A metasurface optimization design method and device, computer equipment and storage medium

Abstract

The application discloses a metasurface optimization design method and device, computer equipment and a storage medium, and the method comprises the steps of establishing a three-dimensional full-wave simulation model for a target metasurface, obtaining transmission spectrum information, and constructing a target function; forward simulation is performed on the target metasurface, first and second forward complex electric fields generated by different planes are obtained, and a dipole companion source array is generated through the second forward complex electric field; the dipole companion array is activated, and backward simulation is performed on the target metasurface, and a companion complex electric field is obtained; the voxel sensitivity is calculated by combining the first forward complex electric field and the companion complex electric field; the lateral radial distance from the voxel center to the center of the micro-nano structure is calculated, and a Gaussian distribution is constructed to approximate a Dirac delta function; the physical gradient parameter of the target function to the physical radius of the micro-nano structure is calculated, and the physical gradient parameter is optimized. The application can solve the problems that the irregular structure generated by the traditional topological optimization is difficult to process, and the continuous gradient of the cylindrical boundary cannot be accurately extracted by the conventional companion optimization.

Description

Technical Field

[0001] This invention relates to the field of micro-nano optical device technology, and in particular to a metasurface optimization design method, apparatus, computer equipment, and storage medium. Background Technology

[0002] Metasurfaces are two-dimensional planar arrays composed of subwavelength artificial microstructures such as nanopillars and nanopores. They enable flexible manipulation of key parameters of electromagnetic waves, such as amplitude, phase, and polarization, at the subwavelength scale. Leveraging their unique advantages in optical field manipulation, they have become core supporting devices in cutting-edge fields such as augmented reality, superlenses, and holographic displays. With the rapid development of these fields, the market demands increasingly stringent performance requirements for metasurface devices. A macroscopic optical metasurface typically contains tens of thousands to millions of nanostructure units, posing extremely high challenges to the design efficiency and quality of metasurfaces.

[0003] In the field of metasurface design, traditional optical design methods often rely on forward parameter scanning or heuristic algorithms such as genetic algorithms and particle swarm optimization. The computational complexity of these methods is O(n). When faced with the huge design freedom brought by large-scale nanostructure units, the number of calculations increases linearly with the number of structural units, which seriously limits the R&D efficiency of large-scale, complex functional metasurfaces and makes it difficult to meet the application needs of current cutting-edge fields.

[0004] To overcome the bottleneck of optimization speed, the adjoint optimization algorithm has been introduced into micro-nano optical design. This method is based on the perturbation theory of Maxwell's equations. By recording the electric field within the structure during forward simulation and the electric field at the target location after propagation, a virtual reverse light source (i.e., the adjoint source) is constructed using the electric field of the target surface. Then, a reverse simulation is performed to record the electric field transmitted back into the structure. Only one forward simulation and one adjoint simulation are needed to calculate the gradient of the objective function with respect to all designed pixels in the entire space. This reverse design method, with a computational complexity of only O(1), greatly improves the global optimization speed of the entire metasurface, providing a new technical path for large-scale metasurface design. However, existing metasurface design technologies based on adjoint optimization still face severe structural constraints and fabrication feasibility challenges in practical engineering applications, failing to effectively balance optical performance and fabrication capabilities.

[0005] Currently, most mainstream adjoint optimization techniques employ the free topology optimization strategy. This strategy divides the design domain into a dense pixel grid, allowing the dielectric constant of each pixel to evolve freely and continuously between the material and the background. While this method can explore a vast design space and optimize structures with excellent optical performance, it also generates highly asymmetric, continuous, irregular structures. These structures exhibit unpredictable sharp edges, extremely small local feature sizes, and complex connectivity, significantly exceeding the manufacturing limits of existing semiconductor micro / nano fabrication processes such as electron beam lithography, deep ultraviolet lithography, and high aspect ratio etching. This leads to a disconnect between simulation results and actual fabrication effects, hindering engineering applications.

[0006] To address the fabrication challenges posed by topology optimization and balance the optical performance of metasurfaces with practical fabrication capabilities, researchers have gradually shifted towards boundary optimization based on regular shapes. However, most of these boundary optimization techniques are currently limited to optimizing rectangular or cuboid structures. The fundamental reason for this lies in the mesh matching problem at the simulation level: mainstream three-dimensional electromagnetic simulation methods (such as the finite-difference time-domain method and rigorous coupled-wave analysis) all use a Cartesian coordinate system, discretizing space into square three-dimensional voxels arranged horizontally and vertically. The right-angled boundaries of rectangular structures naturally fit this square simulation mesh, and their boundary positions can be precisely determined on the coordinate axes. Furthermore, when extracting the gradient of the objective function with respect to geometric dimensions, only a simple difference or step approximation along the X or Y axis is needed to update the dielectric constant, eliminating the need for complex edge processing and greatly reducing the optimization difficulty.

[0007] Compared to rectangular prism structures, cylindrical nanopillars possess natural rotational symmetry, making them ideal structures for realizing polarization-independent metasurface devices such as achromatic superlenses and conventional beam-shaping diffraction optical elements. Furthermore, they exhibit superior stress distribution and morphological fidelity in practical photolithography and etching processes, better meeting the requirements of engineering fabrication. However, directly applying adjoint optimization algorithms to update the physical radius of cylindrical structures remains a gap in current technology. Because the circular physical boundary of a cylinder cannot be perfectly aligned with the square Cartesian grid of simulation software, a severe staircase effect inevitably occurs: when the optimization algorithm attempts to calculate the gradient of the objective function with respect to the continuous radius of the cylinder, a small radius change may not be sufficient to cross a square pixel, leading to gradient vanishing; conversely, when the radius change covers a new pixel, it triggers a drastic gradient change. This inherent contradiction between the discrete grid and the continuous curvature boundary makes it impossible to accurately establish the chain rule for differentiation between the cylinder radius and the objective function, rendering adjoint optimization ineffective for the optimization design of cylindrical nanopillars.

