A broadband metasurface intelligent design method based on a superatom electromagnetic response forward model
By constructing a forward model of the electromagnetic response of superatoms and a diffraction neural network evaluation agent, the problems of high computational overhead and poor manufacturability in broadband metasurface design are solved, enabling efficient parameter design under multi-wavelength conditions and improving design efficiency and consistency.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2026-03-11
- Publication Date
- 2026-06-26
AI Technical Summary
Existing broadband metasurface reverse design suffers from high computational overhead, a gap between trainable modulation parameters and manufacturable structures, and difficulties in constructing and coupling physical consistency assessment proxies, resulting in low design efficiency and poor engineering feasibility.
A forward model of the electromagnetic response of superatoms is constructed, and a diffraction neural network evaluation agent is combined with an optimization algorithm to achieve rapid forward evaluation under multi-wavelength conditions, and output the design results of superatomic geometric parameters that meet the index.
It reduces the computational cost of broadband reverse engineering, improves design efficiency and engineering feasibility, and ensures performance consistency and robustness under multi-wavelength conditions.
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Figure CN122287303A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of intelligent photonic device design and computational electromagnetics, and particularly to a broadband metasurface intelligent design method based on a forward model of superatomic electromagnetic response. Background Technology
[0002] Metasurfaces are artificial electromagnetic structures formed by arranging subwavelength-scale unit structures in a plane. By designing the geometric and material parameters of these unit structures, incident electromagnetic waves can achieve desired amplitude, phase, and polarization modulation after transmission or reflection, thereby enabling functions such as focusing, imaging, beamforming, filtering, holography, and information processing. Compared to traditional bulk optical elements, metasurface devices have advantages such as small thickness, high integration, and ease of array design.
[0003] Broadband metasurface devices must simultaneously meet performance constraints at multiple wavelengths within their operating bandwidth. Furthermore, the device response exhibits dispersion characteristics with wavelength variation, which can easily lead to performance degradation under broadband conditions, such as focal point drift, inhomogeneous in-band efficiency, or increased aberrations. To obtain metasurface structures that meet broadband requirements, existing techniques typically employ full-wave electromagnetic simulation combined with iterative optimization for structure search, or a pre-built response library search combined with re-optimization for design. However, under the combined influence of broadband, multiple constraints, and a high-dimensional structural parameter space, these methods often suffer from shortcomings in efficiency and manufacturability.
[0004] Common difficulties in reverse engineering existing broadband metasurfaces include:
[0005] (1) High computational overhead due to multi-wavelength evaluation. Broadband targets usually require evaluation of candidate structures at multiple discrete wavelength points. If full-wave electromagnetic simulation is frequently called to calculate multi-wavelength response during the optimization iteration process, the computational load will increase significantly with the number of wavelength points and the number of iterations, resulting in a long optimization cycle and high resource consumption.
[0006] (2) The gap between trainable modulation parameters and manufacturable structures. To facilitate optimization, some methods represent the modulation layer as a continuous and trainable complex transmission (or phase / amplitude) distribution, but actual devices need to be realized by superatomic geometric parameters that meet process constraints. If a stable and generalizable "geometric parameter-electromagnetic response" mapping mechanism is lacking, it is difficult to directly obtain manufacturable structures from the optimization results. Usually, additional retrieval, discretization or secondary correction processes are required, which introduces errors and reduces design efficiency.
[0007] (3) The construction and coupling of the physical consistency evaluation agent still requires a systematic solution. In order to reduce the frequency of full-wave simulation calls, the existing technology combines the approximate prediction of the electromagnetic response of the unit structure with the diffraction propagation calculation to achieve rapid forward evaluation. However, under broadband conditions, the complex transmission response of the unit structure exhibits strong dispersion characteristics with wavelength. How to effectively characterize the wavelength dimension, ensure the consistency between the predicted response and the propagation calculation, and form a stable evaluation agent that can be used for iterative optimization still lacks a unified and feasible technical solution.
[0008] Therefore, it is necessary to provide a method for reverse design of broadband metasurfaces, which can achieve rapid forward evaluation under multi-wavelength conditions within the geometrically feasible domain and manufacturability constraints, and can directly output the metaatomic geometric parameter distribution to improve the design efficiency and engineering feasibility of broadband metasurface devices. Summary of the Invention
[0009] Purpose of the invention
[0010] The purpose of this invention is to provide a broadband metasurface intelligent design method based on a forward model of superatomic electromagnetic response: by constructing a rapid prediction model from superatomic geometric parameters to broadband complex transmission response, and combining it with a diffraction propagation evaluation agent based on the angular spectrum method to achieve rapid forward evaluation under multi-wavelength conditions, and with the cooperation of broadband evaluation functions and optimization algorithms to complete the reverse search, thereby reducing the computational cost of broadband reverse design and outputting superatomic geometric parameter design results that meet the indicators.
