Superlens structure optimization method and system based on partition and AI and superlens

Abstract

The invention relates to the technical field of super-lens structure optimization, and provides a super-lens structure optimization method and system based on partition and AI and a super-lens, and the method comprises the steps: firstly dividing the super-lens into a plurality of regions according to the geometric and functional requirements of the super-lens, enabling each region to be relatively independent in space, and facilitating the respective modeling; in each partition, a nonlinear mapping relation among a region coordinate, an initial structure and an expected phase is established by utilizing a forward neural network model, so that preliminary prediction of structure parameters is realized, and time consumption of traditional full-wave simulation is remarkably reduced. After preliminary modeling of all regions is completed, a cross-region collaborative optimization mechanism is adopted, global imaging errors, phase response discontinuity of region boundaries and spatial smoothness of structural parameters are evaluated and fed back by introducing an iterative search strategy based on a disturbance and feedback mechanism, and end-to-end optimization adjustment is performed based on a loss function. Therefore, optimization of structural parameters is realized on the premise of ensuring overall phase continuity and manufacturing feasibility.

Description

Technical Field

[0001] This invention relates to the technical field of superlens structure optimization, specifically to a superlens structure optimization method, system, and superlens based on partitioning and AI. Background Technology

[0002] The statements in this section are merely background information related to the present invention and do not necessarily constitute prior art.

[0003] Driven by the rapid development of metamaterials and micro / nano optics, superlenses, as a novel planar optical device that utilizes subwavelength-scale structures to manipulate light waves, have shown enormous application potential. Especially in fields such as high-resolution imaging, compact optical systems, and novel display technologies, large-aperture, high numerical aperture superlenses have become a key research and application area. However, as the aperture of superlenses increases, their structural complexity grows exponentially, posing unprecedented challenges to traditional design methods. There is an urgent need to develop new, efficient design methods to achieve rapid modeling and precise control of high-performance, large-aperture superlenses.

[0004] Currently, mainstream design methods mainly rely on full-wave electromagnetic simulation and global optimization algorithms, such as finite-difference time-domain (FDTD), RCWA simulation combined with genetic algorithms, topology optimization, and particle swarm optimization. While these methods achieve high accuracy in small-scale device design, they face three major technical bottlenecks in large-aperture superlens design: First, the computational load grows exponentially; simulating massive unit structures to build a database requires enormous time and computing power, severely restricting the design cycle. Second, traditional designs assume planar incidence and use a uniform structure for the entire lens region, neglecting the phase response mismatch caused by differences in incident angles at different radial positions, leading to significant degradation in edge imaging quality. Third, while regional optimization approaches proposed in recent years can reduce local complexity, the lack of inter-regional information exchange mechanisms easily leads to phase abrupt changes or modulation discontinuities at the ring boundaries, resulting in systematic diffraction errors and imaging degradation. This lack of global coordination has become a common and difficult-to-overcome bottleneck in AI-assisted superlens design methods. Summary of the Invention

[0005] To address the aforementioned issues, this invention proposes a method, system, and superlens based on partitioning and AI for superlens structure optimization. By combining regional neural network prediction with cross-regional collaborative optimization, it achieves efficient, low-computational-load, and phase-continuous structural parameter design for large-aperture superlenses while ensuring manufacturing feasibility. This effectively solves key problems of traditional designs, such as high computational load, poor edge imaging quality, and inconsistent partition responses.

[0006] To achieve the above objectives, the present invention adopts the following technical solution: One or more embodiments provide a method for optimizing superlens structures based on partitioning and AI, including the following steps: Based on the target parameters of the superlens to be optimized, the superlens aperture is divided into several regions according to radial or functional requirements; A local partition feedforward neural network model is constructed for each partition. The target phase, region coordinates and sub-region identification parameters of each region are used as input to predict the structural parameters of the subwavelength unit of each region, which are used as the initial prediction results. For the initial prediction results of the subwavelength unit structure parameters of each region, a local perturbation search strategy and a gradient optimization strategy are used for global optimization iteration. In each iteration, the global imaging error, boundary response discontinuity and structural parameter smoothness are fed back. Based on the collaborative optimization mechanism of the global loss function, the initial prediction results of the subwavelength unit structure parameters are iteratively optimized to obtain the optimized design parameters of the superlens. One or more embodiments provide a partitioning and AI-based superlens structure optimization system, including: The partitioning module is configured to divide the aperture of the superlens into several regions based on the target parameters of the superlens to be optimized, either radially or according to functional requirements. The partitioned local optimization module is configured to build a local partitioned feedforward neural network model for each partition. It takes the target phase, region coordinates and sub-region identification parameters of each region as input to predict the structural parameters of the subwavelength unit of each region as the initial prediction result. The cross-regional collaborative optimization module is configured to perform global optimization iterations using a local perturbation search strategy and a gradient optimization strategy for the initial prediction results of the subwavelength unit structural parameters obtained for each region. In each iteration, global imaging error, boundary response discontinuity, and structural parameter smoothness are fed back. Based on the collaborative optimization mechanism of the global loss function, the initial prediction results of the subwavelength unit structural parameters are iteratively optimized to obtain the optimized design parameters of the superlens. An electronic device includes a memory and a processor, as well as computer instructions stored in the memory and running on the processor, wherein the computer instructions, when executed by the processor, perform the steps in the above-described partition-based and AI-based superlens structure optimization method.

