# A New Compact Octagonal Shape Perfect Metamaterial Absorber for Microwave Applications
## 2 Design, Numerical Simulation, and Experiment  
The proposed perfect metamaterial absorber (PMA) consists of three octagonal shape resonators on the dielectric material and a ground plane backside. The proposed perfect metamaterial absorber structure and structural parameters are shown in Figure 1. All of the metallic elements of the PMA are made of copper with a conductivity of 5.8 \(\times\) 10\({}^{7}\) S/m and the thickness of copper resonators are 35 \(\mu\)m that are printed on a substrate with standard relative permittivity \(\varepsilon\) = 4.3, as well as loss tangent \(\delta\) = 0.025. The parameters of the structure are L\({}_{\text{s}}\) = 10 mm, W\({}_{\text{s}}\) = 10 mm, W\({}_{\text{1}}\) = W\({}_{\text{2}}\) = W\({}_{\text{3}}\) = 0.8 mm. The double-sided copper laminated PCB (Printed Circuit Board) (Shenzhen Zhongxinhua Electronics Co., Ltd., Shenzhen, China) is available in the market. Using LPKF S63 PCB prototyping machine (LPKF Laser & Electronics, Tualatin, OR, USA) or chemical process, it is easy to fabricate the design structure. Low cost, high efficient flame retardant4 (FR4) epoxy dielectric material (Shenzhen Zhongxinhua Electronics Co., Ltd., Shenzhen, China) was utilized as substrate material.  
Figure 1: \(Cont.\)  
Finite-integration technique (FIT) based CST microwave studio suite simulator has been implemented to examine this design structure in this paper. The electric field and magnetic field have been polarized along the x-axis and the y-axis, respectively, thus wave propagation is along the z-axis. The boundary conditions of perfect magnetic conductor (PEC) and the perfect electric conductor (PMC) are utilized along the x-axis and y-axis, individually, and two waveguide ports are placed on the positive and negative z-axis. In addition, the periodic boundary conditions with the waveguide ports are used in simulation. The schematic drawing of the proposed structure, unit cell with resistive load, fabricated unit cell, side view of the unit cell, and array of the structure are demonstrated in Figure 1.  
CST based frequency domain solver was used to determine the reflection coefficient in simulation at 1001 frequency samples. The boundary condition and measurement set up are shown in Figure 2. The fabricated sample encloses 18 \(\times\) 22 arrays of the structure of copper materials, and the dimension of the fabricated sample are 180 \(\times\) 220 mm\({}^{2}\). The measurement has been performed with two waveguides in the free-space environment. The scattering parameters have been measured by the PNA network analyser (N5227, Agilent Technologies Sdn. Bhd., Petaling Jaya, Malaysia) where the frequency range of the device was 10 MHz-67 GHz. In addition, a calibration kit (Agilent N4694-60001, Agilent Technologies Sdn. Bhd., Petaling Jaya, Malaysia) was utilized to calibrate the network analyser. For that reason, the measurements were completed precisely. The absorption of the design structure is determined using the following equation, A (\(\omega\)) = 1 \(-\) R (\(\omega\)) \(-\) T (\(\omega\)), where T (\(\omega\)), R (\(\omega\)), and A (\(\omega\)) are the transmittance, reflectance, and absorption at angular frequency \(\omega\), respectively. Absorption depends on the scattering parameters, for instance, \(\left.\right|S_{21}\left.\right|^{2}\) = T (\(\omega\)), and \(\left.\right|S_{11}\left.\right|^{2}\) = R (\(\omega\)). The absorption of the incidence electromagnetic (EM) wave is simplified as A (\(\omega\)) = 1 \(-\) R (\(\omega\)), because back side copper plane blocks the transmission of EM wave. Nonetheless, from the absorption equation, it can be seen that minimizing scattering parameters, which can maximize the absorption of the metamaterials.  
Figure 1: (**a**) The proposed sketch of perfect metamaterial absorber (PMA); (**b**) Unit cell with resistive load; (**c**) The fabricated unit cell structure; (**d**) Side view of PMA; and, (**e**) Fabricated array of PMA.