Kinetic theory of photon acceleration: Time-dependent spectral evolution of ultrashort laser pulses

We investigate the evolution of the space- and time-dependent spectrum of an ultrashort laser pulse in the presence of relativistic plasma waves. A kinetic description of the laser pulse is introduced, generalizing the classical concept of the number of photons. The propagation equation for the generalized photon density is derived. The spectral deformation induced by a relativistic plasma perturbation in the laser pulse is also calculated. We also propose a new diagnostic technique for the electron density gradient, based on the analysis of the induced chirp in ultrashort laser pulses.