Method for reverse design of network multifunctional metasurface based on physical consistency prior

Abstract

The application discloses a method for generating a multifunctional metasurface reverse design based on physical consistency prior, comprising the following steps: obtaining target electromagnetic function parameters of a to-be-designed metasurface; normalizing, embedding coding and multi-task label fusion are performed on the target electromagnetic function parameters to obtain a target function vector; physical consistency prior information is constructed; a plurality of candidate metasurface structures are generated; the candidate metasurface structures are corrected, amplitude-limited, topologically purified or removed according to preset process constraints to obtain manufacturability projection correction results; the corrected candidate metasurface structures are input into a multi-task forward response proxy network to obtain electromagnetic response prediction results; a comprehensive evaluation value is calculated, and the final metasurface structure is obtained according to the comprehensive evaluation value. The application makes the generated structure close to the target electromagnetic response, and meets the basic physical law, the structure topological boundary and the process constraint, thereby improving the design efficiency of the multifunctional metasurface and the realizability of the design result.

Description

Technical Field

[0001] This invention belongs to the fields of electromagnetic metasurfaces, computational electromagnetics, micro / nano structure design, radio frequency and optical device design, and artificial intelligence-assisted reverse design technology. Specifically, it is a reverse design method for multifunctional metasurfaces based on a physically consistent prior generative network. Background Technology

[0002] Metasurfaces are two-dimensional or quasi-two-dimensional electromagnetic structures composed of subwavelength artificial units arranged in a specific spatial pattern. By changing the geometry, size, material parameters, and array arrangement of the units, metasurfaces can control the phase, amplitude, polarization state, and propagation direction of incident electromagnetic waves within a relatively thin thickness. Compared with traditional bulk material devices, metasurfaces have advantages such as compact structure, high degree of controllability, and ease of array integration, and have been used in beam deflection, focusing, polarization conversion, absorption, filtering, holographic modulation, and frequency selection.

[0003] Existing metasurface design methods primarily rely on manual experience, parametric scanning, full-wave simulation, and traditional optimization algorithms. For single operating frequencies, single polarizations, or simple unit structures, these methods can yield structural solutions that meet certain target responses. However, when the target function simultaneously involves frequency, angle, polarization, amplitude and phase response, bandwidth, and fabrication boundaries, the structural parameter space increases significantly. Designers typically need to repeatedly adjust unit periods, linewidths, spacing, layer thicknesses, material dielectric constants, and arrangement methods, and verify these adjustments through successive full-wave simulations, resulting in a lengthy design cycle.

[0004] In recent years, neural networks have been used for both forward prediction and reverse design of metasurfaces. Forward prediction networks can quickly predict electromagnetic responses based on structural parameters, while reverse design networks can directly output structural parameters based on the target response. Related research shows that introducing Jones matrix representation, physically augmented data, forward proxy networks, and conditional generative models into metasurface design helps improve compatibility across different wavelengths, polarizations, and tasks; diffusion models, Transformer generative models, and multi-candidate structure generation methods can provide multiple alternative structures for the same target response, thereby alleviating the one-to-many non-uniqueness problem in reverse electromagnetic design.

[0005] However, existing neural network-based metasurface inverse design still has shortcomings. First, some methods only learn the statistical mapping between the target response and structural parameters, failing to fully embed electromagnetic physics priors such as phase gradient, energy conservation, reciprocity, periodic boundaries, material parameter boundaries, and nearest-neighbor coupling into the generation process. This results in generated structures that may closely approximate the target in surrogate predictions but are difficult to verify through subsequent full-wave simulations or experimental measurements. Second, some methods output a single structural result, while metasurface inverse design inherently involves a one-to-many mapping relationship. The same phase or spectral target may correspond to multiple geometric structures, and a single output can easily lead to the omission of feasible structures.

[0006] Third, some generative models lack manufacturing feasibility constraints, and the generated patterns may have problems such as excessively narrow linewidths, excessively small spacing, isolated metal islands, excessively large aspect ratios, or difficulties in interlayer alignment. These problems will affect the actual manufacturability in micro / nano fabrication, printed circuit fabrication, and multilayer dielectric fabrication. Fourth, if full-wave simulation verification is only performed after generation, high computational costs will still be retained; if only surrogate model prediction is relied upon, the results may be unreliable due to extrapolation errors of the surrogate model.

