  We demonstrate a fibre-based approach that generates mid-infrared femtosecond
pulses in the 3-4 {\mu}m spectral region with microjoule-level single pulse
energy. This is realised in a piece of gas-filled antiresonant hollow-core
fibre that is pumped by a two-micron light source. A rapid variation of the
dispersion near a structural resonance of the fibre creates a phase-matching
point in the mid-infrared, which mediates the frequency-down conversion. We
generate femtosecond pulses centred at 3.16 {\mu}m wavelength with the pulse
energy of more than 1 {\mu}J, achieving the conversion efficiency as high as
9.4%. The wavelength of the radiation is determined solely by the dielectric
wall thickness of the cladding elements, while the yield is subject to other
experimental parameters. This, combined with high power-handling capability of
hollow-core fibres, makes it possible to power scale the mid-infrared output by
either increasing the pulse energy or repetition rate of the pump. The
technique presents a new pathway to build an all-fibre-based mid-infrared
supercontinuum source, which promises to be a powerful new tool for ultrahigh
sensitivity molecular spectroscopy.
