Anomalous Behavior in the Radiation Patterns

A deep physical analysis of the classical electromagnetic problem of calculating the radiation pattern of a dipole located in a dielectric medium 1 at certain distance from the interface to a different dielectric medium 2 is presented. It is shown that an anomalous behavior in the direction of the maximum of the radiation pattern appears. This singularity is physically meaningless. This is shown by applying the Bernstein's theorem and showing that it is violated.