  On the basis of a quantum microscopic approach we study the dynamics of the
afterglow of a dilute Gaussian atomic ensemble excited by pulsed radiation.
Taking into account the vector nature of the electromagnetic field we analyze
in detail the angular and polarization distribution of single-photon
superradiance of such an ensemble. The dependence of the angular distribution
of superradiance on the length of the pulse and its carrier frequency as well
as on the size and the shape of the atomic clouds is studied. We show that
there is substantial dependence of the superradiant emission on the
polarization and the direction of fluorescence. We observe essential
peculiarities of superradiance in the region of the forward diffraction zone
and in the area of the coherent backscattering cone. We demonstrate that there
are directions for which the rate of fluorescence is several times more than
the decay rate of the timed-Dicke state. We show also that single-photon
superradiance can be excited by incoherent excitation when atomic polarization
in the ensemble is absent. Besides a quantum microscopic approach, we analyze
single-photon superradiance on the basis of the theory of incoherent multiple
scattering in optically thick media (random walk theory). In the case of very
short resonant and long nonresonant pulses we derive simple analytical
expressions for the decay rate of single-photon superradiance for incoherent
fluorescence in an arbitrary direction.