[0007] A computer-readable storage medium for storing computer instructions, which, when executed by a processor, perform the steps in the above-described method for optimizing a superlens structure based on partitioning and AI.

[0008] A superlens, employing the steps in the aforementioned partition-based and AI-based superlens structure optimization method, determines structural parameters.

[0009] Compared with the prior art, the beneficial effects of the present invention are as follows: (1) This method transforms the structural design problem, which originally required global high-precision electromagnetic simulation, into several parallel subtasks by introducing a region partitioning strategy and a region-level feedforward neural network model. Each region can independently predict structural parameters, significantly reducing the overall computational complexity of data generation and simulation. At the same time, the fast inference capability of the feedforward neural network greatly improves the modeling efficiency, resulting in an order-of-magnitude reduction in the design cycle compared to full-wave simulation methods such as FDTD / RCWA. This effectively solves the problem of design process delays caused by the long construction time of simulation databases in traditional methods.

[0010] (2) This method introduces radial coordinate information during region division and encodes the incident angle information at different locations into the input features of the neural network, enabling the predicted subwavelength structure parameters to respond more accurately to the local target phase requirements. Combined with the boundary response continuity constraint in the cross-region optimization mechanism, a natural transition of phase response between regions can be achieved, thereby avoiding edge imaging degradation caused by a unified structure dealing with non-uniform incident conditions and improving the overall imaging consistency and clarity of the superlens.

[0011] (3) To overcome the problem of phase discontinuity and abrupt changes at the regional boundaries during traditional regional optimization, this method introduces a collaborative optimization mechanism driven by local perturbation search and global loss function after regional prediction. In each iteration, this mechanism comprehensively considers the boundary phase consistency, overall imaging error, and structural parameter smoothness, realizing the dynamic adjustment and coordination of regional structural parameters, effectively eliminating phase abrupt changes at the partition boundaries and the resulting system diffraction error, and ensuring the dual consistency of the final design results in terms of physical continuity and manufacturing feasibility.

[0012] The advantages of the present invention, as well as its additional advantages, will be described in detail in the following specific embodiments. Attached Figure Description

[0013] The accompanying drawings, which form part of this invention, are used to provide a further understanding of the invention. The illustrative embodiments of the invention and their descriptions are used to explain the invention and do not constitute a limitation thereof.

[0014] Figure 1 This is a flowchart of the superlens structure optimization method based on partitioning and AI according to Embodiment 1 of the present invention; Figure 2 This is a graph of the optimal total loss function during the cross-regional collaborative optimization process of the superlens design example in Embodiment 1 of the present invention; Figure 3 This is a modulation phase diagram of the superlens example of Embodiment 1 of the present invention at different radial radius positions; Figure 4 This is a schematic diagram of the light field intensity curve on the focal plane of the superlens design example of Embodiment 1 of the present invention; Detailed Implementation The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0015] It should be noted that the following detailed descriptions are exemplary and intended to provide further illustration of the invention. Unless otherwise specified, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains.

[0016] It should be noted that the terminology used herein is for describing particular embodiments only and is not intended to limit the exemplary embodiments of the present invention. As used herein, the singular form is intended to include the plural form as well, unless the context clearly indicates otherwise. Furthermore, it should be understood that when the terms "comprising" and / or "including" are used in this specification, they indicate the presence of features, steps, operations, devices, components, and / or combinations thereof. It should be noted that, without conflict, the various embodiments and features within those embodiments can be combined with each other. The embodiments will now be described in detail with reference to the accompanying drawings.

[0017] Example 1 In one or more of the technical solutions disclosed in the embodiments, such as Figures 1 to 4 As shown, a method for optimizing a superlens structure based on partitioning and AI includes the following steps: Step 1: Based on the target parameters of the superlens to be optimized, divide the superlens aperture into several regions according to radial or functional requirements; The target parameters may include the target focal length, design aperture, operating wavelength, and material parameters. The final design must achieve the performance corresponding to these target parameters.

