# A Wideband Terahertz Transmissive Polarization Manipulator Based on Metasurfaces
## 3 Results and Discussion
### Performance Analysis of the LCPC  
We analyzed the effect of different geometrical parameters of the unit cell on the performance of the polarization converter. Figure 10a shows the plot of the axial ratio of the LCPC for different values of \(l\) while keeping all the other parameters constant. It is observed that with the increase in '\(l\)' from 47.3 to 48.5 \(\upmu\)m, the lower end of the frequency band shifts towards the left, while the higher-end remains almost stable, except for '\(l\)' = 48 \(\upmu\)m. As '\(l\)' increases, the width of the outer square ring decreases, changing the resonance frequency of the outer square, hence increasing the bandwidth of the proposed converter. However, after the optimized value, further increase in \(l\) degrades the performance of the polarization converter as the axial ratio increases beyond 3 dB within the band. Figure 10b shows the influence of '\(c\)' on the performance of the converter. '\(c\)' affects the center patch in many ways as it varies the dimensions of the three squares being eliminated from the '\(b\times b\)' patch. Also, it influences many parameters in the equivalent electric circuit (C1, C2, C5, L2, and L3). It can be observed that as '\(c\)' increases from 11.5 \(\upmu\)m to 13.5 \(\upmu\)m, the frequency band shifts towards the right, except at '\(c\)' = 12 \(\upmu\)m, which is the optimized value for our proposed structure. It can be seen from Figure 8b that the '\(c\times c\)' patch confines the highest electromagnetic energy between the two consecutive corners of the '\(c\times c\)' patch. This gap between the two corners cannot be too narrow nor too wide to allow a confined electromagnetic field which will ultimately affect the coupling between the top and ground surfaces and will influence the bandwidth of operation along with a slight shift in the frequency band. Figure 9: Polarized wave trajectory at frequencies of (**a**) 1.085 THz, (**b**) 1.387 THz, (**c**) 1.175 THz, and (**d**) 0.995 THz. Figure 10c shows the effect of '\(a\)' on the performance of the proposed converter. We varied '\(a\)' from 48 \(\upmu\)m to 50.5 \(\upmu\)m while keeping all other parameters constant. Increasing '\(a\)' has a similar effect as what was observed with '\(l\)' as it also affects the width of the outer square ring, which influences the frequency of operation and hence varies the operating bandwidth. However, the tendency of change in the bandwidth varies as at \(a=48\)\(\upmu\)m, the axial ratio goes beyond 3 dB, hence the transmitted wave is not a circularly polarized wave. At \(a=49\)\(\upmu\)m and 51 \(\upmu\)m, the response is almost the same, whereas the optimum response was obtained at \(a=50\)\(\upmu\)m.  
Next, we observed the effect of the thickness of the substrate '\(d\)' on the performance. Figure 10d shows the influence of '\(d\)' on the axial ratio, which shows that when '\(d\)' is varied from 3.3 \(\upmu\)m to 7.3 \(\upmu\)m, the axial ratio of the transmitted wave varies, while keeping bandwidth of operation almost constant. It can be explained quantitatively as follows: the incident electric field on the top metasurface can be divided into two parts; one part reflecting back to the air and the other part transmitting inside the substrate. Here, we assume that conductor thickness is negligible. The transmitted wave travels inside the substrate and upon striking the substrate to ground interface, it is partially reflected back to the substrate, whereas the rest of the portion is transmitted into the air. The portion of the 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 another portion is transmitted into the air. The reflected wave traveling inside the substrate experiences phase delays and upon striking the substrate to ground interface, some portion of this wave reflects back to the substrate, and some is transmitted into the air.