Influence of relaxation on propagation, storage, and retrieving of light pulses in a medium with electromagnetically induced transparency

By solving the self-consistent system of Maxwell and density-matrix equations in the case where the time of relaxations to the ground state is much shorter than the pulse duration we derive an analytical solution for the probe pulse propagation. We obtain an excellent consistency of our analytical solution with direct numerical integration. We investigate the asymptotic behavior of analytical solution and show that under certain conditions it passes to the well-known dark-state polariton propagation regime. We analyzed the dynamics of propagation and, in particular, explain the fact that in the well-known experiments only fractions of pulses were stored.