Super-holographic optimization method and device based on a limited super-atom response library

Abstract

The application discloses a metasurface holographic optimization method based on a limited super atom response library selection, belongs to the metasurface holographic field, and has the steps that a three-dimensional logarithmic probability matrix P (an element represents the logarithmic probability of a structure in a response library selected by a super atom at a grid position) is randomly initialized; a Gumbel-Softmax sampling strategy is used to generate a discrete selection matrix, an index corresponding complex amplitude response is constructed, and a complex amplitude distribution matrix of the whole metasurface is constructed; then, a differentiable wave front propagation algorithm is used to calculate a target complex amplitude distribution; multi-polarization multiplexing is supported, image superposition is realized through time multiplexing; a structural similarity constraint is introduced; a total loss value gradient relative to the probability matrix is calculated; the probability matrix is updated through a stochastic gradient descent; and finally, iteration is performed until convergence, so that a selection matrix and a directly manufacturable metasurface structure layout are obtained. The application can realize high-precision and high-efficiency polarization multiplexing metasurface holographic design.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of holographic metasurface devices, and particularly relates to an end-to-end metasurface holographic optimization method and device based on selection of a limited super atom response library. BACKGROUND

[0002] As a new type of two-dimensional planar optical material composed of sub-wavelength artificial atoms ("super atoms") arranged in a specific sequence, metasurfaces have the ability to flexibly and accurately control the amplitude, phase, polarization, and other multi-dimensional degrees of light waves, providing a revolutionary solution for the miniaturization, integration, and multifunctionalization of new-generation optical systems. In the field of optical holography, metasurfaces effectively compensate for the inherent defects of traditional spatial light modulators (SLMs), such as narrow working bandwidth, small field of view, and multi-stage diffraction crosstalk, enabling high-resolution, large-field holographic display and imaging, and naturally supporting multi-wavelength, multi-polarization channel information multiplexing, with great application potential in high-end display, information encryption, data storage, and computational imaging.

[0003] The core of the inverse design of metasurfaces lies in inversely solving the optimal geometric parameters (such as size, shape, and rotation angle) of each super atom according to the target optical function (such as a specific far-field light field distribution). Currently, the mainstream inverse design method relies heavily on a pre-constructed "super atom response library." This database establishes a mapping relationship between discrete super atom geometric parameters and their corresponding optical complex amplitude responses (i.e., the amplitude and phase of transmission / reflection) through electromagnetic simulation (such as the finite-difference time-domain method, FDTD) or experimental measurement. In recent years, various optimization design methods based on this database have emerged, which can be divided into two categories according to their optimization objects:

[0004] The first method avoids structure optimization and instead optimizes intermediate variables - complex amplitudes. For example, the patent application CN120491222 A (Wideband polarization multiplexing far-field imaging metasurface based on inverse design of Huygens principle) of Guilin University of Electronic Technology. This method directly optimizes the complex amplitude distribution of the metasurface plane (i.e., the ideal phase and amplitude of each point) through a neural network and iteratively calculates the far-field light field using Huygens' principle. However, this method has a key defect: it only produces an ideal complex amplitude distribution, not a manufacturable physical structure. When mapping the optimized complex amplitude back to the real super atom structure, it still needs to rely on a pre-constructed super atom response library for matching lookup. This matching process essentially faces the same dilemma as interpolation methods: the limited discrete library cannot perfectly match the ideal complex amplitude values optimized continuously, introducing errors again in the final manufacturing link, greatly reducing the performance of the previous optimization.

[0005] The second type of method directly optimizes the physical structure parameters of the metasurface, but is heavily dependent on the expansion of the discrete response database. For example:

[0006] Patent application CN117408114A (Method and device for optimizing shape parameters of metasurface) by Tsinghua University proposes training a neural network to fit the continuous and derivable function relationship between the metasurface shape parameters and the optical response. Although this method can perform gradient descent optimization, the neural network is essentially a data-driven interpolator / fitter, and its accuracy is heavily dependent on the completeness of the training data. For regions with dramatic response changes, the prediction accuracy will decrease significantly, and the optimized parameters cannot guarantee that they are discrete values that can be achieved by the process.

[0007] Patent application CN116205111A (Optimization method of multi-dimensional and multi-channel multiplexing metasurface hologram based on reverse design) by Beijing University of Technology is another typical representative. Its core steps include constructing an initial discrete response database through electromagnetic simulation scanning; then, explicitly using data interpolation methods (such as Chebyshev interpolation) to expand and refine the database to create a "pseudo-continuous" response relationship; finally, performing gradient optimization. Although this method is modular, the "interpolation expansion" strategy is the root of its inherent defects.

