Programmable spectral phase transfer to the ultraviolet by gas-filled-fibre four-wave mixing
Programmable shaping of femtosecond ultraviolet (UV) pulses is still much less flexible than at visible and near-infrared wavelengths, mainly because direct UV modulators remain limited in bandwidth, throughput and damage threshold. Here we show that dispersive four-wave mixing (DFWM) in a gas-filled hollow-cappillary fibre (HCF) can transfer programmed spectral phase from the near infrared (NIR) to the UV without relying a narrowband pump. A shaped NIR signal at 1032 nm and a chirped 516-nm pump generate a 344-nm idler, which is characterized with transient-grating frequency-resolved optical gating (TG FROG). As a benchmark, second-order dispersion (SOD) applied to the signal is quantitatively reproduced in the idler. We then demonstrate the transfer of two nontrivial phase patterns: a localized nominal {\pi}-step and a moderate sinusoidal modulation. In the {\pi}-step case, a step imposed on the long-wavelength side of the signal appears on the short-wavelength side of the idler, consistent with the 2*pump - 1*signal mixing relation. In the sinusoidal case, the periodic phase produces a split temporal waveform in both signal and idler. These results show that gas-filled HCF DFWM can act as a practical spectral-phase transducer from the NIR to the UV, while also revealing a trade-off between conversion efficiency and phase-transfer fidelity.