[0008] In summary, existing metasurface adjoint optimization techniques face clear technical bottlenecks. The most significant and critical technical problem is that, due to the Cartesian coordinate system (square mesh) used at the bottom layer, existing adjoint optimization algorithms suffer from severe geometric boundary mismatch when dealing with cylindrical nanopillars that possess polarization-independent properties. This mismatch makes it impossible to establish an accurate chain of derivatives between the continuous physical radius and the objective function, and thus fails to effectively transfer the structural optimization objective to the morphology of the nanopillar. When conventional adjoint optimization is directly applied to such specific optical structures, it cannot achieve global fast optimization that balances workability and polarization independence due to huge gradient calculation errors.

[0009] In addition to the core technical issues mentioned above, there are two major secondary problems: First, because the continuous curvature boundary of the cylinder spans the square pixel grid, a step effect is triggered when extracting the sensitivity of radius evolution. Small changes in the radius parameter may not cause changes in the grid dielectric constant, leading to gradient vanishing or drastic numerical mutations, causing numerical optimization to oscillate and fail to find the optimal value. Currently, there is a lack of effective edge pixel processing mechanisms (such as anti-aliasing or sub-pixel smoothing allocation mechanisms) to solve this problem. Second, it is difficult to balance the efficiency and fabrication feasibility of large-scale optimization. Although traditional boundary optimization with optimization is easy to determine and has a fast optimization speed, it is only applicable to square nanopillar structures. While full-space topology optimization can achieve better optical performance, it generates irregular structures that are difficult to fabricate. Existing technologies cannot establish an effective computational framework that balances "global optimization speed," "polarization-independent optical properties," and "actual semiconductor fabrication feasibility." Therefore, there is an urgent need in this field for a novel optimization calculation method that can retain the extremely high computational speed of global updates of all nanopillars during optimization, and break through the limitations of the existing square mesh system to achieve accurate edge pixel processing and parameter gradient mapping for cylindrical structures (taking into account both processability and polarization independence), thereby promoting the engineering application and performance upgrade of metasurface devices. Summary of the Invention

[0010] This invention provides a metasurface optimization design method, apparatus, computer device, and storage medium, aiming to solve the problems of difficulty in processing irregular structures generated by traditional topology optimization, and the difficulty in accurately extracting continuous gradients at cylindrical boundaries by conventional adjoint optimization.

[0011] In a first aspect, embodiments of the present invention provide a metasurface optimization design method, comprising: A three-dimensional full-wave simulation model is established for the target metasurface, and the transmission spectrum information of the three-dimensional full-wave simulation model is obtained to construct the objective function; wherein, the target metasurface contains multiple micro-nano structures; A forward simulation is performed on the target metasurface to obtain the first forward complex electric field generated on the preset design plane and the second forward complex electric field generated on the target plane. A dipole companion source array is generated through the second forward complex electric field. Then, the dipole companion source array is activated and a reverse simulation is performed on the target metasurface to obtain the companion complex electric field in the design domain of the target metasurface. The voxel sensitivity of the micro / nano structures in the target metasurface in three-dimensional space is calculated by combining the first positive complex electric field and the accompanying complex electric field. Calculate the lateral and radial distances from the centers of all voxels in the three-dimensional space to the center of each micro / nano structure, and construct a Gaussian distribution approximating the Dirac delta function by combining the smoothing scale parameter; Combining the voxel sensitivity and the Gaussian distribution approximation of the Dirac delta function, the partial derivative of the objective function with respect to the physical radius of each of the micro / nano structures is calculated; The partial derivatives are used as gradient parameters for the physical radius of each micro / nano structure, and an optimization algorithm is used to update the physical radius of each micro / nano structure based on the gradient parameters.

[0012] Secondly, embodiments of the present invention provide a metasurface optimization design apparatus, comprising: The model building unit is used to build a three-dimensional full-wave simulation model of the target metasurface and obtain the transmission spectrum information of the three-dimensional full-wave simulation model to construct the objective function; wherein, the target metasurface contains multiple micro-nano structures; An electric field acquisition unit is used to perform forward simulation on the target metasurface, acquire the first forward complex electric field generated by the forward simulation on a preset design plane and the second forward complex electric field generated on the target plane, and generate a dipole companion source array through the second forward complex electric field; then activate the dipole companion source array and perform reverse simulation on the target metasurface to acquire the companion complex electric field in the design domain of the target metasurface. A sensitivity calculation unit is used to calculate the voxel sensitivity of the micro / nano structure in the target metasurface in three-dimensional space by combining the first positive complex electric field and the accompanying complex electric field. The distance calculation unit is used to calculate the lateral and radial distances from the centers of all voxels in the three-dimensional space to the center of each micro / nano structure, and to construct a Gaussian distribution approximating the Dirac delta function by combining the smooth scale parameter. The radius derivative unit is used to combine the voxel sensitivity and Gaussian distribution to approximate the Dirac delta function and calculate the partial derivative of the objective function with respect to the physical radius of each of the micro / nano structures. The parameter optimization unit is used to take the partial derivative as the gradient parameter of the physical radius of each micro-nano structure, and to update the physical radius of each micro-nano structure based on the gradient parameter using an optimization algorithm.

[0013] Thirdly, embodiments of the present invention provide a computer device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the metasurface optimization design method as described in the first aspect.

[0014] Fourthly, embodiments of the present invention provide a computer-readable storage medium storing a computer program that, when executed by a processor, implements the metasurface optimization design method as described in the first aspect.

[0015] This invention provides a metasurface optimization design method, apparatus, computer device, and storage medium. By approximating the Dirac delta function using a Gaussian distribution, the sensitivity of discrete voxels is smoothly mapped to the continuous physical radius of each cylindrical micro / nanostructure. This effectively solves the staircase effect caused by the mismatch between the square Cartesian grid and the cylindrical circular physical boundary, avoiding gradient vanishing and gradient abrupt changes. It also solves the problems of difficulty in fabricating irregular structures generated by traditional topology optimization and the difficulty in accurately extracting the continuous gradient of the cylindrical boundary using conventional adjoint optimization. Furthermore, it can accurately establish the chain derivative of the objective function with respect to the cylindrical radius, obtaining precise gradient parameters. Simultaneously, this invention retains the O(1) complexity advantage of the adjoint optimization algorithm, which requires only one forward and one backward simulation to obtain the gradient across the entire space. It can achieve synchronous global updates of the radii of all nanopillars. While ensuring the efficiency of large-scale metasurface design, the resulting cylindrical structure naturally possesses rotational symmetry, meeting the design requirements of polarization-independent devices. Moreover, its regular morphology conforms to the manufacturing requirements of existing semiconductor micro / nano fabrication processes, effectively balancing the optical performance, polarization characteristics, optimization efficiency, and fabrication feasibility of the metasurface. Attached Figure Description