[0018] Step 2, Local Optimization of Partitions: Construct a local partition feedforward neural network model for each partition. Take the target phase, region coordinates and sub-region identification parameters of each region as input, and use the local partition feedforward neural network model to predict the structural parameters of the subwavelength units of each region as the initial prediction results. Step 3, Cross-regional collaborative optimization: For the initial prediction results of the subwavelength unit structure parameters of each region, a local perturbation search strategy and a gradient optimization strategy are used for global optimization iteration. In each iteration, global imaging error, boundary response discontinuity and structural parameter smoothness are fed back. Based on the collaborative optimization mechanism of the global loss function, the initial prediction results of the subwavelength unit structure parameters are iteratively optimized to obtain the optimized design parameters of the superlens. Specifically, for the initial prediction results of the subwavelength unit structural parameters of each region, a collaborative optimization layer is introduced to construct a complete superlens structure for angular spectrum propagation optical field simulation. A local perturbation search strategy and a gradient optimization strategy are used for global optimization iteration. In each iteration, global imaging error, boundary response discontinuity and structural parameter smoothness are fed back. Based on the collaborative optimization mechanism of the global loss function, the initial prediction results of the subwavelength unit structural parameters are iteratively optimized to obtain the optimized design parameters of the superlens.

[0019] In this embodiment, the overall design space is first divided into multiple regions based on the geometric and functional requirements of the superlens, making each region spatially relatively independent and facilitating separate modeling. Within each region, a feedforward neural network model is used to establish a nonlinear mapping relationship between region coordinates, the initial structure, and the desired phase, enabling preliminary prediction of structural parameters and significantly reducing the time consumption of traditional full-wave simulation. After preliminary modeling is completed in all regions, a cross-regional collaborative optimization mechanism is adopted. By introducing an iterative search strategy based on perturbation and feedback mechanisms, the global imaging error, the phase response discontinuity at region boundaries, and the spatial smoothness of structural parameters are evaluated and fed back. This information is integrated into a global loss function, and end-to-end optimization is performed based on this loss function, thereby optimizing structural parameters while ensuring overall phase continuity and manufacturing feasibility.

[0020] This method transforms the structural design problem, which originally required global high-precision electromagnetic simulation, into several parallel subtasks by introducing a region partitioning strategy and a region-level feedforward neural network model. Each region can independently predict structural parameters, significantly reducing the overall computational complexity of data generation and simulation. Simultaneously, the rapid inference capability of the feedforward neural network greatly improves modeling efficiency, resulting in an order-of-magnitude reduction in the design cycle compared to full-wave simulation methods such as FDTD / RCWA. This effectively solves the problem of design delays caused by the excessively long simulation database construction time in traditional methods.

[0021] By introducing radial coordinate information during region segmentation, the incident angle information at different locations is encoded into the input features of the neural network, enabling the predicted subwavelength structure parameters to more accurately respond to local target phase requirements. Combined with the boundary response continuity constraint in the cross-region optimization mechanism, a natural transition of phase response between regions can be achieved, thereby avoiding edge imaging degradation caused by a uniform structure dealing with non-uniform incident conditions and improving the overall imaging consistency and sharpness of the superlens.

[0022] To overcome the problem of phase discontinuities and abrupt changes at regional boundaries during traditional regional optimization, a collaborative optimization mechanism driven by local perturbation search and a global loss function is introduced after regional prediction. This mechanism comprehensively considers boundary phase consistency, overall imaging error, and structural parameter smoothness in each iteration, achieving dynamic adjustment and coordination of regional structural parameters. This effectively eliminates phase abrupt changes at regional boundaries and the resulting system diffraction errors, ensuring the final design results are consistent in both physical continuity and manufacturing feasibility.

[0023] The radial aperture of the superlens is divided into several collaborative working regions. An end-to-end optimization closed loop is constructed based on a region-level feedforward neural network and a differentiable physics propagation operator. Combined with regional collaborative search and gradient optimization strategies, this solves the problems of long simulation time, difficulty in scaling to large apertures, and easy generation of phase abrupt changes and unmanufacturable structures at the partition boundaries of traditional point-by-point FDTD / RCWA full-field simulation. It realizes efficient, scalable, phase-continuous and manufacturable structural parameter optimization design for large-aperture superlenses under given manufacturing constraints. This significantly reduces the amount of simulation computation while obtaining imaging performance with focal plane light field intensity close to the target focal plane point spread function (PSF). It is also easy to extend to complex design scenarios such as multi-wavelength, multi-focal length or zoom.

[0024] Step 1, based on the target parameters of the superlens to be optimized, divides the aperture of the superlens into several partitions according to radial or functional requirements, including the following steps: Step 11: Obtain the target parameters of the superlens, perform discretization sampling on the superlens, and establish the target phase function based on the phase requirements of each sampling point; Step 111: Obtain target parameters, including working wavelength, target focal length, design aperture, period, and basic design parameters such as material refractive index; A specific design example A has the following superlens design parameters: operating wavelength λ = 1.55μm, target focal length f = 100μm, and superlens aperture radius R. ap = 75μm, silicon nitride Si3N4 material; The element geometry manufacturing constraints include: the minimum radius r of the element cylinder. 1min =40nm, maximum radius r 1max= 220nm; Step 112: Perform uniform sampling along the radial direction r∈[0,Rap], setting the number of sampling points to Nr, thereby constructing a discrete radial coordinate set. The calculation formula is: (1); For example A, the radial sampling point number Nr = 151, that is, 151 points are taken at equal intervals on r∈[0, Rap]. Step 113: Establish the target phase function for each point in the radial coordinate set according to the phase requirements; Specifically, for focusing superlenses, the goal is to achieve wavefront delay compensation at various locations, ensuring coherent superposition of the outgoing light waves at the focal point. Based on the principle of geometrical optics path difference, the target phase function can be defined as: (2); The negative sign indicates the required phase delay. This represents the ideal phase response value of the superlens at each sampling location.

