## 3 Simulation and Analysis  
Using the described design idea, simulation for the proposed structure was carried out using the electromagnetic simulation tool Ansys Electronics. Floquet ports, along with master-slave boundary conditions, were applied to simulate the periodic structure. Let us analyze the proposed structure for an incident horizontally polarized (x-polarized) wave. Since the unit cell is uni-diagonal symmetric (anisotropic structure), it transmits a cross-polarization component of the incident electromagnetic wave, the magnitude and phase of which can be represented as txy and \(\emptyset\)xy. These parameters txy and \(\emptyset\)xy are highly dependent on the geometry of the unit cell. Using the proposed design idea, dimension \(S\) and the size of the square patches C1 \(\times\) C1 and C2 \(\times\) C2 can be tuned in \begin{table}
\begin{tabular}{c c c c c c c c} \hline \(w2\) & C1 & C2 & \(w1\) & \(P\) & \(S\) & \(d\) & \(h\) \\ \hline
0.05 MM & 1.9 mm & 1.5 mm & 0.2 mm & 5.1 mm & 1.8 mm & 2.3 mm & 0.127 mm \\ \hline \end{tabular}
\end{table} 
Table 1: Design parameters for the proposed polarizer. Figure 1: Unit cell for the proposed structure: (**a**) perspective 3D view; (**b**) top view; (**c**) 2D array. such a way that their resonance frequencies lie within the same band. Thus, the proposed structure can transmit co-polarized (txx, \(\oslash\)xx) and cross-polarized (txy, \(\oslash\)xy) components. These components' magnitudes and phases vary over the wide range of frequencies. If their magnitudes become approximately equal--i.e., \(\mid\)txx \(\mid\)txy \(\mid\)--and their phase responses are 90\({}^{\circ}\) apart--i.e., \(\oslash\)dd = \(\oslash\)xy - \(\oslash\)xx = 2n\(\pi\)\(\pi\)\(\pi\)/2--then, n being a whole number, the outgoing wave will be a CP wave. The linear polarization to circular polarization conversion performance can be represented by an axial ratio (AR), as in Equation (1):  
\[AR=\sqrt{\frac{\left|t_{xx}\right|^{2}+\left|t_{xy}\right|^{2}+\sqrt{a}}{\left| t_{xx}\right|^{2}+\left|t_{xy}\right|^{2}-\sqrt{a}}}. \tag{1}\]  
Whereas a can be computed from Equation (2), as follows:  
\[a=\left|t_{xx}\right|^{4}+\left|t_{xy}\right|^{4}+2\left|t_{xx}\right|^{2} \left|t_{xy}\right|^{2}\cos(2\phi_{d}). \tag{2}\]  
For an ideal polarization converter, transmitted orthogonal components are exactly equal--i.e., \(\oslash\)d = \(\oslash\)xx - \(\oslash\)xy =2n\(\pi\)\(\pi\)/2--and their phase angles are exactly 90\({}^{\circ}\) apart. In this case, the outgoing transmitted wave is a perfectly circularly polarized wave, resulting in AR being 1 (0 dB). However, in practical systems, an AR value of 3 dB is acceptable for most systems. Figure 2a,b show that \(\mid\)txx \(\mid\)txy \(\mid\) from 11.05 to 16.75 GHz and 34.16 to 43.03 GHz, and the phases of the two transmitted orthogonal components are approximately \(-\)90\({}^{\circ}\) or +270\({}^{\circ}\) (within \(\pm\)15\({}^{\circ}\) variation). Therefore, the condition required for linear to circular polarization conversion is fulfilled exactly at some frequencies [24], whereas, for a range of frequencies, the transmitted components are not exactly but approximately equal (in this case, the transmitted wave is not perfectly circularly polarized but slightly elliptically polarized). Figure 2c presents the polarizer's performance in terms of axial ratio. Since the axial ratio is lower than 3 dB within 11.05-16.75 GHz and 34.16-43.03 GHz, the transmitted wave's AR condition for linear to circular polarization conversion is maintained. Moreover, from 11.05 to 16.75 GHz, the cross-polarized component (Tyx) is ahead of the co-polarized component (Txx) (phase difference > 0), resulting in a left-handed circularly polarized (LHCP) transmitted wave. Further, from the frequency range 34.16-43.03 GHz, the cross-polarized component lags behind the co-polarized component (phase difference <0); consequently, a right-handed circularly polarized (RHCP) wave is transmitted. Operational bands are highlighted as gray and dark green zones in Figure 2c.