[0007] Therefore, to address the above issues, a novel metasurface inverse design method needs to be proposed, namely, a multifunctional metasurface inverse design method based on a physically consistent prior generative network. Summary of the Invention

[0008] To address the aforementioned problems in existing technologies, this invention provides a reverse design method for multifunctional metasurfaces based on physically consistent prior generative networks. This method integrates target function encoding, physically consistent prior embedding, response manifold constraints, multi-candidate structure generation, manufacturability projection correction, and forward proxy rapid verification into a single closed-loop process. This ensures that the generated structure closely approximates the target electromagnetic response while satisfying fundamental physical laws, structural topological boundaries, and process constraints, thereby improving the design efficiency and feasibility of multifunctional metasurfaces.

[0009] The technical solution to achieve the above objectives is: A multifunctional metasurface inverse design method based on a physically consistent prior generative network includes: Step S1: Obtain the target electromagnetic functional parameters of the metasurface to be designed. The target electromagnetic functional parameters include operating frequency or wavelength, incident angle, exit angle, incident polarization state, target phase response, target amplitude response, target bandwidth, target beam direction, target focal position, and target functional type. Step S2: Normalize, embed, encode, and fuse multi-task tags for the target electromagnetic function parameters to obtain the spectrum-angle-polarization-amplitude-phase joint target function vector; Step S3: Construct physically consistent prior information based on the electromagnetic response law of the metasurface unit, the range of material parameters, the array boundary conditions, and the processing technology boundary. Step S4: Input the target function vector and physical consistency prior information into the physical consistency prior generation network to generate multiple candidate metasurface structures; Step S5: Input multiple candidate metasurface structures into the manufacturability projection correction module, and correct, limit, clean up or eliminate the candidate metasurface structures according to preset process constraints to obtain manufacturability projection correction results. Step S6: Input the candidate metasurface structure after manufacturability projection correction into the multi-task positive response proxy network to obtain the electromagnetic response prediction results corresponding to the candidate metasurface structure. Step S7: Calculate the comprehensive evaluation value based on the target electromagnetic functional parameters, physical consistency prior information, manufacturability projection correction results, and electromagnetic response prediction results, and select the final metasurface structure based on the comprehensive evaluation value.

[0010] Preferably, in step S1, the target function type includes beam deflection, focusing, filtering, absorption, polarization conversion, and holographic modulation; When the target function type is beam deflection, the phase gradient prior satisfies the following equation: ; In the formula, For metasurface along Phase distribution in direction, For free space wavenumber, Angle of incidence The target launch angle; When the target function type is focusing, the target phase distribution satisfies the following formula: ; In the formula, Let the coordinates be those of the metasurface plane. For the target focal length, is the phase constant.

[0011] Preferably, in step S2, the spectrum-angle-polarization-amplitude-phase joint target function vector includes frequency coding components, incident angle coding components, exit angle coding components, polarization state coding components, phase distribution coding components, amplitude distribution coding components, bandwidth coding components, and function type embedding components.

[0012] Preferably, in step S3, the physical consistency prior information includes one or more of the following: phase gradient prior, phase coverage prior, amplitude response prior, energy conservation prior, reciprocity prior, periodic boundary prior, near-field coupling of adjacent units prior, material dielectric constant range prior, and material loss range prior. For passive metasurface structures, the energy conservation prior satisfies the following equation: ; In the formula, For frequency Complex reflection coefficient at that location, For frequency Complex transmission coefficient at that location, For frequency The absorption term at the location.

[0013] Preferably, in step S3, the physically consistent prior generation network includes a conditional diffusion model, a variational autoencoder, a generative adversarial network, a Transformer (self-attention mechanism) generation network, a graph neural network generation network, or a combination thereof. The Physically Consistent Prior Generative Network (PCG) outputs multiple candidate metasurface structural parameters on the target response manifold, conditioned by the target function vector, physically consistent prior information, and structural latent variables. The candidate metasurface structure parameters include unit period, pattern type, pattern boundary coordinates, linewidth, spacing, metal layer thickness, dielectric layer thickness, material dielectric constant, material loss tangent, number of layers, and array arrangement.

[0014] Preferably, in step S4, at least two of the candidate metasurface structures have different pattern shapes, topological connections, or combinations of geometric parameters, and their corresponding electromagnetic responses all meet the error requirements of the same target electromagnetic functional parameter.

[0015] Preferably, in step S5, the preset process constraints include one or more of the following: minimum linewidth, minimum spacing, maximum aspect ratio, minimum fillet radius, structural connectivity, minimum area of ​​metal islands, etching depth, interlayer alignment error, and material thickness range.