[0025] The essence of a superlens is to precisely control the phase of incident light through a subwavelength structure to achieve specific optical effects (such as focusing to a specified focal length). The target phase function serves as a bridge between optical functional requirements and structural design. In the design of superlenses, significant differences exist in incident angle, phase gradient, and effective refractive index at different radial positions. Directly adopting a globally unified strategy makes it difficult to guarantee the accuracy of wavefront control and the overall performance of the device. Step 2 divides the superlens aperture region into spatial regions based on the characteristics of optical parameter variations, laying the structural foundation for subsequent local modeling and regional collaborative optimization.

[0026] Step 12: Based on the characteristics of optical parameter variation, set the division criteria, divide the superlens aperture region into spatial regions, and assign region identifiers to each sampling point of the target phase function based on the divided regions. Optionally, the criteria for spatially dividing the aperture region of the superlens may include: Radial position variation (r): determines the range of incident angles and optical path difference; Equivalent numerical aperture (NA): increases with increasing r, affecting local controllability; Phase gradient distribution: Higher phase change rates are required in edge regions; Effective refractive index variation range: The structure needs to be adapted to a larger refractive index control range; Structural periodicity constraint: Subwavelength conditions must be met to prevent higher-order diffraction; Operating bandwidth of nanopillar units: The bandwidth limitation of nanopillars restricts performance at high incident angles.

[0027] Optionally, any of the following methods can be used to divide the spatial region of the superlens aperture area: (1) Radial partitioning: Taking the center of the superlens as the center, the aperture of the superlens is divided into multiple concentric annular zones along the radial direction. Each zone covers a different radius range, typically set as the central zone, the middle zone, the edge zone, etc. (2) Radial and azimuthal partitioning: On the basis of radial partitioning, further divide along the azimuthal direction (θ direction), cutting the entire aperture region into several fan-shaped sub-regions (similar to "scallop shape"), forming a two-dimensional grid structure of "radial × angle".

[0028] (3) Voronoi partitioning: Based on a set of initial seed points (centers of seed regions), divide the entire metasurface region into multiple sub-regions with irregular but adaptively distributed shapes according to the Euclidean distance. Each region contains all the sampling points closest to a certain seed point.

[0029] The divided regions contain several sub-wavelength units; a sub-wavelength unit refers to a micro-nano structure unit with a size smaller than the working wavelength of the metasurface, such as a nanorod, which is the basic component for the metasurface to achieve optical functions. It precisely regulates the phase of the incident light through its own geometric parameters, such as radius, height, etc., enabling the metasurface to achieve specific optical effects, such as focusing. In this embodiment, radial partitioning is adopted. For example, for a metasurface with an aperture radius R ap = 75μm, the metasurface aperture region is divided into a central region 0 ≤ r ≤ 20μm, an intermediate region 20 < r ≤ 60μm, and an edge region 60 < r ≤ 75μm. A region identification zone ∈ {1, 2, 3} is assigned to each sampling point, that is, the sub-region identification parameter.

[0030] Step 2: Construct a local partition forward neural network model for each partition to predict the structural parameters of the sub-wavelength units that satisfy the local target phase distribution in each partition. The inputs are the regional target phase, regional coordinates, and sub-region identification parameters, and the outputs are the structural parameters of the sub-wavelength units, specifically corresponding to the structural parameters such as the radius, length, and height of the nanorod units. Further, it also includes the training process of the forward neural network model, including the following steps: Step S1: Obtain a metasurface with known structural parameters. After performing region partitioning in Step 1, for each divided region, independently establish the mapping relationship between the structural parameters of the sub-wavelength units and the phase response, and construct the training dataset of the sub-region AI network model. Optionally, for each optical region zone ∈ {1, 2, 3}, scan to obtain the unit radius-phase response curve in the FDTD / RCWA software.

[0031] Specifically, according to each optical region zone ∈ {1, 2, 3}, configure independent scanning tasks for the central region, intermediate region, and edge region respectively. In each region, set the following parameters: Structural parameter range. For example, if the sub-wavelength unit is a vertical columnar structure, set the radius of the scanned sub-wavelength unit. Material settings: Different material combinations can be selected based on factors such as the area's incident angle and loss sensitivity; Geometric variations: Different regions can use different nanopillar heights, cross-sectional shapes (cylindrical, square, elliptical), or period settings; Simulation method: Set up plane wave incident in FDTD or RCWA platform, acquire the output phase of the corresponding structure, and obtain the mapping curve of scanning element radius-phase response. ; To ensure a smooth transition in phase continuity and amplitude consistency between adjacent regions, the density of scanning points is increased near the boundaries of each region, for example, by densifying the sampling interval within ±2 μm of the boundary. This can improve the fitting accuracy of the structural response at the region boundaries; avoid phase abrupt changes when stitching together different AI models; and provide high-resolution transition data for subsequent collaborative optimization mechanisms.