[0016] To more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings used in the following description of the embodiments will be briefly introduced. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0017] Figure 1 A flowchart illustrating a metasurface optimization design method provided in an embodiment of the present invention; Figure 2 A schematic block diagram of a metasurface optimization design device provided in an embodiment of the present invention; Figure 3 This is a schematic diagram of Gaussian smoothing for voxel weighting in a metasurface optimization design method provided in an embodiment of the present invention; Figure 4This is a schematic diagram illustrating the working principle of a color routing metasurface in a metasurface optimization design method provided by an embodiment of the present invention. Figure 5 This is a schematic diagram of the pre-modeling of a color routing metasurface unit in a metasurface optimization design method provided in an embodiment of the present invention; Figure 6 This is a schematic diagram of the objective function curve in the iterative process of a metasurface optimization design method provided in an embodiment of the present invention; Figure 7 This is an optimized color routing metasurface unit structure diagram provided in a metasurface optimization design method according to an embodiment of the present invention; Figure 8 This is a schematic diagram of the target plane light intensity distribution under different wavelengths of incident light in a metasurface optimization design method provided in an embodiment of the present invention. Detailed Implementation

[0018] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0019] It should be understood that, when used in this specification and the appended claims, the terms "comprising" and "including" indicate the presence of the described features, integrals, steps, operations, elements and / or components, but do not exclude the presence or addition of one or more other features, integrals, steps, operations, elements, components and / or collections thereof.

[0020] It should also be understood that the terminology used in this specification is for the purpose of describing particular embodiments only and is not intended to limit the invention. As used in this specification and the appended claims, the singular forms “a,” “an,” and “the” are intended to include the plural forms unless the context clearly indicates otherwise.

[0021] It should also be further understood that the term "and / or" as used in this specification and the appended claims refers to any combination of one or more of the associated listed items and all possible combinations, and includes such combinations.

[0022] Please see below. Figure 1 This invention provides a metasurface optimization design method, specifically including steps S101 to S106.

[0023] Step S101: Establish a three-dimensional full-wave simulation model for the target metasurface and obtain the transmission spectrum information of the three-dimensional full-wave simulation model to construct the objective function; wherein, the target metasurface contains multiple micro-nano structures; Step S102: Perform forward simulation on the target metasurface to obtain the first forward complex electric field generated on the preset design plane and the second forward complex electric field generated on the target plane, and generate a dipole companion source array through the second forward complex electric field; then activate the dipole companion source array and perform reverse simulation on the target metasurface to obtain the companion complex electric field in the design domain of the target metasurface. Step S103: Calculate the voxel sensitivity of the micro / nano structure in the target metasurface in three-dimensional space by combining the first positive complex electric field and the accompanying complex electric field; Step S104: Calculate the lateral radial distance from the center of all voxels in the three-dimensional space to the center of each micro / nano structure, and construct a Gaussian distribution approximating the Dirac delta function by combining the smooth scale parameter; Step S105: Combining the voxel sensitivity and the Gaussian distribution to approximate the Dirac delta function, calculate the partial derivative of the objective function with respect to the physical radius of each of the micro / nano structures; Step S106: Use the partial derivative as the gradient parameter of the physical radius of each micro / nano structure, and update the physical radius of each micro / nano structure based on the gradient parameter using an optimization algorithm.

[0024] In this embodiment, firstly, for a target metasurface containing multiple micro / nano structures, a three-dimensional full-wave simulation model is established and its transmission spectrum information is obtained to construct an objective function. Next, forward simulation is used to obtain the forward complex electric fields generated by the design plane and the target plane, respectively. A dipole adjoint source array is generated using the second forward complex electric field corresponding to the target plane. After activating the array and performing reverse simulation, the adjoint complex electric field of the target plane is obtained. Then, combining the first forward complex electric field and the adjoint complex electric field corresponding to the design plane, the voxel sensitivity of the micro / nano structures in the target metasurface in three-dimensional space is calculated. Simultaneously, the lateral radial distance from the center of all voxels to the center of each micro / nano structure in three-dimensional space is calculated, and a Gaussian distribution is constructed using a smoothing scale parameter to approximate the Dirac delta function. Then, using the voxel sensitivity and the aforementioned Gaussian distribution approximation function, the partial derivative of the objective function with respect to the physical radius of each micro / nano structure is solved. Finally, this partial derivative is set as the gradient parameter of the physical radius of the micro / nano structure, and an optimization algorithm is used to optimize it.

[0025] This embodiment approximates the Dirac delta function using a Gaussian distribution, smoothly mapping the sensitivity of discrete voxels to the continuous physical radius of each cylindrical micro / nano structure. This effectively solves the staircase effect caused by the mismatch between the square Cartesian grid and the circular physical boundary of the cylinder, avoiding gradient vanishing and abrupt changes. It also overcomes the shortcomings of traditional topology optimization, such as the difficulty in fabricating irregular structures and the difficulty in accurately extracting the continuous gradient of the cylindrical boundary using conventional adjoint optimization. Furthermore, it accurately establishes the chain derivative of the objective function with respect to the cylinder radius, obtaining precise gradient parameters. In addition, this embodiment retains the O(1) complexity advantage of the adjoint optimization algorithm, which requires only one forward and one backward simulation to obtain the gradient across the entire space. It enables synchronous global updates of the radii of all nanopillars, ensuring the efficiency of large-scale metasurface design while providing the resulting cylindrical structure with natural rotational symmetry, meeting the design requirements of polarization-independent devices. Moreover, its regular morphology conforms to the requirements of existing semiconductor micro / nano fabrication processes, effectively balancing the optical performance, polarization characteristics, optimization efficiency, and fabrication feasibility of the metasurface.

