  We have studied mesoscopic Josephson junctions formed by highly $n$-doped
InAs nanowires and superconducting Ti/Pb source and drain leads. The
current-voltage properties of the system are investigated by varying
temperature and external out-of-plane magnetic field. Superconductivity in the
Pb electrodes persists up to $ \sim 7$ K and with magnetic field values up to
0.4 T. Josephson coupling at zero backgate voltage is observed up to 4.5 K and
the critical current is measured to be as high as 615 nA. The supercurrent
suppression as a function of the magnetic field reveals a diffraction pattern
that is explained by a strong magnetic flux focusing provided by the
superconducting electrodes forming the junction.
