## 1 Introduction
### Multifunctional Reflective Metasurfaces Combining Distinct Functionalities  
The proposed design strategy is so general that it can also be used to realize multifunctional metasurfaces exhibiting _distinct_ functionalities. For example, the first reflective multifunctional meta-device possessing two distinct functionalities (focusing and PW-to-SW conversion) was demonstrated in [93] in the microwave regime (see Figure 4a,b). Taking meta-atoms the same as shown in Figure 3a, the authors successfully designed a reflective bi-functional metasurface which exhibits two phase distributions satisfying Equations (5) and (6). Shining a \(y\)-polarized microwave at frequency 9.3 GHz normally onto the sample, the authors measured the \(\mathrm{Re}[\vec{E}]\) distributions on two orthogonal planes. Results displayed in Figure 4c indicate clearly that the incoming plane wave has been focused to a focal point. To demonstrate the PW-to-SW conversion effect for the \(\vec{E}\|\hat{x}\) polarization, the authors purposely fabricated a mushroom structure supporting eigen spoof SPP [30; 32] and then put it at the right side of the metasurface to guide out the driven SW (see inset to Figure 4d). Shining the metasurface by an \(x\)-polarized microwave (9.3 GHz), the authors used a near-field scanning technique to map out the \(\mathrm{Re}[\vec{E}_{z}]\) field pattern (see Figure 4d). The measured field pattern represents a very  
Figure 3: **(a)** Schematics of an MIM meta-atom consisting of a metallic patch resonator and a metal ground plane (yellow) separated by a dielectric spacer (blue). **(b)** Tuning the reflection phase \(\varphi_{xx}\) of a microwave MIM meta-atom by varying a and b. Reproduced from [93] with permission. **(c)** A polarization beam splitter made by bifunctional gradient metasurface constructed with MIM meta-atoms consisting of metal-cross planar resonators and metal ground plane (yellow) separated by a dielectric spacer (blue). Reproduced from [79] with permission. **(d)** Experimental characterizations on a unidirectional polarization-controlled SPP (red) coupler at telecom wavelength. Reproduced from [72] with permission. **(e)** A bi-functional meta-hologram device consisting of metal pattern and metal ground plane (yellow) separated by a dielectric spacer (blue) that can generate different hologram image depending on the incident linear polarization. Reproduced from [59] with permission. well-defined spoof SPP with \(k_{spp}=206.5\) m\({}^{-1}\), in good agreement with the theoretically-calculated value (\(k_{spp}=209.4\) m\({}^{-1}\)). For both functionalities, the experimentally-estimated working efficiencies are higher than 90%, which is not surprising since metallic losses are negligible at microwave frequencies. Such a concept was successfully extended to realize the same type of bifunctional meta-device, but working at optical wavelengths (Figure 4e) [94], which is more close to realistic integration-optics applications. Figure 4: A reflective bifunctional metasurfaces that behaves as (**a**) a focusing lens and (**b**) a PW-to-SW (propagating wave to surface wave) convertor when excited by incident waves with polarizations \(E//y\) (red light) and \(E//x\) (blue light), respectively. (**c**) Measured Re\([\overrightarrow{E}]\) distributions on both _xoz_ and _yoz_ planes as the metasurface is illuminated by a normally incident \(y\)-polarized plane wave. (**d**) Measured Re\([\overrightarrow{E}]\) pattern on the _xy_-plane using a monopole antenna placed vertically and 8 mm above the metasurface and the mushroom structure, when the metasurface is illuminated by a normally incident \(x\)-polarized plane wave. Reproduced from [93] with permission. (**e**) The working principle of similar type of bi-functional metasurface operating for visible light realized in [94]. The top panel shows the schematic of the unit cell consisting of an Ag nanobrick (grey) on top of a spacer (green) and Ag substrate. Reproduced from [94] with permission. SPPs, surface plasmon polaritons.