A data-driven hybrid inverse design method for ultra-wideband achromatic lens

Abstract

The application discloses a data-driven hyperbolic lens achromatic design method, which is characterized in that a data-driven reverse dispersion method is adopted to perform reverse dispersion engineering in multiple sub-bands divided by a working frequency band, and spatial multiplexing and global optimization are performed on all unit structures to obtain an overall structure of the hyperbolic lens which has optimal performance and continuous achromaticity in a super wide frequency band. Compared with the prior art, the application has an end-to-end efficient design capability, can realize excellent working performance of the hyperbolic lens, and effectively avoids the dependence of a traditional dispersion engineering method on dispersion regulation and control capability of integrated resonant units, thereby doubling the working bandwidth without sacrificing the performance of the hyperbolic lens, and significantly improving the design precision and efficiency through the data-driven method, thereby providing a new solution for wideband design of achromatic devices and having good application scenarios and prospects.

Description

Technical Field

[0001] This invention relates to the fields of metasurface beam focusing and metasurface reverse design technology, specifically a data-driven hybrid reverse design method for ultrawideband achromatic lenses. Background Technology

[0002] Metasurfaces, composed of subwavelength units, possess exceptional electromagnetic wavefront manipulation capabilities, enabling the control of the amplitude, phase, and polarization of incident electromagnetic waves. They are widely used in fields such as superlenses, holographic imaging, and stealth. Among these, superlenses designed from metasurfaces have demonstrated outstanding capabilities in beam focusing and beamforming applications, finding numerous applications in imaging, sensing, and antenna performance enhancement. However, due to the phase dispersion of the units used in metasurfaces, traditional metasurface-based superlenses suffer from severe chromatic aberration, limiting their broadband performance. Past research has proposed various pioneering methods to mitigate the chromatic aberration effect of superlenses. Currently, the most commonly used method is dispersion engineering, which involves specially designing the resonant properties of the units to compensate for the focusing chromatic aberration of the lens through the phase dispersion of the units themselves.

[0003] Existing achromatic methods based on dispersion engineering are limited by the dispersion control capabilities of the unit cells themselves, making it difficult to broaden the working bandwidth without sacrificing the lens's numerical aperture and focusing efficiency. At the same time, traditional dispersion engineering schemes rely on complex resonance designs, often requiring the construction of a unit cell library and the selection of units that meet the conditions, followed by the overall design of the lens. This process consumes a lot of time and computing power and depends on the designer's experience, resulting in relatively low design efficiency. Summary of the Invention

[0004] The purpose of this invention is to address the shortcomings of existing technologies by proposing a data-driven hybrid reverse design method for ultrawideband achromatic lenses. This method employs data-driven reverse dispersion engineering, dividing the operating frequency band into multiple sub-bands. Dispersion engineering is performed in each sub-band to efficiently reverse design the achromatic lens. A random spatial multiplexing scheme is used to spatially reuse and globally optimize all units, achieving a mapping between the array arrangement and the overall electromagnetic response of the array, thereby outputting a metalens structure with optimal performance. This method utilizes reverse dispersion engineering to map the target electromagnetic response to the metasurface unit structure, avoiding extensive electromagnetic simulations to build a unit library, and efficiently designing units with specified dispersion characteristics within any operating frequency band. Based on a specific integrated resonant unit, the method enables the direct reverse design of the overall structure of the superlens from design specifications, achieving efficient end-to-end design of ultra-wideband achromatic lenses. Without sacrificing numerical aperture, superlens size, or focusing efficiency, it maximizes the achromatic working bandwidth of the superlens, achieving excellent performance. This avoids the reliance of traditional dispersion engineering methods on the dispersion control capabilities of the integrated resonant unit, multiplies the working bandwidth without sacrificing superlens performance, and significantly improves design accuracy and efficiency through a data-driven approach. It provides a new solution for the broadband design of achromatic devices, with promising application scenarios and prospects.

[0005] The specific technical solution to achieve the purpose of this invention is: a data-driven hybrid reverse design method for ultra-wideband achromatic lenses, characterized by dividing the working frequency band into multiple sub-bands, performing dispersion engineering in each sub-band, and performing spatial reuse and global optimization of the units in each sub-band through an optimal random spatial reuse scheme, thereby achieving efficient reverse design of achromatic lenses and transforming the design process from a time-consuming trial-and-error process into a parallel, end-to-end efficient automated process.

