Phase Progression of a Radiation Field From Circular and Square Active Regions

The radiation generated by the current in an active region (ACT-R), specified by propagation phase constant β, is investigated with special interest in its phase progression (PhasProg). The ACT-R is modeled by circular and square loops, and classified into two types: a right-handed ACT-R with positive β and a left-handed ACT-R with negative β. Firstly, a circular ACT-R of a length of n guided wavelengths is formulated. It is found that, at any depression angle θ, the PhasProg with respect to azimuth angle φ is downward-sloping for the right-handed ACT-R and upward-sloping for the left-handed ACT-R. These PhasProgs have a perfectly linear change of 360n degrees (n = 1, 2) with respect to azimuth angle φ. Secondly, a square ACT-R of a length of n guided wavelengths is formulated. When k
₀
/|β| = 1 with k0 being free-space phase constant, the PhasProg is found to be downward-sloping for the right-handed ACT-R and upward-sloping for the left-handed ACT-R, with a quasi-linear change of 360n degrees (n = 1, 2) with respect to azimuth angle φ. Thirdly, the formulated numerical expressions are compared with simulated results obtained using natural and metaloop antennas, and reasonable agreement between these is observed. Fourthly, a comment is made on a singular phenomenon of the PhasProg for n = 2, with an example where k
₀
/β = 2.