[0011] Technical solution
[0012] To achieve the above objectives, this invention provides a broadband metasurface intelligent design method based on a forward model of superatomic electromagnetic response, characterized by the following steps:
[0013] S1: Construction of the Superatomic Dataset
[0014] S1-1) Parameterize the superatomic unit structure to obtain the superatomic geometric parameter vector. The geometric parameter vector includes at least one of geometric parameters such as length, width, and radius.
[0015] S1-2) Set geometrically feasible domain constraints and manufacturability constraints, wherein the constraints include at least one of the following: upper and lower limit constraints for parameters, minimum feature size constraints, boundary margin constraints, minimum spacing constraints, or structural validity determination.
[0016] S1-3) Generate a set of geometric samples in the parameter space that satisfies the constraints, preferably by using hierarchical Latin hypercube sampling to generate samples.
[0017] S1-4) Perform electromagnetic simulation on the geometric sample to obtain the complex transmission response at multiple discrete wavelength points within a preset broadband range as labels. Preferably, the complex transmission response is defined as the ratio of the transmitted complex electric field to the reference complex electric field.
[0018]
[0019] The complex transmission responses at each discrete wavelength point are then used to construct a multi-wavelength tag sequence, thus forming a dataset of "geometric samples - multi-wavelength complex transmission responses".
[0020] S2: Construction and Training of Superatomic Response Prediction Model
[0021] S2-1) Construct and train a superatomic response prediction model, with superatomic geometric parameters and wavelength as inputs and complex transmission response at the corresponding wavelength as output.
[0022] S2-2) Preferably, the output of the complex transmission response is characterized by its real and imaginary parts, i.e., the output vector.
[0023]
[0024] When reasoning, combine the real and imaginary parts to form a complex number. .
[0025] S2-3) Preferably, the input features are normalized: the geometric parameters are normalized according to the superatomic period, and the wavelength is linearly normalized to a preset range.
[0026] S2-4) Preferably, when dividing the dataset, the training set and the validation / test set are divided using "geometric samples" as the basic unit, and then expanded along discrete wavelength points to form training samples.
[0027] S2-5) Preferably, Fourier feature encoding is introduced into the normalized wavelength input, for example:
[0028]
[0029] And It is concatenated with normalized geometric parameters and normalized wavelength as the model input vector.
[0030] S2-6) Preferably, the superatomic response prediction model adopts a fully connected network structure with residual connections, including an input projection layer, several residual blocks and an output layer, wherein the output layer regresses the real part and imaginary part of the complex transmission response.
[0031] (S2-7) Preferably, the model training uses mean squared error as the loss function:
[0032] in For batch size.
[0033] S2-8) Complex transmission modulation array generation: For candidate devices, the first... Each cell location of the layer Its geometric parameters are For any wavelength point Call the prediction model to get And form the complex transmission modulation array of this layer.
[0034]
[0035] This yields a modulation array set under multi-wavelength conditions. .
[0036] S3: Diffraction Neural Network Evaluation Agent Construction
[0037] S3-1) Construct a diffraction neural network evaluation agent, which includes an input surface, several modulation layers, and an output / detector surface; Layer modulation of the incident complex field The effect is determined by the complex transmission function express:
[0038]
[0039] S3-2) Free space propagation is performed between adjacent modulation layers, preferably using the angular spectrum method to achieve interlayer propagation:
[0040]
[0041] S3-3) Predictor Integration: The complex transmission function of the modulation layer is generated by the prediction model in step S2 based on the geometric parameters and wavelength.
[0042]
[0043] The modulation array is formed by steps S2-8. Substituting the modulation array into an alternating cascaded link of "point-by-point modulation - angular spectrum propagation" yields the complex field of the output surface.
[0044] S3-4) Generation of multi-wavelength output response set: Selecting a set of discrete wavelength points For each Each layer of modulation array is generated separately. and perform forward propagation to obtain The output / detection surface intensity can be determined by...
[0045]
[0046] This results in a multi-wavelength output response set.