[0006] The specific steps of the hybrid reverse engineering include:

[0007] 1) Determine the operating frequency band, focal length, numerical aperture, and unit structure of the target achromatic lens;

[0008] 2) The target operating frequency band is divided into k sub-bands using the sub-band decomposition method;

[0009] 3) Using the reverse dispersion engineering method, the unit of each sub-band is reverse designed to obtain the size parameters of all units that meet the requirements of phase dispersion, operating frequency band, and amplitude.

[0010] 4) The optimal random spatial reuse method is used to perform spatial reuse and global optimization on the units of each sub-band obtained by reverse design, and finally the overall structure of the superlens is obtained.

[0011] Specifically, the hybrid reverse design, based on the sub-band division method, first employs data-driven reverse dispersion engineering. Based on the calculated target phase dispersion distribution, a neural network is used to perform parallel reverse design of the required units within each sub-band, rapidly predicting the geometric structure of all units that meet the conditions. Subsequently, units within each sub-band are randomly sampled, and the sampled units are recombined and reused to form a complete superlens structure. A genetic algorithm is used to iterate the sampling matrix, capturing the nonlinear relationship between the superlens structure corresponding to different sampling matrices and the achromatic focusing effect. Finally, the sampling matrix with optimal achromatic focusing performance and its corresponding complete superlens structure are output. This step is called the optimal random space reuse method. Unlike traditional random space reuse methods, this method can generate intelligent patterns, learn the nonlinear relationship between the random atomic arrangement and the corresponding electromagnetic response, and thus output the optimal random reuse scheme, achieving global optimization while realizing the reuse of sub-band units. Through the steps described above, the hybrid reverse design framework can achieve end-to-end design of achromatic lenses, that is, directly provide the optimal achromatic lens structure based on design requirements, and endow the superlens with ultra-wideband operating characteristics through sub-band decomposition.

[0012] The sub-band decomposition method divides the operating frequency band into multiple sub-bands and performs dispersion engineering in each sub-band to avoid the performance limitations of the integrated resonant unit's phase dispersion modulation capability on the broadband operation of the achromatic lens, as is present in traditional methods. Based on the sub-band decomposition scheme, a hybrid reverse design is introduced to efficiently reverse design the achromatic lens, avoiding complex resonant structure design and the construction of a primitive atom library. This transforms the design process from a time-consuming trial-and-error process into a parallel, end-to-end, highly efficient, and automated process.

[0013] Compared with the prior art, the present invention has the following beneficial technical effects and significant technical progress:

[0014] 1) The sub-band decomposition scheme effectively avoids the constraints of unit dispersion control capability on the working bandwidth, numerical aperture and lens size of achromatic lenses in traditional dispersion engineering schemes, as well as the complex resonance design of integrated resonant units. It can also expand the working bandwidth of the lens by a factor of two with relatively high focusing efficiency without sacrificing the numerical aperture, and achieve excellent broadband continuous achromatic focusing effect.

[0015] 2) A data-driven reverse dispersion engineering scheme is adopted, which effectively avoids the traditional dispersion engineering scheme's design process of spending a lot of time and computing power to build a cell library and select cells that meet the conditions. Instead, through neural networks and optimization algorithms, cells that meet the conditions can be quickly predicted and retrieved, enabling efficient reverse design. Combined with the sub-band decomposition scheme, parallel cell structure design of multiple sub-bands can be completed, significantly improving design efficiency. Moreover, the designed cells can approach the performance limit of the cells themselves.