[0008] What is particularly critical is that all the above methods of directly optimizing structure parameters (the second type) have the core bottleneck of how to deal with the limitations of the "discrete response database". Whether it is neural network fitting (CN117408114A) or explicit interpolation (CN116205111A), it is trying to bypass the discreteness problem by building a continuous proxy model. This approach faces three serious challenges in actual industrial application:

[0009] 1) The cost of database construction and expansion is high, and the technical threshold is high.

[0010] 2) The interpolation and fitting methods are difficult to adapt to the inherent strong nonlinearity and non-continuous response characteristics of the metasurface, leading to design errors;

[0011] 3) There is a fundamental contradiction between the continuous optimization idea and the "limited discrete library" constraint of industrial production;

[0012] In summary, the existing technology is in a dilemma: the optimization of complex amplitudes (the first type of method) cannot solve the structure matching problem in the final manufacturing; and the method of directly optimizing the structure parameters (the second type) is severely limited by the discrete database, and has to rely on interpolation or fitting to simulate continuity, bringing a series of problems of cost, accuracy and manufacturability. The fundamental reason is that there is an irreconcilable contradiction between the "continuity" requirement of the optimization algorithm and the "discreteness" nature of the metasurface response and manufacturing.

[0013] Therefore, there is an urgent need in the art for a new framework that can directly perform efficient, gradient-based optimization in discrete space. Such a framework must be able to directly utilize a limited, uninterpolated, validated library of superatom responses to transform a continuous optimization process into a discrete optimization process that selects the optimal superatom structures from the library, in order to simultaneously guarantee design accuracy, physical reality, and manufacturing feasibility at their roots, and completely eliminate the dependence on interpolation techniques. SUMMARY

[0014] In order to solve the problems of existing super surface design methods, such as dependence on interpolation database, disconnection between optimization process and physical implementation, and difficulty in adapting to large-scale manufacturing, the present application provides a super surface holographic optimization method and device based on limited super atom response library selection. By introducing a three-dimensional logarithmic probability distribution matrix as an optimization parameter, the super surface structure design is modeled as a classification problem of optimal selection from a limited and validated super atom response library, and the Gumbel-Softmax reparameterization technique is used to realize gradient backpropagation of discrete selection. This method avoids the interpolation or fitting step, and can realize high-precision, high-efficiency, and directly manufacturable polarization multiplexing super surface holographic design.

[0015] The technical scheme adopted by the present application to solve its technical problems is:

[0016] A super surface holographic optimization method based on limited super atom response library selection, comprising the following steps:

[0017] Step one, randomly initialize an unnormalized three-dimensional logarithmic probability distribution matrix P, and the elements in the logarithmic probability distribution matrix P represent the logarithmic probability of the super atom located at the grid position being selected as the super atom response library The super atom response library is a set of discrete super atom structure parameters and their corresponding complex amplitude responses calibrated in advance through electromagnetic simulation or experiment. Step two, based on the current logarithmic probability distribution matrix P, use the Gumbel-Softmax sampling strategy to generate a discrete selection matrix

[0018] , and according to the selection matrix , index the corresponding complex amplitude response from the super atom response library to construct the complex amplitude distribution matrix of the entire super surface, which is used for subsequent light field propagation calculation. Step three, use a differentiable wavefront propagation algorithm to calculate the complex amplitude distribution of the light field generated by the super surface on the target plane in the far field

[0019] Step four, calculate the difference between the calculated complex amplitude distribution and the target complex amplitude distribution, and update the logarithmic probability distribution matrix P based on the difference ;

[0020] ​Step four, supporting multi-polarization multiplexing, realizing image superposition through time multiplexing;

[0021] Step five, introducing structural similarity constraints, adopting a local periodicity approximation simplification modeling strategy to calculate the total loss value;

[0022] Step six, calculating the total loss value Relative probability matrix Gradient;

[0023] Step seven, according to the gradient calculated in step six, using a random gradient descent to update the probability matrix , obtaining the optimized metasurface shape structure parameters and the complex amplitude response under each polarization state ;

[0024] Step eight: repeating steps two to seven, constantly optimizing the log probability distribution matrix until the loss function converges to a preset threshold or reaches a maximum iteration number, and finally obtaining the discrete selection matrix from the converged probability matrix through the argmax operation, and further obtaining the discrete metasurface structure layout which can be directly used for manufacturing .

