Characteristics of formation of a signal pulse in the field of a short high-power pump pulse for a double resonance in a system with a common upper level

A theoretical investigation is made of an essentially nonstationary double resonance excited in a system with a common upper level in the field of a 2π pump pulse and of constant low-intensity signal radiation. The conditions are found for the formation of an exponentially amplified signal pulse of asymptotically constant profile moving at the velocity of the pump pulse. A study is made of the relationship between the signal pulse parameters and the parameters of the medium and of the pump pulse. It is shown that competition between the local and wave transient processes is responsible for the existence of an optimal pump pulse energy which depends on the values of the detuning from a resonance in the pump and signal channels. When this optimal energy is exceeded, the output signal pulse energy decreases. It is demonstrated that when the initial values of the detuning in the two channels are unequal the formation of a signal pulse is accompanied by pulling of the signal frequency to the value which satisfies the conditions of equality of the detuning values. During the early stages of formation of the signal pulse this results in splitting into a train of several pulses which are shorter than the pump pulse.