Photoelectron Momentum Spectra Of H And H₂⁺ By The Extreme Ultraviolet Attosecond Pulses

In recent years,the generation and application of ultra-short and ultrafast pulsed lasers have become a prominent frontier in physics and optical research with significant potential for various applications.As a result,countries worldwide are actively developing related light sources,such as ELI in Europe,Dalian Light Source,and Shanghai Light Source in China.By utilizing ultrafast and powerful pulsed lasers to irradiate matter with high coherence,we can gain in-depth insights into numerous high-order nonlinear phenomena.The photoelectric effect,a fundamental phenomenon in modern physics,is of particular importance,and we can study the photoelectron spectrum by combining different light sources to examine the ionized photoelectron momentum spectrum of hydrogen atoms and hydrogen molecule ions and their governing principles.This study can be divided into three main aspects:By solving the time-dependent Schr?dinger equation,we investigated the momentum spectrum of linearly polarized light acting on hydrogen molecular ions.Firstly,we analyzed the photoelectron momentum distribution of linear laser pulses acting parallel and perpendicular to the molecular axis of hydrogen molecules ions with internuclear distance of 2 a.u.The results showed a six-petal distribution parallel to the molecular axis and a two-petal distribution perpendicular to the molecular axis.Secondly,we explored the influence of micro declination angle on the distribution of the photoelectron ionization momentum spectrum.We found that when the laser polarization direction and the hydrogen ion molecular axis angle are 4°,the momentum spectrum changes significantly.Moreover,when the angle between the linearly polarized laser and the hydrogen molecule ion with internuclear distance of 2a.u.is 45°,the momentum spectrum shows a two-petal distribution.However,when the molecular internuclear distance is 4 a.u.,and the linear polarization laser pulse acts parallel and perpendicular to the momentum distribution of hydrogen molecular ions,the momentum distribution map has no significant change,and the alignment sensitivity is poor.We introduce a low-order perturbation theory model to divide the direction of the total electric field into x and y directions,while considering the relationship between the internuclear distance and the ionization interface,when the internuclear distance is 2 a.u.,the ionization section in the y direction is much larger than the ionization section in the x direction,so when it is offset by a small angle,the momentum spectrum changes significantly.We investigated the effects of a set of counter-circular polarization laser pulses acting on hydrogen molecule ions.Specifically,we studied the momentum distribution of hydrogen molecules with internuclear distance 2 a.u.under the influence of time delay and carrier envelope phase.Our results showed that increasing the time delay in one optical period resulted in an increase in the electric field in the x direction,which was greater than the field in the y direction.However,due to the significantly larger ionization interface in the y direction than in the x direction,the momentum distribution was biased towards the y direction.We then further adjusted the time delay of the two pulses to a very large time,which could be approximated as the electric fields in the x and y directions being equal.This resulted in a double two-petal distribution in the momentum distribution.When the time delay becomes very large,it is equivalent to two independent circular pulses acting on hydrogen molecular ions before and after,which presents as a double two-petal distribution.We conducted a study on the photoelectron momentum distribution of a pair of chirped and count-circular polarized light acting on hydrogen atoms.Our results showed that when time delay is 2 o.c.optical cycles and the wavelength is 30 nm,the photoelectron momentum distribution appears as a vortex structure.Furthermore,when we added coaxial linear chirping to the laser pulses,the resulting phase difference remained stable,and the structural change was not significant.However,when we took two count-circular pulses with opposite linear chirp parameters,the vortex structure was significantly different.Specifically,when one pulse had a positive chirp parameter and the other had a negative chirp parameter,the phase difference of the low-frequency part of the spectrum was large,and the phase difference of the high-frequency part was small,resulting in no significant change in the vortex structure.However,when one pulse had a negative linear chirp parameter,and the other pulse had a positive negative chirping parameter,the phase difference of the low-frequency part of the spectrum was small,and the phase difference of the high-frequency part was large,resulting in a significant change in the vortex structure.