[0016] Preferably, in step S6, the multi-task positive response agent network is trained using training samples before candidate structure screening; The training samples include metasurface structure parameters and their full-wave simulation or test responses; The full-wave simulation response or test response includes one or more of the following: complex reflection coefficient, complex transmission coefficient, phase, amplitude, and far-field distribution. The electromagnetic response prediction results include one or more of the following: complex reflection coefficient, complex transmission coefficient, phase response, amplitude response, polarization conversion efficiency, operating bandwidth, absorptivity, far-field pattern, beam deflection angle, and focusing efficiency.

[0017] Preferably, in step S7, the comprehensive evaluation value is calculated based on the target response error, response manifold consistency error, energy conservation error, manufacturing constraint error, and structural diversity evaluation item, and its comprehensive loss function satisfies the following formula: ; In the formula, For the target response error, For phase consistency error, For energy conservation error, To create constraint errors, For structural diversity evaluation items, , , , and All are weighting coefficients; Among them, the manufacturing constraint error includes linewidth constraint, spacing constraint, aspect ratio constraint and topological connectivity constraint. The linewidth constraint and spacing constraint are calculated based on the deviation between the actual linewidth and actual spacing of the candidate structure and the lower limit of the process.

[0018] Preferably, in step S7, after the final metasurface structure is obtained by screening, a full-wave simulation verification is performed on the final metasurface structure. When the deviation between the full-wave simulation verification result and the prediction result of the multi-task positive response agent network exceeds a preset threshold, the final metasurface structure and its full-wave simulation verification result are added to the training samples, and the multi-task positive response agent network is updated by bootstrapping.

[0019] Compared with the prior art, the beneficial effects of the present invention are: This invention combines target function encoding, physical consistency prior construction, cross-scale condition generation, multi-candidate structure output, manufacturability projection correction, and multi-task forward response proxy into the same process, so that metasurface reverse design no longer relies solely on human experience or single neural network regression results. By incorporating physical consistency priors into the generation and screening of candidate structures, the risk of generated structures violating phase modulation laws, energy conservation relationships, or material boundary conditions can be reduced. By comprehensively evaluating response manifold constraints and multiple candidate structures, the problem of non-uniqueness of multiple structures corresponding to the same target response can be alleviated. Through manufacturability projection correction, unmanufacturable structures such as excessively narrow linewidths, excessively small spacing, isolated patterns, and excessively large aspect ratios can be reduced; Rapid verification through a multi-task forward response agent network can reduce the number of repeated full-wave simulations and improve the efficiency of reverse engineering of multifunctional metasurfaces. Attached Figure Description

[0020] The accompanying drawings are provided to further illustrate the invention and form part of the specification. They are used in conjunction with embodiments of the invention to explain the invention and do not constitute a limitation thereof. In the drawings: Figure 1 This is a flowchart of the reverse design method for multifunctional metasurfaces based on a physically consistent prior generative network, as described in this invention. Figure 2 This is another flowchart of the reverse design method for multifunctional metasurfaces based on physical consistency prior generation networks according to the present invention; Figure 3 This is a schematic diagram comparing the generated full-wave simulation phase response of the structure with the target phase response in this invention; Figure 4 This is a schematic diagram comparing the generated full-wave simulation amplitude response of the structure with the target amplitude response in this invention; Figure 5 This is a schematic diagram comparing the proportion of candidate structure constraint violations before and after manufacturability projection correction in this invention; Figure 6 This is a schematic diagram comparing the far-field radiation pattern of the target and the far-field radiation pattern of the generated structure in the beam deflection task of this invention. Detailed Implementation

[0021] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0022] To address the problems of high workload for manual parameter tuning, numerous full-wave simulations, non-unique inverse mapping, insufficient physical consistency of generated structures, and difficulty in guaranteeing manufacturing feasibility in existing metasurface reverse design methods, this invention proposes a multifunctional metasurface reverse design method based on a physically consistent prior generative network. This method does not simply use a neural network to directly regress a structural parameter from the target response. Instead, it establishes a closed-loop process between target function encoding, physically consistent prior embedding, response manifold constraints, multi-candidate structure generation, manufacturability projection correction, and forward surrogate verification. This ensures that candidate structures are jointly constrained by the target function, physical laws, structural topology, and manufacturing boundaries during the generation, correction, and selection stages. The specific implementation process is as follows.

[0023] like Figure 1 , 2 As shown, a reverse design method for multifunctional metasurfaces based on physically consistent prior generative networks includes: Step S1: Obtain the target electromagnetic functional parameters of the metasurface to be designed. The target electromagnetic functional parameters include operating frequency or wavelength, incident angle, exit angle, incident polarization state, target phase response, target amplitude response, target bandwidth, target beam direction, target focal position, and target functional type.

