Design method of large-aperture large-field-of-view broadband achromatic superlens

Abstract

This invention provides a design method for a large-aperture, wide-field-of-view, broadband achromatic superlens. By mimicking the structure of a traditional fisheye lens, incident light from different field-of-view angles is mapped onto different unit regions on the superlens surface after passing through an aperture stop. Optical design software is then used to optimize the equivalent lens system to correct large-field-of-view aberrations. Based on this, a hybrid algorithm framework and a forward mapping algorithm are constructed to screen and arrange a large-scale unit structure library, reducing the computational complexity of the traditional point-by-point compensation method from O(N^2) to O(N^2). 2 The computational complexity is reduced to O(N), which greatly reduces the consumption of computing resources, speeds up the calculation and improves the accuracy, enabling the design of large-aperture, wide-band, and large-field achromatic superlenses that do not rely on large computer clusters.

Description

Technical Field

[0001] This invention belongs to the field of superlens technology, specifically relating to a design method for a large-aperture, large-field-of-view, wide-band achromatic superlens. Background Technology

[0002] Metalens utilize subwavelength scale unit structures to finely control the phase, amplitude, and polarization of the light field. Compared with traditional refractive optical elements, they have advantages such as being ultra-thin, lightweight, and easy to integrate, making them key components for realizing next-generation compact imaging systems. However, achieving large-aperture, large-field-of-view, and wide-band achromatic imaging in the continuous band still faces significant challenges, mainly in the following aspects: (1) Severe coupling between aberrations and chromatic aberration: In large-field-of-view imaging, aberrations such as field curvature, coma, and distortion increase rapidly with the field angle. When working in the wide band, chromatic aberration is coupled with structural dispersion, making it extremely difficult to simultaneously correct large-field-of-view aberrations and wide-band chromatic aberration on a single metalen lens; (2) Computational bottleneck caused by the huge number of units: To achieve a large aperture and high numerical aperture, metalens require extremely high sampling density, with the number of units reaching 10. 8 The traditional “point-by-point compensation + point-by-point selection” design process usually requires independent solution and optimization for each unit position, with a computational complexity of about O(N²). In large-scale design, it must rely on high-performance computing clusters, which seriously limits engineering applications; (3) Difficulty in balancing multiple indicators globally: The three indicators of large aperture, large field of view, and wide band achromaticity often restrict each other. Expanding the aperture and field of view will amplify the difficulty of aberration and chromatic aberration correction, while widening the working band will exacerbate the dispersion contradiction. Existing design schemes mostly weigh one or two indicators, making it difficult to take into account all three and form a general design paradigm that can be promoted.

[0003] Therefore, it is necessary to propose a superlens design method that can achieve large aperture, large field of view and wide band achromatic imaging, while significantly reducing computational complexity and having high universality. Summary of the Invention

[0004] The purpose of this invention is to overcome the shortcomings of the prior art and provide a superlens design method that can achieve large aperture, large field of view and wide band achromatic imaging, while significantly reducing computational complexity.

[0005] To achieve the above objectives, the technical solution of the present invention is implemented as follows:

[0006] The present invention provides a design method for a large-aperture, large-field-of-view, wide-band achromatic superlens, comprising the following steps:

[0007] S1: Set the target imaging parameters, which include the working band range, field of view range, effective aperture radius of the superlens, and expected position of the image plane;

[0008] S2: Construct an equivalent traditional fisheye superlens system and model it as a binary surface in optical design software. Given the fixed parameter design values ​​of the superlens system, set the physical structure parameter variables and optimize the superlens system through optical design software to obtain the binary surface polynomial expansion coefficients at several discrete working wavelengths within the working band range. Construct the theoretical phase distribution of the superlens surface as follows:

[0009] in, Indicates the first One operating wavelength, , The total number of the operating wavelengths. This indicates that a grid cell on the surface of the superlens is in the first... Theoretical phase distribution at each operating wavelength Denotes the coefficients of a two-dimensional surface polynomial expansion. Indicates the effective aperture radius of the superlens. This represents the radial distance from the center point of a grid cell on the surface of the superlens to the center point of the superlens surface. Represents the normalized radial coordinates, The number of terms in the coefficients of a two-dimensional surface polynomial expansion. , Indicates only with the operating wavelength Related constant parameter factors, It is an area that needs optimization. dimensional vector, any The range of values ​​is ;

[0010] S3: Divide the effective aperture region of the superlens surface into... A Cartesian coordinate system is established with the center of the superlens surface as the origin, and the coordinates of the center points of all grid cells in the first quadrant are obtained to form a first target point set. The angle between the origin and the x-axis in the first quadrant is calculated as follows: The rays passed through in sequence The coordinates of the center points of each grid cell constitute a second reference point set. Based on the principle of minimum Euclidean distance, the points in the first quadrant are then... Each grid cell is divided into the second reference point set. Each grid cell corresponds to one Each grid category;

[0011] S4: Set the evaluation function, and use global optimization algorithm and local optimization algorithm to evaluate the second reference point set. The cell structure of each grid cell is iteratively optimized to obtain an optimal one. Thus, the aforementioned The optimal theoretical phase distribution of each grid cell;

[0012] S5: For the above For any given grid cell, based on the optimal theoretical phase distribution, find the best matching optimal cell structure in the preset cell structure library, and then, based on the cell structure within the first quadrant... The grid category to which each grid cell belongs will be... The optimal unit structure of any grid cell in the grid cells is taken as the optimal unit structure of each grid cell under the corresponding grid category, thereby obtaining the optimal unit structure arrangement of the entire superlens surface;

[0013] S6: Based on the optimal unit structure arrangement of the entire superlens surface, the electromagnetic field data contained in the unit structure at any grid unit on the superlens surface are stitched together to form the near-field data of the entire superlens surface. Far-field propagation calculation is performed based on scalar diffraction theory. Then, the obtained far-field data is compared with the preset target imaging index. If the far-field data meets the target imaging index, the design is completed. If the far-field data does not meet the target imaging index, the process returns to step S4 for re-optimization until the far-field data meets the target imaging index.

[0014] In one embodiment, given fixed parameter design values ​​for the superlens system, physical structure parameter variables are set, and the superlens system is optimized using optical design software to obtain the bidimensional polynomial expansion coefficients at several discrete working wavelengths within the working band range, including:

[0015] S21: Select several discrete working wavelengths within the working band range, and select several discrete incident field angles within the field of view range;

[0016] S22: Given the aperture stop position, incident field of view angle and design values ​​of the superlens substrate material, set the physical structure parameter variables of the superlens system and give initial values. The physical structure parameter variables include the number of terms in the binary polynomial expansion coefficients, aperture stop diameter, superlens diameter, superlens substrate thickness, preset focal length, and image plane size.

[0017] S23: Set the expected optimization index and operands in the optical design software, input the maximum working wavelength, and optimize the superlens system according to the direction indicated by the operands. If the current optimization result does not meet the expected optimization index, then re-assign the value of the physical structure parameter variable and enter a new round of optimization. If the current optimization result meets the expected optimization index, then fix the physical structure parameter variable given in the current optimization to obtain the superlens system with a determined configuration and the binary polynomial expansion coefficients at the maximum working wavelength.

