Quantum fluctuations and transverse effects in superfluorescence

Superfluorescence emission profiles are computed using one-way coupled Maxwell-Bloch equations. Transverse effects are included in the full three-spatial-dimension case as well as in the cylindrical-symmetry case. Initiating quantum fluctuations are approximated by a random polarization source with a completely random phase and root-mean-square tipping angle of $\frac{2}{\sqrt{N}}$, where $N$ is the number of atoms in each volume element. These fluctuations reduce the tail of the output obtained with transverse effects alone. In fact, the fluctuations in output pulse shapes encompass the Cs data of Gibbs, Vrehen, and Hikspoors. The standard deviation for the delay time is found to be (12.5±4)% for Fresnel number of 0.8 compared with the value (10±2)% recently measured by Vrehen and der Weduwe, also for Cs. Inhomogeneous-broadening effects are also included in some simulations.