[0024] In the embodiments, the target function types include beam deflection, focusing, filtering, absorption, polarization conversion, and holographic modulation; The target function vector can be represented as: ; In the formula, The operating frequency or the frequency derived from the wavelength. Angle of incidence The target launch angle, It is a polarization state. For the target phase response, For the target amplitude response, For target bandwidth, Encode the target function type; When the target function type is beam deflection, the phase gradient prior satisfies the following equation: ; In the formula, For metasurface along Phase distribution in direction, For the free space wavenumber, this formula is derived from the generalized Snell phase gradient relation and is used to constrain the phase change along the metasurface direction; When the target function type is focusing, the target phase distribution satisfies the following formula: ; In the formula, Let the coordinates be those of the metasurface plane. For the target focal length, It is the phase constant; For beam deflection tasks, the target phase gradient is constructed based on the generalized phase gradient relationship; for focusing tasks, the target phase distribution is constructed based on the focal length and aperture coordinates; for passive transmission or reflection metasurfaces, energy conservation priors are constructed based on the relationship between reflection, transmission, and absorption; for polarization control tasks, polarization conversion priors can be constructed based on the cross-polarization and co-polarization response relationship in the Jones matrix.

[0025] Step S2 involves normalizing, embedding, and fusing multi-task labels to obtain a spectrum-angle-polarization-amplitude-phase joint target function vector. Specifically, continuous parameters are first normalized based on the frequency, angle, and size ranges of the training samples, while discrete parameters are categorically encoded or embedded. For phase and amplitude distributions, they can be represented by sampling point vectors, low-order basis function coefficients, or feature maps. After encoding, different functional tasks are converted into a unified spectrum-angle-polarization-amplitude-phase joint target function vector, enabling the same generative network to handle multiple metasurface design tasks.

[0026] In the embodiment, the spectrum-angle-polarization-amplitude-phase joint target function vector includes frequency coding components, incident angle coding components, exit angle coding components, polarization state coding components, phase distribution coding components, amplitude distribution coding components, bandwidth coding components, and function type embedding components.

[0027] Step S3: Construct physical consistency prior information based on the electromagnetic response law of the metasurface unit, the range of material parameters, the array boundary conditions, and the processing technology boundary.

[0028] In the embodiments, the physical consistency prior information includes one or more of the following: phase gradient prior, phase coverage prior, amplitude response prior, energy conservation prior, reciprocity prior, periodic boundary prior, near-field coupling of adjacent cells prior, material dielectric constant range prior, and material loss range prior. For passive metasurface structures, the energy conservation prior satisfies the following equation: ; In the formula, For frequency Complex reflection coefficient at that location, For frequency Complex transmission coefficient at that location, For frequency The absorption term at the location.

[0029] In the embodiments, the physical consistency prior generation network includes a conditional diffusion model, a variational autoencoder, a generative adversarial network, a Transformer generation network, a graph neural network generation network, or a combination thereof. The Physically Consistent Prior Generative Network (PCG) outputs multiple candidate metasurface structural parameters on the target response manifold, conditioned by the target function vector, physically consistent prior information, and structural latent variables. The candidate metasurface structure parameters include unit period, pattern type, pattern boundary coordinates, linewidth, spacing, metal layer thickness, dielectric layer thickness, material dielectric constant, material loss tangent, number of layers, and array arrangement.

[0030] Step S4: Input the target function vector and physical consistency prior information into the physical consistency prior generation network to generate multiple candidate metasurface structures; specifically, the physical consistency prior generation network takes the target function vector, physical consistency prior information and structural latent variables as conditional inputs, and structural parameters or structural patterns as outputs.

[0031] In this embodiment, in order to retain the multiple solutions characteristic in reverse design, the generative network outputs multiple candidate structures instead of just a single structure. At least two of the multiple candidate metasurface structures have different pattern shapes, topological connections or combinations of geometric parameters, and the corresponding electromagnetic responses all meet the error requirements of the same target electromagnetic function parameter.

[0032] Step S5: Input multiple candidate metasurface structures into the manufacturability projection correction module, and correct, limit, topologically clean or eliminate the candidate metasurface structures according to preset process constraints to obtain manufacturability projection correction results.

