Steady propagation of pulses in resonant media

Steady propagation of pulses of radiation in a resonant medium is studied by taking into account the loss for the case in which pulse duration is small as compared to the relaxation time of the resonant atoms. Expressions for the amplitude profile, chirped frequency, envelope velocity, propagation number and the atomic variables are evaluated in terms of the known quantities. For negligible loss, a nonchirped hyperbolic-secant 2π-pulse of arbitrary frequency and duration is obtained and the results agree with those of Eberly and Matulic. For nonzero loss, chirped 2π-pulses of arbitrary frequency and duration is obtained and a small assymetry which depends on the pulse duration and detuning. If the medium is inverted, one can also get exactly resonant chirped π-pulses of duration greater than a critical value and having an arbitrary small asymmetry. The expression for the pulse area in this case is different from that given in the literature. Exactly resonant nonchirped hyperbolic-secant π-pulses of duration equal to this critical value and having the usual expression for pulse area obtained by Arecchi and Bonifacio and by Lamb are a special case of the results obtained by taking asymmetry equal to zero and pulse duration equal to the critical value. For π-pulses the product of the envelope and mean phase velocities is almost equal to the square of the velocity of nonresonant light. Consideration of nonlinear Kerr effect leads to an extra term in chirping. (author)