Parametric light bullets: a multiscale analysis

We generalize to a (3 + 1)-dimensional version the known model equations describing the evolution of the modulation of two short and localized pulses, fundamental and second harmonic, propagating together in a bulk uniaxial crystal with nonvanishing second-order susceptibility chi((2)) and interacting The derivation is performed in a rigorous way that allows the determination of the physical conditions under which the model is valid: the order of magnitude of the walk-off, phase mismatch and anisotropy must have determined values. These conditions are made explicit for a few particular materials, showing that parametric light bullets exist for femtosecond pulses only, and that the problem is not scale invariant. It is also shown that the phase mismatch term can be completely removed from the model.