Terahertz metasurface reverse design method based on cascade neural network

Abstract

The invention discloses a terahertz metasurface reverse design method based on a cascade neural network, and belongs to the crossing field of terahertz technology and artificial intelligence, the method aims at a specific target frequency, the complex amplitude of a metasurface unit structure is extracted as training input, and metasurface unit structure parameters are taken as output; firstly, a forward prediction network is trained, the weight is frozen, then the forward prediction network is cascaded with a reverse design network, a complex amplitude mean square error is used as unique loss, only reverse propagation is carried out on the reverse network, and therefore one-to-one mapping of parameters and responses of a unit structure is established. According to the method, the terahertz metasurface structure parameters can be efficiently and accurately predicted, and the effectiveness of the terahertz metasurface structure parameters is verified through holographic imaging experiments. Through the cascaded bidirectional network structure, the problem of one-to-many mapping in a deep learning reverse design method is effectively solved, and rapid, accurate and reliable reverse design of the terahertz metasurface is realized.

Description

Technical Field

[0003] This invention belongs to the interdisciplinary field of terahertz technology and artificial intelligence, and in particular relates to a reverse design method for terahertz metasurfaces based on cascaded neural networks. Background Technology

[0005] Metasurfaces, as two-dimensional artificial electromagnetic materials, allow for arbitrary manipulation of the amplitude and phase of electromagnetic waves through the precise design of subwavelength structural unit arrays. This ability to precisely control electromagnetic waves at the subwavelength scale is the physical foundation for advanced functional applications such as anomalous refraction, efficient focusing, high-order vortex beam generation, and holographic imaging. Therefore, determining the optimal structural parameters of metasurface units quickly and accurately based on a pre-defined target optical response has become a core challenge in achieving specific electromagnetic functions.

[0006] To achieve the aforementioned precise wavefront control, traditional design methods mainly rely on an iterative combination of numerical optimization algorithms and full-wave electromagnetic simulation. However, this iterative search paradigm has two inherent drawbacks: first, its dependence on high computational costs, requiring a complete electromagnetic simulation for each iteration, resulting in an extremely long design cycle; second, when exploring high-dimensional parameter spaces, it is prone to getting trapped in local optima, thus limiting the final performance of the device.

[0007] With the rise of machine learning, deep learning has been introduced into the field of inverse design. This method aims to construct an end-to-end mapping model from the target electromagnetic response to structural parameters, thereby transforming the time-consuming optimization search process into a one-time network forward inference, thus promoting faster and more accurate designs and achieving a qualitative leap in design efficiency. However, current mainstream single inverse network models have a fundamental flaw: they ignore the non-uniqueness of solutions that is prevalent in electromagnetic physics systems. This "one-to-many" mapping relationship makes it difficult for the network to converge during training due to fuzzy gradient information.

[0008] This invention provides a reverse design method for terahertz metasurfaces based on cascaded neural networks. While maintaining the high efficiency advantage of deep learning methods, it effectively overcomes the instability and inaccuracy caused by the "one-to-many" mapping problem of single reverse models, thereby achieving fast, accurate and reliable reverse design of terahertz metasurfaces. Summary of the Invention

[0010] Purpose of the invention: The purpose of this invention is to provide a reverse design method for terahertz metasurfaces based on cascaded neural networks, enabling fast, accurate and reliable reverse design of terahertz metasurfaces.

[0011] Technical solution: A reverse design method for terahertz metasurfaces based on cascaded neural networks, characterized by the following steps:

[0012] S1. Constructing the dataset: First, design and determine the target metasurface unit structure. By changing its structural parameters, obtain the complex amplitude of the optical response corresponding to multiple metasurface units and represent it as two components: real part and imaginary part. Thus, construct a dataset containing the mapping relationship between structural parameters and real and imaginary parts. This dataset is then divided into training set and test set according to a predetermined ratio.

[0013] S2. Construct and train a forward prediction network. Construct a forward prediction network model that maps unit structure parameters to optical response. The input of the model is the metasurface structure parameters, and the output is the real and imaginary parts of the predicted complex amplitude of the corresponding optical response. Then, train the forward prediction network using the training set divided in step S1, and fix its network parameters after the network training is completed.

