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The standard model of femtosecond filamentation is based on phenomenologicalassumptions which suggest that the ionization-induced carriers can be treatedas free according to the Drude model, while the nonlinear response of the boundcarriers follows the all-optical Kerr effect. Here, we demonstrate that theadditional plasma generated at a multiphoton resonance dominates the saturationof the nonlinear refractive index. Since resonances are not captured by thestandard model, we propose a modification of the latter in which ionizationenhancements can be accounted for by an ionization rate obtained fromnon-Hermitian Floquet theory. In the adiabatic regime of long pulse envelopes,this augmented standard model is in excellent agreement with direct quantummechanical simulations. Since our proposal maintains the structure of thestandard model, it can be easily incorporated into existing codes of filamentsimulation.

Adiabatic Floquet model for the optical response in femtosecond filaments