Generation of 0π pulses from a zero-area pulse in coherent pulse propagation

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Abstract
The generation of 0π pulses in coherent pulse propagation is studied for a simple initial pulse profile consisting of two separated square pulses with one inverted to give a total pulse area of zero. When the two pulses are close together, it is found that the threshold for lossless propagation occurs at an absolute area of 2½π. But as the pulses become farther separated, one finds two thresholds. The first one occurs for an absolute area of about π and the second one at about 2π. Although one can have lossless propagation occurring for the absolute area between π and 2π, it is accomplished only by generating very low amplitude 0π pulses. It is only after the second threshold, 2π, is achieved that one can expect to find moderate to large amplitude 0π pulses, and these may be accompanied by several low amplitude 0π pulses.