I. Introduction
Besides being the operating principle of optical fibers, the total internal reflection (TIR) has numerous other applications at optical frequencies such as in microscopes [1] and in spatial filtering of light [2]. Although less popular than at optical frequencies, TIR also has applications at microwave frequencies. Dielectric waveguides [3], dielectric resonators [4], and long distance communication based on ionospherical TIR [5] are among a host of important applications. The TIR law, which is a special case of Snell’s law, can be extracted from classical electromagnetic theory quite easily. Based on TIR, if the incident angle of a TM wave on a boundary is larger than the critical angle, the wave will be totally reflected. This is similar to the case in which a TM wave impinges on a PEC boundary. However, the two cases are different in the phase shift of the reflected electric field, as clarified in Fig. 1. Reflection from a PEC boundary preserves the phase of the magnetic component of a TM wave. In contrast, TIR adds 180° phase change to the magnetic component of a TM wave. This phase shift difference is crucial to the antenna design described here.