[0047] S4: Construction of Broadband Evaluation Function
[0048] A broadband evaluation function is established to comprehensively evaluate the output response of multiple discrete wavelength points within a preset broadband range, thereby obtaining an evaluation value for optimization. The evaluation function can adopt a multi-wavelength weighted synthesis form or a multi-objective form.
[0049] S5: Iterative Optimization
[0050] Under the constraints of geometrically feasible region and manufacturability, an optimization algorithm is used to iteratively update the superatomic geometric parameters. In each iteration: a set of complex transmission modulation arrays for each modulation layer is generated. The multi-wavelength output response set is obtained, and the evaluation value is calculated based on step S4 to guide the update of geometric parameters. Preferably, iterative optimization can be implemented using a gradient optimization algorithm or an evolutionary optimization algorithm; in one embodiment, the evolutionary optimization algorithm is a multi-objective genetic algorithm, such as the NSGA-II multi-objective genetic algorithm.
[0051] S6: Output Results
[0052] Output a set of superatomic geometric parameters that satisfy a preset threshold or convergence condition. The set of geometric parameters is represented in the form of a parameter vector or a geometric parameter matrix.
[0053] Beneficial effects
[0054] Compared with the prior art, the present invention has at least the following beneficial effects:
[0055] 1) By evaluating the agent, multi-wavelength output responses can be obtained quickly during optimization iterations, reducing the computational overhead caused by repeated full-wave simulations in broadband reverse engineering;
[0056] 2) By establishing a “geometric parameter-complex transmission response” mapping through the superatom response prediction model, the optimization variables can be directly mapped to the superatom geometric parameters, and the device geometric parameter distribution results can be directly output.
[0057] 3) Improve the consistency and robustness of broadband performance through broadband evaluation and multi-objective / constraint optimization strategies. Attached Figure Description
[0058] Figure 1 The diagram shows the superatomic structure used in the embodiments of the present invention; the left diagram is a three-dimensional structural diagram of the superatomic structure; the right diagram is a top view of the superatomic structure and a schematic diagram of the structural parameter definition, where L is the length of the cross arm, W is the width of the cross arm, R1 is the outer radius of the central ring, R2 is the inner radius of the central hole, P is the structural period, and H is the structural height.
[0059] Figure 2 This is a schematic diagram illustrating the forward propagation principle of the diffraction neural network evaluation agent that integrates a superatomic response predictor in this invention.
[0060] Figure 3 This is a schematic diagram of the network structure of the superatomic response predictor in the embodiment.
[0061] Figure 4 This is a schematic diagram of the reverse design process of the broadband achromatic superlens in the embodiment.
[0062] Figure 5 The diagram shows the distribution of superatomic geometric parameters of the broadband achromatic superlens reverse-engineered in this embodiment.
[0063] Figure 6 The light field intensity distribution diagram of the broadband achromatic superlens reverse-designed in the embodiment is shown on the x–z section. Detailed Implementation
[0064] The specific embodiments of the present invention will be further described below with reference to the accompanying drawings. The following embodiments are for illustrative purposes only and are not intended to limit the scope of protection of the present invention. Those skilled in the art can make various modifications or substitutions to the embodiments without departing from the spirit of the present invention, and all such modifications or substitutions should fall within the scope of protection of the present invention.
[0065] Example 1
[0066] This embodiment adopts Figure 1 The cross-shaped superatomic structure shown is used as an example of a unit cell structure, and combined with... Figure 2 and Figure 3 The process and network structure shown demonstrate the construction, training, and integration of the superatomic response predictor with the diffraction neural network.
[0067] (a) Structural and material design
[0068] The superatomic material is ZnSe, the substrate material is CaF2, and the structural height is [missing information]. The cycle is The geometric parameters are defined as: the length of the crossarm. Cross arm width Outer radius of the central circular hole Inner radius of the central circular hole And denote the geometric parameter vector .
[0069] (II) Geometric Constraints, Sampling Mapping and Sample Selection
[0070] Set boundary margin Minimum feature size With minimum inner radius Under one example constraint:
[0071]
[0072]
[0073] Generation using hierarchical Latin hypercube sampling And generate physical parameters by mapping step by step:
[0074]
[0075] The generated samples are evaluated for validity. Those that do not meet the constraints are removed or resampled to obtain a set of valid samples that meet the geometrically feasible region constraints.
[0076] (III) Electromagnetic Simulation and Complex Transmission Tag Generation
[0077] Electromagnetic simulation was performed on the effective geometric sample, selecting multiple discrete wavelength points within a preset bandwidth. Obtain the transmitted complex electric field at the monitoring surface. With reference complex electric field Define complex transmission coefficient
[0078]
[0079] and with
[0080]
[0081] As a supervisory label, among which and They are respectively The real and imaginary parts of .