[0018] S24: Based on the superlens system with a determined configuration, the maximum working wavelength is replaced one by one with the other working wavelengths in the optical design software, and optimization is performed at least once based on each working wavelength to obtain the corresponding binary polynomial expansion coefficients, thereby obtaining the binary polynomial expansion coefficients for each working wavelength within the field of view.

[0019] S25: Based on the determined configuration of the superlens system, establish a mapping relationship between the incident field of view and the radial coordinates of the superlens surface, and divide the superlens surface into multiple unit regions, each unit region corresponding to a field of view range.

[0020] In one embodiment, a Cartesian coordinate system is established with the center of the superlens surface as the origin. The coordinates of the center points of all grid cells in the first quadrant are obtained to form a first target point set. The coordinates of the points in the first quadrant with the origin as the endpoint and the x-axis as the coordinate system are obtained. The rays passed through in sequence The coordinates of the center points of each grid cell constitute a second reference point set. Based on the principle of minimum Euclidean distance, the points in the first quadrant are then... Each grid cell is divided into the second reference point set. Each grid cell corresponds to one There are several grid categories, including:

[0021] S31: Establish a Cartesian coordinate system Oxy with the center of the superlens surface as the origin O, and normalize the coordinates of the center points of all grid cells with the effective aperture radius R of the superlens as the normalization coefficient, so that the normalized coordinates are in the interval [-1,1].

[0022] S32: Construct a first target point set A, which contains the normalized coordinates of the center points of all grid cells within the first quadrant of the superlens surface, denoted as: ,in, For grid cells ( m,u The normalized coordinates of the center point, and , It is a positive integer, ( m,u ) represents the grid cell index of the first target point set A;

[0023] S33: Construct a second reference point set B, which contains points in the first quadrant that have the origin O as their endpoint and make an angle of θ with the x-axis. The rays pierced through in sequence The normalized coordinates of the center point of each grid cell are denoted as: ,in, It is a positive integer. This represents the grid cell index of the second reference point set B;

[0024] S34: Calculate each element in the first target point set A Each element in A and the second reference point set B Euclidean distance of B: , ;

[0025] S35: Based on the principle of minimum Euclidean distance, assign each element... Partition to the element with the smallest distance. The first target point set A is thus divided into the corresponding grid categories. Mutually exclusive subsets of grid cells Each of the said mesh cell subsets All are related to an element in the second reference point set B Unique correspondence.

[0026] In one embodiment, the evaluation function is set as follows:

[0027]

[0028]

[0029] in, For the second reference point set The grid index of each grid cell. Represents grid cells Normalized coordinates of the center point Indicates the first The aforementioned operating wavelengths Represents grid cells At the operating wavelength The theoretical phase below, Represents grid cells The operating wavelength matched from the preset unit structure library The actual phase below, Indicates the first Grid cells in the second reference point set at the operating wavelength The difference between the theoretical phase and the theoretical phase caused by the actual matching unit structure is normalized. This indicates that the first target point set is mapped to the grid cells of the second reference point set. The ratio of the total number of elements in the corresponding grid category to the total number of elements in the first target point set. Indicates the first The sum of the normalized differences between the actual phase and the theoretical phase of the entire surface of the superlens at the specified operating wavelength.

[0030] In one embodiment, the global optimization algorithm and the local optimization algorithm are used to optimize the second reference point set. The cell structure of each grid cell is iteratively optimized to obtain an optimal one. Thus, the aforementioned The optimal theoretical phase distribution of each grid cell includes:

[0031] S41: Set the number of iterations, the dimension of the optimization variables, and the range of values ​​for the optimization variables in the global optimization algorithm; run the global optimization algorithm based on the evaluation function; and connect any unit structure in the unit structure library with the... Phase matching is performed on any grid cell in the grid cells to optimize the reduced range of values ​​for the optimization variable, where the optimization variable is... ;

[0032] S42: Set the number of iterations and the dimension of the optimization variables in the local optimization algorithm, use the obtained narrowed value range as the value range of the optimization variables in the local optimization algorithm, run the local optimization algorithm based on the evaluation function, and connect any unit structure in the unit structure library with the... Phase matching is performed on any one of the grid cells to obtain an optimal one. Thus, the aforementioned The optimal theoretical phase distribution of each grid cell.

[0033] In one embodiment, the global optimization algorithm is Bayesian optimization (BO) or gradient descent (GD), and the local optimization algorithm is particle swarm optimization (PSO) or genetic algorithm (GA).

[0034] In one embodiment, the statement regarding the For any given grid cell, based on the optimal theoretical phase distribution, find the optimal cell structure that best matches it in a preset cell structure library, including:

[0035] S51: For the aforementioned For any grid cell among the grid cells, the optimal theoretical phase distribution is used to obtain the phase distribution of the grid cell. The sum of the optimal theoretical phases at each of the aforementioned operating wavelengths;

[0036] S52: Multiply the phase of any unit structure in the unit structure library by... Then with the grid cells in The difference between the sum of the optimal theoretical phases at each of the operating wavelengths is calculated, and the cell structure with the smallest difference is taken as the optimal cell structure of the grid cell.

[0037] In one embodiment, it further includes:

[0038] Based on the parametric scanning method, the operating wavelengths are established. The mapping relationship between the geometric parameters, material parameters and electromagnetic response characteristics of the lower unit structure is established, and a unit structure library covering the working waveband range is constructed based on the mapping relationship; wherein, the electromagnetic response characteristics include at least phase delay, transmission efficiency and electromagnetic field data.

[0039] In one embodiment, the far-field propagation calculation based on scalar diffraction theory includes:

[0040] Optical field propagation calculations are performed using angular spectrum theory or band-limited angular spectrum.

[0041] Specifically, for light fields with different incident angles, the incident angle light fields are applied to the corresponding local regions of the superlens, and the forward transmission and emission of the incident angle light fields are calculated; the propagation distance for the propagation calculation is set to the superlens focal length optimized by the optical design software.

[0042] In one embodiment, the superlens substrate material is a low-dispersion glass material within the operating wavelength range, the number of unit structures is greater than or equal to two, and the phase response of the period and height of the unit structures within the operating wavelength range covers at least 0-2π.

[0043] The period of the structural units on the surface of the superlens Satisfying the Nyquist sampling criterion:

[0044] Where λ is the operating wavelength and NA is the numerical aperture of the superlens. , where a is the refractive index and β is the aperture angle.

