Basic concepts of three-dimensional wave packets are applied to the description of transverse effects on the propagation of ultrashort (femtosecond) pulses. The frequency-dependent nature of diffraction acts as a kind of dispersion that modifies the pulse front surface, its group velocity, the envelope form, and the carrier frequency. If the diffracted field in the monochromatic case is known, these changes can be straightforwardly quantified. Finding the propagated pulsed beam field reduces to a well-known and simpler problem of one-dimensional pulse propagation with group velocity dispersion. The method is applied to pulsed Gaussian beams and pulsed Bessel beams. Anomalous pulse front behavior, including superluminality in pulsed Gaussian beams is found. The carrier phase at any point of space is calculated.

• Received 16 September 2001

DOI:https://doi.org/10.1103/PhysRevE.65.026606