FLOQUET-LIOUVILLE SUPER-MATRIX APPROACH FOR MULTIPHOTON NON-LINEAR OPTICAL PROCESSES IN INTENSE LASER FIELDS

A practical non-penurbative approach is presented for the treatment 01 multiphoton non-linear optical prcxerses in intense monochromatic or polychromatic field. By extending the many-mode Floque ~ 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 wwsronned into an equivalent rime-independenr Floquet-Liouville super-matrix eigenvalue problem. The method is illustrated by a study of the mulfiphoron resonance fluorescence spectra of two-level systems. The study of non-linear optical processes such as multiphoton dissociation of molecules, resonance fluorescence, Raman scattering, and wave mixings, etc. is a subject of much current interest [1,2] both theoretically and experi-ment&y. At lower fields, perturbative and diagrammatic methods [2] are often used for non-resonant phenomena, whereas the rotating wave approximation (RWA) is most commonly adopted for near resonant processes [2,3]. The semiclassical Floquet approaches based on the SchrXnger equation, while providing non-perturbative means for the studies of multiphoton ionization, excitation, and dissociation _ processes at high fields [4], cannot be ap-plied to processes undergoing relaxations due to radiative decays and collision dampings, etc. In this Letter we ad-vance a general non-perturbative semiclassical treabnent of the Liouville equation (allowing for relaxation mecha-nisms) for the density matrix operator of atomic or molecular systems exposed to intense monochromatic or poly-chromatic fields. By extending the many-mode Floquet theory (MMFT) recently developed [S], the time-depen