Light bullets from femtosecond filamentation

A model for the propagation of femtosecond laser pulses in transparent media and the formation of light bullets is proposed. This model enable us to generalize Marburger's formula for the position of the nonlinear focus of the beam in the presence of delayed Kerr effect. It is shown that an instantaneous higher-order saturation tuned to mimic the defocusing effect due to the plasma generated by multiphoton ionization does not properly represent the dynamics of femtosecond filamentation as it violates causality and artificially promotes long distance propagation in the form of periodic oscillations around a spatial soliton. A causal description of multiphoton ionization leads to an extended moving focus model from which the formation of a synchronized structure exhibiting several focusing-defocusing cycles before eventual diffraction can be inferred.