Analysis of Phase-matching Conditions for Isolated Attosecond Pulses Generated by Three-color Lasers in a Gas-filled Waveguide(Invited)
The interaction between ultrafast femtosecond laser pulse and an intense gas medium gives rise to High-order Harmonic Generation(HHG),which finds crucial applications in tracking ultrafast electron dynamics,molecular orbital and structural imaging,as well as observing ultrafast processes.Moreover,HHG holds significant potential in synthesizing even shorter attosecond-level pulses.Previously,single or bichromatic coherent synthesized waveform has been commonly employed to excite HHG in the gas medium for generating attosecond pulses.With advancements in relevant technologies,the coherent synthesis of multicolor lasers has gradually matured.Utilizing synthesized multicolor waveforms,HHG can be induced within a gas-filled waveguide to generate an Isolated Attosecond Pulse(IAP).Previous studies have demonstrated that,compared to two-color and single-color waveforms,optimized three-color synthesized waveform in the gas-filled waveguide can effectively extend the cutoff frequency of HHG,enhance harmonic yield,and generate high-quality IAP.However,these studies have not indicated whether arbitrarily three-color synthesized waveforms can also generate isolated attosecond pulses within the waveguide.Specifically,whether the instantaneous phase-matching mechanism of isolated attosecond pulses is correlated with the selection of three-color waveforms remains unexplored.Furthermore,it remains uncertain whether any three-color laser waveforms within the waveguide can produce isolated attosecond pulses superior to the three-color optimized waveforms,including their pulse widths and energies.In order to answer these questions,a three-color optimized waveform is selected in this paper and it is compared with two other unoptimized waveforms.Five different sets of three-color waveforms are also compared to examine the impact factors of forming an isolated attosecond pulse,i.e.,the interplay of the single-atom response of different optical waveforms and the macroscopic phase-matching conditions.The comparison between optimized and unoptimized three-color waveforms reveals that the effective generation of IAP occurs only when a single emission peak occurring in the single-atom response is consistently maintained or when redundant emission peaks in the single-atom response are suppressed under appropriate phase-matching conditions during the propagation of HHG in the waveguide.Further comparison of different single-atom responses of three-color waveforms and macroscopic phase-matching conditions with the eventual formation of IAP confirms the aforementioned conclusion,indicating that both factors determine whether three-color waveforms can generate isolated attosecond pulses within the gas-filled waveguide,which are the single-atom response and the macroscopic phase-matching.By comparing the electric fields of three-color waveforms,it is preliminarily proved that the single-atom response depends on the synthesized electric field waveform,which dominates ionization and movement of the electron in an external field.While the macroscopic phase matching has been confirmed in other studies to be related to the propagation process of high harmonics in the waveguide.Finally,the ratio of the attosecond pulse intensity to the attosecond pulse width is used as a quantitative index to analyze the outcome of attosecond pulses.The three-color waveform consisting of the fundamental laser(1 600 nm),its second harmonic field(800 nm),and its fourth harmonic field(400 nm)is considered to be the optimal waveform for generating the IAP within the waveguide.These findings emphasize the important role of reasonably optimized light combinations in the process of producing the IAP by three-color waveforms through the gas-filled waveguide.It also shows that not any three-color waveforms can produce the IAP in the gas-filled waveguide.The compromise or the competition of the single-atom response due to the waveform and the macroscopic phase matching caused by the waveguide affects the final production of the IAP.This study provides the theoretical support for generating isolated attosecond pulse of shorter duration and higher intensity based on the technologies of the multicolor waveform synthesis and the gas-filled waveguide.On the other hand,this work also provides insights into the development of alternative"gating"schemes for generating isolated attosecond pulses,laying the theoretical foundation for experimental work with the ultimate goal of generating useful attosecond pulses for wide applications.
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