[0032] Step S2: Based on the mapping relationship between the unit structure parameters and phase response of each region, extract the target phase and concatenate it with the region coordinates and sub-region identifier parameters corresponding to the target phase as input data. The subwavelength unit structure parameters of the corresponding region are used as output and input into the local partition feedforward neural network model constructed for the current region for training. Based on the trained feedforward neural network model, the structural parameters of the subwavelength units that satisfy the local target phase distribution of each region can be predicted, i.e., the subwavelength structural parameters. Among them, the local partition feedforward neural network model is the local partition feedforward neural network model; Specifically, the radial radius of the superlens is normalized to the range [0,1], and one-hot encoding is used for zones ∈ {1,2,3}. A fully connected neural network structure MLP is constructed for the three radial regions of the superlens. If it is a large-aperture superlens, a complex convolutional neural network CNN can be constructed for each radial region of the superlens, with MSE as the loss function. The training hyperparameters are set as follows: learning rate lr = 1e-3, batch size = 256, and training epoch = 300. The optimizer is Adam. During training, the average loss per epoch is printed for monitoring. After training, the model weights are saved. The region-level neural network is trained using the unit radius-phase data scanned by FDTD / RCWA in step three. The training set data is organized in three columns: radius (μm), zone_id (1 / 2 / 3), and phase (rad), i.e., a data table is constructed, with corresponding data set for each column.

[0033] Step 3: Establish a cross-regional collaborative optimization mechanism. After outputting the initial structural parameters of each region, a collaborative optimization layer is introduced to control the collaborative optimization between different regions, ensuring the consistency of the overall wavefront. This step is based on the initial prediction results of the subwavelength unit structural parameters output by the pre-trained regional AI model. By introducing a collaborative optimization mechanism, it achieves phase response coordination and structural continuity optimization between different regions, improving the global wavefront control performance and manufacturing feasibility of the large-aperture superlens. This process adopts a local perturbation search strategy and feeds back global imaging errors, boundary response discontinuities, and structural parameter smoothness in each iteration, achieving progressive optimization of the overall structure.

[0034] In step 3, the constructed global loss function is a weighted sum of global imaging error, region boundary continuity penalty, and cell radius smoothing term; the global loss function is: (3); in, For global imaging error, Penalty for regional boundary continuity, For the unit radius smoothing term, For adaptive weights; Global imaging error is a measure of the difference between the actual imaging effect of the superlens (the light field intensity obtained from angular spectrum propagation simulation) and the ideal imaging effect (such as the target point spread function PSF); the calculation formula is: (4); The formula for calculating the continuity penalty at the region boundary is as follows: (5); This embodiment defines a continuity penalty at the boundary of the region to make the phase response at the boundary of adjacent partitions transition as smoothly as possible, avoiding abrupt phase changes caused by independent optimization of each partition, such as a sudden change in phase at the boundary between the axial region and the intermediate region, thus ensuring the continuity of the overall wavefront. The formula for the element radius smoothing term is: (6); Where MSE represents the mean square error of the solution. The symbol for summation is 'mean', and the symbol for average is 'mean'. To find the sign of the absolute value; They represent the simulated light field intensity and the target light field intensity, respectively. These represent the modulation phases of two adjacent regions; These represent the maximum and minimum values ​​of the radius of the subwavelength unit (such as a nanopillar), respectively. Let represent the radii of the superlens at the (i+1)th sampling point and the ith sampling point, respectively. In this embodiment, r represents the radius of the superlens, and r1 represents the radius of the subwavelength unit (such as a nanopillar). In this embodiment, a smoothing term constraint is set for the radius of the subwavelength unit (such as nanopillar) of the superlens to suppress sharp jumps in the unit radius, such as a sudden jump from 40nm to 220nm in the radius of a certain unit, to ensure that the structural changes meet the manufacturing process requirements (such as photolithography precision). In this embodiment, the initial prediction results of the subwavelength unit structure parameters obtained by the model prediction, i.e. the structure parameters of the superlens, are used to perform global optical field simulation using the angular spectrum propagation algorithm to detect the performance of the superlens. Initial predictions of subwavelength structure parameters are obtained. The complex field integral and light field intensity distribution from the superlens to the focal plane are calculated using the angular spectrum propagation algorithm. This is the simulation output of the actual optical performance of the superlens. Under radial symmetry conditions, the radial component from the superlens to the focal plane is calculated using the angular spectrum propagation algorithm. ρ Replay points The formula is: (7); The formula for calculating light field intensity is: (8); in, Indicates the radius r of the superlens in Integral over a range To find the sign of the absolute value; The amplitude and intensity of the light field, Represents the phase information of the optical field; This represents the wave vector of each plane wave being integrated; The global imaging error can be calculated based on the light field intensity obtained from the angular spectrum propagation algorithm. Furthermore, the dynamically adjustable weights of the global imaging error, region boundary continuity penalty, and cell radius smoothing term in the total loss function of the superlens optimization design are expressed as follows: ; In the formula, For the number of iterations, hour, , , These represent the weights of the global imaging error, the region boundary continuity penalty, and the cell radius smoothing term, respectively.