[0082] (iv) Predictor construction and training
[0083] Periodic geometric parameters Normalization involves linearly normalizing the wavelength and constructing Fourier features from the normalized wavelength. ,Will
[0084]
[0085] The data is concatenated as input to the predictor. The dataset is divided into training and validation / test sets with "geometric samples" as the smallest unit, and then expanded along the wavelength to avoid data leakage caused by different wavelength points of the same geometric sample appearing in both the training and test sets.
[0086] like Figure 3 As shown, the predictor employs a residual fully connected network structure, which includes an input projection layer, several residual fully connected blocks, and an output layer:
[0087] 1) The input projection layer is used to map the input features to the hidden feature dimension, and can be combined with the normalization layer and SiLU activation function to improve training stability;
[0088] 2) The residual fully connected block includes at least a fully connected transformation, a SiLU activation function, and residual connections. Multiple residual fully connected blocks are cascaded to extract the nonlinear mapping relationship between "geometric parameters - wavelength - complex transmission response".
[0089] 3) The output layer is a linear regression layer, used to output the real and imaginary parts of the complex transmission response. .
[0090] Using mean squared error as the loss function With tags Conduct supervised training.
[0091] In one example training configuration, the number of residual blocks is 6, and the hidden dimension is... Fourier characteristic frequency count The AdamW optimizer was used, with a batch size of 4096, training for 200 epochs, and a learning rate decay based on validation loss. The above network structure and parameters are example parameters and can be adjusted according to computational resources and accuracy requirements.
[0092] (v) Forward evaluation of diffractive neural networks with integrated predictors
[0093] For wavelength point , for the Each position of the layer geometric parameters Call the predictor to get
[0094]
[0095] And form a modulation array .Will Substituting the "point-by-point modulation-angular spectrum propagation" alternating cascaded link, the output complex field is obtained. , and by
[0096]
[0097] The intensity of the probe surface is obtained. For By executing the above process step by step, a set of multi-wavelength output responses is obtained for broadband evaluation and optimization.
[0098] Example 2
[0099] The following is combined Figures 4 to 6This paper illustrates an example application of the method of the present invention in the reverse design of a broadband achromatic superlens. In this embodiment, the diffraction neural network with the integrated predictor obtained in Example 1 is used as the forward estimator, and a multi-objective genetic algorithm is used for multi-objective optimization. In this embodiment, the NSGA-II algorithm is preferably used.
[0100] (a) Design task and parameter setting
[0101] In one example, the superlens operates in the 3–6 μm wavelength range, and the superlens diameter... Target focal length Let the lens radius Its numerical aperture NA is determined by geometric relationships:
[0102]
[0103] Under the example parameters described above, NA is approximately 0.447. It should be understood that the band, aperture, focal length, and NA are example parameters and can be adjusted according to application requirements in other implementations.
[0104] Geometric parameter matrix of superatomic units within the aperture range of candidate superlens structures This indicates that each position corresponds to the cross-shaped superatomic parameter described in Example 1. And satisfy the geometric constraints and manufacturability constraints in Example 1.
[0105] (ii) Discrete wavelength set and multi-wavelength forward evaluation
[0106] Select within the preset bandwidth =30 discrete wavelength points As a set of evaluation wavelengths.
[0107] For any candidate structure For each wavelength point :
[0108] 1) The predictor of Example 1 generates the complex transmission modulation array of each modulation layer. ;
[0109] 2) The amplitude prediction at this wavelength point is obtained by the evaluation agent calculation of the diffraction neural network of the integrated predictor. Phase prediction (in (Index of sampling location within the caliber).
[0110] 3) Based on this, construct the evaluation quantity at this wavelength point.
[0111] (III) Construction of evaluation indicators (Example: intensity-weighted phase error)
[0112] 1) Target phase distribution: for focal length of An ideal superlens, at wavelength The lower and radial coordinates are The target phase is given by the following formula:
[0113]
[0114] (Note: The above is an example of target phase representation; equivalent target phase definitions can also be used in other implementations.)
[0115] 2) Periodic phase difference:
[0116]
[0117] 3) Intensity weighting and normalization: Intensity is obtained from amplitude prediction. And normalize it:
[0118]
[0119] in To prevent tiny constants with a denominator of zero.
[0120] Define weights:
[0121]
[0122] In one example, take , .
