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The motion of a wave packet in a nonuniform medium is discussed. It is found that the wave-packet motion, obtained by WKB method, is the same as one obtained by geometrical optics. The wave packet, in general, undulates around the axis. As the direction of the beam and the local refractive index change as the packet travels, the axial velocity component of the beam is modulated. This seems to be in contradiction to the constancy of the group velocity. This apparent contradiction is eliminated by examining the shape of a wave packet composed of a single transverse mode, which turns out to be warped. As an example, a medium is assumed in which the dielectric constant decreases quadratically, away from some spatial axis. The group velocity of several undulating packets in the medium is very close to that of a straight ray. Numerical calculation is presented.
Kawakami et al. (1967) studied this question.