## 1 Introduction
### Multifunctional Transmissive Metasurfaces Combining Distinct Functionalities  
Compared to reflective devices, high-efficiency multifunctional meta-devices in transmission geometry are much more difficult to realize, simply because more channels (transmission and reflection ones) exist in this geometry and thus Equation (2) is difficult to meet. People utilized the concept of Huygens' surface to construct transmission-mode metasurfaces with high efficiencies, but such devices usually require complex 3D non-flat meta-atoms with both electric and magnetic resonators incorporated [24; 26]. Due to the complexities in meta-atom design, multifunctional meta-devices realized based on such a scheme are rarely seen, except a transmissive functionality-tunable device recently realized with controllable active elements incorporated [96].  
Meanwhile, meta-atoms in multilayer geometry (with deep-subwavelength total thicknesses) are found as alternative candidates to construct high-efficiency transmission-mode metasurfaces. Many functional meta-devices are fabricated using such kind of meta-atoms [27; 49], generating interesting effects such as high-efficiency SPP excitations [31] and photonic spin-Hall effect [54]. Straightforwardly, there appear recent efforts on using such meta-atoms to construct transmissive multifunctional meta-devices with very high efficiencies.  
[PERSON] et al. proposed to use a four-layer structure, with each layer containing a metallic mesh coupled with a metal patch [93], as the basic meta-atom to construct transmissive bifunctional meta-devices (Figure 6a). Each single layer exhibits perfect EM transmission at a particular frequency due to the interaction between the patch resonator and the opaque mesh. Mutual interactions between different layers can significantly enlarge the transparency window and the transmission-phase variation range (see Figure 6b). With such a high-performance structure, the authors designed and fabricated a transmissive metasurface (see Figure 6a for sample picture) with meta-atoms carefully adjusted to yield transmission phases (\(\varphi_{xx}\) and \(\varphi_{yy}\)) satisfying Equations (5) and (6). Experimental results shown in Figure 6e,f indicate that the device can focus \(y\)-polarized PW to a point and can refrac \(x\)-polarized PW anomalously, illustrating the desired bi-functionality. The achieved working efficiency is 72%, much higher than those of other transmissive metasurfaces [25; 26; 27; 49].  
Figure 6: (**a**) Photograph of a microwave transmissive bifunctional metasurface. Inset illustrates a typical meta-atom composed by four metallic layers (yellow) separated by three F4B spacers (blue). (**b**) Transmission amplitude (blue lines) and phase (red lines) for a periodic metasurface constructed by the 4-layer meta-atom, under the excitations of \(y\)-polarized (solid lines) and \(x\)-polarized (dotted lines) incident waves, respectively. Schematics and working principles of a transmissive bifunctional metasurfaces, which behaves as (**c**) a focusing lens and (**d**) a beam deflector when excited by incident waves with polarizations \(E//y\) and \(E//x\), respectively. (**e**) Measured Re\([\overset{\rightarrow}{E}]\) distributions on both \(x\)oz and \(y\)oz planes as the metasurface is illuminated by a normally-incident \(y\)-polarized plane wave. (**f**) Measured scattered wave intensity as function of frequency and detection angle when the metasurface is illuminated by \(x\)-polarized normally incident plane waves. Reproduced from [93] with permission.