We suggest a technique to amplify a train of attosecond pulses, produced by high-harmonic generation (HHG) of an infrared (IR) laser field, in an active medium of a plasma-based X-ray laser. This technique is based on modulation of transition frequency of the X-ray laser by the same IR field, as used to generate the harmonics, via linear Stark effect, which results in redistribution of the resonant gain and simultaneous amplification of a wide set of harmonics in the incident field. We propose an experimental implementation of the suggested technique in active medium of C 5+ ions at wavelength 3.4 nm in the "water window" range and show the possibility to amplify by two orders of magnitude a train of attosecond pulses with pulse duration down to 100 as. We show also a possibility to isolate a single attosecond pulse from the incident attosecond pulse train during its amplification in optically deep modulated medium.
Abstract:In this supplemental material we derive an analytical solution describing an amplification of the highharmonic field in an active medium of a plasma-based X-ray laser in the linear regime within the three-level medium model and constant population inversion approximation. We provide also more detailed numerical study of an amplification process in both linear and nonlinear regimes taking into account a saturation effect within the fivelevel medium model.