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A technique combining the finite-difference time-domain method and the imaginary-distance beam-propagation method is used to demonstrate the discontinuity-radiation concept for a dielectric rod antenna. The field near the rod is decomposed into a guided and an unguided wave. Using the two waves, the feed and terminal patterns are evaluated. It is numerically revealed that superposing the two patterns forms the radiation field of the antenna. The decomposition technique enables us to efficiently evaluate the directivity of a long rod antenna.