[0045] Compared with existing technologies, the large-aperture, wide-field-of-view, and broadband achromatic superlens design method of this invention constructs an equivalent traditional fisheye superlens system by mimicking a traditional fisheye lens. It then uses ray tracing software to perform macroscopic optimization of the superlens system, correcting aberrations across the large field of view and obtaining the target phase distribution map at full aperture. To address the high computational cost of traditional methods, a forward mapping method is designed, combined with a hybrid algorithm framework, reducing the computational complexity from O(N^2) to O(N^2). 2 The optical density (O(N)) is significantly reduced. This design methodology successfully achieves the unification of large aperture, wide field of view, and continuous-band achromatic capabilities, eliminating reliance on large computer clusters and significantly lowering the design threshold and time cost. This design paradigm is not only applicable to visible light imaging but can also be extended to other bands such as infrared and terahertz, as well as more complex optical function designs, providing a practical solution for next-generation compact imaging systems such as mobile phone lenses, endoscopes, automotive cameras, and AR / VR devices. Attached Figure Description

[0046] Figure 1 This is a flowchart illustrating an embodiment of a design method for a large-aperture, wide-field-of-view, and wide-band achromatic superlens according to this application.

[0047] Figure 2 for Figure 1 The diagram shows a fisheye-like optical path structure used in the design method of a large-aperture, large-field-of-view, wide-band achromatic superlens.

[0048] Figure 3 for Figure 1 The superlens design method shown presents two unit structures selected when constructing the unit structure library;

[0049] Figure 4 for Figure 3 The phase distribution and transmittance distribution obtained by scanning the two unit structures are shown; where (a) is Figure 3 Simulation results of the phase variation of the medium-length cuboid prism with wavelength and cross-sectional side length, (b) is Figure 3 Simulation results of the phase variation of the medium cylinder with wavelength and cross-sectional diameter; (c) is Figure 3 The simulation results of the transmittance of a medium-sized cuboid prism as a function of wavelength and cross-sectional side length, (d) is... Figure 3 Simulation results of the transmittance of a medium cylinder as a function of wavelength and cross-sectional diameter;

[0050] Figure 5 for Figure 1The diagram shows the overall phase, standard dot plot, and MTF curve of the unit structure array 103 after Zemax optimization of the equivalent conventional fisheye superlens system in step S2 of the superlens design method. (a) represents the overall phase of the unit structure array 103; (b) represents the standard dot plot of the unit structure array 103; OBJ (Object) represents the object plane; IMA (Image) represents the image plane; Deg (Degree) represents degrees; (c) represents the MTF curve of the unit structure array 103; Diff.Limit-Tangential represents the meridional diffraction limit; Diff.Limit-Sagittal represents the sagittal diffraction limit; Tangential represents the meridional direction; and Sagittal represents the sagittal direction.

[0051] Figure 6 for Figure 1 The phase-matching images of each grid cell in the second reference point set obtained after optimization by the global optimization algorithm and the local optimization algorithm in the superlens design method shown;

[0052] Figure 7 for Figure 1 The xz plane intensity distribution of the equivalent conventional fisheye superlens system calculated in the far field of the superlens design method shown;

[0053] Figure 8 for Figure 1 Comparison of focal lengths of equivalent traditional fisheye superlens systems under different incident conditions in the superlens design method shown;

[0054] Figure 9 for Figure 1 The full width at half maximum (FWHM) of the equivalent conventional fisheye superlens system is calculated by unfolding along the y-axis at the focal plane in the superlens design method shown.

[0055] Figure 10 for Figure 1 The MTF curve in the superlens design method shown is calculated based on the point spread function (PSF) of the equivalent traditional fisheye superlens system.

[0056] Figure 11 for Figure 1 The diagram illustrates the combination of the forward mapping method and the hybrid optimization algorithm framework in the superlens design method.

[0057] Figure labeling: 101 aperture; 102 superlens substrate; 103 unit structure array. Detailed Implementation

[0058] See also Figure 1-11This embodiment provides a design method for a large-aperture, wide-field-of-view, and wide-band achromatic superlens. Large aperture refers to a lens containing more than 10 unit structures. 8 The term "large field of view" refers to an overall field of view greater than 60°, and "wide-band achromatic" means that within a continuous operating wavelength range, focal length shift errors of different wavelengths of light can be offset by a long depth of focus. The design method for the large-aperture, wide-band achromatic superlens includes the following steps:

[0059] S1: Set the target imaging parameters, which include the working band range, field of view range, effective aperture radius of the superlens, and expected image plane position. The working band range can be any continuous band.

[0060] In this embodiment, the superlens substrate 102 is made of a low-dispersion glass material within the operating wavelength range. The number of unit structures should be greater than or equal to two, and the period and height of the unit structures are pre-optimized to achieve a phase response covering at least 0-2π within the operating wavelength range. The period of the structural unit on the superlens surface... The Nyquist sampling criterion must be met: Where λ is the operating wavelength and NA is the numerical aperture of the superlens. , where a is the refractive index and β is the maximum semi-cone angle formed by the line connecting the focal point of the superlens and the edge of its effective aperture in the image-side medium.

[0061] S2: Construct an equivalent traditional fisheye superlens system and model it using the binary surface Binary2 in the optical design software Zemax. Optimize the physical parameters of the equivalent traditional fisheye superlens system macroscopically using Zemax. Given fixed design values ​​for the superlens system parameters, set physical structure parameter variables, and optimize the equivalent traditional fisheye superlens system using Zemax to obtain the globally corrected binary surface polynomial expansion coefficients at several discrete working wavelengths within the working wavelength range, as well as the physical structure parameters of the equivalent traditional fisheye superlens system. This allows for the construction of the theoretical phase distribution of the superlens surface as follows: .

[0062] in, Indicates the first One operating wavelength, , This represents the total number of operating wavelengths. This indicates that a grid cell on the surface of the superlens is in the first... Theoretical phase distribution at each operating wavelength Denotes the coefficients of a two-dimensional surface polynomial expansion. Indicates the effective aperture radius of the superlens. This represents the radial distance from the center point of a grid cell on the surface of the superlens to the center point of the superlens surface. Represents the normalized radial coordinates, The number of terms in the coefficients of a two-dimensional surface polynomial expansion. , Indicates only with the operating wavelength The relevant constant parameter factor is a dimensional vector, any The range of values ​​is Normalized The range of values ​​is .

[0063] Based on the theoretical phase distribution of the superlens surface, the phase at any grid cell on the superlens surface can be calculated, along with constant parameter factors. Used to shift the phase up or down without affecting the waveform and focal length; optimal constant parameter factor. This helps to match the actual phase with the smallest theoretical phase error within the pre-defined unit structure library, thus achieving the effect of achromatic correction. This is still something that needs to be optimized in the subsequent step S4. Dimensional vector.

[0064] like Figure 2 As shown, the equivalent conventional fisheye superlens system of this embodiment includes a superlens and an aperture 101 disposed on the superlens substrate 102. The aperture 101 is used to define the incident light beam diameter.

[0065] Zemax uses the Binary2 plane, with the evaluation function being the RMS of the centroid reference. It primarily observes the standard point plot and MTF curve, with EFFL (Effective Power of Light) as the operand. Binary2 is specifically designed to simulate a plane, and its phase formula is: By using the optical design software Zemax to obtain the binary polynomial expansion coefficients for each selected working wavelength, the focal length shift under a large field of view can be compensated for, ensuring that the light is focused on the same plane at least at the same working wavelength.

