  We numerically investigate the energy and arrival-time noise of ultrashort
laser pulses produced via resonant dispersive wave emission in gas-filled
hollow-core waveguides under the influence of pump-laser instability. We find
that for low pump energy, fluctuations in the pump energy are strongly
amplified. However, when the generation process is saturated, the energy of the
resonant dispersive wave can be significantly less noisy than that of the pump
pulse. This holds for a variety of generation conditions and while still
producing few-femtosecond pulses. We further find that the arrival-time jitter
of the generated pulse remains well below one femtosecond even for a
conservative estimate of the pump pulse energy noise, and that photoionisation
and plasma dynamics can lead to exceptional stability for some generation
conditions. By applying our analysis to a scaled-down system, we demonstrate
that our results hold for frequency conversion schemes based on both small-core
microstructured fibre and large-core hollow capillary fibre.