[0025] In the present application, the structure layout obtained by the above optimization can be used to manufacture high-precision metasurface devices for wave control applications such as holographic display, optical imaging, augmented reality / virtual reality display, communication, sensing, energy regulation, and quantum information.

[0026] Further, in the step one, the three-dimensional log probability distribution matrix , wherein represents the number of spatial grids of the metasurface, represents the number of candidate structures in the superatom response library, and the superatom response library is a set of discrete superatom structure parameters and corresponding complex amplitude responses calibrated in advance through electromagnetic simulation or experiment, represented as:

[0027] ;

[0028] , wherein represents the th structure, which usually includes the long axis length l, the short axis length w, the height h, and the period length c of the unit, and represent the amplitude and phase response of the th structure under the polarization state .

[0029] Further, in the step two, the discrete selection matrix , wherein each element The superatom sequence number representing the actually selected superatom response library, and the complex amplitude distribution matrix is ;

[0030] The selection matrix is a state matrix represented by one-hot encoding, indicating that the selected superatom in each unit of the metasurface comes from the sequence number in the superatom response library, and the selection process is realized by the following formula:

[0031] ;

[0032] Wherein, is the noise sampled from the Gumbel(0, 1) distribution, is a temperature parameter, which controls the sharpness of the sampling process; in the forward propagation, the discrete selection is obtained by taking the argmax operation; in the backward propagation, the continuous softmax approximation is used to calculate the gradient.

[0033] In step three, the differentiable wavefront propagation algorithm is an angular spectrum method or a Fresnel diffraction method.

[0034] In step four, for different polarization states of incident light, steps two and three are repeated to obtain the far-field complex amplitude distribution under each polarization state , the reconstructed image and the target image are brought into the loss function to calculate the image loss value .

[0035] In step five, in order to adapt to the process requirements of large-scale manufacturing, the invention introduces a structural similarity constraint in the optimization process. The invention uses a local periodic approximation (LPA) simplification modeling strategy, which requires the calculation result to satisfy the periodic boundary condition (PBC) in the metasurface plane; through the discrete selection matrix , the corresponding structure distribution S is indexed from the superatom response library, and the similarity of the structure parameters of adjacent superatoms is calculated as a structure regularization term:

[0036] ;

[0037] The total loss function is the weighted sum of the image loss and the structure loss: , wherein, is a weight coefficient, which is used to balance the image quality and the structure smoothness.

[0038] In the step six, the gradient of the discrete sampling (index) operation is estimated by Gumbel-Softmax reparameterization trick, so that the whole optimization process is derivable, and the gradient calculation is realized through the automatic differentiation framework, realizing the differentiability of the continuous relaxation approximation.

[0039] In the step seven, the process of updating the probability matrix

[0040]

[0041] Wherein, T is the learning rate, and the simulated annealing strategy is adopted, and the temperature parameter is gradually reduced in the optimization process So that the sampling process gradually changes from exploration to certainty.

[0042] A metasurface holographic optimization device based on a limited hyperatom response library selection, comprising:

[0043] A response library storage module is used to store the hyperatom response library obtained through electromagnetic simulation or experimental calibration, and the response library contains discrete geometric structure parameters and corresponding complex amplitude responses;

[0044] A probability matrix generation module is used to randomly initialize and maintain a three-dimensional logarithmic probability distribution matrix, which is used to represent the selection probability between each grid position of the metasurface and the candidate hyperatom structure;

[0045] A sampling and indexing module is used to sample from the probability matrix based on the Gumbel-Softmax reparameterization technique to obtain a discrete selection matrix, and index the hyperatom response library to construct the complex amplitude distribution of the metasurface;

[0046] A wavefront propagation module is used to execute a differentiable wavefront propagation algorithm to calculate the complex amplitude distribution of the metasurface on the far-field target plane;

[0047] An optimization calculation module is used to construct an image loss and a structure similarity constraint loss for a multi-polarization state reconstruction image, form a total loss function, and update the probability matrix by using a gradient descent type optimization algorithm combined with a simulated annealing strategy;

[0048] A structure generation module is used to output the discrete selection matrix and the corresponding metasurface structure layout after optimization convergence, so as to obtain a directly manufacturable metasurface device.

