## 3 Metasurfaces
### Wavefront Control/Shaping Using Metasurfaces  
In the past, wavefront shaping in the microwave regime has been achieved with the help of reflect- and transmit-arrays [45; 46]. Such arrays have used variable element size and rotation (in case of reflect-arrays), and aperture coupled miniaturized delay lines (with a patched ground) for the transmit-array, in order to shape the wavefronts [47; 48]. Such arrays, however, have a periodicity of the order \(\lambda/4-\lambda/2\), therefore, they do not provide sub-wavelength resolution (sub-wavelength resolution can improve the aperture efficiency of such arrays) [31; 49]. Due to large periodicity, the induced electric and magnetic polarizabilities can no longer completely define their response and they cannot be considered 'homogenised', hence they are not classified as metasurfaces.  
Metasurfaces allow the \(360^{\circ}\) control of the phase by introducing anisotropy through its individual elements. V-shaped anisotropic elements have been used to obtain full control of the phase, however, reflection losses reduce the efficiency of the structure to \(50\%\) and since anisotropy exploits the cross-polar  
Figure 1: An illustration of generalised law of refraction. \(\Phi\) and \(\Phi+\mathrm{d}\Phi\) are phase discontinuities at A\({}^{\prime}\) and A while dx is the distance between them. \(\Theta^{\prime}\) and \(\theta\) represent the angles of incidence and refraction to the normal (dotted line).  
component to achieve a full 360\({}^{\circ}\) of phase manipulation, the efficiency of the structure is further halved [16; 35]. In order to unlock further potential of metasurface design, multi-layered Huygens surfaces have been proposed [50]. These surfaces eliminate the reflection losses completely. [PERSON]'s metasurfaces with an efficiency of 86% at 10 GHz have been shown in [34]. This design also showed a wide 3-dB bandwidth of 24%.  
The local phase manipulation by metasurfaces has also been used to shape the wavefronts of the reflected wave. The variation in the dimensions of square patches on a dielectric layer backed by a ground plane has been shown to tailor the reflected wavefront [51]. By carefully controlling the size and response of each sub-wavelength inclusion in along both perpendicular axes, a birefringent metasurface has been successfully constructed in [52]. This metasurface showed an efficiency of 92% with the additional advantage of splitting the incoming non-polarised electromagnetic wave into two orthogonal linear polarisations. A similar approach using perpendicular strip dipoles in a triangular lattice in terahertz range has been presented in [53]. Another technique has been developed to replicate the behaviour of arbitrary materials by using heterogeneous layers [54]. By varying the weight percentage of polyaniline micro-powder, carbon nanotubes, carbon nanofibers or graphene nanoplatelets, a series of artificial dielectrics were designed with a range of relative permittivities and loss tangents at microwave frequencies. Precise combinations of different thickness of these materials were developed via a mathematical model in conjunction with a particle swarm optimization. They were used to replicate the phase jumps of the wave going through the composite material over a frequency range. It was found that these multiple layers of artificial dielectrics could replicate the reflection coefficient of real materials, frequency selective surfaces, and even complex reflection profiles of arbitrary bespoke materials [54]. In related work, it was found that layered Cadmium iodide crystals of different sizes could be used to control the absorption over optical wavelengths [55].