Coherent-optical-pulse propagation as an inverse problem

Various coherent-optical-pulse profiles are known to exhibit lossless propagation during transmission through a resonant atomic medium. It is shown that the requirement of lossless propagation provides asymptotic information that is sufficient to determine these profiles by the inverse method. Pulse profiles are obtained as solutions to the Marchenko equation. The analysis is applied explicitly to the propagation of 2, 4, and 0 pulses in an inhomogeneously broadened medium.