  We investigate the stimulated emission of superradiant atoms coupled to a
waveguide induced by a coherent-state photon pulse. We provide an analytical
result when a short $\pi$ pulse is incident, which shows that the atoms emit
photons coherently into the output pulse, which remains a coherent state in the
short pulse limit. An incident pulse is amplified in phase-preserving manner,
where noise is added almost entirely in the phase direction in phase space.
This property improves the ratio of intensity signal to noise after the
amplification for sufficiently short pulses. This is a unique feature different
from general phase-preserving linear amplifiers, where the signal-to-noise
ratio deteriorates in the amplification process. We also discuss the dependence
of the photon-emission probability on pulse parameters, such as the pulse area
and the duration.
