Non-linear resonance frequency shifts and saturation effects by oscillating and static applied fields in multi-level systems

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A previously developed exact semiclassical method is used to evaluate multi-photon spectra and Floquet characteristic exponents (dressed-atom energies) for several multi-level systems interacting with both strong oscillating and static fields under varying degrees of saturation. The usefulness of characteristic exponent plots in extracting the physically significant features of the spectrum, without the necessity of evaluating portions of the complete spectrum, is demonstrated for a number of model three-level systems which are not directly amenable to study by the often used rotating-wave approximation. The effect of neighbouring non-resonant states on two-photon resonance profiles is also discussed using three to six level systems (H and Na atoms) as models.