  Spectral broadening of ultrashort laser pulses is simultaneously described by
either self-phase modulation (SPM) or four-wave mixing (FWM). The latter
implies the instantaneous conservation of both the photon number and energy,
while the former describes a time-dependent frequency shift, implying a
violation of the energy conservation if the number of photons is to be
conserved in each time slice. We resolve this paradox by considering the
transient energy storage in the propagation medium, that can be calculated in
the SPM formalism via the dephasing between the incident pulse and the medium
polarization leading to an effective imaginary part in the third-order
susceptibility. In parallel, considering the temporal variation of the incident
intensity in FWM offsets the instantaneous frequency.
