## 3 Metasurfaces
### Definition and Salient Characteristics of Metasurfaces  
Metasurfaces are defined as the periodic (or aperiodic) structures where the thickness and periodicity of the individual elements (scatterers) are small in comparison to the wavelength of operation. These two-dimensional structures can be sub-classified further; an array of apertures in a reflective screen are classified as metascreens while separate individual scatterers are called metafilms [1]. However, this classification has not been usually adopted in the published literature. Metasurfaces can also be defined as a (symmetric or asymmetric) array of sub-wavelength resonant scatterers which control the electromagnetic response of the surface [16]. The distribution of individual scatterers is pivotal in determining the response of a surface. This property differentiates the metasurfaces from traditional frequency selective surfaces (FSS). A traditional FSS has individual elements (periodicity) which are of the order of the operating wavelength (generally--\(\surd\)2). Another difference between metasurfaces and FSSs is closely related to the sub-wavelength nature of the individual elements of a metasurface. The sub-wavelength nature of building blocks of metasurfaces allows them to be treated as a classic homogenous structure, thereby characterising their response with effective parameters. For a metasurface, the fields and the polarizations must be the average of the surface fields as the surface is thin. An analytical approach based on the reflection and transmission dyadic is given in [22]. Generalized sheet-transition conditions allow the complex distribution of the meta-elements to be replaced with boundary conditions by using the electric and magnetic surface susceptibilities [23]. This homogenization technique has been used to design leaky-wave antennas [24]; fractal metasurfaces [25]; and non-linear metasurfaces [26]. It is pertinent to mention that aperiodic arrangements of elements have been carried out in the design of reflect-arrays. For a reflected beam to have a specific direction, each element is designed so that it imparts the desired phase shift. Some examples are given in [27; 28; 29; 30]. Since the response of the metasurfaces sheet is dependent on the localized behaviour of each unit, each individual unit cell is allowed to be spatially varied [16]. Such variations can be used to design metasurface lenses and shape wavefronts. The applications of the metasurfaces will be discussed in this paper. The miniaturized individual \"meta-atoms\" of the metasurfaces allow the sub-wavelength resolution of the wavefronts ranging from microwave to optical scale. This property of metasurfaces also allows them to behave like homogeneous or nearly homogenous sheets [31]. Another perspective to define a metasurface goes via [PERSON]'s principle [32]. [PERSON]'s principle states that \"each point on a wavefront acts as a secondary source\", thus allowing the control of wavefronts beyond the source. When an electromagnetic wave strikes a surface, it induces electric and magnetic dipole moments. These moments generate surface currents. According to [PERSON]'s principle, these surface currents are equivalent to the tangential electric and magnetic fields which control the electromagnetic response of a surface [33]. A surface can then be only characterised as a metasurface when its every individual element is polarizable and sub-wavelength. This is achieved by careful design of the individual element(s) [31]. Metasurfaces have the ability to tailor both the electric and magnetic field component of the electromagnetic waves. Therefore, metasurfaces can have negligible mismatch losses as their impedance can be matched by tailoring the electric and magnetic polarizabilities [34; 35]. Metasurfaces without reflection losses are characterised as Huygens metasurfaces [34].