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 Floquet 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-independent Floquet-Liouville super-matrix eigenvalue problem. The method is illustrated by a study of the multiphoton resonance fluorescence spectra of two-level systems.