Required little help to explain Resonant (leading to Kerr, Kerr-quintic nonlinearities) and nonresonant (leading to the transitions in quantum levels) optical nonlinearities.
A nonresonat regime is when the photon energy is not enough to induce a transition to an excited state, i.e. in a transparency regime. In this regime you are basically moving electrons that tend to return to their original state very fast, in 1 fs or so. In this case you can consider that the NLO response is purely a chi^(3) process. In the resonant regime, you are inducing a transition to a higher lying excited state. this process is best described by saturable absorption, since ground state absorption is usually large. Saturable absorption (and its associated nonlinear refraction) is not a purely chi^(3) process, but can rather been seen as a process containing many nonlinear orders, or a nonlinearity that cannot be decompose into orders at all. Moreover, there is usually excited state absorption to other higher lying states, and the response time will depend on the decay mechanism of the actual states involved. Is good you take a good look at Boyd's Nonlinear Optics
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