Energy density characterization of complex ultrashort laser pulses

We introduce the concept of energy density flux as a characterization tool for the propagation of ultrashort laser pulses with spatio-temporal coupling. This energy density flux is calculated in the local frame moving at the velocity of the envelope of the wave packet under examination, and it can also be extended to the case of nonlinear propagation. We perform a detailed numerical study of the energy density flux in the particular case of conical waves. We also experimentally characterize the energy density flux for the cases of Bessel-X pulse in linear propagation and complex ultrashort pulses generated by filamentation in a nonlinear Kerr medium.