Spectrum and wave shape of intense laser pulse propagating through Raman active medium

Results of the analytical solution of non-linear equations describing the propagation of an ultra-short intense laser pulse through a Raman-active medium are presented. The pulse passing through the medium generates a large number of high-order harmonics if the pulse intensity is close to some thresholds. The medium is described by the density matrix for two-level systems. The laser pulse duration was much shorter than both the period of oscillation and the relaxation times of an oscillator. Using this solution, the spectrum of such a pulse was expressed in terms of integrals of the initial field. The solution allows the harmonic spectrum dependence on the pulse intensity and effects of propagation to be investigated. Estimations of the conversion efficiency of the initial pumping frequency into high-order harmonics are given. The evolution of the pulse shape as a function of the distance passed by the pulse through the media was investigated.