[0033] In the embodiments, the preset process constraints include one or more of the following: minimum linewidth, minimum spacing, maximum aspect ratio, minimum fillet radius, structural connectivity, minimum area of ​​metal islands, etching depth, interlayer alignment error, and material thickness range. Specifically, for the generated candidate structures, we first check whether their linewidth is less than the minimum linewidth threshold, whether the spacing is less than the minimum spacing threshold, whether the ratio of structure height to linewidth exceeds the allowable range of the process, and whether there are isolated metal islands or suspended areas in the pattern. For correctable structures, we perform boundary smoothing, minimum linewidth expansion, topology connectivity purification, island merging, hole filling, and size limiting. For structures that cannot be corrected, we directly reject them.

[0034] Step S6: Input the candidate metasurface structure after manufacturability projection correction into the multi-task positive response proxy network to obtain the electromagnetic response prediction results corresponding to the candidate metasurface structure.

[0035] In this embodiment, the multi-task positive response agent network is trained using training samples before candidate structure screening; Input structural parameter samples into a multi-task positive response agent network, and use the full-wave simulation response or test response as the supervision output; For parametric structures, inputs may include period, linewidth, spacing, thickness, material dielectric constant, and loss tangent; for pixelated structures, inputs may include pattern mask and material layer information. The multi-task positive response agent network outputs responses such as complex reflection coefficient, complex transmission coefficient, phase, amplitude, and far-field distribution. After training, the network is used for rapid screening of candidate structures; The candidate metasurface structure, after manufacturability projection correction, is input into a trained multi-task forward response proxy network to obtain the electromagnetic response prediction results corresponding to the candidate metasurface structure. The electromagnetic response prediction results include one or more of the following: complex reflection coefficient, complex transmission coefficient, phase response, amplitude response, polarization conversion efficiency, operating bandwidth, absorptivity, far-field pattern, beam deflection angle, and focusing efficiency.

[0036] Step S7: Calculate the comprehensive evaluation value based on the target electromagnetic functional parameters, physical consistency prior information, manufacturability projection correction results, and electromagnetic response prediction results, and select the final metasurface structure based on the comprehensive evaluation value.

[0037] Specifically, the predicted response is compared with the target function parameters, and the target response error and response manifold consistency error are calculated. For passive structures, the energy conservation error is also calculated. For structures whose manufacturing boundaries are close to the threshold, while preserving manufacturing constraint errors; The comprehensive evaluation value consists of the target response error, response manifold consistency error, energy conservation error, manufacturing constraint error, and structural diversity evaluation items.

[0038] In this embodiment, the comprehensive evaluation value is calculated based on the target response error, response manifold consistency error, energy conservation error, manufacturing constraint error, and structural diversity evaluation item, and its comprehensive loss function satisfies the following formula: ; In the formula, For the target response error, For phase consistency error, For energy conservation error, To create constraint errors, For structural diversity evaluation items, , , , and All are weighting coefficients; The manufacturing constraint error includes linewidth constraint, spacing constraint, aspect ratio constraint, and topological connectivity constraint. The linewidth constraint and spacing constraint are calculated based on the deviations between the actual linewidth and actual spacing of the candidate structure and the lower limit of the manufacturing process, respectively. ; In the formula, For the candidate structure Line width, Minimum linewidth threshold, For the first Spacing, Minimum spacing threshold For the first At structural height, The height limit corresponds to the process capability; the aforementioned manufacturing constraint error is used to penalize structures that do not meet the processing boundaries.

[0039] In the embodiment, during the screening process, structures that do not meet the hard manufacturing constraints are first eliminated, and then the structures with smaller comprehensive evaluation values ​​and response indicators that meet the target threshold are selected from the remaining candidate structures. If multiple structures meet the target requirements at the same time, structures with larger manufacturing margins, simpler patterns, or more stable bandwidth responses can be given priority. After the final metasurface structure is obtained through screening, a full-wave simulation is performed to verify the final metasurface structure. If the deviation between the full-wave simulation verification result and the prediction result of the multi-task positive response agent network is within a preset range, the structure is output as the final design result. If the deviation exceeds a preset threshold, the structure and its full-wave simulation result are added to the sample database, and the multi-task positive response agent network is updated before re-screening candidate structures.

[0040] To verify the effectiveness of the method of this invention in the reverse design of multifunctional metasurfaces, a parameterized simulation database was constructed, encompassing four typical electromagnetic control tasks: beam deflection, focusing, bandpass filtering, and polarization conversion. Under unified material range, geometric boundaries, and process constraints, the method of this invention was systematically compared with several representative baseline methods. The experiments focused on examining design accuracy, design efficiency, manufacturability pass rate, and generalization ability under different functional tasks.