[0049] The beneficial effects of the present application mainly include:

[0050] 1、The method directly searches for geometric parameters in the hyperatom response library verified by simulation and experiment, which guarantees the compatibility with the manufacturing process and is suitable for wafer-level nanoimprinting and other large-scale processes.

[0051] ​​​2、Compared with the inverse optimization method relying on polynomial fitting or interpolation, the present application does not need to construct a continuous amplitude and phase space, avoids interpolation error, and improves accuracy and universality.

[0052] 3、The method directly acts on the target holographic image in the optimization process, saves the intermediate step in the traditional method, has higher optimization efficiency, and saves calculation time.

[0053] 4、The present application adopts a gradient-based optimization method combined with a simulated annealing strategy, and can obtain a metasurface design scheme closer to the global optimum. BRIEF DESCRIPTION OF DRAWINGS

[0054] Figure 1 It is a holographic optimization method flowchart of the metasurface based on the selected finite super atom response library of the present application;

[0055] Figure 2 It is a schematic diagram of the metasurface super atom response database obtained by scanning the super atom structure unit based on the finite difference time domain method;

[0056] Figure 3 It is a schematic diagram of the probability matrix, selection matrix and Gumbel-Softmax sampling process;

[0057] Figure 4 It is the change of the amplitude of the GaN material metasurface unit relative to the super atom structure;

[0058] Figure 5 It is the change of the phase of the GaN material metasurface unit relative to the super atom structure;

[0059] Figure 6 It is the change of the amplitude of the Si material metasurface unit relative to the super atom structure;

[0060] Figure 7 It is the change of the phase of the Si material metasurface unit relative to the super atom structure;

[0061] Figure 8 It is a structural schematic diagram of the metasurface holographic optimization device based on the selected finite super atom response library of the present application;

[0062] Figure 9 It is a holographic reconstruction schematic diagram of the metasurface designed by the present application;

[0063] Figure 10 It is a comparison of the metasurface holographic reconstruction diagrams of the present application and the direct selection method on the silicon material;

[0064] Figure 11 It is a comparison of the metasurface holographic reconstruction diagrams of the present application and the continuous interpolation method designed on the silicon material. DETAILED DESCRIPTION

[0065] The present invention will now be further described with reference to the accompanying drawings.

[0066] Reference Figures 1-11 This paper presents a metasurface holographic optimization method based on a finite superatomic response library. This embodiment uses the design of a silicon material multichannel polarization multiplexing holographic metasurface based on the angular spectrum algorithm as an example. The multichannel polarization multiplexing specifically adopts x and y dual polarization multiplexing. In this embodiment, FDTD simulation is based on the Lumerical software platform, and matrix operations and gradient optimization are implemented based on the PyTorch algorithm library.

[0067] The metasurface holographic optimization method based on a finite superatomic response library includes the following steps:

[0068] Step 1: Randomly initialize an unnormalized three-dimensional logarithmic probability distribution matrix. ,in This represents the number of spatial grids on the metasurface. This represents the number of candidate structures in the superatom response library. In this example, N is 500, M is 500, and K is 625. (Log probability distribution matrix) Middle elements Indicates the location on the grid. The superatoms were selected as the first superatoms in the superatom response library. The logarithmic probability of the structure.

[0069] The aforementioned superatomic response library is based on the following conditions: incident wavelength of 637 nm, fixed height of nanobricks of 600 nm, fixed period of superatoms of 400 nm, and dual-channel polarization states in the x and y directions, respectively. For example... Figure 2 The set of discrete superatomic structure parameters and their corresponding complex amplitude responses, calibrated by FDTD electromagnetic simulation, is shown below:

[0070] ;

[0071] in, Indicates the first The structure includes the major axis length *l* and minor axis length *w* of atoms. In the simulation, the length ranges of *l* and *w* are selected as 150 nm to 390 nm, and the sampling step size is 10 nm. and They represent polarization states respectively In the case of the first The amplitude and phase response of the structure The value is along The axial direction is denoted as Or denoted along the y-axis as .

[0072] Step two, as shown in Figure 3 , the Gumbel-Softmax trick is used to convert the discrete selection into a differentiable continuous approximation to support gradient optimization. Based on the current log probability distribution matrix , the Gumbel-Softmax sampling strategy is used to generate a discrete selection matrix , where each element represents the actual selected superatom response library of the superatom sequence number. According to the selection matrix , the corresponding complex amplitude response is indexed from the superatom response library, and the complex amplitude distribution matrix of the entire super surface is constructed, which is used for subsequent light field propagation calculation.

