Generation of Intense Low-Divergence Isolated Soft-X-Ray Attosecond Pulses in a Gas-Filled Waveguide Using Three-Color Synthesized Laser Pulses

Isolated attosecond pulses (IAPs) in the soft-x-ray (SXR) region have been successfully produced via high-order harmonic generation in a gas medium at several laboratories, but pulse energies are much lower compared to the IAPs in the extreme ultraviolet. Here, we show that in a gas-filled hollow waveguide, an efficient gating method using a few-cycle three-color synthesizer is able to generate stronger SXR IAPs. We show that an 104-as IAP in the SXR region (central energy of 210 eV) with a higher pulse energy (0.9 nJ) and a lower divergence (within 1.5 mrad) can be generated with a three-color laser beam for input pulse energy at 0.62 mJ, under the condition of optimal gas pressure and waveguide length. The enhancement of the IAP is attributed to favorable phase matching of SXR high harmonics caused by the evolution of the three-color waveform during its propagation in the waveguide, which can be understood by analyzing the time shift of the waveform due to the interplay of the waveguide mode, atomic dispersion, and plasma dispersion. We check that the gating method is quite robust with respect to the phase jitter in the waveform. The advantage of this method is further demonstrated by comparing the generation of SXR high harmonics and attosecond pulses with two other schemes: the three-color waveform in a gas cell and a previously optimized two-color waveform in a gas-filled waveguide.