[0066] In step S2, specifically, given the fixed parameter design values ​​of the superlens system, the physical structure parameter variables are set, and the equivalent traditional fisheye superlens system is optimized using the optical design software Zemax to obtain globally corrected superlens systems at various operating wavelengths within the field of view. The following are the coefficients of the bidimensional polynomial expansion and the physical structural parameters of the equivalent traditional fisheye superlens system, including:

[0067] S21: Select several discrete operating wavelengths within the operating band range. , The number of working wavelengths should be selected, and the selected working wavelengths should be distributed as evenly as possible within the working band. Several discrete incident field angles should be selected within the field of view, and the selected field angles should be distributed as evenly as possible within the working field of view (e.g., 0°, 10°, 20°, 30°, 40°, 50°).

[0068] S22: Given the aperture position, incident field of view, and design values ​​of the superlens substrate material, set the physical structure parameter variables of the superlens system and give initial values ​​through experience. The physical structure parameter variables include the number of terms in the binary polynomial expansion coefficients, aperture diameter, superlens diameter, superlens substrate thickness, preset focal length, and image plane size.

[0069] In the optical design software Zemax, the expected optimization indices and operands are set. The operands, as evaluation functions in Zemax, indicate the direction of optimization and can be set according to the function or the expected result. The expected optimization indices include standard point plots and MTF curves. If the current optimization result does not meet the expected optimization indices, the values ​​of the physical structure parameters are redefined and a new round of optimization is initiated. If the current optimization result meets the expected optimization indices, the physical structure parameters given in the current optimization are fixed, resulting in a superlens system with a defined configuration and the bidimensional polynomial expansion coefficients at the maximum operating wavelength.

[0070] S24: Based on a superlens system with a defined configuration, the maximum working wavelength is replaced one by one with the other working wavelengths in the optical design software Zemax, and optimization is performed at least once based on each working wavelength to obtain the corresponding binary polynomial expansion coefficients, and then the binary polynomial expansion coefficients for each working wavelength selected within the field of view are obtained.

[0071] First, set the wavelength to the maximum value among several selected working wavelengths. Input the maximum working wavelength and optimize the superlens system according to the direction indicated by the operand. Observe the standard dot plot, MTF curve, etc. If it is close to the expected effect, proceed to the next step; otherwise, adjust the initial value in S22 and re-optimize. The physical structure of the lens is determined based on the optimization result of the maximum wavelength. At this time, it is necessary to change the other parameters except for the working wavelength and the expansion coefficient to fixed values. Then, adjust the working wavelength and optimize. The optimization here is to replace the working wavelength with the next working wavelength with the working wavelength that has been optimized to obtain the expansion coefficient under the current working wavelength. At this time, only the coefficients of a few expansion terms change, and then the corresponding binary polynomial expansion coefficients for each working wavelength are obtained one by one.

[0072] S25: Based on the determined configuration of the superlens system, establish the mapping relationship between the incident field of view and the radial coordinates of the superlens surface, dividing the superlens surface into multiple unit regions, each corresponding to a field of view range. By setting the aperture stop, light at a specific incident field of view will hit a specific area of ​​the superlens surface. Therefore, after the configuration of the superlens system model in Zemax is determined, it is necessary to establish the mapping relationship between the incident field of view and the radial coordinates of the superlens surface to divide the superlens surface into multiple unit regions corresponding one-to-one with multiple field of view ranges and associate them one by one. This is used in the subsequent optical path simulation for superlens system performance optimization to indicate the effective unit region from which the incident light at the corresponding incident field of view exits the superlens surface, thereby observing far-field imaging and performing phase adjustment of the unit structure, serving the subsequent optimization of the unit structure arrangement of the superlens system.

[0073] S3: Divide the effective aperture region of the superlens surface into... A Cartesian coordinate system is established with the center of the superlens surface as the origin, using a grid of cells. The coordinates of the center points of all grid cells in the first quadrant are obtained to form the first target point set. The angle between the origin and the x-axis in the first quadrant is calculated as follows: The rays passed through in sequence The center point coordinates of each grid cell constitute a second reference point set. This ensures that the distribution of all grid cells within the second reference point set is unique across the entire superlens surface. Uniqueness means that the elements within the second reference point set are distinct. Based on the principle of minimum Euclidean distance, the elements in the first quadrant are then grouped together. Each grid cell is divided into a set of second reference points. Each grid cell corresponds to one Each grid category.

[0074] Step S3 is called the forward mapping method. Through dimensionality reduction processing by partitioning the first quadrant into nearest neighbor units and second nearest neighbor units, it maps the data within the first quadrant... Each grid cell is divided into a set of second reference points. Each grid cell corresponds to one For each grid category, only the second reference point set needs to be considered. The forward mapping method selects and arranges the cell structure for each grid cell. Compared to the traditional point-by-point compensation method, the computational complexity is reduced from O(N) to O(N). 2 The computational complexity is reduced to O(N), but the overall computational complexity increases linearly with the number of units. The forward mapping method reduces N... 2 Mapping the set space of parameters to a set of N elements significantly reduces the computational complexity from O(N²) to O(N), greatly reducing the computational burden of designing large-aperture superlenses.

[0075] In step S3, specifically, a Cartesian coordinate system is established with the center of the superlens surface as the origin. The coordinates of the center points of all grid cells in the first quadrant are obtained to form the first target point set. The angle between the origin and the x-axis in the first quadrant is obtained. The rays passed through in sequence The coordinates of the center points of each grid cell constitute a second reference point set. Based on the principle of minimum Euclidean distance, the points in the first quadrant are then... Each grid cell is divided into a set of second reference points. Each grid cell corresponds to one There are several grid categories, including:

[0076] S31: Establish a Cartesian coordinate system Oxy with the center of the superlens surface as the origin O, divide the superlens surface into 4 symmetrical parts, and normalize the coordinates of the center points of all grid cells with the effective aperture radius R of the superlens as the normalization coefficient, so that the normalized coordinates are in the interval [-1,1].

[0077] S32: Construct the first target point set A, which contains the normalized coordinates of the center points of all grid cells within the first quadrant of the superlens surface, denoted as: ,in, For grid cells ( m,u The normalized coordinates of the center point, and , It is a positive integer, ( m,u ) represents the grid cell index of the first target point set A. The elements of the first target point set A are the distances between the center point and the origin of all grid cells in the first quadrant.

[0078] S33: Construct a second reference point set B, which contains points in the first quadrant that have endpoints at the origin O and make an angle of θ with the x-axis. The rays pierced through in sequence The normalized coordinates of the center point of each grid cell are denoted as: ,in, It is a positive integer. This represents the grid cell index of the second reference point set B.

[0079] In this embodiment, the second reference point set B is composed of the normalized coordinates of the center points of N grid cells that are traversed by the positive x-axis (i.e., at an angle of 0° to the x-axis). Therefore, the second reference point set B is denoted as: .

[0080] S34: Calculate each element in the first target point set A Each element in A and the second reference point set B Euclidean distance of B: , .

