# Design Procedure of a Frequency Reconfigurable Metasurface Antenna at mmWave Band
## 1 Introduction
### Metamaterials and Metasurface Structures  
In recent years, scientists have embarked on research regarding the use of artificial materials, which generate significant benefits and introduces various applications. Metamaterials are among these artificial materials, as they are composed of closely spaced sub-wavelength meta-atoms, which resonantly couple to both the electric or magnetic components of the incident electromagnetic fields, thereby exhibiting properties that are not found in nature, as shown in Figure 1[18, 19, 20]. Consequently, they have physical properties that are largely determined by their structures rather than their individual attributes. Furthermore, different structures influence the categorization of metamaterials according to their electrical  
Figure 1: From meta-atoms to metamaterials. permeability, denoted as \(\epsilon\) and (\(\mu\)) values, respectively [23]. The authors in [24] made it possible to classify these materials in four different classes, as shown in Figure 2.  
The first quadrant from Figure 2 is characterized by the existence of both positive \(\epsilon\) and \(\mu\) values. Such materials are known as double positive (DPS). These can be found in nature, for example, in dielectric materials where EM waves propagate. The second quadrant consists of materials that are represented by a plasma and are known as epsilon negative medium (ENG) due to \(\epsilon<0\) and \(\mu>0\) values [25]. The third quadrant is of interest, being that both \(\epsilon\) and \(\mu\) values of materials are negative and not found in nature, hence why it is called the double negative medium (DNG). Furthermore when plane waves propagate in metamaterials, the electric field, magnetic field, and wave vector adopt the left-hand rule, hence why they are referred to as left-handed materials [26]. The fourth quadrant is called the mu negative medium (MNG), represented by magnetic materials as it entails positive \(\epsilon\) and negative \(\mu\) values. From Figure 2, one can see that the majority of waves propagate through two mediums namely; region I and III. Presently, most metamaterials are being designed with two basic types of structures: dense arrays of thin wires (the electric dipoles) and arrays of split-ring resonators (SRRs) (the magnetic loops), which are metallic rings etched onto a dielectric substrate in a concentric pattern [27; 28]. According to the authors in [29], SRRs are considered as unit cells of DNG metamaterials. In order to attain DNG mediums, ENG and MNG mediums are combined, as shown in Figure 3. This paper will focus on the third quadrant as they give metamaterials the property /ability to control EM waves. Figure 2: (**I–IV**) Metamaterial classifications based on permittivity and permeability values. Metasurface unit cells consist of SRRs, which comprise negative effective permeability at frequencies closer to the resonant frequency and are used to make left handed media with negative refractive index [30]. The geometric parameters of the ring resonator and the resonant frequency are dependent on each other [28]. Over the course of development of metasurfaces, the limitations of fixed response metasurfaces in realistic applications, i.e., limited working bandwidths and fixed wave manipulation capabilities, were realized [31]. As a result, many efforts have been devoted to developing reconfigurable metasurfaces (RMS) that can actively control EM waves with external tunings. RMSs involve adding tunability to each unit cell which allows for more capabilities of metasurface applications. In the context of wireless communication, they are mostly considered passive reflecting devices used to shape the propagation environment [32, 33, 34, 35]. As an alternative, recent studies presented an application of RMSs as massive MIMO active reconfigurable antennas with developed analog signal processing capabilities for next generation transceivers [8, 14, 36]. RMS antennas achieve higher power efficiency as they eliminate the need for active phase shifters.