Superradiant amplification in an optically dense gas

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We solve numerically the coupled integro-differential Maxwell-Bloch equations describing the amplification of a pulse in an inverted pressure broadened resonant medium, without assuming the Slowly Varying Envelope Approximation in space. Our algorithm incorporates the effects of the backward wave and that of the Local Field Corrections. We show that the superradiant regime sets on for much smaller values of αL than that predicted by the Forward Wave Approximation, and that it is possible to convert most of the energy stored in the atomic system into transmitted and reflected bursts whose duration are substantially shorter than either the dephasing or relaxation times of the atomic system, for sample lengths that are only few wavelengths long. Furthermore, we show that in the superradiant regime, except for sample lengths that are in the neighborhood of an integer multiple of the half-wavelength, the atomic polarizability possesses definite spatial symmetry with respect to the midpoint of the sample, resulting there in equal energy release for the transmitted and reflected signals. The transition domain between two consecutive opposite spatial symmetry sectors is manifested through unequal intensity for the transmitted and reflected bursts and in different frequency shifts in the spectral distributions of the two output signals.