The traditional design of metamaterial absorber depends on the experience of researchers to obtain excellent optical performance by modifying geometric parameters. The design pattern of trial and error leads to low efficiency but high cost. Therefore, deep learning is proposed as an inverse design method to improve design productivity and shorten the design circle of terahertz (THz) metamaterial absorber due to the powerful learning ability. It can map the relationship of structural parameters with its absorption performance to predict the optimum value of structural parameters. However, the response spectrum composed of multiple sampling points is employed as the input, which results in a complex network system with a large number of input nodes, output nodes, and hidden layers. Therefore, this paper puts forward a way to simplify the structure of the neural network and apply it to the design of a THz metamaterial absorber with a novel top pattern of the circular ring and double-opening resonance ring.

The whole design process is divided into four steps in Fig. 1: determining key structural parameters of the top layer, processing data sets, analyzing the structure of the neural network, and predicting structural parameters. Step 1 is determining key structural parameters. The absorber designed in this paper is composed of three layers. The copper with conductivity σ=5.71×10⁷ S/m, permeability μ=4π×10^-7 H/m, and thickness of 0.2 μm is selected for the top layer and bottom layer. The intermediate medium layer is FR-4 with the dielectric constant εr=4.3 and thickness of 50 μm. The pattern of the top layer is shown in the upper right of Fig. 1. According to the theory of LC electromagnetic resonance, the resonant characteristics of the unit are easily affected by the width of the circular ring (r₁-r₂), the width of the double-opening resonant square ring (L₁-L₂), and the opening width G. Step 2 is processing data sets. With the quality factor and absorptivity as inputs, and the structural parameters including the inner diameter of metal ring r₁, the inner side length of double-opening resonance ring L₁, and opening width G as outputs, 1000 sample data sets are calculated through CST simulation and divided into training sets and test sets according to the ratio of 7∶3. Step 3 is analyzing the structure of the neural network. The Sigmoid function is employed as the activation function of neurons. The error rate fluctuates with the changing number of hidden layers but reaches a minimum of 0.9% at five layers. Thus, the hidden layer is set to five. The mean square error is smaller when the number of nodes m=6, 9, and 12, and the error rate has an obvious minimum value when the number of nodes m = 6, 9, and 12. Therefore, the number of hidden layer nodes is set to be 6, 9, or 12. Step 4 is predicting structural parameters. When the demand performance is set as A=100% and Q=23, the structural parameters calculated by the neural network are r₁=42.5 μm, L₁=37 μm, and G=19 μm. The optical performance calculated by CST simulation is 99.99% and the quality factor Q is 23.2. Thus, the error of target absorption performance is 0.9%. When the required performance is set as A=85% and Q=30, the structural parameters calculated by the neural network are r₁=45 μm, L₁=35 μm,and G=21 μm. The optical performance by CST simulation is 85.86% and the quality factor Q is 31.7. Therefore, the error of the target absorption performance is 1.05%.

This paper analyzes the influence of structural parameters r₁, L₁, and G on the absorption performance of the absorber. When r₁=45 μm, the change trend of absorbance and Q value with L₁ and G is shown in Fig. 3. The absorbance increases and the Q value gradually decreases as L₁ increases and G decreases. When L₁=36 μm and G=25 μm, the change trend of absorbance and Q value with r₁ is shown in Fig. 4. The absorption rate decreases and the Q value increases with the rising r₁. Additionally, the electric field distribution and surface current distribution of the high absorption structure at the resonance frequency f₀=1.192 THz are analyzed as shown in Fig. 5. The electric field is mainly distributed at the four parts of the circular ring and the double-opening resonant ring. For the double-opening resonant ring, the surface current flows down through the left and right sides respectively to generate electric dipole resonance. For the external ring, the current mainly converges at the four parts of the adjacent double-open resonant ring, as the upper and lower of the ring, thus producing electric dipole resonance. The two absorbers of Model A and Model B designed for the requirements of high absorptivity and high Q value respectively with the same top layer pattern can be produced by micro-nano fabrication. When the fabrication tolerance of Model A is -2%-2%, the absorption rate fluctuates between 97.40%-99.99%, the absolute error is -2.6%-0, and the maximum relative error is 2.6%. The Q value fluctuates between 22.5 and 24.3, with an absolute error of -0.7-1.1 and a maximum relative error of 4.7%. Table 6 shows that when the fabrication tolerance of Model B is -3%-3%, the absorption rate fluctuates between 84.98%~89.10%, the absolute error is -0.88%-3.24%, and the maximum relative error is 3%. The Q value fluctuates between 30.8 and 31.7, the absolute error is -0.9-0, and the maximum relative error is 2.8%. This indicates that Model A is within the fabrication tolerance of -2%-2%, and Model B is within the fabrication tolerance of -3%-3%, with good fabrication tolerance.

In this paper, an absorber structure with a top pattern of the circular ring and double-opening resonant ring is proposed, and the reverse design of THz metamaterial absorber is realized through neural networks. The input and output nodes are simplified by electromagnetic resonance theory and absorption performance characterization to reduce the complexity of the neural network. The maximum absorption rate of metamaterial absorber designed by the proposed neural network can reach 99.99% at the frequency of 1.192 THz, which is close to perfect absorption. The maximum Q value can be 31.7 at frequency of 1.22 THz. The maximum relative error should not exceed 4.7% within the fabrication tolerance of -2%-2%. Additionally, this paper analyzes the influence of three geometric parameters on the absorptivity and quality factor in detail and discusses the absorption mechanism of the absorber from three aspects of current, electric field distribution, and equivalent circuit. The proposed method can effectively improve the design efficiency of metamaterial absorber according to the performance requirements and has great application prospects in terahertz functional device design.