[0041] All candidate structures were generated under the same material parameter range and processing constraints, which mainly included minimum linewidth, minimum spacing, maximum aspect ratio, pattern connectivity, and minimum island area. The candidate structures output by the comparison method were first uniformly formatted, then rapidly predicted using a multi-task positive response proxy network. Representative schemes were selected for full-wave simulation verification to ensure consistency in the comparison results.

[0042] For the simulation platform, CST Microwave Studio (electromagnetic simulation software) was used to establish a parametric full-wave simulation model of the metasurface. Rogers RO4003C was selected as the dielectric substrate, and a copper material model was used for the metal layer. The operating frequency band covered 8–12 GHz. By randomly sampling and constraining geometric parameters such as unit period, pattern boundary, linewidth, spacing, metal thickness, and dielectric thickness, a structural parameter space was formed. Then, the complex reflection coefficient, complex transmission coefficient, phase response, amplitude response, and far-field radiation pattern were obtained through full-wave simulation to construct a structure-response pair sample.

[0043] To ensure statistical independence between training and testing, the samples were randomly divided into model building samples, parameter tuning samples, and evaluation samples. Model building samples were used for parameter learning of the physically consistent prior generator network and the multi-task positive response agent network; parameter tuning samples were used for hyperparameter tuning and early stopping; and evaluation samples were used for final performance evaluation. The corresponding simulation and dataset settings are shown in Table 1. Table 1 Simulation Platform and Dataset Settings

[0044] To comprehensively evaluate the effectiveness of the method of this invention, traditional search methods, intelligent optimization methods, and generative methods were set as controls, including Random Search, Particle Swarm Optimization (PSO), Bayesian Optimization, Conditional Generative Adversarial Network (cGAN), Variational Autoencoder (VAE), and Diffusion Model. Among these, Random Search, PSO, and Bayesian Optimization all iteratively minimize the target response error; cGAN, VAE, and Diffusion Model directly output candidate structures conditioned on the target function vector.

[0045] The evaluation metrics mainly include: 1) Phase RMSE, used to evaluate the consistency between the generated structure's phase response and the target response; 2) Amplitude Error, used to evaluate the degree to which the generated structure approximates the target amplitude response; 3) Number of full-wave simulations, used to evaluate the dependence on high-overhead simulations during the design process; 4) Average design time, used to evaluate the overall design efficiency; and 5) Proportion of meeting manufacturing constraints, used to evaluate the proportion of candidate structures that meet process boundaries and manufacturability constraints. The corresponding evaluation metric settings are shown in Table 2. Table 2. Overall performance comparison of different reverse engineering methods

[0046] Taking beam deflection mission as an example, the target exit angle is set to 30° and the incident angle is 0°, and it is required to maintain a relatively stable phase gradient distribution and amplitude response within the working frequency band. Figure 3 A comparison of the target phase response and the full-wave simulated phase response of the structure generated by this invention is presented. Figure 4 The comparison results between the target amplitude response and the generated structure amplitude response are presented. It can be seen that the proposed method can approximate the target phase trend well in the element position dimension, and the amplitude fluctuation remains within a small range, indicating that the physical consistency prior has a positive effect on the generation of stable structures.

[0047] Table 2 presents the overall performance of different reverse design methods on the evaluation samples. The results show that while traditional search and optimization methods can find feasible structures that meet some of the target requirements, they incur significant overhead in terms of the number of full-wave simulations and design time. Generative methods significantly reduce design time, but without explicit physical constraints, they still have certain shortcomings in phase consistency and the proportion of manufacturing constraints met. In contrast, the method of this invention demonstrates superior overall performance in terms of design accuracy, design efficiency, and manufacturing feasibility.

[0048] To verify the manufacturability projection correction module's effect on improving the quality of candidate structures, the proportions of linewidth violations, spacing violations, isolated metal islands, average manufacturing margin, and response error exceeding the threshold were statistically analyzed before and after correction. The results are shown in Table 3. Table 3 Comparison of candidate structure quality before and after manufacturability projection correction

[0049] From Table 3 and Figure 5 As can be seen, after manufacturability projection correction, the unmanufacturability problems caused by excessively small linewidths, insufficient spacing, and isolated patterns in the candidate structures are significantly reduced; at the same time, the average manufacturing allowance is increased from 0.11 mm to 0.27 mm, indicating that the proposed correction process can not only eliminate obviously unmanufacturable structures, but also improve the structure's tolerance to manufacturing errors while preserving the target response trend.

