Spatial evolution of short laser pulses under coherent population trapping

The spatial and temporal evolution is studied of two powerful short laser pulses having different wavelengths and interacting with a dense three-level Λ-type optical medium under coherent population trapping. The general case of unequal oscillator strengths of the transitions is considered. The durations of the probe pulse and the coupling pulse $T_{1,2}\hspace{0.5em}{(T}_2>T_1)$ are assumed to be shorter than any of the relevant atomic relaxation times. We propose analytical and numerical solutions of a self-consistent set of coupled Schrödinger equations and reduced wave equations in the adiabatic limit taking account of the first nonadiabatic correction. The adiabaticity criterion is also discussed taking account of pulse propagation. The dynamics of propagation is found to be strongly dependent on the ratio of the transition oscillator strengths. It is shown that the envelopes of the pulses slightly change throughout the medium length in the initial stage of propagation. This distance can be large compared to the one-photon resonant absorption length. Eventually, the probe pulse is completely reemitted into the coupling pulse during propagation. An effect of localization of the atomic coherence was observed similar to the one predicted by Fleischhauer and Lukin [Phys. Rev. Lett. 84, 5094 (2000)].