Initiation of superfluorescence from a sphere

Three-dimensional theory of the initiation of superfluorescence from a spherical medium with a radius much larger than the optical wavelength is developed. Time evolution of the average intensity of the superfluorescence pulse from its initial spontaneous stage to the exponential-growth limit is found. It is shown that light propagates along rays, governed by laws of geometrical optics. Amplification of light along each ray is the same as determined from the conventional one-dimensional theory. It is proved that although the average intensity is isotropic, each pulse is strongly directional.