Abstract
The resonant propagation of an optical pulse in a two-photon absorber with a coherent initial excitation of the medium may lead to a pulse steepening growing exponentially in space. In addition another example is given wherein the steepening is followed by flattening. These results are new although, principally, they could be obtained from the general solution of the respective Goursat problem of an amplitude-modulated initial wave (H Steudel and D J Kaup 1996 J. Mod. Opt. 43 1851). In addition, we also give a simple theorem whereby it is demonstrated that the spatial derivative of the phase of the electric field will always be bounded. Furthermore, it is also shown that there can be certain critical points at which the atomic state, as well as the electric field, can become stationary in time and the spatial direction.
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