[0014] S3. Construct and train the reverse design network model. Construct a reverse design network model for learning the reverse mapping from the target optical response to the metasurface structure parameters. The training process involves cascading the forward prediction network trained and fixed in step S2 with the reverse design network. During training, the real and imaginary parts of the training set are input into the reverse design network to obtain a set of predicted structure parameters. Then, the set of predicted structure parameters are input into the fixed forward prediction network to obtain a reconstructed real and imaginary part. Finally, the network weights of the reverse design network are iteratively updated until training is completed by calculating the loss function between the reconstructed value and the actual value input into the reverse network.

[0015] S4. Input the desired target optical response complex amplitude into the trained inverse design network to obtain structural parameters, and use micro-nano fabrication technology to form the corresponding pattern on the substrate based on the parameters to complete the metasurface sample.

[0016] Furthermore, the steps for constructing the dataset are as follows: the rotation angles of the upper and lower resonators of the metasurface unit are used as variable structural parameters. By changing the rotation angles, the unit structure under each set of structural parameters is simulated using simulation software to obtain its transmission optical response within a certain frequency range. Finally, the complex amplitude value (including the real and imaginary parts) at a specific frequency is extracted, and the complex amplitude and the corresponding rotation angle are combined to form a data sample, thereby constructing a complete dataset.

[0017] Furthermore, both the forward prediction network and the reverse design network are deep fully connected neural networks with similar network structures. The network structure includes an input layer, an output layer, and eight hidden layers. The number of neurons in the eight hidden layers is set to a combination of 200, 500, 800, 800, 800, 500, and 200. Each fully connected layer is followed by a normalization layer and an activation function layer.

[0018] Furthermore, both the training processes of the forward prediction network and the reverse design network use PReLU as the activation function, the Adam optimizer for updating network weights, and the mean squared error (MSE) as the loss function to quantify the prediction error.

[0019] The terahertz metasurface reverse design method based on cascaded neural networks proposed in this invention has the following advantages:

[0020] (1) The present invention provides a terahertz metasurface reverse design method based on cascaded neural networks, which can effectively overcome the instability and inaccuracy caused by the "one-to-many" mapping problem of a single reverse model by means of the physical constraint mechanism of cascaded networks while maintaining the high efficiency advantage of deep learning methods, thereby realizing fast, accurate and reliable reverse design of terahertz metasurfaces.

[0021] (2) The reverse design method of terahertz metasurface based on cascaded neural network of the present invention does not depend on the specific metasurface unit configuration and has good versatility and scalability. Attached Figure Description

[0023] Figure 1 This is a schematic diagram of the overall process of the reverse design method in this embodiment of the invention;

[0024] Figure 2 This is a schematic diagram of the metasurface unit structure used in the embodiments of the present invention;

[0025] Figure 3 This is a schematic diagram of the model framework of the cascaded neural network model described in this invention;

[0026] Figure 4 This is a graph showing the change of the loss function during the training process of the present invention, where (a) is the convergence curve of the loss function of the forward prediction network and (b) is the convergence curve of the loss function of the reverse design network.

[0027] Figure 5 These are experimental images of the reverse design method of this invention in holographic applications, where (a) is the target image, (b) is the pixelated target image, (c) is the simulated holographic image obtained based on the design of this invention, and (d) is the corresponding experimentally measured holographic image. Detailed Implementation

[0029] The present invention will now be described in further detail with reference to the embodiments and accompanying drawings.

[0030] like Figure 1 As shown in the figure, this embodiment demonstrates the complete process of designing a terahertz holographic metasurface using the method of the present invention. First, the complex amplitude distribution curve is determined, and the target features are extracted from the curve as input. The features are then fed into a deep neural network model, which can quickly and directly predict the optimal structural parameters corresponding to each unit constituting the metasurface array, thereby completing the design of the entire metasurface array.

[0031] like Figure 2 As shown, the metasurface unit used in this embodiment comprises a three-layer structure, consisting of a top-layer metal C-ring resonator, an intermediate dielectric substrate, and a bottom-layer metal C-ring resonator stacked sequentially from top to bottom. The intermediate dielectric substrate is a cyclic olefin copolymer (COC) with a thickness h of 100 μm. The period P of the entire unit structure is set to 109 μm, and the radius R of the C-ring is 86 μm. In this unit, the geometry of the metal C-ring remains fixed, while its functional adjustment is achieved by independently rotating the top-layer C-ring by an angle θ1 and the bottom-layer C-ring by an angle θ2.

