  We explore the effect of pulsars, in particular those born with millisecond
periods, on their surrounding supernova ejectas. While they spin down,
fast-spinning pulsars release their tremendous rotational energy in the form of
a relativistic magnetized wind that can affect the dynamics and luminosity of
the supernova. We estimate the thermal and non thermal radiations expected from
these specific objects, concentrating at times a few years after the onset of
the explosion. We find that the bolometric light curves present a high
luminosity plateau (that can reach $10^{43-44}\,$erg/s) over a few years. An
equally bright TeV gamma-ray emission, and a milder X-ray peak (of order
$10^{40-42}\,$erg/s) could also appear a few months to a few years after the
explosion, as the pulsar wind nebula emerges, depending on the injection
parameters. The observations of these signatures by following the emission of a
large number of supernovae could have important implications for the
understanding of core-collapse supernovae and reveal the nature of the remnant
compact object.