[0035] Furthermore, the initial prediction results of the subwavelength structure parameters are obtained, and the light field simulation is performed using the angular spectrum propagation algorithm. The complex field integral and light field intensity distribution from the superlens to the focal plane are calculated, and the light field intensity and global imaging error are calculated. The global imaging error is then passed back to the AI ​​model optimizer of the local feedforward neural network model of each partition to update the model parameters. This ensures that the local optimization of each partition is no longer isolated, but adjusts its direction according to the global performance, thereby achieving information coordination between partitions. In step 3, for the initial prediction results of the subwavelength unit structure parameters of each region, a local perturbation search strategy is adopted to perform inter-regional collaborative iteration. In each iteration, the global imaging error, boundary response discontinuity and structural parameter smoothness are fed back. Based on the collaborative optimization mechanism of the global loss function, the initial prediction results of the subwavelength structure parameters are optimized to obtain the optimized design parameters of the superlens. The inputs to the optimization process include initial subwavelength unit structural parameters, target phase distribution, zone identifier parameters (zone∈{1,2,3}), angular spectrum propagation model, and loss function weight parameters. The output is the superlens parameter design results, including the structural parameters of a large-aperture superlens and the global imaging intensity distribution.

[0036] Specifically, the optimization process can be achieved by constructing a collaborative optimization layer. The process of optimizing the design parameters of the superlens includes the following steps: Step 31: Initialization. Use the initial prediction results of the local partition feedforward neural network as the initial design parameters and set the number of iterations k. Specifically, the initial results predicted by the local partitioning neural network are used as the starting point for collaborative optimization, denoted as... , k Indicates the iteration round of collaborative optimization; Step 32: In each round of collaborative iteration, using the partition as the smallest collaborative optimization unit, perform local perturbation search on each partition in sequence: Local perturbation search, specifically: for the first m partitions ( m =1,2,3), determine the optimized input parameters for the current hyperlens partition, including the current global structure parameters and the radial index (sampling point) corresponding to the partition. The allowed range of structural parameters for this partition (the range of possible values ​​for the sampling points) ); in the current number m Several sampling points are randomly selected from the radial index of each partition, and local perturbation is performed on the structural parameters of the selected sampling points to form candidate solutions; The range of values ​​that a sampling point can take is the radius range of the superlens corresponding to each sampling point within the divided region; Step 33, Trimming and Structural Smoothing: Trimming and smoothing the disturbed structural parameters; Specifically, to randomly perturb the radius of several sampling points, a local perturbation strategy can be adopted. This involves selecting several random sampling point radii within a certain region, applying a Gaussian perturbation to these radii, and then clipping the perturbed radii to the range of [r] within that region. min , r max To ensure local continuity, a small-scale convolutional smoothing process is performed on the region. Step 34: Combine the candidate structural parameters with the structural parameters of other partitions to construct the complete superlens structure. Simulate and calculate the focal plane light field distribution using the angular spectrum propagation model, and calculate the global loss function. ; Step 35, Update Strategy: Compare the global loss value of the current candidate solution with the loss value of the current structural parameters to determine whether to accept the current candidate solution. If the current candidate solution is accepted, update the current structural parameters; otherwise, keep the original structural parameters unchanged. Step 36: Determine whether the local search of all partitions has been completed. If not, switch to the next partition and execute steps 32 to 35 to perform the local search of the partition. If completed, proceed to the next step. Step 37: After completing a round of local search of all partitions, determine whether the convergence condition is met. If not, proceed to steps 32 to 36 to continue the next round of collaborative iteration. If the condition is met, output the current superlens parameter design result. The convergence condition can be a slow decrease in loss or a tendency for structural changes to stabilize. For example, if the global imaging error, the region boundary continuity penalty, and the unit radius smoothing term all satisfy the convergence condition, then global consistency correction of the large-aperture superlens design can be achieved, and the set number of iterations can also be reached. k ; In this step, a "local random search" collaborative optimization is performed on a zone-by-zone basis. For each iteration, a local search is performed sequentially on the three zones. For each zone, the radius values ​​of several sampling points are randomly perturbed on its radial index set, the loss of candidate solutions is calculated, and improvements that reduce the loss are adopted. After multiple iterations, a globally approximate optimal solution is obtained.

