Phase of Radiation From a Square Principal Source Region

The radiation from a square-shaped principal radiation source ring (Sq-PriSoR) is simulated using a metaloop antenna supporting a traveling wave current with dual propagation phase constants (
$\beta < 0$
and
$\beta > 0$
). It is found that the phase progression as a function of azimuth angle
$\phi$
does not change in a perfectly linear fashion. It is also found that the phase progression singularly behaves when the Sq-PriSoR has a loop length of two guided wavelengths, depending on
$\beta/k_{0}$
with
$k_{0}$
being the free-space phase constant. As an example, the phase progression for
$\beta/k_{0}=+0.5$
is demonstrated; the gradient of the phase progression is changed at specific depression angle
$\theta_{\Gamma}$
.