# A Wideband Terahertz Transmissive Polarization Manipulator Based on Metasurfaces
## 3 Results and Discussion  
### Simulation and Analysis of the LCPC  
In order to validate the performance of the proposed structure, the optimized unit cell was resimulated in the Computer Simulation Technology (CST) time-domain solver. Close agreement between HFSS and CST results validate the performance of the proposed structure. Figure 3a,b depict the transmission characteristics for the incident x-polarized and y-polarized wave traveling in the '-z' direction in CST and HFSS. The phase difference between the transmitted x-polarized and y-polarized components with an incident x-polarized wave is shown in Figure 4. The phase difference between the two polarized components from 0.94 THz to 1.47 THz is close to \(-90^{\circ}\) or \(+270^{\circ}\). There is a slight mismatch between the two results obtained from the two software packages. This might be due to different computational techniques; HFSS works on the finite element mesh (FEM) method, whereas CST's time-domain solver works on the finite difference time domain (FDTD) method to solve Maxwell Equations. Two similar responses from different computational techniques confirm the validity of our proposed design; therefore, further simulations were carried out in HFSS. Figure 3: Transmission characteristics with incident (**a**) x-polarized (**b**) y-polarized waves. In order to understand the operation of the LCPC, we consider a plane horizontal (x polarized) wave traveling in the '-z' direction. The incident wave can be expressed as Equation (1). The magnitudes of this incident wave are expressed in Equation (2). \[E_{xi}=E_{xi}e_{x} \tag{1}\]  
\[E_{xi}=E_{0}e^{i\xi z} \tag{2}\]  
The transmitted wave can be expressed as the sum of two components, i.e., x-polarized and y-polarized, as shown in Equation (3):  
\[E_{t}=E_{xt}e_{x}+E_{yt}e_{y}=t_{xx}e^{i\psi_{xx}}E_{0}e^{i\xi z}e_{x}+t_{xy}e^ {i\psi_{xy}}E_{0}e^{i\xi z}e_{y} \tag{3}\]  
\[t_{xx}=\frac{E_{xt}}{E_{xi}} \tag{4}\]  
\[t_{xy}=\frac{E_{yt}}{E_{xi}} \tag{5}\]  
where \(t_{xx}\) and \(t_{xy}\) represent transmission coefficients for \(x\) to \(x\) and \(x\) to \(y\) polarization conversion as shown in Equations (4) and (5), respectively. \(\varphi_{xx}\) and \(\varphi_{xy}\) are phase angles corresponding to \(t_{xx}\) and \(t_{xy}\), respectively. Since the proposed structure has an anisotropic structure, the magnitudes and phases for x-polarized and y-polarized transmitted waves may be different. However, if for a certain frequency range these transmission coefficients become comparable and their phase angles are \(90^{\circ}\) apart, i.e., \(t_{xx}\) = \(t_{xy}\) and \(\ \varphi_{xy}=2n\pi\pm\pi/2\), \(n\) being an integer. This would be the condition where linear horizontal (x-polarized) wave will be converted into a perfectly circularly polarized wave. In order to describe the transmission conversion performance for the proposed structure, we calculate the axial ratio for the transmitted wave as in Equation (6):  
\[AR=\left(\frac{\left|t_{xx}\right|_{2}+\left|t_{xy}\right|^{2}+\sqrt{a}}{\left| t_{xx}\right|_{2}+\left|t_{xy}\right|^{2}-\sqrt{a}}\right)^{1/2} \tag{6}\]  
where '\(a\)' can be calculated from Equation (7) as:  
\[a=\left|t_{xx}\right|_{4}+\left|t_{xy}\right|^{4}+2|t_{xx}|^{2}\left|t_{xy} \right|^{2}\cos\left(2\varphi_{xy}\right) \tag{7}\]  
Figure 4: The phase difference between x-polarized and y-polarized transmitted waves with incident x-polarized wave. For a perfect LCPC, AR should be 1 (0 dB); however, in most of the systems, a 3 dB value of the axial ratio is acceptable. It is clear from Figure 3a that in the frequency range from 0.94 THz to 1.47 THz, the transmission coefficient magnitudes are comparable, whereas the phase difference between them is \(-90^{\circ}\) or \(+270^{\circ}\) with \(\pm 10^{\circ}\) variation. Therefore, the condition for linear to circular polarization is fully met at some frequencies. For a range of frequencies, it partially fulfils the requirement (in this case, the transmitted wave will be slightly elliptically polarized).