Theory of propagation of ultrashort light pulses in a threelevel medium

The results are given of a theoretical investigation of the interaction between two ultrashort pulses J₁ and J₂ of frequencies ω₃₁ and ω₂₁ with a three-level amplifying medium. It is assumed that the signal J₁ of frequency ω₃₁ is a steady-state π pulse and the signal J₂ is weak so that its influence on the level populations can be ignored. The case when the signal J₂ has a steady-state amplitude profile and an exponential gain is considered. The analysis is made ignoring the group delay effects and also allowing for the mismatch of the group velocities of the signals. The results obtained can be used in studies of the amplification of ultrashort pulses in molecular media such as organic dyes or CO₂ molecules.