## 6 Performance Analysis  
For design considerations, the effect of different dimensions of the unit cell on the performance of the dual-band polarization converter was analyzed. Figure 11 shows the plot of the axial ratio for the proposed converter for different values of \(p\) keeping all the other parameters constant. It is observed that with the increase in \(p\) from 49.9 \(\upmu\)m to 51.9 \(\upmu\)m, the lower end of the first frequency band remains almost constant while higher-end shifts towards the right cause the bandwidth of the first band to increase. In the second band, increasing \(p\) has greater impact: it shifts the lower frequency towards the left while the higher-end remains almost stable with some exceptions. Thus, periodicity \(p\) has an impact on both conversion bands. This can be explained as follows: increasing \(p\) increases the length of the outer square ring on the metasurface, since this square ring contributes to the electric field strength at f1 less than that at f2 (as seen in Figure 8). Thus, variation in the second conversion band is found to be larger than for the first conversion band. Figure 11 shows the plot of the axial ratio for different values of \(c\) from 13.2 \(\upmu\)m to 14.2 \(\upmu\)m. It is clear that with the increase in \(c\), the first frequency band shifts towards the left, which decreases operational bandwidth. A similar tendency is observed for the second frequency band due to the larger variation per wavelength as compared to the first frequency band. This change is supported by Figure 8, in which both conversion bands' operation depends upon corner square-conducting patches. The effect of substrate thickness \(d\) and inner square dimension \(c_{1}\) is analyzed as shown in Figure 12,b, respectively. Figure 12 shows that as \(d\) is increased from 3.2 \(\upmu\)m to 4.2 \(\upmu\)m, the performance of dual-band LP-to-CP deteriorates in terms of axial ratio. A slight decrease in bandwidth is observed  
Figure 11: Effect of (**a**) \(p\) and (**b**) \(c\) on the performance of dual-band LP-to-CP converter. as the higher frequency end of the first band moves towards the left. This variation in second frequency band seems to be abrupt due to higher sensitivity at high frequency, although performance remains more or less stable (within 3 dB), except at \(d\) = 4.2 \(\upmu\)m. This phenomenon can be explained quantitatively as follows: the incident electric field on the top metasurface can be divided into two parts: the reflected wave to the air and the transmitted wave inside the substrate. Assuming the conductor thickness to be negligible, the transmitted wave travels inside the substrate and upon striking the substrate to the ground interface, is partially reflected back to the substrate, whereas the remainder of the portion is transmitted into the air. The portion of electromagnetic wave which was reflected back to the substrate travels back to the top surface to the substrate interface and, upon striking that interface, is again divided into two portions. One portion is reflected back to the substrate, while the other portion is transmitted into the air. The reflected wave traveling inside the substrate experiences the phase delays and, upon striking the substrate to ground interface, some portion of this wave reflects back to the substrate, while some part is transmitted into the air. These multiple transmitted waves interfere with each other constructively and destructively producing two polarized waves: one X polarized and the other Y polarized. These waves generate circularly polarized waves when they have comparable magnitudes and differences in phase angles around 90\({}^{\circ}\). Varying the substrate thickness changes the phase angles and hence affects the axial ratio for the proposed converter. Figure 12b shows the effect of \(c1\) on the performance of dual-band LP-to-CP converter. It shows that the first frequency band remains almost stable with a change in \(c1\), whereas the second frequency band is sensitive towards \(c1\).