[0037] The optimal total loss function curve obtained by the regional collaborative optimization AI model designed in this embodiment changes during the iterative process of step 3 above as follows: Figure 2 As shown, the modulation phase of the superlens designed for a specific example at different radial radius positions is as follows: Figure 3 As shown in the figure, the solid curves represent the actual modulation phase at different radial radii of the superlens, and the dashed curves represent the target modulation phase at different radial radii of the superlens. The light field intensity curve on the focal plane of the designed superlens is shown in the figure. Figure 4As shown, the solid curve represents the simulated light field intensity curve of the superlens, and the dashed curve represents the ideal light field intensity curve of the superlens. From... Figure 2 It can be seen that in the initial iteration phase, the total loss decreases rapidly, and as the number of iterations increases, the total loss gradually stabilizes and eventually converges; from Figure 3 It can be seen that the modulation phase changes continuously with the radial radius, and the overall phase curve is consistent with the trend of the theoretical target phase curve. At the boundaries of each partition, no significant abrupt change in phase variation occurs. Figure 4 It can be seen that the light intensity distribution is basically consistent with the target point spread function (PSF) profile.

[0038] The proposed partitioned collaborative AI optimization-based superlens design method, with its advantages of efficient design capabilities for large-aperture superlenses and low aberrations and high imaging quality, has broad application prospects in multiple fields: In the field of optical imaging, it can support the development of large-aperture superlens camera lenses, enabling the miniaturization of portable high-resolution imaging devices; in the field of virtual reality display, it can provide AR / VR headsets with lightweight, thin, and wide-field-of-view superlens optical systems, enhancing user immersion; in the field of laser processing, it can assist in the design of high-precision large-aperture laser focusing superlenses, improving the processing efficiency and accuracy of complex workpieces; in the field of biological detection, it can be applied to high-resolution microscopic imaging superlenses, enabling precise observation at the single-cell level. Furthermore, the rapid and automated design characteristics of this method will accelerate the implementation of superlenses in high-end optical applications such as autonomous driving vehicle optics and satellite remote sensing imaging, promoting technological upgrading and innovative development in related industries.

[0039] Example 2 Based on Example 1, this example provides a superlens structure optimization system based on partitioning and AI, including: The partitioning module is configured to divide the aperture of the superlens into several regions based on the target parameters of the superlens to be optimized, either radially or according to functional requirements. The partitioned local optimization module is configured to build a local partitioned feedforward neural network model for each partition. It takes the target phase, region coordinates and sub-region identification parameters of each region as input to predict the structural parameters of the subwavelength unit of each region as the initial prediction result. The cross-regional collaborative optimization module is configured to perform global optimization iterations using a local perturbation search strategy and a gradient optimization strategy for the initial prediction results of the subwavelength unit structural parameters obtained for each region. In each iteration, global imaging error, boundary response discontinuity, and structural parameter smoothness are fed back. Based on the collaborative optimization mechanism of the global loss function, the initial prediction results of the subwavelength unit structural parameters are iteratively optimized to obtain the optimized design parameters of the superlens. It should be noted that each module in this embodiment corresponds one-to-one with each step in embodiment 1, and their specific implementation process is the same, so it will not be repeated here.

[0040] Example 3 Based on Embodiment 1, this embodiment provides an electronic device, including a memory and a processor, as well as computer instructions stored in the memory and running on the processor. When the processor executes the computer instructions, it completes the steps in the partition-based and AI-based superlens structure optimization method described in Embodiment 1.

[0041] Example 4 Based on Embodiment 1, this embodiment provides a computer-readable storage medium for storing computer instructions. When the computer instructions are executed by a processor, they complete the steps in the partitioning and AI-based superlens structure optimization method described in Embodiment 1.

[0042] Example 5 Based on Embodiment 1, this embodiment provides a superlens, which uses the steps in the superlens structure optimization method based on partitioning and AI described in Embodiment 1 to determine the structural parameters.

[0043] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

[0044] While the specific embodiments of the present invention have been described above in conjunction with the accompanying drawings, this is not intended to limit the scope of protection of the present invention. Those skilled in the art should understand that various modifications or variations that can be made by those skilled in the art without creative effort based on the technical solutions of the present invention are still within the scope of protection of the present invention.

Claims

1. A method for optimizing superlens structures based on partitioning and AI, characterized in that, Includes the following steps: Based on the target parameters of the superlens to be optimized, the superlens aperture is divided into several regions according to radial or functional requirements; A local partition feedforward neural network model is constructed for each partition. The target phase, region coordinates and sub-region identification parameters of each region are used as input to predict the structural parameters of the subwavelength unit of each region, which are used as the initial prediction results. For the initial prediction results of the subwavelength unit structure parameters of each region, a local perturbation search strategy and a gradient optimization strategy are used for global optimization iteration. In each iteration, the global imaging error, boundary response discontinuity and structural parameter smoothness are fed back. Based on the collaborative optimization mechanism of the global loss function, the initial prediction results of the subwavelength unit structure parameters are iteratively optimized to obtain the optimized design parameters of the superlens.

