Nonlinear propagation of strong multi-mode fields

We develop a strict theory of nonlinear propagation of few interacting strong light beams. The key idea of our approach is a self-consistent solution of the nonlinear wave equation and the density matrix equations of the material beyond the rotatory wave approximation. We assume a Fourier expansion of the density matrix which goes beyond the conventional Taylor expansions of the polarization over the field amplitudes which is inadequate for the field strengths that we are interested in. Two qualitatively different situations are considered, with and without phase matching. Unlike in our previous paper (Baev et al 2003 J. Opt. Soc. Am. B at press) devoted to the three-photon (TP) absorption induced upconverted lasing, we obtain here a strict solution for the nonlinear interaction between different light beams. The general theory is applied to a numerical study of the role of saturation in TP photoabsorption by an organic chromophore in solution.