[0026] To address the staircase effect and gradient extraction failure caused by the mismatch between the Cartesian mesh and the continuous cylindrical boundary in underlying finite-difference time-domain or strictly coupled-wave analysis, this embodiment innovatively introduces a sub-pixel Gaussian smoothing mapping algorithm. This algorithm assigns continuous weights to boundary voxels by calculating radial distances, successfully and accurately resolving discrete spatial sensitivity to the gradient of the structure's physical radius. Simultaneously, this embodiment also integrates an optimization algorithm that effectively suppresses numerical noise in mesh partitioning, as well as an objective function that achieves multi-objective adaptive equilibrium. This overcomes the bottleneck of existing technologies that cannot simultaneously achieve polarization independence, extremely high optimization speed, and practical fabrication feasibility, realizing a globally fast and stable solution for the parameters of large-scale metasurface arrays.

[0027] It should be noted that, in addition to isotropic cylindrical nanopillars, the Gaussian smooth boundary mapping concept described in this embodiment can also be extended to elliptical cylinders, rectangular cylinders, or other regular cross-section micro-nano structures by constructing corresponding boundary distance functions or sign distance functions. Furthermore, the underlying electromagnetic simulation engine used in this embodiment is based on the finite-difference time-domain method, but it can also be replaced by a bottom-level electromagnetic simulation engine based on a fixed spatial discrete grid, such as the strictly coupled wave analysis method (RCWA).

[0028] In practical applications, polarization-independent color separation devices, such as a color routing metasurface, can be generated based on the superlens optimization design method provided in this embodiment. The metasurface includes a transparent substrate and a high-refractive-index cylindrical nanopillar array on the substrate. The array has a specific sub-pixel arrangement (such as a red-green-green-blue (RGGB) array or a red-green-blue-infrared (RGB-IR) array with a specific period), and the nanopillar radius distribution of the array is calculated and generated by the above method.

[0029] In one embodiment, step S101 includes: The objective function is constructed based on the transmission spectral information according to the following formula: ; Wherein, FOM represents the objective function, and T1, T2, and T3 represent the effective transmittance at the first, second, and third wavelengths for the micro / nano structure, respectively. , and These represent the effective dielectric constants of the micro / nano structure at the first wavelength, the second wavelength, and the third wavelength, respectively.

[0030] This embodiment first constructs a three-dimensional full-wave simulation model of the metasurface array and sets the initial cylindrical radius distribution parameters. The structure is then excited by broadband or multiple narrowband light sources to obtain the transmission field spectrum information of the model. To achieve conventional multi-objective optimization (such as multi-wavelength or multi-focus equalization optimization), this embodiment constructs a log-sum (FOM, Figure of Merit) function as the objective function: ; In the above formula, T1 refers to the effective transmittance of the device for the first wavelength, which is calculated by dividing the energy of that wavelength at the expected receiving position by the total energy of the incident wavelength. Specifically, it is obtained by setting a fixed position in the simulation software and collecting data. Similarly, T2 and T3 refer to the effective transmittance of the device for the second and third wavelengths, respectively. The effective dielectric constant of the device at the first wavelength can be calculated from the difference between the dielectric constant of the effective refractive index medium and the background medium at the first wavelength (the effective refractive index medium refers to the target design structure of the device when it is actually working, such as the nanopillars of the metasurface; the background medium is air, or the material filled between the nanopillars to ensure the stability of the nanopillar structure and prevent it from collapsing). , Similarly, these refer to the effective dielectric constants of the device at the second and third wavelengths, respectively. These values ​​vary with wavelength and material, and are generally measured in the laboratory using the materials. To make the result of the optimization function close to the single-digit order of magnitude (facilitating subsequent gradient calculation), the entire optimization function needs to be multiplied by 10. The mathematical structure of this optimization function allows channels with lower transmittance to automatically receive larger weighting coefficients when calculating gradients, thus avoiding the attrition effect caused by traditional linear summation (i.e., when transmittance increases in one band, transmittance in another band decreases sharply).

[0031] This embodiment uses a logarithmic sum or equivalent exponential smoothing formula to construct the objective function, enabling it to automatically assign high-amplitude companion source weights to low-transmittance channels during back-derivative calculation. In practical applications, this embodiment, in constructing the objective function, in addition to using a logarithmic sum form to dynamically balance the transmittance of multiple target channels, can also employ normalized exponential functions (such as Softmin or Softmax functions) and dynamic linear weighting methods.

[0032] In one embodiment, step S102 includes: The target metasurface is illuminated by an actual forward light source to perform forward simulation of the target metasurface; Record the first positive complex electric field generated by the target metasurface on the preset design plane and the second positive complex electric field generated on the target plane; A dipole adjoint source array is generated based on the second positive complex electric field corresponding to the target plane; wherein, the dipole adjoint source array is set in the target region corresponding to the target plane, and the complex amplitude of the dipole adjoint source is determined by the positive complex electric field distribution in the target region and the weighting coefficient corresponding to the objective function; The forward light source is turned off, and the dipole adjoint source array is activated for reverse simulation. Then, the adjoint complex electric field generated by the target plane is collected.

[0033] In this embodiment, when implementing the adaptive construction of the accompanying source and the collection of the accompanying field, a forward simulation is first performed. That is, the actual light source is used as the incident light source to illuminate the device, and the complex electric field component readings E collected by the preset collection plane in the design domain (e.g., within a cylindrical nanoparticle) are recorded. fwd This refers to the first positive complex electric field; simultaneously, the target plane is extracted to calculate the effective transmittance of each wavelength device for the objective function, and the second positive complex electric field generated by the target plane is also extracted. Here, the electric field distribution in the target plane is used to automatically generate a dipole companion source array, such as sampling the collected target plane electric field at equal intervals and creating an electric field consistent with the positive electric field at the sampling position as a return light source. The complex amplitude can be determined by the second positive complex electric field distribution in the target area and the weighting coefficient corresponding to the objective function. Under the condition of maximizing the optical power or transmission efficiency in the target area, the complex amplitude is obtained by weighting the complex conjugate of the second positive complex electric field in the target area. Subsequently, the positive light source is turned off, the above-mentioned companion dipole source is activated, and a reverse simulation is performed to collect the companion complex electric field E in the preset target plane within the design domain. adj .

[0034] In one embodiment, step S103 includes: The three-dimensional space corresponding to the three-dimensional full-wave simulation model is meshed to obtain the mesh space; Based on the perturbation theory of Maxwell's equations, the sensitivity distribution of each voxel in the grid space to the objective function is calculated, and the voxel sensitivity is obtained: ; Where g(r) represents the voxel sensitivity, E fwd E represents the first positive complex electric field. adj Represents the associated complex electric field, r represents the position vector of a single voxel, and Re represents the calculation using the real part. The wave number is represented by λ, and the wavelength used is represented by λ. This represents the effective dielectric constant.