[0050] Considering that this invention is not limited to a single beam deflection scenario, but also targets multiple target electromagnetic functions such as focusing, filtering, and polarization conversion, further generalization tests were conducted on multi-functional tasks. Test samples were randomly selected for each type of task, and the target response error and corresponding functional efficiency were statistically analyzed under the same evaluation system. The results are shown in Table 4. As can be seen from Table 4, the method of this invention can maintain low response error and high functional efficiency across different types of tasks, indicating that the proposed target function encoding method, physically consistent prior embedding strategy, and multi-task positive response proxy mechanism have good versatility. Taking the beam deflection task as an example... Figure 6 A comparison of the far-field radiation pattern of the target and the far-field radiation pattern of the structure generated in this invention is presented. The main lobe direction maintains good consistency with the target angle, and the side lobe suppression is also within an acceptable range. The results are shown in Table 4: Table 4 Test results under different functional tasks

[0051] The method of this invention can achieve better target response approximation results with less full-wave simulation overhead in the reverse design of multifunctional metasurfaces, and significantly improve the fabrication feasibility of candidate structures.

[0052] In one beam deflection embodiment, the operating frequency is set to... The angle of incidence is The target launch angle is The target function coding module will , , The polarization state is encoded as the target function vector; the physical consistency prior construction module generates the target phase gradient according to the phase gradient formula; the physical consistency prior generation network outputs multiple candidate unit structures that satisfy the phase gradient trend and response manifold constraints; the manufacturability projection correction module eliminates structures whose linewidth and spacing do not meet the processing requirements; the multi-task positive response surrogate network predicts the far-field radiation pattern and outputs the beam deflection angle, and finally selects the metasurface structure that meets the target deflection angle and efficiency requirements.

[0053] In one focusing embodiment, the operating wavelength, focal length F, and aperture size are set. The target function encoding module converts the focal length, aperture coordinates, and polarization state into a target phase distribution; the physical consistency prior construction module generates constraint information based on the focusing phase formula; the physical consistency prior generation network outputs multiple metasurface unit structures and their arrangements; the multi-task positive response surrogate network predicts the focal position and focusing efficiency; and the comprehensive evaluation and screening module selects the structure with smaller focal position error, focusing efficiency meeting the threshold, and larger manufacturing margin as the final design result.

[0054] In one absorption or filtering embodiment, the target center frequency, bandwidth, and target reflection amplitude are input. A physical consistency prior generation network generates multiple candidate metal-dielectric-metal structures or other structures suitable for frequency-selective responses; physical consistency prior information limits the material loss range and passive energy relationships; a manufacturability projection correction module checks pattern connectivity, linewidth, and dielectric layer thickness; a multi-task positive response proxy network outputs the reflection or transmission spectrum; and a comprehensive evaluation and screening module selects structures whose frequency band location matches the target and whose fabrication constraints are met.

[0055] Finally, it should be noted that the above are merely preferred embodiments of the present invention and are not intended to limit the present invention. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art can still modify the technical solutions described in the foregoing embodiments or make equivalent substitutions for some of the technical features. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A reverse design method for multifunctional metasurfaces based on physically consistent prior generative networks, characterized in that, include: Step S1: Obtain the target electromagnetic functional parameters of the metasurface to be designed. The target electromagnetic functional parameters include operating frequency or wavelength, incident angle, exit angle, incident polarization state, target phase response, target amplitude response, target bandwidth, target beam direction, target focal position, and target functional type. Step S2: Normalize, embed, encode, and fuse multi-task tags for the target electromagnetic function parameters to obtain the spectrum-angle-polarization-amplitude-phase joint target function vector; Step S3: Construct physically consistent prior information based on the electromagnetic response law of the metasurface unit, the range of material parameters, the array boundary conditions, and the processing technology boundary. Step S4: Input the target function vector and physical consistency prior information into the physical consistency prior generation network to generate multiple candidate metasurface structures; Step S5: Input multiple candidate metasurface structures into the manufacturability projection correction module, and correct, limit, clean up or eliminate the candidate metasurface structures according to preset process constraints to obtain manufacturability projection correction results. Step S6: Input the candidate metasurface structure after manufacturability projection correction into the multi-task positive response proxy network to obtain the electromagnetic response prediction results corresponding to the candidate metasurface structure. Step S7: Calculate the comprehensive evaluation value based on the target electromagnetic functional parameters, physical consistency prior information, manufacturability projection correction results, and electromagnetic response prediction results, and select the final metasurface structure based on the comprehensive evaluation value.

