Floquet-Liouville super-matrix approach for multiphoton non-linear optical processes in intense laser fields

A practical non-perturbative approach is presented for the treatment of multiphoton non-linear optical processes in intense monochromatic or polychromatic field. By extending the many-mode Floques theory recently developed by the authors, the time-dependent Liouville equation for the density matrix of atoms or molecules undergoing radiative and/or collisional relaxations can be transformed into an equivalent time-dependent Floquet-Liouville super matrix eigenvalue problem. The method is illustrated by a study of the multiphoton resonance fluorescence spectra of the two-level systems.