As shown in Figure 2b, this wavelength corresponds to an intersection between the transmission spectra of \(x\)- and \(y\)-polarized incident plane waves. Figure 3 presents the variations of the three parameters \(T\) in (a), \(\xi\) in (b) and \(P\) in (c) and the \(FOM\) as a function of the beam-waist \(W_{0}\) when this anisotropic metasurface (\(\lambda/2\) plate) is illuminated by a linearly-polarized Gaussian beam. Due to the structure anisotropy, these parameters will depend on the polarization of the incident beam especially for highly focused beams (small \(W_{0}\)). To account for this anisotropy, we choose the polarization of the incident beam to be directed along the bisector of \(\widehat{XOY}\) by setting \(a=1\) and \(\phi=45^{\circ}\) in Equations (12) and (13), respectively. As we can see from Figure 3a-c, all three parameters tend asymptotically to the value corresponding to a plane wave illumination. A \(FOM\) of \(10^{-2}\) is reached for a beam-waist \(W_{0}^{min}=5p\) (see the inset of Figure 3d). The latter corresponds to a polarization degree of \(P=0.9944\), a phase change of \(\xi=1.011\pi\) and a transmission efficiency of \(T=0.9252\). This result demonstrates the robustness of the structure with respect to the beam-size. In fact, one might qualitatively expect this outcome because the underlying physical effect (the phase change) is not a collective effect, but results from the excitation of two guided modes inside the apertures with different phase velocity. The quarter-wave plate is obtained in [14] by only modifying the dimensions of one rectangular aperture. Thus, after optimizing the transmission coefficient, we set here \(a_{y}=0.658p\) instead of \(a_{y}=0.653p\) in that reference. All the other geometrical parameters are kept the same as for the half-wave plate. The operation wavelength is now equal to \(\lambda_{0}=1.182p\). This small modification of the parameter \(a_{y}\) leads to a more efficient transmission coefficient of \(T_{\rm pw}=0.5995\) instead of \(0.57\) and to \(\xi_{\rm pw}=0.5001\pi\) and \(P_{\rm pw}=1\) for a plane wave illumination under normal incidence. Figure 4 shows the variations of the three parameters \(T,\xi,P\) and of the \(FOM\) as a function of the beam-waist \(W_{0}\) value when this anisotropic metasurface (\(\lambda/4\) plate) is illuminated by a linearly-polarized Gaussian beam. The criterion of \(FOM\leq 10^{-2}\) is met for a minimum beam-waist of \(W_{0}=6p\). The condition is quite similar to the half-wave plate's, demonstrating again the high robustness of such a metasurface to act as anisotropic plates in the domain of THz or microwave. Figure 4: Same study as in Figure 3, but for the quarter-wave plate operating at \(\lambda=1.182p\). Figure 3: Variations of (**a**) the transmission efficiency \(T\), (**b**) the polarization degree \(P\), (**c**) the phase change \(\xi\) and (**d**) the \(FOM\) defined by Equation (10) in the case of the half-wave plate operating at \(\lambda=1.194p\) as a function of the illumination Gaussian beam size \(W_{0}/p\). The beam is impinging the structure under normal incidence and is polarized at \(45^{\circ}\) from the \(x\)-axis in order to get transmission across the two perpendicular rectangles. The angular spectrum expansion of the beam is described with \(128\times 128\) harmonics. The inset in (d) corresponds to a zoom made around \(FOM=10^{-2}\). To illustrate the angular filtering effect that can occur for a highly focused Gaussian beam (\(W_{0}=2p=1.67\lambda_{0}\)), we present in Figure 5 the spatial distribution of the incident electric intensity (\(|E_{i}(x,y,z_{0})|^{2}\)) in comparison with the transmitted electric field intensity (\(|E_{t}(x,y,z_{0})|^{2}\)) calculated at different distances \(z_{0}\) from the output side of the anisotropic metasurface for a half-wave plate (Figure 5a-h) and for a quarter-wave plate (Figure 5i-p). For both cases, the transmitted beam is distorted and does not exhibit a 2D Gaussian shape.