[0081] S35: Based on the principle of minimum Euclidean distance, assign each element... Partition to the element with the smallest distance. The corresponding grid categories are used to divide the first target point set A into... Mutually exclusive subsets of grid cells Each grid cell subset All are related to an element in the second reference point set B. Unique correspondence.

[0082] By dividing the target point set A into nearest neighbor and next nearest neighbor units, all elements of the first target point set A are mapped to the second reference point set B. Based on this, all elements of the first target point set A are divided into N classes, such as... Figure 11 As shown, for example: Suppose the second reference point set B contains elements 1, 2, and 3, and the first target point set A contains elements 1, 1.1, 1.6, 2.1, 2.6, and 3.1. In this case, elements 1 and 1.1 in the first target point set A are mapped to 1, 1.6 and 2.1 are mapped to 2, and 2.6 and 3 are mapped to 3. Finally, the hybrid optimization algorithm framework only needs to optimize the cell structure of N types of mesh cells.

[0083] S4: Set the evaluation function, and use global and local optimization algorithms to evaluate the second reference point set. The cell structure of each grid cell is iteratively optimized to obtain an optimal one. And thus obtain The optimal theoretical phase distribution of each grid cell.

[0084] In this embodiment, the evaluation function Set to:

[0085]

[0086]

[0087] in, For the second reference point set B The grid index of each grid cell. Represents grid cells The normalized coordinates of the center point, in this embodiment, are for any grid cell in the second reference point set B. , . Indicates the first One operating wavelength, Represents grid cells At operating wavelength The theoretical phase below, Represents grid cells Operating wavelength matched from the preset unit structure library The actual phase below, Indicates the first Grid cells in the second reference point set B at each operating wavelength The difference between the theoretical phase and the theoretical phase resulting from the actual matched unit structure is normalized.

[0088] This indicates that the first target point set is mapped to the grid cells in the second reference point set B. The ratio of the total number of elements in the corresponding grid category to the total number of elements in the first target point set. Assuming the second reference point set B contains elements 1, 2, and 3, and the first target point set A contains elements 1, 1.1, 1.6, 2.1, 2.6, and 3.1, and that elements 1 and 1.1 in the first target point set A are mapped to 1, 1.6 and 2.1 are mapped to 2, and 2.6 and 3 are mapped to 3, then... , , . Indicates the first The sum of the normalized differences between the actual phase and the theoretical phase of the entire surface of the superlens at the specified operating wavelength.

[0089] Global optimization algorithms can be Bayesian optimization or gradient descent, etc., while local optimization algorithms can be particle swarm optimization or genetic algorithms, etc., and they can be combined arbitrarily.

[0090] Specifically, global optimization algorithms and local optimization algorithms are used to optimize the second reference point set. The cell structure of each grid cell is iteratively optimized to obtain an optimal one. And thus obtain The optimal theoretical phase distribution of each grid cell includes:

[0091] S41: Set the number of iterations, the dimension of the optimization variables, and the range of values ​​for the optimization variables in the global optimization algorithm. The range of values ​​for the optimization variables is given empirically. The initial value is determined, and a global optimization algorithm is run based on the evaluation function, combining any unit structure in the unit structure library with... Phase matching is performed on any one of the grid cells to optimize the result. The narrowed range of values ​​for (i.e., the optimization variable).

[0092] In the global optimization algorithm, each iteration updates According to the evaluation function In each iteration, the sum of the normalized differences between the actual and theoretical phases of the entire superlens surface at each working wavelength in the current iteration is calculated. The smaller the sum of the normalized differences, the better the matching in that iteration. The more suitable it is, the more it can be determined at the end of the iteration cycle based on the value of the evaluation function for each iteration. The narrowed range of values.

[0093] This represents the phase at each of the J operating wavelengths plus a constant, which is an optimization variable that the global optimization algorithm needs to set. In this embodiment... Therefore, the number of variables in the global optimization algorithm (i.e., the dimension of the optimization variables) is 8. The global optimization algorithm is a Bayesian optimization algorithm with 200 iterations and a weight coefficient of 0.01. The global optimization algorithm is an existing algorithm, and its specific settings should be configured according to the specific problem when using it; it will not be elaborated further here.

[0094] Global optimization algorithms in the initial parameter space (i.e., given) The initial value is determined later. The reduced parameter space obtained by shrinking within the range of values ​​of () is used as the initial parameter space for the new local optimization algorithm. If for (range of values) If the query points are 1000 for each working wavelength, then... The space of optional parameters pointed to by an 8-dimensional vector is very large, with a range of values ​​of 1000. 8 By using a global optimization algorithm, obviously useless parameter space can be eliminated, leaving some potentially usable parameter space. Then, a local optimization algorithm is used to find the best parameter in the remaining potentially usable parameter space. .

[0095] S42: Set the number of iterations and the dimension of the optimization variables in the local optimization algorithm. Use the narrowed range of values ​​as the range of values ​​for the optimization variables in the local optimization algorithm. Run the local optimization algorithm based on the evaluation function, and compare any unit structure in the unit structure library with... Phase matching is performed on any one of the grid cells to obtain an optimal one. And thus obtain The optimal theoretical phase distribution of each grid cell. The local optimization algorithm is particle swarm optimization, with a population size of 100, 500 iterations, learning factors C1 and C2 both of 2, and an inertia factor w of 0.8. Based on the evaluation function... In each iteration, the sum of the normalized differences between the actual and theoretical phases of the entire superlens surface at each working wavelength in the current iteration is calculated. The minimum sum of the normalized differences indicates that the current iteration is a good match. The optimal solution is found at the end of the iteration cycle, based on the evaluation function value of each iteration. The local optimization algorithm is an existing algorithm. When using it, the specific settings should be adjusted according to the specific problem. It will not be elaborated here.

[0096] In this embodiment, to improve efficiency, a hybrid optimization algorithm framework is adopted. The global optimization algorithm and the local optimization algorithm are combined to form a hybrid optimization algorithm framework. The global optimization algorithm is used to quickly identify potential intervals in a large parameter space, pre-determining several potential intervals. The local optimization algorithm is used to find local optimization within these potential intervals. In this embodiment, combining the nearest neighbor and second nearest neighbor unit partitioning of the forward mapping method, all elements of the first target point set A are mapped to the second reference point set B. Based on this, the first target point set A is divided into N classes. Finally, the hybrid optimization algorithm framework is used to solve the target phase and chromatic difference compensation requirements of the N grid units in the second reference point set B. This allows for rapid selection and matching of the N types of grid unit structures from the structural unit library, reducing the computational complexity of the traditional point-by-point compensation method from O(N²) to O(N).

[0097] S5: For For any given grid cell, based on the optimal theoretical phase distribution, find the best matching optimal cell structure in the preset cell structure library, and then, based on the cell structure in the first quadrant... The grid category to which each grid cell belongs will be... The optimal cell structure of any cell in a given grid cell is taken as the optimal cell structure of each cell under the corresponding grid category, thereby obtaining the optimal cell structure arrangement of the entire superlens surface.

