Four-wave mixing of quasi-monochromatic waves and few-cycle pulses

Four-wave coherent mixing models for two quasi-monochromatic pumping fields and pulses of a two-component Stokes field with an elliptic polarization and a duration on the order of the period of oscillations have been derived for a two-level medium with a forbidden dipole transition. It is shown that, under the unidirectional wave propagation conditions and in the absence of depletion of pumping, the system of Maxwell-Bloch equations can be reduced to a new completely integrable system of equations. Nonsoliton radiation dynamics of generation of Stokes field pulses is studied in the framework of the integrable reduction of this model. The apparatus for the inverse problem algorithm corresponding to the solvable problem is developed. An approximate asymptotic expression for the leading front of the pulse packet being generated is obtained for various initial and boundary conditions. The application of these results for describing parametric processes involving various types of waves is discussed.