Shape evolution of a light pulse in a linear birefringent medium

The spreading of a three-dimensional quasi-monochromatic progressive directional wave packet (such as a laser pulse) propagating freely in a linear and transparent birefringent medium is described geometrically by means of the ellipsoid representative of the pulse's second-order moments. The medium is characterized by a second-order expansion of its dispersion relation omega(K) about the mean wave vector Km of the pulse, i.e., by its Hessian matrix (H(Km)omega), which plays two important roles. Then, for some elements of(H(Km)omega), practical expressions are provided that are related to the curvature and dispersion properties of the normal surface of the medium. Then cases in which these properties determine completely the asymptotic transverse or axial spreadings of the wave packet are specified, and the results of an experiment are discussed.