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

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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 △t when △t 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.
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