# Wide-Band Wide-Beam Circularly-Polarized Slot-Coupled Antenna for Wide-Angle Beam Scanning Arrays
## 4 Numerical Assessment
To better illustrate the _EM_ phenomena and interactions, Figure 6 shows the 2D plot of the magnitude of the electric field, \(|\mathbf{E}(x,\,z)|\), on a vertical surface parallel to the \((x,\,z)\)-plane and crossing the barycenter of the antenna. As it can be observed, the air coupling between the bottom (primary) and the top (secondary) element of the radiator at hand guarantees a proper excitation of the parasitic element by enabling the generation of a wide beam in the far-field region. The wide-beam behavior of the synthesized _WWCS_ antenna in a wide frequency is \"detailed\" in Figure 7a,b, where the two elevation gain patterns at \(O=4\) frequencies \(f_{o}=f_{\text{min}}+(o-1)\times\frac{(f_{\text{max}}-f_{\text{min}})}{(O-1)},\,o=1,\ldots,O\) are given. The remarkable stability, also in frequency, of the wide-beam radiation is pointed out by the plot of the _HPBW_ versus the frequency being \(HPBW(f,\,\varphi=0)\geq 169\) [deg] and \(HPBW(f,\,\varphi=90)\geq 146\) [deg] for \(f\in[f_{\text{min}},\,f_{\text{max}}]\) [Figure 7c]. To better understand the advantages of the proposed design, the behavior of the \(HPBW\) of a planar radiator obtained by removing the top layer (i.e., \(\ell_{3}\)--Figure 1) is shown as well [Figure 7c]. It turns out that the presence of the parasitic ring in the synthesized _WWCS_ radiator (Figure 1) almost doubles the \(HPBW\) at the central frequency, thus verifying its effectiveness in yielding a wide-beam behavior [Figure 7c]. Figure 6: _Numerical assessment_ (\([f_{\rm min}\), \(f_{\rm max}]=[2.3,\,2.6]\) [GHz], \(f=f_{0}=2.45\) [GHz])—2D map of the magnitude of the electric field, \(|{\bf E}(x,z)|\), in a vertical surface parallel to the \((x,z)\)-plane and crossing the center of the _WWCS_ antenna. The optimized _WWCS_ layout exhibits the desired _LHCP_ operation and is pointed out by both the co-polar, \(G_{LHCP}(f_{0},\,\theta,\,\varphi)\), and the cross-polar, \(G_{RHCP}(f_{0},\,\theta,\,\varphi)\), gain patterns in Figure 5, where it can be clearly observed that \(G(f_{0},\,\theta,\,\varphi)\approx G_{LHCP}(f_{0},\,\theta,\,\varphi)\) and \(G_{LHCP}(f_{0},\,\theta,\,\varphi)\gg G_{RHCP}(f_{0},\,\theta,\,\varphi)\) for \(0\leq\theta\leq 90\) [deg] with broadside \(AR\) and \(XPD\) equal to \(AR(f_{0},\,\theta=0,\,\varphi=0)=3.2\) [dB] and \(XPD(f_{0},\,\theta=0,\,\varphi=0)=15\) [dB], respectively. Moreover, such a good polarization purity is kept almost unaltered in the complete radiating upper semi-sphere with the exception of the elevation angles close to the antenna end-fire as illustrated by the 2D maps of \(AR(f_{0},\,\theta,\,\varphi)\) [Figure 8a] and \(XPD(f_{0},\,\theta,\,\varphi)\) [Figure 8c] as well as by the corresponding thresholded pictures aimed at highlighting the fulfilment of the design requirements [Figure 8b,d]. It is worth remarking that the slight degradation of both \(AR\) and \(XPD\) appears only in the most challenging region (i.e., \(\theta\simeq 90\) [deg]) and is possibly due to the spurious radiation by the slot along the directions of its major arms (i.e., \(\varphi=135\) [deg] and \(\varphi=315\) [deg]--Figure 8 and Figure 3). Figure 7: _Numerical Assessment_(\([f_{\rm min},\,f_{\rm max}]=[2.3,\,2.6]\) [GHz])—Plot of (**a**,**b**) the gain pattern at different frequencies in the elevation planes (**a**) \(\varphi=0\) [deg] and (**b**) \(\varphi=90\) [deg] and of (**c**) the half-power beamwidth, \(HPBW(f,\,\varphi)\) on both planes, comparing the synthesized _WWCS_ radiator with a planar layout obtained by removing the top layer (\(\ell_{3}\)—Figure 1) hosting the parasitic ring. In order to assess the excitation of a _LHCP_, the plot of the magnitude of the instantaneous surface current density, \(\left|\mathbf{J}_{surf}(x,\,y;\,t)\right|\), is reported in Figure 9 at four consecutive instants [i.e., \(t=0\) [sec]--Figure 9a; \(t=\frac{T_{0}}{8}\) [sec]--Figure 9b; \(t=\frac{T_{0}}{4}\) [sec]--Figure 9c; \(t=\frac{3}{8}T_{0}\) [sec]--Figure 9d \(T_{0}\) being the period at \(f_{0}\), \(T_{0}=\frac{1}{f_{0}}\)].