[0035] In this embodiment, when calculating voxel sensitivity, the three-dimensional space is first divided into a square grid, and then the calculation is performed layer by layer and grid by grid. Subsequently, based on the perturbation theory of Maxwell's equations, the sensitivity distribution of each voxel to the objective function in the grid space is calculated. Specifically, the first positive complex electric field E is used... fwd With the accompanying complex electric field E adj The inner product of the two is used to calculate the analytical gradient g(r) of the change in spatial dielectric constant. This gradient is the voxel sensitivity.

[0036] Furthermore, during the code implementation, if the spatial resolutions of the forward field and the adjoint field are inconsistent, bilinear interpolation can be used to resample and align the real and imaginary parts of the complex field to ensure the spatial accuracy of the sensitivity calculation.

[0037] In one embodiment, step S104 includes: Calculate the radial distance from the center of all voxels to the center of the cylinder using the following formula: ; Where ρ represents the radial distance, x c and y c y and y represent the x and y coordinates of the center of the micro / nano structure, respectively, and x and y represent the x and y coordinates of the voxel center, respectively. According to the following formula, a Gaussian distribution is constructed to approximate the Dirac delta function based on the smoothing scale parameter. : ; Where, α smooth R represents the smoothing scale parameter, and R represents the radius of the micro / nano structure.

[0038] Traditional methods directly map the voxel sensitivity g(r) to the gradient of the cylinder radius R. However, this leads to severe numerical abrupt changes and gradient vanishing problems because the square mesh crosses the circular boundary. To address this, this embodiment introduces a sub-pixel smoothing mapping algorithm: for pixels centered at (x... cy c For a nanopillar of radius R, calculate the radial distance from the center of all voxels to the center of the pillar. And a smoothing scale parameter is introduced. (It can be adaptively set to 0.7 times the square root of the voxel area), construct the following Gaussian distribution to approximate Dirac. function: ; Wherein, the smoothing scale parameter α smooth It is a constant that can be modified and adjusted (related to the spatial mesh density used in the actual simulation). Mathematically, The function can calculate the accumulation of a certain mutation over a very short distance (in adjoint optimization, the nanocylinder's material differs from the background material, resulting in a different dielectric constant; therefore, there is a mutation in the dielectric constant from the outer voxel to the inner voxel of the cylinder. This mutation occurs at the cylinder's edge, and only the edge voxels contribute to the integral of the "dielectric constant change"; however, during adjoint optimization, this value is used as the basis for calculating the optimization gradient (i.e., determining whether the nanocylinder diameter should increase or decrease, and by how much)). The exponential term constructs a width in the form of a Gaussian function, α smooth The larger the value, the wider the envelope. Integrating this function at the voxel position (R-ρ, the edge of the cylinder) yields its maximum value. Since the meshes used in actual optical calculations are often quite coarse, typically on the order of 5 nm or higher, the square lattice containing the square voxels around the circumference of the nanocylinder is not fine and smooth. Therefore, the calculated results for voxels along the cylinder's diameter deviate from the actual ideal positions. This can be addressed by... Figure 3 Understanding: For example, the voxels involved on the right edge of a circle are in a vertical column, while Gaussian smoothing broadens the focus from the absolutely fine edge. This is equivalent to applying a Gaussian weighting to the voxels around the edge (the grayscale of the grid represents the weight), with higher weights closer to the center and lower weights at the edge. α smooth The range of voxels covered by the focus determines the overall size of the α range. smooth Giving the function a width is equivalent to smoothing out the coarse grid.

[0039] This embodiment extracts the spatial gradient of three-dimensional discrete voxels to construct the radial distance from the voxel center to the nanopillar center. With respect to the physical radius of the nanopillar Continuous smoothing functions (such as Gaussian weights) The smoothing function is then used to spatially integrate the discrete voxel gradients near the boundary, analytically yielding the continuous gradient with respect to the target's physical radius. In practical applications, the edge smoothing mapping function in this embodiment uses a Gaussian distribution to approximate the Dirac function, calculating the distance weights from pixels to the cylindrical boundary using an exponential function. Furthermore, a continuous step model can be constructed using the Sigmoid or Tanh functions to replace the Gaussian kernel for boundary smoothing.

[0040] In one embodiment, step S105 includes: The partial derivatives of the objective function and the physical radius of each of the micro / nano structures are calculated according to the following formula, based on the chain rule: ; Where F represents the objective function FOM, R j Let g(r) represent the radius of the j-th micro / nano structure on the metasurface. i ) represents the voxel sensitivity corresponding to the i-th voxel, N pix ρ represents the total number of voxels. i,j ϵ represents the radial distance between the i-th voxel and the j-th micro / nanostructure. in With ϵ out Dielectric constants of the structural material and the background environment at the same wavelength, V vox Represents the geometric volume of each voxel.

[0041] This embodiment uses the objective function FOM to guide the update of the radius of the micro / nano structure (e.g., circular nanopillar), which requires calculating the derivative of the objective function with respect to the derivative. According to the chain rule, we can obtain: ; Where F represents the objective function FOM, R j Denotes the j-th nanocylinder of the metasurface. represent Dielectric constant at the vector position. This is the calculation formula already proposed in traditional adjoint optimization, namely the analytical gradient mentioned earlier. , Item is The derivative of the vector position dielectric constant with respect to the radius of the j-th cylinder shows a significant abrupt change at the edge of the cylinder; this partial derivative is... Where i is the voxel index. Finally, by combining the above equations, the voxel sensitivity, Gaussian smoothing weights, and voxel volume can be calculated. By integrating and summing the products in space, we can analytically obtain the partial derivative of the objective function with respect to the physical radius of a single nanopillar: ; in, and The dielectric constant of the structural material and the background environment at the same target wavelength. Corresponding to the effective dielectric constant , Representing the geometric size of each voxel, Gaussian smoothing is applied to the voxel weights. Figure 3 .

[0042] The above method can directly obtain the partial derivative of the objective function with respect to the radius of the circular nanocylinder, smoothly resolving the conflict between the Cartesian simulation mesh and the boundary of the cylindrical surface, thereby realizing the extraction of the physical gradient parameters required for optimization.