[0098] The pre-defined unit structure library is a unit structure library covering the working waveband, built based on the electromagnetic simulation software FDTD. The unit structure library records the phase, electromagnetic field, and transmittance response of each unit structure at different wavelengths. The unit structure array in the first quadrant of the superlens surface is obtained by screening and arranging the unit structures in a two-dimensional plane through a forward mapping method and a hybrid optimization algorithm framework. Then, based on the symmetry relationship between the other quadrants and the first quadrant, the unit structure array of the entire superlens surface can be obtained.

[0099] Specifically, in step S5, for For any given grid cell, the optimal cell structure that best matches its theoretical phase distribution is found in a pre-defined cell structure library, including:

[0100] S51: Regarding For any grid cell in a given grid cell, the optimal theoretical phase distribution is obtained from the grid cell's position within the grid cell. The sum of the optimal theoretical phases at each working wavelength;

[0101] S52: Multiply the phase of any unit structure in the unit structure library by... Then with the grid cells in The sum of the optimal theoretical phases at each working wavelength is subtracted, and the cell structure with the smallest difference is taken as the optimal cell structure of the mesh.

[0102] In this embodiment, before finding the optimal cell structure that best matches the optimal theoretical phase distribution in a preset cell structure library, the method further includes:

[0103] The element structure is scanned in the simulation software FDTD. Element structure parameters include incident light wavelength, material properties, and structural dimensions. Based on a parametric scanning method, the operating wavelengths are established. The mapping relationship between the geometric parameters, material parameters, and electromagnetic response characteristics of the lower unit structure is established, and a unit structure library covering the operating wavelength range is constructed based on the mapping relationship; among which, the electromagnetic response characteristics include at least phase delay, transmission efficiency, and electromagnetic field data. During parameter scanning, all selected discrete operating wavelengths must be scanned.

[0104] like Figure 3 As shown, the unit structure needs to have good axisymmetry for polarization-insensitive designs, such as combinations of circular, square, or related holes in the cross-section. The simulation boundary conditions are periodic, with a mesh accuracy of 2 or higher, and linearly polarized light can be used for simulation. The unit structure library stores phase, transmittance, and electromagnetic field data for different structural parameters and wavelengths.

[0105] S6: Based on the optimal unit structure arrangement of the entire superlens surface, the electromagnetic field data contained in the unit structure at any grid unit on the superlens surface are stitched together to form the near-field data of the entire superlens surface. Far-field propagation calculations are then performed based on scalar diffraction theory. The obtained far-field data is then compared with preset target imaging indicators, including achromatic effect and large field-of-view imaging effect. If the far-field data meets the target imaging indicators, the design is complete. If the far-field data does not meet the target imaging indicators, the process returns to step S4 for re-optimization until the far-field data meets the target imaging indicators. When returning to step S4 for re-optimization, the iteration count or weight coefficients of the global optimization algorithm can be reset, or the initial values ​​of the optimization variables can be reset based on the difference between the far-field data and the target imaging indicators. Through the iterative optimization of steps S4-S6, a superlens structure that meets the requirements of large aperture, large field of view, and wide-band achromatic effect is finally obtained.

[0106] Due to the complexity and computational difficulty of accurately solving Maxwell's equations, researchers widely employ scalar diffraction theories, such as angular spectrum theory and improved band-limited angular spectra, to reduce computational load and increase speed while maintaining accuracy. In this design method, incident light at different angles acts on different superlens unit regions. The transmitted outgoing light only needs to propagate in a forward direction (0°) using the angular spectrum, without simulating large-angle propagation. The propagation distance is set to the superlens focal length obtained from Zemax.

[0107] Therefore, in step S6, far-field propagation calculations are performed based on scalar diffraction theory, including: using angular spectrum theory or band-limited angular spectrum to calculate the light field propagation. Specifically, for light fields with different incident angles, the incident angle light field is applied to the corresponding local region of the superlens, and the forward transmission and emission of the incident angle light field are calculated; the propagation distance for the propagation calculation is set to the superlens focal length optimized by the optical design software Zemax.

[0108] Based on the design method of this embodiment, a superlens with a diameter of 4.584 mm, a working wavelength of 400–680 nm, and a field of view of 100° was designed. The main design process is as follows: Figure 1 .

[0109] Optical path construction reference Figure 2 A circular aperture 101 is placed at a set distance in front of the superlens substrate 102 (made of H-FK95N glass). The function of the aperture 101 is to transform the large field-of-view problem into a local area correction problem. For example, 0° incident light mainly passes through the central area of ​​the lens, while 50° incident light mainly passes through the edge area of ​​the lens. This structure mimics the principle of a fisheye or a traditional wide-angle lens, effectively separating the aberration correction areas of different fields of view.

[0110] Figure 3 The two unit structures selected are a cuboid prism with a square cross-section and a cylinder. A high refractive index material (TiO2) is selected as the micro-nano structure material, with a height of 600nm and a period of 400nm. Figure 4 The phase and transmittance of two types of nanopillars are obtained by scanning them using the finite-difference time-domain method (FDTD), and a large database containing information such as phase, electromagnetic field and transmittance is established. Figure 4 (a)-(d) represent the simulation results of the phase of the cuboid prism changing with wavelength and cross-sectional side length, the simulation results of the phase of the cylinder changing with wavelength and cross-sectional diameter, the simulation results of the transmittance of the cuboid prism changing with wavelength and cross-sectional side length, and the simulation results of the transmittance of the cylinder changing with wavelength and cross-sectional diameter, respectively.

[0111] Create in Zemax software Figure 2The optical path model is designed with the evaluation function set as minimizing the radius of the dot plot under the full field of view (0° to 50° half field of view), while ensuring that the effective focal length is controlled near the preset value. During optimization, eight discrete working wavelengths are selected, and six phase expansion coefficients are set accordingly. Figure 5 (a)-(c) represent the overall phase, standard dot plot, and MTF curve of the superlens after Zemax optimization, respectively. Table 1 lists the optimized coefficients. The final optimized result is a substrate 2 with a thickness of 3 mm, an aperture 101 with a diameter of 0.8 mm, a superlens 3 with a radius of 2.292 mm, and a preset focal length of 2.381 mm.

[0112] Table 1

[0113]

[0114] The specific parameters of the computing equipment are as follows: the CPU is an AMD Ryzen 5 5600H with 6 cores and 12 logical processors; the RAM is 16GB with a speed of 3200MT / s; the GPU is an NVIDIA GeForce RTX 3050 with a total RAM of 12GB. The final calculation time was close to 4 hours, and the resulting data size was 7.9GB in pkl format. Figure 6 The phase-matching image is obtained through a hybrid optimization algorithm framework and a forward mapping method. The straight line and the sphere represent the theoretical phase and the actual phase caused by the unit structure, respectively. Since the obtained phase data is periodic, the effect of data winding needs to be considered. Therefore, after restoring it to the original, continuous and uninterrupted state, the phase-matching result is observed to be very good.

