Metasurfaces are highly valuable for their unique electromagnetic properties. Since the introduction of the generalized Snell’s law, metasurfaces have seen significant applications across various fields. However, the inverse design of metasurfaces has remained a major challenge. Solving the coupling problem between parameters and finding the unit structure that most closely matches the target light field are key steps in metasurface applications. With the development of deep learning, neural network algorithms have demonstrated strong computational capabilities. Although many neural network architectures have been applied to metasurface inverse design due to their convenience, there is still significant room for improvement in terms of design accuracy, computational speed, and handling of parameter coupling. In this paper, we present an innovative improvement to the traditional residual network (ResNet) and analyze its application in metasurface inverse design by comparing different architectures. We design a unit structure that can effectively control both the amplitude and phase of the light field at a frequency of 1 THz. The fabrication of this structure can be compatible with semiconductor manufacturing technologies. We apply the improved ResNet architecture to the metasurface design process to address the parameter coupling problem inherent in metasurface inverse design. This approach demonstrates a strong practical effect, with fast speed and high precision. In addition, we compare the differences caused by various residual blocks in detail and verify the proposed method through the design of a focusing metasurface.

The metasurface unit structure consists of three parts (Fig. 1): an open-ring cylinder made of silicon material, a silicon cylinder, and a square silicon dioxide substrate. This unit structure has a total of eight parameters: q₁ and q₂ regulate the opening angle of the open-ring cylinder; W is the thickness of the open-ring cylinder; R₁ is the maximum diameter of the open-ring cylinder; R is the radius of the cylinder; h₁ is the height of both the cylinder and open-ring cylinder; h₂ is the side length of the square substrate; h is the thickness of the square substrate. Among these parameters, h₂ and R₁ are set to fixed values based on the overall proportions of the unit structure during the sweeping process. Through testing, we determine that h₂ is 100 μm and R₁ is 79.89 μm. Since the thickness W of the ring has minimal influence on the light field control, it is fixed. The height h₁ of the nanopillar is set uniformly to 100 μm, and the thickness h of the square substrate is fixed at 10 μm. We primarily focus on the three parameters: R, q₁, and q₂. The core ResNet architecture consists of a fully connected layer and an activation function layer. Each residual block contains four hidden layers. The fully connected layer, linked to the output vector of the residual block, has an activation function, with a rectified linear unit (ReLU) function applied in the two fully connected layers. The final fully connected layer serves as the output layer, and the output data is two-dimensional. Unlike previous ResNet architecture, this design does not include a convolutional layer, and the database used for ResNet training is based on the parameter sweeps of the unit structure designed in this paper. After 12000 sweeps, the resulting data fully meet the requirements for light field amplitude and phase coverage. We retain 6500 sets of data for neural network training, with an 80∶20 split for the training and test sets.

The metasurface unit structure we designed demonstrates excellent control over right-handed circularly polarized (RCP) light. By adjusting just two parameters of the unit structure, the required amplitude and phase coverage for the inverse design of the metasurface can be achieved (Figs. 3 and 4). The dataset is generated based on the unit structure’s sweeping results. By improving the ResNet architecture (Fig. 5), we analyze the training performance of the neural network with different numbers of residual blocks. It is found that the design proposed in this paper achieves the best parameter decoupling effect when using three residual blocks (Table 1). Compared to the actual values of the unit structure parameters, the predicted values from the trained ResNet are within a small margin of error (Table 2). To further verify the effectiveness of the method, we design a metalens based on the output data from the trained ResNet. The designed metalens exhibit the expected focusing effect (Fig. 10).

We propose a unit structure capable of covering and controlling the amplitude and phase of the RCP light field in the 1 THz range. To address the parameter coupling issue in the inverse design, we improve the residual architecture and apply it to this problem. The results show that the shallow ResNet model effectively handles data coupling. By using the optimal neural network architecture, we inversely design the metasurface, verifying the accuracy and feasibility of the method. The results demonstrate that the method is highly effective for metasurface inverse design, with the designed metasurface showing the expected focusing effect and high focusing efficiency. This work provides a valuable reference for the inverse design of optical metasurfaces and has potential applications in light field wavefront manipulation.