Coherent propagation of an optical pulse in a fibre waveguide containing quasiresonant impurities. Adiabatic following approximation

An analysis is made of the propagation of ultrashort pulses in a fibre waveguide doped with resonant impurities. Equations describing the evolution of a pulse in the case of one-photon and two-photon resonances are derived on condition that the Rabi frequency is considerably less than the detuning from an exact resonance. The influence of impurity atoms on the parameters of a pulse and on the characteristics of its evolution (ultrashort pulse duration, 'soliton threshold', and ultrashort pulse collapse threshold) is determined. The corrections to these quantities have different signs for different types of resonance.