The asymptotic theory of eikonal approximation permits electromagnetic fields to be described locally in terms of plane waves and the trajectory to be described as space–time rays. Properties of these space–time rays in a dispersive medium can be studied through the effective index of refraction defined by the higher-order space–time eikonal equation. From the analysis it is shown that the diffraction effects due to the finite size of the beam and the dispersion effects due to the finite pulse width can be treated in a unified manner in the generalized space–time eikonal equation. The space–time rays of a Gaussian pulse in a dispersive medium can be readily solved analytically and shown to provide results similar to those obtained by the Fourier transformation method.
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