2. The method for reverse design of multifunctional metasurfaces based on physically consistent prior generative networks according to claim 1, characterized in that, In step S1, the target function types include beam deflection, focusing, filtering, absorption, polarization conversion, and holographic modulation. When the target function type is beam deflection, the phase gradient prior satisfies the following equation: ； In the formula, For metasurface along Phase distribution in direction, For free space wavenumber, Angle of incidence The target launch angle; When the target function type is focusing, the target phase distribution satisfies the following formula: ； In the formula, Let the coordinates be those of the metasurface plane. For the target focal length, is the phase constant.

3. The method for reverse design of multifunctional metasurfaces based on physically consistent prior generative networks according to claim 1, characterized in that, In step S2, the spectrum-angle-polarization-amplitude-phase joint target function vector includes frequency coding components, incident angle coding components, exit angle coding components, polarization state coding components, phase distribution coding components, amplitude distribution coding components, bandwidth coding components, and function type embedding components.

4. The method for reverse design of multifunctional metasurfaces based on physically consistent prior generative networks according to claim 1, characterized in that, In step S3, the physical consistency prior information includes one or more of the following: phase gradient prior, phase coverage prior, amplitude response prior, energy conservation prior, reciprocity prior, periodic boundary prior, near-field coupling of adjacent units prior, material dielectric constant range prior, and material loss range prior. For passive metasurface structures, the energy conservation prior satisfies the following equation: ； In the formula, For frequency Complex reflection coefficient at that location, For frequency Complex transmission coefficient at that location, For frequency The absorption term at the location.

5. The reverse design method for multifunctional metasurfaces based on physically consistent prior generative networks according to claim 1, characterized in that, In step S3, the physical consistency prior generation network includes a conditional diffusion model, a variational autoencoder, a generative adversarial network, a Transformer generation network, a graph neural network generation network, or a combination thereof. The Physically Consistent Prior Generative Network (PCG) outputs multiple candidate metasurface structural parameters on the target response manifold, conditioned by the target function vector, physically consistent prior information, and structural latent variables. The candidate metasurface structure parameters include unit period, pattern type, pattern boundary coordinates, linewidth, spacing, metal layer thickness, dielectric layer thickness, material dielectric constant, material loss tangent, number of layers, and array arrangement.

6. The reverse design method for multifunctional metasurfaces based on physically consistent prior generative networks according to claim 1, characterized in that, In step S4, at least two of the candidate metasurface structures have different pattern shapes, topological connections, or combinations of geometric parameters, and their corresponding electromagnetic responses all meet the error requirements of the same target electromagnetic functional parameter.

7. The reverse design method for multifunctional metasurfaces based on physically consistent prior generative networks according to claim 1, characterized in that, In step S5, the preset process constraints include one or more of the following: minimum linewidth, minimum spacing, maximum aspect ratio, minimum fillet radius, structural connectivity, minimum area of ​​metal islands, etching depth, interlayer alignment error, and material thickness range.

8. The method for reverse design of multifunctional metasurfaces based on physically consistent prior generative networks according to claim 1, characterized in that, In step S6, the multi-task positive response agent network is trained using training samples before candidate structure screening. The training samples include metasurface structure parameters and their full-wave simulation or test responses; The full-wave simulation response or test response includes one or more of the following: complex reflection coefficient, complex transmission coefficient, phase, amplitude, and far-field distribution. The electromagnetic response prediction results include one or more of the following: complex reflection coefficient, complex transmission coefficient, phase response, amplitude response, polarization conversion efficiency, operating bandwidth, absorptivity, far-field pattern, beam deflection angle, and focusing efficiency.

9. The method for reverse design of multifunctional metasurfaces based on physically consistent prior generative networks according to claim 1, characterized in that, In step S7, the comprehensive evaluation value is calculated based on the target response error, response manifold consistency error, energy conservation error, manufacturing constraint error, and structural diversity evaluation item, and its comprehensive loss function satisfies the following formula: ； In the formula, For the target response error, For phase consistency error, For energy conservation error, To create constraint errors, For structural diversity evaluation items, , , , and All are weighting coefficients; Among them, the manufacturing constraint error includes linewidth constraint, spacing constraint, aspect ratio constraint and topological connectivity constraint. The linewidth constraint and spacing constraint are calculated based on the deviation between the actual linewidth and actual spacing of the candidate structure and the lower limit of the process.

10. The method for reverse design of multifunctional metasurfaces based on physically consistent prior generative networks according to claim 1, characterized in that, In step S7, after the final metasurface structure is obtained, a full-wave simulation is performed on the final metasurface structure. When the deviation between the full-wave simulation verification result and the prediction result of the multi-task positive response agent network exceeds a preset threshold, the final metasurface structure and its full-wave simulation verification result are added to the training samples, and the multi-task positive response agent network is updated by bootstrapping.

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