2. The superlens structure optimization method based on partitioning and AI as described in claim 1, characterized in that: Based on the target parameters of the superlens to be optimized, a method for dividing the superlens aperture into several partitions according to radial or functional requirements includes the following steps: Obtain the target parameters of the superlens, discretize and sample the superlens, and establish the phase requirements for each sampling point to establish the target phase function; Based on the characteristics of optical parameter variation, the spatial region of the superlens aperture is divided, and a region identifier is assigned to each sampling point of the target phase function based on the divided region.

3. The superlens structure optimization method based on partitioning and AI as described in claim 2, characterized in that: Obtain the target parameters of the superlens, perform discretization sampling on the superlens, and establish the phase requirements for each sampling point to establish the target phase function, including: Obtain the target parameters, including the basic design parameters such as operating wavelength, target focal length, design aperture, period, and material parameters; Uniform sampling is performed along the radial direction r∈[0,Rap], with the number of sampling points set to Nr, thereby constructing a discrete radial coordinate set. The calculation formula is: A target phase function is established for each point in the radial coordinate set based on its phase requirements.

4. The superlens structure optimization method based on partitioning and AI as described in claim 1, characterized in that: For each partition, a local partition feedforward neural network model is constructed to predict the subwavelength unit structure parameters that satisfy the local target phase distribution of each partition. The inputs are the regional target phase, regional coordinates, and sub-regional identifier parameters; the outputs are the subwavelength unit structure parameters, including the structural parameters of the radius, length, and height of the nanopillar units. It also includes the training process of the feedforward neural network model, which includes the following steps: For a superlens with known structural parameters, for each region after division, independently establish the mapping relationship between subwavelength unit structural parameters and phase response, and construct a training dataset for the regional AI network model; Based on the mapping relationship between the unit structure parameters and phase response of each region, the target phase is extracted and concatenated with the region coordinates and sub-region identifier parameters corresponding to the target phase as input data. The subwavelength unit structure parameters of the corresponding region are used as output and input into the local partition feedforward neural network model constructed for the current region for training.

5. The superlens structure optimization method based on partitioning and AI as described in claim 1, characterized in that: The constructed global loss function is a weighted sum of global imaging error, region boundary continuity penalty, and cell radius smoothing term. ； in, For global imaging error, Penalty for regional boundary continuity, For the unit radius smoothing term, For adaptive weights; The global imaging error is calculated using the following formula: ； The formula for calculating the continuity penalty at the region boundary is as follows: ； ； Where MSE represents the mean square error of the solution. The symbol for summation is 'mean', and the symbol for average is 'mean'. To find the sign of the absolute value; They represent the simulated light field intensity and the target light field intensity, respectively. These represent the modulation phases of two adjacent regions, respectively. These represent the maximum and minimum values ​​of the subwavelength element radius, respectively; Let represent the radii of the superlens at the (i+1)th sampling point and the ith sampling point, respectively.

6. The superlens structure optimization method based on partitioning and AI as described in claim 1, characterized in that: The initial prediction results of the subwavelength unit structure parameters are obtained. The complex field integral and light field intensity distribution from the superlens to the focal plane are calculated using the angular spectrum propagation algorithm. The light field intensity and global imaging error are calculated. The global imaging error is then passed back to the AI ​​model optimizer of the local partition feedforward neural network model of each partition to update the model parameters.

7. A superlens structure optimization system based on partitioning and AI, characterized in that, include: The partitioning module is configured to divide the aperture of the superlens into several regions based on the target parameters of the superlens to be optimized, either radially or according to functional requirements. The partitioned local optimization module is configured to build a local partitioned feedforward neural network model for each partition. It takes the target phase, region coordinates and sub-region identification parameters of each region as input to predict the structural parameters of the subwavelength unit of each region as the initial prediction result. The cross-regional collaborative optimization module is configured to perform global optimization iterations using a local perturbation search strategy and a gradient optimization strategy for the initial prediction results of the subwavelength unit structural parameters obtained for each region. In each iteration, global imaging error, boundary response discontinuity, and structural parameter smoothness are fed back. Based on the collaborative optimization mechanism of the global loss function, the initial prediction results of the subwavelength unit structural parameters are iteratively optimized to obtain the optimized design parameters of the superlens.

8. An electronic device, characterized in that, It includes a memory and a processor, as well as computer instructions stored in the memory and running on the processor, which, when executed by the processor, perform the steps in the partition-based and AI-based superlens structure optimization method according to any one of claims 1-6.

9. A computer-readable storage medium, characterized in that, Used to store computer instructions, which, when executed by a processor, complete the steps in the partition-based and AI-based superlens structure optimization method according to any one of claims 1-6.

10. A superlens, characterized in that, The structural parameters are determined by using the steps in the superlens structure optimization method based on partitioning and AI as described in any one of claims 1-6.

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