camera can provide complete phase information of attosecond pulse trains to better support the study of electron dynamics in atoms.

Research purpose 　This work is dedicated to the investigation of the generation, measurement, and characterization of attosecond pulse train (APT), which are essential for probing ultrafast dynamics in atomic, molecular, and electronic systems. The focus is on the generation of APTs through interactions between femtosecond lasers and gases, as well as the extraction of temporal and dynamic information from these pulses by using advanced spectroscopic techniques such as the RABITT method.

Methods 　The experimental approach involves the use of a homebuilt femtosecond titanium sapphire regenerative amplifier to produce high-order harmonics, leading to the generation of APTs. The setup includes the homebuilt titanium sapphire chirped pulse amplifier and a collinear attosecond pulse generation and measurement beamline, which are used to conduct RABITT experiments. The process requires the interaction of femtosecond lasers with gas targets to generate high-energy photons in the extreme ultraviolet and soft X-ray spectral ranges. By optimizing the phase-matching conditions within the gas target, strong high-order harmonic signals are observed on an XUV spectrometer. The temporal information of the attosecond pulses is indirectly measured through the photoelectron spectrum produced by the interaction of attosecond pulses with femtosecond lasers. The research also employs the FROG-CRAB algorithm and the extended phase retrieval and iterative engine (ePIE) algorithm for temporally reconstructing APTs and attempts to use a genetic algorithm to extract phase information.

Results 　The study yields three sets of RABITT spectrograms, which are analyzed by using the RABITT sideband phase method to directly reconstruct APTs. Fourier transform analysis is used to extract phase differences between sidebands, offering insights into the phase differences between corresponding high-order harmonics. This method, however, provides an estimation of the phase in the center of each harmonic order, which does not fully represent the actual pulse shape. The FROG-CRAB algorithm and ePIE algorithm successfully reconstructs the attosecond pulse trains from the RABITT spectrograms, revealing similar temporal pulse train morphologies. In contrast, the genetic algorithm, despite its potential for high constraint optimization, does not yield satisfactory results, possibly due to the sensitivity of the algorithm to discrepancies between theoretical simulations and experimental data.

Conclusions 　The research concludes that achieving ideal inversion results for APTs necessitates small time delay steps and a wide scanning range in the experimental data collection process to ensure a rich dataset for inversion. The FROG-CRAB algorithm and ePIE algorithm demonstrate their effective performance in reconstructing APTs, with ePIE showing higher computational efficiency. The genetic algorithm, while offering a high degree of constraint, faces challenges and requires to be further refined. The study underscores the importance of the signal-to-noise ratio in experimental data for the accuracy of inversion results. This work provides significant guidance for future measuring electron dynamics and explaining their evolution patterns, contributing valuable experimental methods and data analysis techniques to the field of attosecond science.