## 2 Design of the Ultra-Wide Band Absorber
### Proposed Genetic Algorithm  
This section describes an optimization algorithm, the so-called genetic algorithm. To design the optimal metasurfaces shown in Figure 2, a genetic algorithm that can find the ultimately optimized metasurface patterns mimicking the meiosis of the chromosome was proposed.  
Figure 1: Proposed composite absorber. (**a**) Principle of operating mechanism, (**b**) Layer configuration.  
Figure 2 shows the flow chart of the genetic algorithm to design the pixelated metasurfaces. To achieve the design goals, a condition for evaluating performance of metasurfaces is required and there is a step to determine whether the goal has been achieved or not. In the beginning of the algorithm, two random 1-bit quantized chromosomes need to be generated. A dominant factor is selected from the two chromosomes, and then the next generations are prepared by crossover and mutation operations from the chromosomes. In the next step, the performance of the chromosome is evaluated repeatedly to find the optimal dominant gene. The cost function for the evaluation is as follows:  
\[\text{Cost function }=\frac{1}{\text{N}}\sum_{n=1}^{\text{N}}\text{W}_{1}| \Gamma_{\text{f}1}|+\text{W}_{2}|\Gamma_{\text{f}2}|+\cdots\text{W}_{n}|\Gamma _{\text{f}n}|\]  
where, \(\Gamma_{\text{f}n}\) is a reflection coefficient of the selected nth frequency and \(\text{W}_{n}\) is a weighing factor for the nth reflection coefficient. The factor of the evaluation is an arithmetic mean of reflection coefficients in the frequency range from 2 to 18 GHz. Reflection coefficients of the absorber are computed from a full-wave electromagnetic simulation, COMSOL Multiphysics [31]. Finally, with the optimal gene, the validation of the finalized results is completed. So, an optimized result can be obtained through the above procedure.  
Figure 3 shows a schematic of an example of the proposed pixelated pattern for the metasurfaces. As mentioned above, the upper and lower metasurface layers are discretized into 20 \(\times\) 20 square pixels of size 1 \(\times\) 1 mm\({}^{2}\). The gap between the neighboring unit-cells is 1 mm at the external boundaries of the square pixel arrays. The reason for the size and number of pixels is that the target lowest frequency band of the proposed absorber is 2 GHz, so the half-wavelength at 2 GHz is about 7.5 cm. Since the goal is to reduce the area and thickness of the unit cell to less than lambda/5, the unit cell was set to 20 \(\times\) 20 mm\({}^{2}\), and the pixel was set to 1 mm in consideration of the appropriate number of variables within the unit cell size.  
Figure 2: Flow chart of the proposed genetic algorithm.  
To optimize the 20 \(\times\) 20 pixels, in the first step, 55-random 1-bit arrays are generated. Each bit is filled with 'zero' or 'one' corresponding to the area of dielectric or conductive ink. An example is shown in the Figure 2 inset. The final pattern is built by performing \(x\)-axis symmetry and then \(y\)-axis symmetry with respect to the pattern of the first quadrant. A random bit array is created iteratively and evaluated for optimization by the genetic algorithm. Therefore, to find the global optimum, 110-binary variables are needed for the upper and lower layers while at the same time for the absorber structure an iterative computation is performed. As a result, an optimized combination of metasurface satisfying the criterion of the figure of merit, in this case less than \(-\)10 dB reflectance, in the target frequency range, is obtained.