[0016] 3) An optimal random spatial multiplexing scheme is adopted. Compared with traditional spatial multiplexing schemes, the proposed scheme can effectively alleviate the sidelobe effect in traditional shared aperture methods. Meanwhile, for general random spatial multiplexing schemes, the sampling of sub-regions is completely random. Although effective in some cases, it still has certain shortcomings in terms of sidelobe suppression, coupling reduction, and interpretability. Therefore, completely random sampling is insufficient to optimize the metasurface performance. By embedding global optimization into the traditional random spatial multiplexing scheme, the nonlinear relationship between the atomic arrangement and electromagnetic response is captured, thereby effectively mitigating the efficiency degradation and focal spot shift phenomena that occur in the phase distribution after random interleaving. Attached Figure Description

[0017] Figure 1 This is a schematic diagram of the process of the present invention;

[0018] Figure 2 This is a schematic diagram of the hybrid design in Example 1;

[0019] Figure 3 A schematic diagram of the achromatic lens and integrated resonant unit designed for Example 1;

[0020] Figure 4 The phase and dispersion distribution diagrams of the achromatic lens in Example 1 are shown.

[0021] Figure 5 This is a schematic diagram of a deep neural network structure;

[0022] Figure 6 This is a schematic diagram illustrating the prediction effect of a neural network.

[0023] Figure 7 Here is a flowchart of the reverse dispersion engineering method;

[0024] Figure 8 A comparison chart of the achromatic focusing performance of the achromatic lens designed for Example 1;

[0025] Figure 9 The simulation result diagram of the achromatic lens designed in Example 1;

[0026] Figure 10The graph shows the actual focal length, full width at half maximum (FWHM), and relative focusing efficiency of the achromatic lens in Example 1. Detailed Implementation

[0027] See Figure 1 The present invention specifically includes:

[0028] 1) Determine the operating frequency band, focal length, incident surface diameter, and numerical aperture of the target achromatic superlens.

[0029] 2) Determine the structure of the integrated resonant unit used to control the phase and phase dispersion of the incident wave.

[0030] 3) Based on the operating frequency band range, focal length, incident surface aperture, and integrated resonant unit structure, the operating frequency band is decomposed using a sub-band decomposition scheme, including the number of sub-bands and the range of each sub-band.

[0031] 4) Determine the phase distribution required for the superlens to achieve focusing at the starting frequency of each sub-band using the following formula:

[0032] .

[0033] Where F is the focal length of the lens, and r is the radial position along the aperture surface of the superlens. For the target operating frequency, This represents the additional phase constant.

[0034] 5) Determine the phase dispersion distribution required for the superlens to achieve achromatic dispersion compensation within each sub-band using the following formula:

[0035] .

[0036] in, This indicates the starting frequency of the corresponding operating frequency band. This indicates the introduction of an additional phase shift to better compensate for the initial phase of the unit, enabling the hyperbolic phase distribution of the superlens to be shifted upwards or downwards as a whole without affecting the focal length and achromatic focusing effect.

[0037] 6) Based on the determined integrated resonant unit structure and the calculated target phase dispersion, the inverse dispersion engineering method is used to automatically reverse design the integrated resonant unit in each sub-band, and quickly obtain all the unit structure and unit performance prediction results required in each sub-band.

[0038] This invention utilizes the sub-band units obtained from reverse dispersion engineering and employs an optimal random spatial multiplexing scheme for global design and optimization. The units designed based on reverse dispersion engineering are randomly multiplexed in an optimal arrangement to optimize the overall performance of the superlens, resulting in the final superlens layout and overall structure. The combination of reverse dispersion engineering and the optimal random multiplexing scheme ultimately constitutes a hybrid design framework for end-to-end design of ultra-wideband achromatic lenses. This method, through sub-band decomposition, avoids the constraint of the integrated resonant unit's dispersion control capability on the overall performance of the achromatic lens. Simultaneously, it optimizes the superlens performance through a data-driven scheme and improves design efficiency.

[0039] This invention, based on the overall operating frequency band required by the design goals and considering the phase dispersion control range achievable by the integrated resonant unit, divides the total operating frequency band into multiple sub-bands. This allows the integrated resonant unit to achieve the required phase dispersion value and reflection amplitude for achromatic focusing at the target focal length and lens size within each sub-band, thus avoiding the limitation imposed by the integrated resonant unit's own dispersion control capability on the operating bandwidth and numerical aperture of the achromatic lens. Specifically, for an achromatic lens, its lens diameter... Numerical aperture (NA), operating frequency band And the phase dispersion control range that the integrated resonant unit can achieve. The following relationship must be satisfied:

[0040] .