[0043] In one embodiment, step S106 includes: The physical gradient parameters are optimized using an adaptive moment estimation optimizer according to the following formula: ; in, This represents the radius update amount in each round of optimization. Here, m represents the reference step size, v represents the mean of the first-order momentum, and v represents the variance of the second-order gradient. This represents a constant term used to avoid zero denominators and improve numerical stability.

[0044] Because the Finite-Difference Time-Domain (FDTD) method used in micro-nano optical simulations arranges electromagnetic field components through a spatially staggered grid and iteratively derives the time-domain electromagnetic field using the central difference method and the leapfrog method, the grid exhibits discreteness when dealing with nanoscale radius variations. This can cause the conventional steepest descent method to stagnate or oscillate violently, increasing the difficulty for the optimizer to calculate the optimization direction. Therefore, this embodiment employs an Adaptive Moment Estimation (Adam) optimizer in the outer loop optimization. This optimizer retains the historical optimization direction by introducing the first-order momentum mean m and the second-order gradient variance v, while adaptively normalizing based on the fluctuation amplitude of the accompanying gradient. Combined with boundary constraints (limiting the radius variation range), it enables parallel synchronous updates of all nanopillar array radius parameters in each simulation round, effectively improving the convergence speed and physical accuracy of the overall metasurface optimization.

[0045] In practical applications, for parameter optimizers, the adaptive moment estimation optimization algorithm in this embodiment can be replaced by other first-order or second-order quasi-Newton numerical optimization methods, such as the RMSProp algorithm, L-BFGS-B algorithm, etc.

[0046] In one specific embodiment, an optimization process for a metasurface color router with a unit size of 1280nm × 1280nm is provided. This device aims to precisely separate incident broadband or multi-wavelength light in space and focus it onto the four sub-pixel regions (R (red), G (green), G (green), and B (blue)) corresponding to the image sensor, thereby improving the sensor's light sensitivity efficiency for the three primary colors. Specifically, as follows... Figure 4 As shown. Specifically, it includes the following processes: (1) Initial physical model modeling In the 3D electromagnetic simulation software Lumerical FDTD, a square design domain RGGB pixel unit with a period of 1280nm is established (four channels receive light in the red, green, green, and blue bands respectively). In practical applications, the metasurface is constructed by periodically repeating this unit. Titanium dioxide is selected as the high-refractive-index nanopillar material, and silicon dioxide is used as the substrate and filling material. 100 cylindrical nanopillars with a height of 1μm are arranged in a grid within the unit design domain. Considering the diagonal mirror structure symmetry, their physical radius can be regarded as a 55-dimensional design variable. To adapt to the processing limits of actual electron beam lithography (EBL) or deep ultraviolet lithography (DUV), the diameter search range is set to D. min To D max ; where D max Take 90nm, D min This is the minimum radius allowed by the process, or 0nm when vacancy is allowed in the design.

[0047] Figure 5 A top view of an unoptimized 1280nm×1280nm unit metasurface structure is shown. All structures are cylindrical to ensure the feasibility of semiconductor processing and polarization independence.

[0048] (2) Objective function and simulation parameter configuration Center wavelengths of 450nm (blue light), 550nm (green light), and 650nm (red light) were selected as optimization targets. A transmittance monitor corresponding to the RGGB sub-pixel was set 1μm below the nanopillar to simulate the sensor plane; at the same time, the associated dipole source action region corresponding to each wavelength was limited to the central part of the corresponding target sub-pixel region, for example, 1 / 4 of the area of ​​the center of the corresponding sub-pixel region, to enhance beam focusing contrast and suppress crosstalk.

[0049] A logarithmic algorithm and an objective function are used to achieve dynamic balancing of the RGB three channels. The outer loop calls a custom Adam optimization algorithm with an initial fixed step size of 0.3 nm, a first-order momentum decay coefficient of 0.4, and a second-order momentum decay coefficient of 0.8 to suppress numerical abrupt noise caused by mesh division in each iteration.

[0050] (3) Iterative process based on subpixel smoothing In each iteration, a forward broadband light source simulation is first performed. Then, data is extracted based on the complex amplitude of the objective function at a specific wavelength, and an adjoint dipole source is adaptively constructed in the corresponding sub-pixel region. After obtaining the voxel sensitivity through inverse simulation, sub-pixel Gaussian smoothing mapping is performed. Smoothing scale parameters... The size is set to 0.7 times the voxel mesh size. This smoothing mapping transforms the discrete electric field inner product in 3D space into the analytical gradient of each cylinder radius by calculating the distance weight of each square voxel to the cylinder boundary, enabling the Adam optimizer to complete one round of physical parameter updates.

[0051] (4) Results obtained from optimization After the set 270 iterations, the model converged during the process, as follows: Figure 6 As shown. Select the best model from the optimization history, such as... Figure 7 As shown.

[0052] Figure 8 This demonstrates the spatial light field energy distribution on the sensor target plane after forward incident light passes through the metasurface. It is evident that crosstalk between wavelengths is effectively suppressed, and red, green, and blue light are guided to designated areas of the sensor: 450nm blue light is precisely routed to the B sub-pixel region, 550nm green light is distributed to the two diagonally opposite G sub-pixel regions, and 650nm red light is efficiently converged to the R sub-pixel region. The light spot morphology is complete and the energy is concentrated, achieving high-fidelity spatial color separation at a 1280×1280 subwavelength scale.

[0053] Figure 2 This is a schematic block diagram of a metasurface optimization design apparatus 200 provided in an embodiment of the present invention. The apparatus 200 includes: The model building unit 201 is used to build a three-dimensional full-wave simulation model of the target metasurface and obtain the transmission spectrum information of the three-dimensional full-wave simulation model to construct the objective function; wherein, the target metasurface contains multiple micro-nano structures; The electric field acquisition unit 202 is used to perform forward simulation on the target metasurface, acquire the first forward complex electric field generated by the forward simulation on the preset design plane and the second forward complex electric field generated on the target plane, and generate a dipole companion source array through the second forward complex electric field; then activate the dipole companion source array and perform reverse simulation on the target metasurface to acquire the companion complex electric field in the design domain of the target metasurface. Sensitivity calculation unit 203 is used to calculate the voxel sensitivity of the micro-nano structure in the target metasurface in three-dimensional space by combining the first positive complex electric field and the accompanying complex electric field. The distance calculation unit 204 is used to calculate the lateral and radial distances from the center of all voxels in the three-dimensional space to the center of each micro-nano structure, and to construct a Gaussian distribution approximating the Dirac delta function by combining the smooth scale parameter. The radius derivative unit 205 is used to combine the voxel sensitivity and Gaussian distribution to approximate the Dirac delta function and calculate the partial derivative of the objective function with respect to the physical radius of each of the micro / nano structures. The parameter optimization unit 206 is used to use the partial derivative as the gradient parameter of the physical radius of each micro-nano structure, and to update the physical radius of each micro-nano structure based on the gradient parameter using an optimization algorithm.

