Analytical solution of carrier-envelope phase drift of linearly chirped pulsed Gaussian beam

The propagation of the linearly chirped few-cycle pulse Gaussian beam in the free space is studied by q parameters methods. The distribution of carrier-envelope phase drift in the temporal and spatial domain is analyzed by a zero-order amplitude and first-order phase approximation independent on the chirp coefficient. The carrier-envelope phase drift undergoes a π shift from minus infinity to infinity and evolution to －π/2 on and off the axis, and the position of carrier-envelope phase drift is zero around a certain point originated from the modulation of the chirped on the relation between the phase front and the pulse front in the spatially domain．