An angular-spectrum representation is obtained of the electromagnetic field in a homogeneous medium, arising from any prescribed motion of a charged particle in a plane. The field on either side of the plane of motion is expressed as a superposition of monochromatic waves in general, homogeneous as well as evanescent ones. The homogeneous waves are propagated away from the plane of motion of the particle, the evanescent ones decay exponentially with increasing distance from this plane. For each plane wave, the appropriate dispersion relation is satisfied and hence the representation is a true mode expansion in each of the two half-spaces. The results are illustrated by considering the field of a uniformly moving charged particle. In free space, the Coulomb field of the particle, as would be observed in a fixed laboratory system, is shown to arise from the superposition of evanescent waves to which the moving particle gives rise. The main formulas relating to the Čerenkov field both above and below threshold are also obtained, as an illustration of this technique.
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