[0054] In one embodiment, the model building unit 201 includes: The first function construction unit is used to construct a target function based on the transmission spectrum information according to the following formula: ; Wherein, FOM represents the objective function, and T1, T2, and T3 represent the effective transmittance at the first, second, and third wavelengths for the micro / nano structure, respectively. , and These represent the effective dielectric constants of the micro / nano structure at the first wavelength, the second wavelength, and the third wavelength, respectively.

[0055] In one embodiment, the electric field acquisition unit 202 includes: The forward simulation unit is used to irradiate the target metasurface with an actual forward light source as the incident light source in order to perform forward simulation of the target metasurface. An electric field recording unit is used to record the first positive complex electric field generated by the target metasurface on a preset design plane and the second positive complex electric field generated on the target plane. An array generation unit is used to generate a dipole adjoint source array based on a second positive complex electric field corresponding to the target plane; wherein the dipole adjoint source array is disposed in a target region corresponding to the target plane, and the complex amplitude of the dipole adjoint source is determined by the positive complex electric field distribution in the target region and the weighting coefficient corresponding to the objective function; An array activation unit is used to turn off the forward light source and activate the dipole companion source array to perform reverse simulation, and then collect the companion complex electric field generated by the target plane.

[0056] In one embodiment, the sensitivity calculation unit 203 includes: Spatial partitioning unit is used to divide the three-dimensional space corresponding to the three-dimensional full-wave simulation model into a mesh space; The distributed computation unit is used to calculate the sensitivity distribution of each voxel in the grid space to the objective function based on the perturbation theory of Maxwell's equations, thereby obtaining the voxel sensitivity: ; Where g(r) represents the voxel sensitivity, E fwd E represents the first positive complex electric field. adj Represents the associated complex electric field, r represents the position vector of a single voxel, and Re represents the calculation using the real part. The wave number is represented by λ, and the wavelength used is represented by λ. This represents the effective dielectric constant.

[0057] In one embodiment, the distance calculation unit 204 includes: A radial calculation unit is used to calculate the radial distance from the center point of all voxels to the center of the cylinder according to the following formula: ; Where ρ represents the radial distance, x c and y c y and y represent the x and y coordinates of the center of the micro / nano structure, respectively, and x and y represent the x and y coordinates of the voxel center, respectively. The second function construction unit is used to construct a Gaussian distribution approximating the Dirac delta function based on the smoothing scale parameter according to the following formula. : ; Where, α smooth R represents the smoothing scale parameter, and R represents the radius of the micro / nano structure.

[0058] In one embodiment, the radius derivative unit 205 includes: The partial derivative calculation unit is used to calculate the partial derivatives of the objective function and the physical radius of each of the micro / nano structures according to the following formula, based on the chain rule: ; Where F represents the objective function FOM, R j Let g(r) represent the radius of the j-th micro / nano structure on the metasurface. i ) represents the voxel sensitivity corresponding to the i-th voxel, N pix ρ represents the total number of voxels. i,j ϵ represents the radial distance between the i-th voxel and the j-th micro / nanostructure. in With ϵ out Dielectric constants of the structural material and the background environment at the same wavelength, V vox Represents the geometric volume of each voxel.

[0059] In one embodiment, the parameter optimization unit 206 includes: An adaptive optimization unit is used to optimize the physical gradient parameters using an adaptive moment estimation optimizer according to the following formula: ; in, This represents the radius update amount in each round of optimization. Here, m represents the reference step size, v represents the mean of the first-order momentum, and v represents the variance of the second-order gradient. This represents the numerical stability constant used to avoid a denominator of zero.

[0060] Since the embodiments of the apparatus and the embodiments of the method correspond to each other, please refer to the description of the embodiments of the method for the embodiments of the apparatus, which will not be repeated here.

[0061] This invention also provides a computer-readable storage medium storing a computer program thereon, which, when executed, can perform the steps provided in the above embodiments. The storage medium may include various media capable of storing program code, such as a USB flash drive, a portable hard drive, a read-only memory (ROM), a random access memory (RAM), a magnetic disk, or an optical disk.

[0062] This invention also provides a computer device, which may include a memory and a processor. The memory stores a computer program, and when the processor calls the computer program in the memory, it can implement the steps provided in the above embodiments. Of course, the computer device may also include various network interfaces, power supplies, and other components.

[0063] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on its differences from other embodiments. Similar or identical parts between embodiments can be referred to interchangeably. For the systems disclosed in the embodiments, since they correspond to the methods disclosed in the embodiments, the descriptions are relatively simple; relevant parts can be referred to in the method section. It should be noted that those skilled in the art can make various improvements and modifications to this application without departing from the principles of this application, and these improvements and modifications also fall within the protection scope of the claims of this application.

[0064] It should also be noted that, in this specification, relational terms such as "first" and "second" are used only to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Without further limitations, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes said element.

Claims

1. A metasurface optimization design method, characterized in that, include: A three-dimensional full-wave simulation model is established for the target metasurface, and the transmission spectrum information of the three-dimensional full-wave simulation model is obtained to construct the objective function; wherein, the target metasurface contains multiple micro-nano structures; A forward simulation is performed on the target metasurface to obtain the first forward complex electric field generated on the preset design plane and the second forward complex electric field generated on the target plane. A dipole companion source array is generated through the second forward complex electric field. Then, the dipole companion source array is activated and a reverse simulation is performed on the target metasurface to obtain the companion complex electric field in the design domain of the target metasurface. The voxel sensitivity of the micro / nano structures in the target metasurface in three-dimensional space is calculated by combining the first positive complex electric field and the accompanying complex electric field. Calculate the lateral and radial distances from the centers of all voxels in the three-dimensional space to the center of each micro / nano structure, and construct a Gaussian distribution approximating the Dirac delta function by combining the smoothing scale parameter; Combining the voxel sensitivity and the Gaussian distribution approximation of the Dirac delta function, the partial derivative of the objective function with respect to the physical radius of each of the micro / nano structures is calculated; The partial derivatives are used as gradient parameters for the physical radius of each micro / nano structure, and an optimization algorithm is used to update the physical radius of each micro / nano structure based on the gradient parameters.

