Simultaneous stationarity and localization of linear wave packets: The importance of dimensionality and broad spectral support

In this paper we review the conditions needed for the localization and stationarity of a wave packet during propagation in a linear transparent medium. The requirements on the dimensionality and spatiotemporal frequency content for wave packets with such characteristics are discussed. In particular, we demonstrate how the localization of the stationary two-dimensional solution of the propagation equation depends on the features and shape of its spatiotemporal spectral bandwidth. The spatiotemporal properties of the one-dimensional (1D) spatial and 1D temporal beams stationarily propagating in dispersive materials are illustrated both in the normal and in the anomalous dispersion regime.