[0123] 4) Single-wavelength weighted error (weighted MAE):
[0124]
[0125] 5) Definition of Broadband Multi-Objective:
[0126]
[0127] NSGA-II also focuses on the optimization process To achieve a more even achromatic color difference effect within the band.
[0128] (iv) NSGA-II Optimization Process and Hyperparameters
[0129] like Figure 4 As shown, NSGA-II uses a candidate structure For each individual, the optimization process includes: initializing the population; calling the diffraction neural network evaluation agent for each individual in the population to obtain multi-wavelength amplitude and phase predictions and calculating... Perform crossover and mutation to generate offspring; merge the parent and offspring and perform non-dominated sorting to select the next generation of population; iterate until the termination condition is met.
[0130] In one example setup: the population size is 50, the number of iterations is 210, the crossover probability is 0.9, and the mutation probability is 0.05. Termination conditions can include reaching a preset number of iterations, the Pareto front change satisfying the convergence criterion, or the evaluation value reaching a threshold. The above parameters are example parameters and can be adjusted in other implementations according to computational resources and accuracy requirements.
[0131] (v) Output and Verification
[0132] A representative solution is selected from the Pareto solution set as the output. In one example, a representative solution is selected. The minimum solution is used as the representative structure. The distribution of the superatomic geometric parameters corresponding to this solution is output (see...). Figure 5 ), and provides the light field intensity distribution diagram of the x–z cross section to illustrate the achromatic results (see Figure 6 ).
Claims
1. A broadband metasurface intelligent design method based on a forward model of superatomic electromagnetic response, characterized in that, Includes the following steps: S1: Construct or obtain a dataset containing the correspondence between superatomic geometric parameters and their electromagnetic responses at multiple discrete wavelength points within a preset bandwidth; S2: Construct and train a superatomic response prediction model based on the dataset, so that it outputs the complex transmission response of the corresponding wavelength when the superatomic geometric parameters and wavelength are input; S3: Construct a diffraction neural network evaluation agent, take the complex transmission response of the metasurface to be optimized at multiple wavelength points as the modulation parameter input, and calculate the output response of the target plane based on the diffraction propagation model; S4: Establish an evaluation function for the output response at multiple wavelength points within a preset bandwidth, so as to comprehensively evaluate the output response at multiple wavelength points and generate evaluation values. S5: Under the constraints of geometric feasible region and manufacturability, the superatomic geometric parameters are updated iteratively using an optimization algorithm. In each iteration, the diffraction neural network evaluation agent is called to calculate the evaluation value and update the superatomic geometric parameters accordingly. S6: Output the combination of superatomic geometric parameters that meets the preset threshold or convergence condition as the design result of broadband metasurface.
2. The method according to claim 1, characterized in that, In step S1, hierarchical Latin hypercube sampling is used to sample the superatomic geometric parameters, and geometrically feasible region constraints are applied to the sampling results to obtain effective samples.
3. The method according to claim 1 or 2, characterized in that, In step S1, the electromagnetic response is obtained through electromagnetic simulation. The complex transmission response is determined by the ratio of the transmitted complex electric field at the monitoring surface to the reference complex electric field, and a tag sequence is formed at multiple discrete wavelength points within the preset broadband.
4. The method according to claim 1, characterized in that, The output of the superatomic response prediction model in step S2 is the real and imaginary parts of the complex transmission response.
5. The method according to claim 1, characterized in that, In step S2, the input features are normalized and the wavelength input is Fourier feature encoded.
6. The method according to claim 1, characterized in that, The diffraction propagation model described in step S3 uses the angular spectrum method to achieve interlayer propagation, and performs propagation calculations at multiple discrete wavelength points to obtain the target plane output response at the corresponding wavelength points.
7. The method according to claim 1, characterized in that, The evaluation function in step S4 performs a weighted synthesis of the output responses at multiple discrete wavelength points or constructs a multi-objective evaluation vector, and includes at least one of error terms and constraint terms.
8. The method according to claim 1, characterized in that, The optimization algorithm mentioned in step S5 is a gradient optimization algorithm or an evolutionary optimization algorithm.
9. The method according to claim 1, characterized in that, In step S5, manufacturability constraints are applied to the superatomic geometric parameters. These manufacturability constraints include upper and lower limits of geometric parameters, minimum feature size constraints, or structural validity determinations.
10. The method according to claim 1, characterized in that, The design results output in step S6 include a set of geometric parameters for each superatomic unit in the metasurface, which is characterized in the form of a parameter vector or a geometric parameter matrix.