Exact solution of a π-pulse problem

The exact solution describing steady-state resonant pulse propagation in a two-level inverted medium is given. This steady-state pulse is often referred to as a 180° or π-pulse. No approximation of a slowly varying envelope is made, and hence the solution satisfies the second-order wave equation as well as the equations of motion of the density matrix of the system. As a result the theory is able to describe very short pulses, whose width can be of the order of the period of the optical carrier. The model for the system includes a nonresonant loss and a finite value of the transverse relaxation time T2, but neglects dispersion in the host medium. The steady-state pulse is found to be frequency modulated and asymmetric in shape.