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

Abstract

The radiation generated by the current in an active region (ACT-R), specified by propagation phase constant $\beta $ , 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 $\beta $ and a left-handed ACT-R with negative $\beta $ . Firstly, a circular ACT-R of a length of $n$ guided wavelengths is formulated. It is found that, at any depression angle $\theta $ , the PhasProg with respect to azimuth angle $\phi $ 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 $\phi $ . Secondly, a square ACT-R of a length of $n$ guided wavelengths is formulated. When $k_{0}/\vert \beta \vert =1$ with $k_{0}$ 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 $\phi $ . 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 $k_{0}/\beta =2$ .