# A 60-GHz Ultra-Thin and Flexible Metasurface for Frequency-Selective Wireless Applications
## 2 Materials and Methods
### Design and Modelling of 60-GHz Metasurface in Simulation  
A metasurface is designed and developed by the addition of a thin interface with an array of subwavelength-scaled resonators to dramatically alter the reflection and transmission coefficients due to the resultant change in boundary conditions and excitation of effective currents on the surface.  
Figure 1: An illustration of a conventional screen printing process.  
The subwavelength resonator size becomes critical to implement at higher frequencies and generally requires sophisticated micro-fabrication techniques. It is important to design such geometries which can ensure stability in performance against the fabrication tolerances that can cause minor variations in the size and radiating length. This concern has been fully considered in this work while designing a resonator geometry, and a stable structure comprised of a circular loop embedded with the square loop has been introduced. The proposed design offers more angular stability and lesser deviation in the resonant frequency than the I-shaped resonator reported in Reference [23]. The design and modelling of the metasurface, as well as the parametric analysis of the design variables, is carried out by using the Computer Simulation Technology (CST) Microwave Studio software established on the Finite Integral Techniques (FIT) for EM computations.  
Two flexible substrate materials with excellent flexibility and durability, i.e., Melinex (thickness, h\({}_{1}\) = 125 \(\upmu\)m, dielectric constant, \(\varepsilon_{\mathrm{r1}}\) = 2.9, loss tangent, tan\(\delta\) = 0.06) and Kapton (h\({}_{2}\) = 75 \(\upmu\)m, \(\varepsilon_{\mathrm{r2}}\) = 3.5, tan\(\delta\) = 0.002), have been selected. The optimized dimensions of the metasurface unit-cell designed at 60-GHz are 2.8 mm (0.56 \(\lambda_{\mathrm{o}}\)) \(\times\) 2.8 mm (0.56 \(\lambda_{\mathrm{o}}\)) \(\times\) 0.135 mm (0.027 \(\lambda_{\mathrm{o}}\)). The increased fraction value of the wavelength in the dimensions of the design in comparison with the [23] has made this design more convenient to realize without using highly complex small-scale fabrication techniques. Figure 2 shows the metasurface with a dual loop ring resonator, i.e., a circular ring embedded with a square-shaped ring, designed on a substrate film. Figure 2a shows the optimized design of the unit cell which has been subsequently fabricated and tested. The top layer consists of the array of electrically resonant dual loop metallic resonators with the optimized dimensions of the parameters as, a = 1.16 mm, b = 0.99 mm, c = 0.20 mm and d = 0.25 mm. The flexible manipulation of the EM waves at the subwavelengths is accomplished by a repeated patterning of the designed unit-cell in an infinite 2D plane to realize a metasurface, where a 5 \(\times\) 5 unit-cell section is shown in Figure 2b as a periodicity representation. Simulation of a single unit-cell is performed with periodic boundary conditions and floquet ports to construct an infinite metasurface excited by a plane-wave. The infinite is positioned at z = 0 and the impinging plane wave impinges on the surface at an incidence angle \(\theta\). The surface radiates a collimated beam, which shows a waveguide-like ability of the designed medium.