Reshaping of femtosecond pulses by the Gouy phase shift

It is shown that;because of the phase anomaly a femtosecond pulse propagate s on the optical axis with a velocity greater than c in the vicinity of the focus not only for large but also small values of the Fresnel number. The group velocity is calculated and its physical meaning discussed. Analytical expressions are derived for the electric field. The causality of the syste m is proved. The mechanism of the superluminality is a reshaping process ca used by the interference. Contrary to other superluminal phenomena, the sup erluminal propagation occurs in a classically not forbidden region. [S1063- 651X(99)11108-5].