Gaussian packets are high-frequency asymptotic space-time solutions of the wave equation. We briefly review the derivation of the evolution equations for paraxial Gaussian packets propagating in a smooth stationary non-dissipative isotropic medium. The central point of a Gaussian packet moves along the spatial central ray according to the ray tracing equations. The first derivatives of the complex-valued phase function of the Gaussian packet at the central point are determined by ray tracing, and are real-valued. The shape of a Gaussian packet is determined by the second derivatives of the complex-valued phase function. The equations for these second derivatives, derived in general Cartesian coordinates, nicely decouple in ray-centred coordinates. The 2 x 2 matrix of the second derivatives of the phase function in the plane perpendicular to the central ray describes the Gaussian beam corresponding to the Gaussian packet, and is calculated by dynamic ray tracing in the same way as for the Gaussian beam. The evolution of the remaining second derivatives of the phase function of the Gaussian packet may be expressed in terms of the complex-valued matrix of geometrical spreading of the Gaussian beam.
Gaussian packets, Gaussian beams, space-time ray theory, complex-valued phase function, inhomogeneous media.
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