[0115] The electromagnetic field data of the optimal cell structure matched at all grid cells are stitched together to form the near-field data of the entire superlens, and then the band-limited spectral algorithm is used to perform far-field diffraction calculations. The band-limited spectral method can solve the inherent defects (aliasing error) of the traditional angular spectral method in discrete numerical calculations. By introducing a bandwidth-limited transfer function, it improves the numerical accuracy and reliability of the calculation. Figure 7 This is the intensity distribution in the xz plane calculated in the far field; the dashed line represents the preset focal length. Figure 8 This is a comparison of focal lengths under different incident conditions; the dashed line represents the preset focal length. The focal lengths calculated for different wavelengths and incident angles have very small deviations, which can be compensated for by a longer depth of focus.

[0116] MTF (Modulation Transfer Function) is a key indicator for measuring the imaging resolution and contrast reproduction capability of an optical system. Figure 9 , Figure 10These are the full width at half maximum (FWHM) calculated along the y-axis at the focal plane and the MTF curve calculated based on the system's point spread function (PSF). Both have numerical distributions close to the diffraction limit, demonstrating good performance.

[0117] As can be seen from the simulation results above, the large-aperture superlens designed in this embodiment not only has an ultra-large field of view of 100°, but also achieves clear achromatic imaging. Compared with traditional fisheye systems, the fisheye lens system composed in this embodiment has a simpler structural characteristic.

[0118] This embodiment's superlens design method mimics a traditional fisheye lens by constructing an equivalent traditional fisheye superlens system, including a superlens and an aperture stop mounted on the superlens substrate. Incident light from different field angles is mapped onto different unit regions on the superlens surface after passing through the aperture stop. Combined with the aperture stop structure, achromatic focusing imaging of light rays at different incident angles is achieved. Furthermore, the equivalent superlens system is optimized using the optical design software Zemax to correct large field-of-view aberrations. Based on this, a forward mapping algorithm and a hybrid algorithm framework are constructed, and a large-scale unit structure library is selected and arranged, reducing the computational complexity of the traditional point-by-point compensation method from O(N^2) to O(N^2). 2 The computational complexity is reduced to O(N), significantly decreasing computational resource consumption, accelerating computation speed and accuracy, and enabling the design of a large-aperture, wide-band, and large-field-of-view achromatic superlens without relying on large computer clusters. Simulation results show that the superlens described in this embodiment achieves good achromatic imaging in the 400–680 nm operating band and a near 100° full field of view, while maintaining a large aperture of 4.584 mm. The design method of this application is universal and scalable, and can be extended to the design of superlenses in other bands and with more complex optical functions, providing a new design solution for next-generation compact high-performance imaging systems.

[0119] Those skilled in the art should understand that the discussion of any of the above embodiments is merely exemplary and is not intended to imply that the scope of protection of this application is limited to these examples; within the framework of this application, the technical features of the above embodiments or different embodiments can also be combined, the steps can be implemented in any order, and there are many other variations of different aspects of one or more embodiments of this application as described above, which are not provided in detail for the sake of brevity.

[0120] One or more embodiments in this application are intended to cover all such substitutions, modifications, and variations that fall within the broad scope of this application. Therefore, any omissions, modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of one or more embodiments in this application should be included within the protection scope of this application.

Claims

1. A design method for a large-aperture, wide-field-of-view, wide-band achromatic superlens, characterized in that, Includes the following steps: S1: Set the target imaging parameters, which include the working band range, field of view range, effective aperture radius of the superlens, and expected position of the image plane; S2: Construct an equivalent traditional fisheye superlens system and model it as a binary surface in optical design software. Given the fixed parameter design values ​​of the superlens system, set the physical structure parameter variables and optimize the superlens system through optical design software to obtain the binary surface polynomial expansion coefficients at several discrete working wavelengths within the working band range. Construct the theoretical phase distribution of the superlens surface as follows: in, Indicates the first One operating wavelength, , The total number of the operating wavelengths. This indicates that any grid cell on the surface of the superlens is in the first... Theoretical phase distribution at each operating wavelength Denotes the coefficients of a two-dimensional surface polynomial expansion. Indicates the effective aperture radius of the superlens. This represents the radial distance from the center point of any grid cell on the surface of the superlens to the center point of the superlens surface. Represents the normalized radial coordinates, The number of terms in the coefficients of a two-dimensional surface polynomial expansion. , Indicates only with the operating wavelength Related constant parameter factors, It is an area that needs optimization. dimensional vector, any The range of values ​​is ; S3: Divide the effective aperture region of the superlens surface into... A Cartesian coordinate system is established with the center of the superlens surface as the origin, and the coordinates of the center points of all grid cells in the first quadrant are obtained to form a first target point set. The angle between the origin and the x-axis in the first quadrant is calculated as follows: The rays passed through in sequence The coordinates of the center points of each grid cell constitute a second reference point set. Based on the principle of minimum Euclidean distance, the points in the first quadrant are then... Each grid cell is divided into the second reference point set. Each grid cell corresponds to one Each grid category; S4: Set the evaluation function, and use global optimization algorithm and local optimization algorithm to evaluate the second reference point set. The cell structure of each grid cell is iteratively optimized to obtain an optimal one. Thus, the aforementioned The optimal theoretical phase distribution of each grid cell; S5: For the above For any given grid cell, based on the optimal theoretical phase distribution, find the best matching optimal cell structure in the preset cell structure library, and then, based on the cell structure within the first quadrant... The grid category to which each grid cell belongs will be... The optimal unit structure of any grid cell in the grid cells is taken as the optimal unit structure of each grid cell under the corresponding grid category, thereby obtaining the optimal unit structure arrangement of the entire superlens surface; S6: Based on the optimal unit structure arrangement of the entire superlens surface, the electromagnetic field data contained in the unit structure at any grid unit on the superlens surface are stitched together to form the near-field data of the entire superlens surface. Far-field propagation calculation is performed based on scalar diffraction theory. Then, the obtained far-field data is compared with the preset target imaging index. If the far-field data meets the target imaging index, the design is completed. If the far-field data does not meet the target imaging index, the process returns to step S4 for re-optimization until the far-field data meets the target imaging index.

2. The design method for a large-aperture, large-field-of-view, wide-band achromatic superlens as described in claim 1, characterized in that, Given fixed parameter design values ​​for the superlens system, physical structure parameter variables are set, and the superlens system is optimized using optical design software to obtain the bidimensional polynomial expansion coefficients for several discrete working wavelengths within the working band range, including: S21: Select several discrete working wavelengths within the working band range, and select several discrete incident field angles within the field of view range; S22: Given the aperture stop position, incident field of view angle and design values ​​of the superlens substrate material, set the physical structure parameter variables of the superlens system and give initial values. The physical structure parameter variables include the number of terms in the binary polynomial expansion coefficients, aperture stop diameter, superlens diameter, superlens substrate thickness, preset focal length, and image plane size. S23: Set the expected optimization index and operands in the optical design software, input the maximum working wavelength, and optimize the superlens system according to the direction indicated by the operands. If the current optimization result does not meet the expected optimization index, then re-assign the value of the physical structure parameter variable and enter a new round of optimization. If the current optimization result meets the expected optimization index, then fix the physical structure parameter variable given in the current optimization to obtain the superlens system with a determined configuration and the binary polynomial expansion coefficients at the maximum working wavelength. S24: Based on the superlens system with a determined configuration, the maximum working wavelength is replaced one by one with the other working wavelengths in the optical design software, and optimization is performed at least once based on each working wavelength to obtain the corresponding binary polynomial expansion coefficients, thereby obtaining the binary polynomial expansion coefficients for each working wavelength within the field of view. S25: Based on the determined configuration of the superlens system, establish a mapping relationship between the incident field of view and the radial coordinates of the superlens surface, and divide the superlens surface into multiple unit regions, each unit region corresponding to a field of view range.

