Formation of a signal pulse as a result of a transient double resonance in a medium with a strong inhomogeneous broadening of spectral transitions

A theoretical study is made of a linear, in respect of the field of lower frequency (signal), transient double resonance in a system with a shared upper level. The radiation of higher frequency (pump) is selected to be a 2π pulse which is spectrally much narrower than the contour of the Doppler scatter of the frequencies of a transition which is in resonance with this pulse. A condition is found for the appearance of a signal pulse of constant profile moving at the velocity of the pump pulse and growing exponentially in the course of its propagation into a resonant medium. It is shown that in general the energy of a signal pulse depends nonmonotonically on the energy of the pump pulse: there is an optimal value of the pump energy at which the rate of rise of the signal energy is maximal. A study is made of the efficiency of a double resonance on the detuning from a resonance in the pump and signal channels.