[0073] The selection matrix is a state matrix represented by one-hot encoding, which represents the selected superatom in each unit of the super surface from the sequence number in the superatom response library. The selection process is realized by the following formula:

[0074] ;

[0075] wherein is the noise sampled from the Gumbel(0, 1) distribution, is the initial value of the temperature parameter, which is 1, and controls the sharpness of the sampling process. In the forward propagation, the discrete selection is obtained by taking the argmax operation; in the backward propagation, the continuous softmax approximation is used to calculate the gradient.

[0076] Step three, the angular spectrum method is used to calculate the complex amplitude distribution of the light field generated by the super surface on the target plane in the far field , the expression of the angular spectrum method:

[0077] ;

[0078] The complex amplitude light field distribution of the reconstruction plane under different propagation distances is calculated {i}(i=1, 2), wherein represents the phase distribution, f x , f y represents the spatial frequency, represents the complex amplitude distribution of the super surface near field, represents the transfer function in the angular spectrum method, and the calculation formula is:

[0079] ;

[0080] wherein λ represents the wavelength, and z represents the light field transmission distance.

[0081] Step four, the method supports multiple polarization multiplexing, and image superposition can be realized by time multiplexing or other manners to improve the display information capacity. Steps two and three are repeated to obtain the far-field complex amplitude distribution under each polarization state

[0082] Step five, to adapt to the process requirements of large-scale manufacturing, the present application introduces a structural similarity constraint in the optimization process. The present application uses a local periodic approximation (LPA) simplification modeling strategy, which requires that the calculation results satisfy the periodic boundary condition (PBC) in the metasurface plane. A discrete selection matrix is used to index the corresponding structure distribution S from the super-atom response library. The similarity of the structure parameters of adjacent super-atoms is calculated as a structure regularization term:

[0083] ;

[0084] The total loss function is the weighted sum of the image loss and the structure loss: . Where is the weight coefficient, used to balance the image quality and the structure smoothness.

[0085] Step six, calculate the gradient of the total loss value relative to the probability matrix . The Gumbel-Softmax reparameterization trick is used to estimate the gradient of the discrete sampling (indexing) operation, so that the entire optimization process is differentiable. The gradient calculation is realized through an automatic differentiation framework, realizing the differentiability of continuous relaxation approximation.

[0086] Step seven, according to the gradient calculated in step six, the probability matrix is updated using the stochastic gradient descent or its variants (such as the Adam optimizer), to obtain the optimized metasurface shape structure parameters and the complex amplitude response under each polarization state . The process of updating the probability matrix :

[0087] ;

[0088] Where, is the gradient of the loss function with respect to the independent variable P , and is the learning rate, and the simulated annealing strategy is used to gradually reduce the temperature parameter ​​​​​The sampling process gradually changes from exploratory to deterministic.

[0089] Step eight, repeat steps two to seven, constantly optimize the logarithmic probability distribution matrix until the number of iterations reaches 2000. Finally, the discrete selection matrix is obtained from the converged probability matrix by argmax operation , and then the discrete metasurface structure layout directly used for manufacturing is obtained .

[0090] As Figure 9 shown, the metasurface structure layout obtained by the above optimization is used to simulate the holographic reconstruction images of the metasurface at and two reconstruction plane positions under the conditions of XX and YY polarization states. According to the above steps, the holographic reconstruction results of the present method and other comparative methods are simulated and compared, and further quantitative evaluation of the quality of the reconstructed images is made by using the structural similarity index (SSIM) and peak signal-to-noise ratio (PSNR).

[0091] As Figure 10 shown, the holographic reconstruction results obtained by the present method after selecting the super atom structure are compared with the holographic reconstruction results obtained by the direct selection method. The core difference between the direct selection method and the present method is that specifically, the direct selection method is based on the complex amplitude proximity criterion to select the target super atom structure from the limited discrete super atom response library, while the present method selects the super atom structure from the limited discrete super atom response library through the aforementioned design logic. As Figure 10 can be seen, the present method can obtain more accurate holographic reconstruction results. Further analysis shows that the direct selection method is worse than the present method in actual holographic reconstruction effect because it does not take into account the local periodic approximation.

