Linear regime of time-varying double resonance in a medium with Doppler-broadened spectral lines

A time-varying regime of a double resonance in a system with a common upper level, with Doppler-broadened spectral lines, is described theoretically. The light field with the lower frequency (the signal) is assumed to be weak in comparison with that with the higher frequency (the pump). The nature of the interaction between the fields is determined substantially by the parameter n, which is the square root of the ratio of oscillator strengths in the pump and signal channels. At n > 0.5, and at sufficiently large distances, the resultant optical field is described as a superposition of the fields of a 2π pump pulse and an exponentially growing signal pulse of steady-state shape which is coupled with the pump pulse. The signal gain coefficient is described as a function of the pump frequency and the pump pulse energy by means of a probability integral of complex argument. At n ≤ 0.5, the signal pulse undergoes a pronounced dispersive spreading with increasing distance traversed, and the rate of amplification of this pulse is lower than exponential. The shaping of the signal pulse is studied as a function of the detuning from resonance in the signal and pump channels.