[0032] like Figure 3 As shown, the cascaded neural network model constructed in this invention consists of a reverse design network on the left and a forward prediction network on the right. Its training process first requires using the numerical simulation software CST Studio Suite to change the combination of rotation angles θ1 and θ2 of the two metal C-rings, and extracting the corresponding complex amplitudes (real and imaginary parts) at a fixed frequency, using the angles and complex amplitudes as the dataset. During training, the forward network is first trained independently to accurately predict the real and imaginary parts based on the input θ1 and θ2. Then, after fixing the weights of the forward network, the weights of the reverse design network are iteratively optimized by calculating the error between the reconstructed complex amplitude corresponding to the structure predicted by the reverse network and the target complex amplitude.

[0033] like Figure 4 As shown in the figure, the loss function convergence curves of the forward prediction network and the reverse design network during the training process are shown. It can be seen from the figure that the training loss and test loss of both networks can decrease rapidly in the early stage of training and eventually converge, which proves the effectiveness of model training.

[0034] like Figure 5 As shown, in order to verify the practicality and accuracy of the method of the present invention through application examples, a terahertz holographic metasurface capable of generating the digital "1234" pattern was designed. Figure 5(a) is the target image set in this embodiment, namely the number "1234". Figure 5 (b) is the pixelated image. The target complex amplitude distribution required for each unit structure that makes up the metasurface is calculated and input into a trained inverse design network to obtain the unit structure parameters that make up the entire metasurface array. Based on this design, we conducted simulations and experimental sample tests. Figure 5 (c) is the holographic image obtained from the simulation. Figure 5 (d) is a holographic image of the actual prepared metasurface sample measured at 0.6 THz. The high consistency between the simulation and experimental results confirms that the reverse design method proposed in this invention is functionally feasible and has high design accuracy and reliability.

Claims

1. A metasurface reverse design method based on cascaded neural networks, characterized in that, Includes the following steps: S1. Change the structural parameters of the metasurface unit, obtain the structure of each unit and the corresponding complex amplitude of the optical response, establish a dataset and divide it into training set and test set; S2. Construct a forward prediction network, which is a deep neural network that takes unit structure parameters as input and optical response complex amplitude as output; train the forward prediction network using the training set and fix its network weights after training is completed. S3. Construct a reverse design network, which is a deep neural network that takes the complex amplitude of the optical response as input and the unit structure parameters as output. The reverse design network is cascaded with the forward prediction network with fixed weights. The complex amplitude of the optical response in the training set is input into the reverse design network. The network weights of the reverse design network are iteratively updated only by minimizing the mean square error between the reconstructed complex amplitude output by the forward prediction network and the actual complex amplitude input to the reverse design network. S4. Input the desired target optical response complex amplitude into the trained inverse design network to obtain the unit structure parameters, and use micro-nano fabrication technology to form the corresponding pattern on the substrate based on the parameters to complete the metasurface sample.

2. The method according to claim 1, characterized in that, The optical response complex amplitude obtained in step S1 is a value at a specific target frequency. This method avoids the complex process of calculating or defining the complete target response spectrum during application, thereby simplifying the input conditions for reverse design.

3. The method according to claim 1, characterized in that, Both the forward prediction network and the reverse design network are deep neural networks, each containing an input layer, an output layer, and multiple hidden layers. Each hidden layer is followed by a batch normalization layer and a nonlinear activation layer to accelerate model convergence and enhance the network's nonlinear fitting ability.

4. The method according to claim 1, characterized in that, In the training method described in S3, the weights of the forward network are kept frozen during training, the forward and inverse networks are cascaded, and only the inverse network is updated via backpropagation. This method overcomes the problem of mapping ambiguity caused by insufficient features when using only a single frequency point complex amplitude as the target by using the physical mapping relationship solidified by the forward network as a hard constraint. It can force the network to converge to a unique, physically self-consistent structural parameter solution, thereby ensuring the uniqueness and high accuracy of the prediction results.

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