The Carrier--Envelope Phase of Focused Few-Cycle Laser Pulses

The Gouy phase shift modulates the carrier-envelope phase of a focused few-cycle laser pulse. We investigate the variations of the carrier--envelope (CE) phase of a pulsed Gaussian beam on and off the axis by the first-order approximation and numerical calculation. The CE phase undergoes a π shift from minus infinity to infinity, and it changes fastest with distance at the focus. The variation of CE phase on propagation distance is nearly independent of pulse duration Δt when Δt is greater than 10fs and the first order approximation fits this result very well. The maximum difference of CE phase between a pulse with duration of one cycle and the result of first-order approximation is 0.09.