We have formulated the quantum theory of formation of the superfluorescence pulse from a pencil-like amplifier. The coupled system of the linearized Bloch equations for two-level atoms and the three-dimensional wave equation for the electric field has been solved in the geometrical-optics approximation for Fresnel numbers F ≥ 1. Several properties of the superfluorescence pulse are discussed. The spatial coherence function of the pulse has been found as a function of the Fresnel number. This function provides a precise formulation of the concept of "diffraction modes." The delay-time distribution function for various Fresnel numbers has been found. The results are consistent with experimental data and numerical simulations.
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Mostowski et al. (1984) studied this question.
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