Can optical phase conjugators produce a very short conjugate pulse

In studying the transient behavior of phase conjugation via four-wave mixing, it has been found that very short probe pulses invariably produce considerably broadened conjugate pulses unless the conjugator is inordinately short. It is sought here to determine whether a short conjugate pulse might be produced by judicious programming of the probe. It is found that the probe can indeed be tailored to produce an arbitrarily short conjugate signal and that, if the conjugating medium exhibits linear absorption, then the total energy in the probe signal is finite. The probe programming required can be determined by numerical evaluation of a Fourier transform.