Influence of transverse inhomogeneity of the radiation field and of the active medium on the dynamics of superradiance from an extended system

A study is made of the dynamics of a superradiance pulse in a transversely inhomogeneous active medium inside a tubular waveguide with dielectric walls. The problem is solved numerically in the approximation of a given field profile by expanding the radiation field in terms of the normal modes of the waveguide and the polarization and inversion of the medium in terms of basis functions dependent on the transverse coordinates. It is shown that an inhomogeneous transverse distribution of the field and of the initial inversion can suppress the appearance of oscillatory replicas (superradiant "ringing") of the main superradiance field and also can result in incomplete utilization of the energy stored in the active medium because of coherent dephasing of the polarization of the medium in different parts of a transverse cross section of the waveguide.