2. The metasurface optimization design method according to claim 1, characterized in that, The target metasurface is subjected to forward simulation to obtain the first forward complex electric field generated by the forward simulation on the preset design plane and the second forward complex electric field generated on the target plane, and a dipole adjoint source array is generated through the second forward complex electric field; Then, the dipole adjoint source array is activated and the target metasurface is simulated in reverse to obtain the adjoint complex electric field within the design domain of the target metasurface, including: The target metasurface is illuminated by an actual forward light source to perform forward simulation of the target metasurface; Record the first positive complex electric field generated by the target metasurface on the preset design plane and the second positive complex electric field generated on the target plane; A dipole adjoint source array is generated based on the second positive complex electric field corresponding to the target plane; wherein, the dipole adjoint source array is disposed in the target region corresponding to the target plane, and the complex amplitude of the dipole adjoint source array is determined by the positive complex electric field distribution in the target region and the weighting coefficient corresponding to the objective function; The forward light source is turned off, and the dipole adjoint source array is activated for reverse simulation. Then, the adjoint complex electric field generated by the target plane is collected.

3. The metasurface optimization design method according to claim 1, characterized in that, The calculation of the voxel sensitivity of the micro / nano structures in the target metasurface in three-dimensional space by combining the first positive complex electric field and the accompanying complex electric field includes: The three-dimensional space corresponding to the three-dimensional full-wave simulation model is meshed to obtain the mesh space; Based on the perturbation theory of Maxwell's equations, the sensitivity distribution of each voxel in the grid space to the objective function is calculated, and the voxel sensitivity is obtained: ； Where g(r) represents the voxel sensitivity, E fwd E represents the first positive complex electric field. adj Represents the associated complex electric field, r represents the position vector of a single voxel, and Re represents the calculation using the real part. The wave number is represented by λ, and the wavelength used is represented by λ. This represents the effective dielectric constant.

4. The metasurface optimization design method according to claim 1, characterized in that, The calculation of the lateral radial distance from the center of all voxels in the three-dimensional space to the center of each micro / nano structure, and the construction of a Gaussian distribution approximating the Dirac delta function by combining smoothing scale parameters, includes: Calculate the radial distance from the center point of all voxels to the center of the micro / nano structure using the following formula: ； Where ρ represents the radial distance, x c and y c y and y represent the x and y coordinates of the center of the micro / nano structure, respectively, and x and y represent the x and y coordinates of the voxel center, respectively. According to the following formula, a Gaussian distribution is constructed to approximate the Dirac delta function based on the smoothing scale parameter. : ； Where, α smooth R represents the smoothing scale parameter, and R represents the radius of the micro / nano structure.

5. The metasurface optimization design method according to claim 1, characterized in that, The process of combining the voxel sensitivity and Gaussian distribution to approximate the Dirac delta function, and calculating the partial derivative of the objective function with respect to the physical radius of each micro / nano structure, includes: The partial derivatives of the objective function and the physical radius of each of the micro / nano structures are calculated according to the following formula, based on the chain rule: ； Where F represents the objective function FOM, R j Let g(r) represent the radius of the j-th micro / nano structure on the metasurface. i ) represents the voxel sensitivity corresponding to the i-th voxel, N pix ρ represents the total number of voxels. i,j This represents the radial distance between the i-th voxel and the j-th micro / nanostructure. and V represents the dielectric constant of the structural material and the background environment at the same wavelength. vox Represents the geometric volume of each voxel.

6. The metasurface optimization design method according to claim 1, characterized in that, The step of using the partial derivative as a gradient parameter for the physical radius of each micro / nano structure, and updating the physical radius of each micro / nano structure using an optimization algorithm based on the gradient parameter, includes: The gradient parameters are optimized using an adaptive moment estimation optimizer according to the following formula: ； in, This represents the radius update amount in each round of optimization. Here, m represents the reference step size, v represents the mean of the first-order momentum, and v represents the variance of the second-order gradient. This represents a constant term used to avoid zero denominators and improve numerical stability.

7. A metasurface optimization design device, characterized in that, include: The model building unit is used to build a three-dimensional full-wave simulation model of the target metasurface and obtain the transmission spectrum information of the three-dimensional full-wave simulation model to construct the objective function; wherein, the target metasurface contains multiple micro-nano structures; An electric field acquisition unit is used to perform forward simulation on the target metasurface, acquire the first forward complex electric field generated by the forward simulation on a preset design plane and the second forward complex electric field generated on the target plane, and generate a dipole companion source array through the second forward complex electric field; then activate the dipole companion source array and perform reverse simulation on the target metasurface to acquire the companion complex electric field in the design domain of the target metasurface. A sensitivity calculation unit is used to calculate the voxel sensitivity of the micro / nano structure in the target metasurface in three-dimensional space by combining the first positive complex electric field and the accompanying complex electric field. The distance calculation unit is used to calculate the lateral and radial distances from the centers of all voxels in the three-dimensional space to the center of each micro / nano structure, and to construct a Gaussian distribution approximating the Dirac delta function by combining the smooth scale parameter. The radius derivative unit is used to combine the voxel sensitivity and Gaussian distribution to approximate the Dirac delta function and calculate the partial derivative of the objective function with respect to the physical radius of each of the micro / nano structures. The parameter optimization unit is used to take the partial derivative as the gradient parameter of the physical radius of each micro-nano structure, and to update the physical radius of each micro-nano structure based on the gradient parameter using an optimization algorithm.

8. A computer device, characterized in that, It includes a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the metasurface optimization design method as described in any one of claims 1 to 6.

9. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores a computer program that, when executed by a processor, implements the metasurface optimization design method as described in any one of claims 1 to 6.

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