Numerical simulations of an extended sample of three-level atoms with
slow dipole dephasing exhibit a superfluorescent pulse shortly after i
ncoherent pumping begins. The operator Maxwell-Bloch equations are sim
ulated by classical Langevin equations. The counterpropagating fields
are solved for in the (one-dimensional) limit of the Fresnel number ne
ar unity, with open-end boundary conditions. An initial, ''quiet'' bui
ldup of the inversion is followed by superfluorescence. Oscillation of
the populations, coherences, and fields is observed. The superfluores
cence delay time is compared with analytical predictions made in the l
inear regime. A transition to amplified spontaneous emission is found
as the pump rate is decreased.