Chirp compensation of water-window attosecond pulses with thin liquid sheets

Chirp control remains a key challenge for practical applications of water-window isolated attosecond pulses. In this numerical investigation, we propose thin liquid sheets as continuously tunable dispersive optical elements for chirp compensation of water-window attosecond pulses. The complex refractive indices of representative liquids are reconstructed by combining near-edge absorption data with tabulated X-ray optical constants and through the Kramers-Kronig relation. The resulting transmission and group-delay dispersion are then used to evaluate the compression of isolated attosecond pulses obtained from strong-field-approximation simulations. We show that the pre-edge dispersion of liquid water below the oxygen K-edge can compensate for the negative attochirp of long-trajectory harmonic emission in the 470-530 eV range, compressing the pulse from approximately 201 as to 67 as with a transmitted energy fraction of about 31.8%. Near the nitrogen K-edge, liquid nitrogen and liquid ammonia enable analogous compression in the 320-400 eV range, yielding pulse durations of approximately 54-56 as. These results indicate that free-standing liquid sheets can serve as flexible, self-refreshing, and thickness-tunable dispersive soft-X-ray optics for attosecond pulse compression.