Initiation of superfluorescence in a large sphere

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Abstract
We investigate the early stages of superfluorescent emission from a large spherical volume containing atoms all initially in the same excited state. The electric polarization fluctuations that characterize a fully inverted atomic system, and which trigger superfluorescence, are found to cause field amplification only in vector spherical-harmonic multipole modes of limited order. The field and polarization fluctuations obey Gaussian statistics, a result that has been used to calculate the angular correlation of intensities radiated in any two directions. Components of the electric field radiated in two arbitrary directions and circularly polarized in opposite senses are found to be uncorrelated. They thus have no intensity-intensity or higher-order correlations. Field components which are circularly polarized in the same sense, however, are shown to be correlated over an angular range that is proportional to the ratio of the wavelength to the radius of the sphere.