[0092] As Figure 11 shown, the holographic reconstruction images corresponding to the metasurface made by the present method are compared with the holographic reconstruction images corresponding to the metasurface made by the traditional continuous interpolation inverse design method. Figure 11 The results shown in Figures 4-7As shown, since the phase and amplitude change greatly with the super surface structure in the Si material, even if the method of the application can only select the super atom structure within the preset limited super atom response library, the final obtained holographic reconstruction quality is still better than that of the traditional continuous interpolation reverse design method. Further analysis shows that since the parameters outside the super atom response library selected by the continuous interpolation method have not been completely verified and experimentally demonstrated, the corresponding complex amplitude is easy to deviate in the actual manufacturing process, thereby leading to the actual holographic reconstruction effect of the method being worse than that of the method of the application.

[0093] In addition, in order to facilitate engineering implementation, the embodiment also provides a super surface holographic optimization device based on a limited super atom response library selection, which is used to execute the foregoing optimization method and can be realized by software, hardware or a combination of software and hardware. The device includes the following modules:

[0094] A response library storage module is configured to store a super atom response library obtained through electromagnetic simulation or experimental calibration, the response library including a plurality of discrete geometric structure parameters and corresponding complex amplitude responses, the structure parameters including a long axis length and a short axis length of a nano brick, and the responses including amplitude and phase information under a specific polarization state;

[0095] A probability matrix generation module is configured to randomly initialize and dynamically maintain a three-dimensional logarithmic probability distribution matrix , wherein represents a number of spatial grids of the super surface, represents a number of candidate structures in the super atom response library, and the matrix is configured to represent a probability of selecting different super atom structures at each position;

[0096] A sampling and indexing module is configured to sample and generate a discrete selection matrix from the probability matrix based on a Gumbel-Softmax reparameterization technique, and obtain complex amplitude responses of corresponding super atom structures from the response library through an indexing operation, and further construct a complex amplitude distribution matrix of the entire super surface;

[0097] A wave front propagation module is configured to perform a differentiable wave front propagation calculation, and calculate a complex amplitude distribution of a light field generated by the super surface on a target reconstruction plane by using an angular spectrum method or other diffraction propagation models;

[0098] An optimization calculation module is configured to construct a multi-channel image reconstruction loss function and a structure smoothing constraint term, form a total loss , and update the probability matrix based on gradient back propagation by using a stochastic gradient descent or a variant thereof (such as an Adam optimizer) , and simultaneously integrate a simulated annealing mechanism to gradually reduce a temperature parameter in the Gumbel-Softmax .

[0099] a structure generation module, which outputs a final discrete selection matrix by performing argmax operation on the log-probability matrix after the optimization process converges and the corresponding metasurface structure layout The obtained result can be directly used for processing and manufacturing of the metasurface device.

[0100] The device is suitable for design and implementation of the metasurface in holographic display, optical imaging, augmented reality (AR), virtual reality (VR), optical communication, sensing, energy regulation and quantum information processing, etc.

[0101] The embodiments described in the specification are only enumerations of implementation forms of the inventive concept, and are only used for purposes of illustration. The protection scope of the present application should not be regarded as being limited to the specific forms presented in the embodiments, and the protection scope of the present application also encompasses equivalent technical means that can be thought of by those skilled in the art according to the inventive concept.

Claims

1. A metasurface holographic optimization method based on a finite superatomic response library, characterized in that, The method includes the following steps: Step 1: Randomly initialize an unnormalized three-dimensional logarithmic probability distribution matrix P. The elements in the logarithmic probability distribution matrix P... Indicates the location on the grid. The superatoms were selected as the first superatoms in the superatom response library. The logarithmic probability of the structure; the superatomic response library is a set of discrete superatomic structure parameters and their corresponding complex amplitude responses, pre-calibrated through electromagnetic simulation or experiment; Step 2: Based on the current log probability distribution matrix The discrete selection matrix is ​​generated using the Gumbel-Softmax sampling strategy. According to the selection matrix Index the corresponding complex amplitude response from the superatomic response library to construct the complex amplitude distribution matrix of the entire metasurface for subsequent optical field propagation calculations; Step 3: Calculate the complex amplitude distribution of the light field generated by the metasurface on the far-field target plane using a differentiable wavefront propagation algorithm. ; Step 4: Support multi-polarization multiplexing and achieve image overlay through time multiplexing; Step 5: Introduce structural similarity constraints, adopt a local periodic approximation simplification modeling strategy, and calculate the total loss value; Step 6: Calculate the total loss value relative probability matrix The gradient; Step 7: Update the probability matrix using stochastic gradient descent based on the gradient calculated in Step 6. The optimized metasurface shape and structure parameters were obtained. and complex amplitude response under various polarization states ; Step 8: Repeat steps 2 through 7, continuously optimizing the logarithmic probability distribution matrix until the loss function converges to a preset threshold or reaches the maximum number of iterations. Finally, obtain the discrete choice matrix from the converged probability matrix through the argmax operation. This leads to discrete metasurface structure layouts that can be directly used for manufacturing. .