3. The design method for a large-aperture, large-field-of-view, wide-band achromatic superlens as described in claim 1, characterized in that, A Cartesian coordinate system is established with the center of the superlens surface as the origin. The coordinates of the center points of all grid cells in the first quadrant are used to form a first target point set. The angle between the origin and the x-axis in the first quadrant is calculated as follows: The rays passed through in sequence The coordinates of the center points of each grid cell constitute a second reference point set. Based on the principle of minimum Euclidean distance, the points in the first quadrant are then... Each grid cell is divided into the second reference point set. Each grid cell corresponds to one There are several grid categories, including: S31: Establish a Cartesian coordinate system Oxy with the center of the superlens surface as the origin O, and normalize the coordinates of the center points of all grid cells with the effective aperture radius R of the superlens as the normalization coefficient, so that the normalized coordinates are in the interval [-1,1]. S32: Construct a first target point set A, which contains the normalized coordinates of the center points of all grid cells within the first quadrant of the superlens surface, denoted as: ,in, For grid cells ( m,u The normalized coordinates of the center point, and , It is a positive integer, ( m,u ) represents the grid cell index of the first target point set A; S33: Construct a second reference point set B, which contains points in the first quadrant that have the origin O as their endpoint and make an angle of θ with the x-axis. The rays pierced through in sequence The normalized coordinates of the center point of each grid cell are denoted as: ,in, It is a positive integer. This represents the grid cell index of the second reference point set B; S34: Calculate each element in the first target point set A Each element in A and the second reference point set B Euclidean distance of B: , ; S35: Based on the principle of minimum Euclidean distance, assign each element... Partition to the element with the smallest distance. The first target point set A is thus divided into the corresponding grid categories. Mutually exclusive subsets of grid cells Each of the said mesh cell subsets All are related to an element in the second reference point set B Unique correspondence.

4. The design method for a large-aperture, large-field-of-view, wide-band achromatic superlens as described in claim 1, characterized in that, The evaluation function is set as follows: in, For the second reference point set The grid index of each grid cell. Represents grid cells Normalized coordinates of the center point Indicates the first The aforementioned operating wavelengths Represents grid cells At the operating wavelength The theoretical phase below, Represents grid cells The operating wavelength matched from the preset unit structure library The actual phase below, Indicates the first Grid cells in the second reference point set at the operating wavelength The difference between the theoretical phase and the theoretical phase caused by the actual matching unit structure is normalized. This indicates that the first target point set is mapped to the grid cells of the second reference point set. The ratio of the total number of elements in the corresponding grid category to the total number of elements in the first target point set. Indicates the first The sum of the normalized differences between the actual phase and the theoretical phase of the entire surface of the superlens at the specified operating wavelength.

5. The design method for a large-aperture, large-field-of-view, wide-band achromatic superlens as described in claim 4, characterized in that, The global optimization algorithm and the local optimization algorithm are used to optimize the second reference point set. The cell structure of each grid cell is iteratively optimized to obtain an optimal one. Thus, the aforementioned The optimal theoretical phase distribution of each grid cell includes: S41: Set the number of iterations, the dimension of the optimization variables, and the range of values ​​for the optimization variables in the global optimization algorithm; run the global optimization algorithm; and connect any unit structure in the unit structure library with the... Phase matching is performed on any grid cell within a grid cell. In each iteration, the sum of the differences between the actual phase and the theoretical phase of the superlens surface at each working wavelength in the current iteration is calculated using the evaluation function. This optimizes the narrowed range of values ​​for the optimization variable, where the optimization variable is... ; S42: Set the number of iterations and the dimension of the optimization variables in the local optimization algorithm, and use the obtained narrowed value range as the value range of the optimization variables in the local optimization algorithm. Then, connect any unit structure in the unit structure library with the... Phase matching is performed on any one of the grid cells to obtain an optimal one. Thus, the aforementioned The optimal theoretical phase distribution of each grid cell.

6. The design method for a large-aperture, large-field-of-view, wide-band achromatic superlens as described in claim 1, characterized in that, The global optimization algorithm is Bayesian optimization or gradient descent, and the local optimization algorithm is particle swarm optimization or genetic algorithm.

7. The design method for a large-aperture, large-field-of-view, wide-band achromatic superlens as described in claim 1, characterized in that, The for the For any given grid cell, based on the optimal theoretical phase distribution, find the optimal cell structure that best matches it in a preset cell structure library, including: S51: For the aforementioned For any grid cell among the grid cells, the optimal theoretical phase distribution is used to obtain the phase distribution of the grid cell. The sum of the optimal theoretical phases at each of the aforementioned operating wavelengths; S52: Multiply the phase of any unit structure in the unit structure library by... Then with the grid cells in The difference between the sum of the optimal theoretical phases at each of the operating wavelengths is calculated, and the cell structure with the smallest difference is taken as the optimal cell structure of the grid cell.

8. The design method for a large-aperture, large-field-of-view, wide-band achromatic superlens as described in claim 1, characterized in that, Also includes: Based on the parametric scanning method, the operating wavelengths are established. The mapping relationship between the geometric parameters, material parameters and electromagnetic response characteristics of the lower unit structure is established, and a unit structure library covering the working waveband range is constructed based on the mapping relationship; wherein, the electromagnetic response characteristics include at least phase delay, transmission efficiency and electromagnetic field data.

9. The design method for a large-aperture, large-field-of-view, wide-band achromatic superlens as described in claim 1, characterized in that, The far-field propagation calculation based on scalar diffraction theory includes: Optical field propagation calculations are performed using angular spectrum theory or band-limited angular spectrum. Specifically, for light fields with different incident angles, the incident angle light fields are applied to the corresponding local regions of the superlens, and the forward transmission and emission of the incident angle light fields are calculated; the propagation distance for the propagation calculation is set to the superlens focal length optimized by the optical design software.

10. The design method for a large-aperture, large-field-of-view, wide-band achromatic superlens as described in claim 1, characterized in that, The substrate material of the superlens is a low-dispersion glass material within the working band range. There are two or more types of unit structures, and the phase response of the period and height of the unit structure within the working band range covers at least 0-2π. The period of the structural units on the surface of the superlens Satisfying the Nyquist sampling criterion: Where λ is the operating wavelength and NA is the numerical aperture of the superlens. , where a is the refractive index and β is the aperture angle.

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