Coherent soft x-ray attosecond waveform synthesis through echo-enabled harmonic generation free-electron lasers

Attosecond pulse trains (APTs) are indispensable for probing electron dynamics at their intrinsic timescales. High-harmonic generation (HHG) has long been a successful and widely used technique in producing extreme ultraviolet APTs. However, in the soft x-ray regime, HHG suffers from low conversion efficiency and lacking flexibility in the waveform and spectrum control. Here in this study, based on the waveform synthesis of the echo-enabled harmonic generation (EEHG) free-electron laser (FEL), we propose a method that can generate soft x-ray APTs with high temporal and spectral tunability. EEHG scheme is well-known in forming phase-locked high-harmonic bunching combs down to the soft x-ray regime. Here, the EEHG scheme is employed to facilitate successive FEL lasing in several different harmonic numbers and then perform the coherent waveform synthesis to generate soft x-ray APTs. Three-dimensional simulation results indicate that reproducible generation of coherent APTs in the soft x-ray regime with peak power of 3.5 GW and micropulse duration of 160 as can be achieved by five-harmonic synthesis. The micropulse duration together with the spectral components of the APTs can be adjusted easily according to the programmable high-harmonic bunching combs in the EEHG scheme. This method has the potential to establish a robust platform for attosecond sciences in the soft x-ray regime, which can enable unprecedented studies of electron dynamics in physical and chemical reactions, biological systems, and quantum materials.