2. The metasurface holographic optimization method based on a finite superatomic response library as described in claim 1, characterized in that, In step one, the three-dimensional logarithmic probability distribution matrix ,in This represents the number of spatial grids on the metasurface. This indicates the number of candidate structures in the superatomic response library, which is a set of discrete superatomic structure parameters and their corresponding complex amplitude responses that have been pre-calibrated through electromagnetic simulation or experiments.

3. The metasurface holographic optimization method based on a finite superatomic response library as described in claim 1 or 2, characterized in that, In step two, the discrete selection matrix , where each element This represents the superatom index in the actually selected superatom response library, and the complex amplitude distribution matrix is... ; The selection matrix It is a state matrix represented by one-hot encoding, indicating that the selected superatoms in each unit of the metasurface are from the index of the superatom response library. In forward propagation, discrete selections are obtained by taking the argmax operation; in backward propagation, the gradient is calculated by using continuous softmax approximation.

4. The metasurface holographic optimization method based on a finite superatomic response library as described in claim 1 or 2, characterized in that, In step three, the differentiable wavefront propagation algorithm is either the angular spectrum method or the Fresnel diffraction method.

5. The metasurface holographic optimization method based on a finite superatomic response library as described in claim 1 or 2, characterized in that, In step four, steps two and three are repeated for incident light with different polarization states to obtain the far-field complex amplitude distribution under each polarization state. Calculate the light intensity distribution of the reconstructed image under each polarization state. The image will be reconstructed. and target image Calculate the image loss value by substituting it into the loss function. .

6. The metasurface holographic optimization method based on a finite superatomic response library as described in claim 1 or 2, characterized in that, In step five, the discrete selection matrix is ​​used. The corresponding structure distribution S is indexed from the superatomic response library, and the similarity of adjacent superatomic structure parameters is calculated as the structure regularization term. The total loss function is the weighted sum of image loss and structure loss.

7. The metasurface holographic optimization method based on a finite superatomic response library as described in claim 1 or 2, characterized in that, In step six, the gradient of the discrete sampling operation is estimated using the Gumbel-Softmax reparameterization technique, making the entire optimization process differentiable. The gradient calculation is implemented through an automatic differentiation framework, achieving the differentiability of the continuous relaxation approximation.

8. The metasurface holographic optimization method based on a finite superatomic response library as described in claim 1 or 2, characterized in that, In step seven, the probability matrix is ​​updated. Simultaneously, a simulated annealing strategy was adopted, gradually reducing the temperature parameter during the optimization process. This allows the sampling process to gradually shift from exploratory to deterministic.

9. An apparatus for implementing the metasurface holographic optimization method based on a finite superatomic response library as described in claim 1, characterized in that, The device includes: The response library storage module is used to store the superatomic response library obtained through electromagnetic simulation or experimental calibration. The response library contains discrete geometric structural parameters and their corresponding complex amplitude responses. The probability matrix generation module is used to randomly initialize and maintain a three-dimensional logarithmic probability distribution matrix, which is used to characterize the selection probability between each grid position on the metasurface and the candidate superatomic structure; The sampling and indexing module is used to sample from the probability matrix based on the Gumbel-Softmax reparameterization technique to obtain a discrete selection matrix, and to index the superatom response library to construct the complex amplitude distribution of the metasurface; The wavefront propagation module is used to execute a differentiable wavefront propagation algorithm to calculate the complex amplitude distribution of the metasurface in the far-field target plane; The optimization calculation module is used to construct image loss and structural similarity constraint loss for multi-polarization reconstructed images, form the total loss function, and update the probability matrix using gradient descent-type optimization algorithms combined with simulated annealing strategy; The structure generation module is used to output a discrete selection matrix and the corresponding metasurface structure layout after optimization convergence, thereby obtaining a directly fabricable metasurface device.

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