[0041] For the target operating frequency band The sub-band decomposition method used first divides it into N consecutive sub-bands. ( For each sub-band The dispersion modulation range of the integrated resonant unit The above inequality is also satisfied, as shown in the following equation:

[0042] .

[0043] Therefore, for the operating bandwidth, lens size, and numerical aperture required by the design goals, the phase dispersion control range that the given integrated resonant unit structure needs to satisfy after adopting the sub-band decomposition scheme can be reduced to the following formula:

[0044] .

[0045] By rationally dividing the sub-band range, it is possible to avoid complex resonant design of the unit and reduce the constraints on bandwidth and numerical aperture during the design of achromatic lenses.

[0046] The described inverse dispersion engineering method comprises a neural network for forward prediction and an adaptive differential evolution algorithm for inverse retrieval. Based on the integrated resonant unit structure used, the method employs full-wave simulation to obtain a dataset containing unit structure parameters and reflection coefficients. A neural network is then trained on this dataset to rapidly predict the electromagnetic response of different structural units, including the real and imaginary parts of the reflection coefficients. Next, the amplitude and phase dispersion values ​​of different structural units are calculated based on the real and imaginary parts of the reflection coefficients. Finally, the adaptive differential evolution algorithm is used to rapidly inversely design units operating in a specific frequency band that meet specific phase dispersion and amplitude requirements.

[0047] The specific process of reverse engineering includes:

[0048] 1-1) The initial population was generated using Latin hypercube sampling;

[0049] 1-2) Neural networks are used to predict the phase dispersion and amplitude of the initial population in the target operating frequency band;

[0050] 1-3) Calculate the difference between the phase dispersion curve and the target phase dispersion curve for each individual, as well as the amplitude score for each individual, based on the prediction results;

[0051] 1-4) Based on the calculated phase error and amplitude score, assess the fitness of each individual and determine whether the conditions are met;

[0052] 1-5) Perform the selection, crossover, and mutation processes using the differential evolution algorithm;

[0053] 1-6) Update the population and repeat steps 1-2) to 1-5) until the convergence condition is met;

[0054] 1-7) Output the optimal unit structure.

[0055] This invention employs a random staggered scheme for spatial reuse of metasurface units, with the specific random reuse pattern given by the sampling matrix. By loading deep learning methods and a global optimization algorithm, the nonlinear relationship between the metasurface arrangement scheme and the electromagnetic field response is adaptively learned, thereby obtaining the optimal random spatial reuse scheme, enabling the reused metasurface to have the best performance. The specific process is as follows:

[0056] 2-1) Generate a sampling matrix with k distinct elements from k sets of metasurface units to be reused as needed. ;

[0057] 2-2) Based on the sampling matrix, generate a sampling mask, sample the structural parameter tensors of each group of metasurface units, and obtain the structural parameter tensors of all units after multiplexing based on the sampled tensors containing the structural parameters of each channel.

[0058] 2-3) Input the structural parameter tensors of all reused units into the neural network to predict the amplitude and phase distribution of the metasurface;

[0059] 2-4) Based on the amplitude and phase distribution of the metasurface, the electric field intensity distribution of the metasurface in the target plane is calculated using the point source approximation scheme;

[0060] 2-5) Based on the design objectives and the calculated field strength distribution, calculate the fitness function and evaluate the current sampling matrix. The properties of the obtained reusable metasurface;

[0061] 2-6) Update using genetic algorithm Repeat steps 2-2) to 2-5) until the convergence condition is met or the maximum number of iterations is reached;

[0062] 2-7) Optimal Output ,based on The final layout and overall structure of the metasurface are obtained.

[0063] The aforementioned hybrid design, along with a dual-layer integrated resonant unit design, yields a microwave-band reflective ultra-wideband achromatic lens. Its operating frequency band is 8-16 GHz, with a bandwidth of 66.7%, a focal length of 215 mm, an effective aperture size of 310 mm, and a numerical aperture of 0.58. This achromatic lens achieves achromatic focusing of the reflected beam within the 8-16 GHz ultra-wideband, with an average relative focusing efficiency of 52.91% within its operating bandwidth.

[0064] This invention, based on design goals, divides the target operating frequency band into multiple sub-bands and performs inverse dispersion engineering within each sub-band. Metasurface units are automatically designed according to theoretical dispersion compensation values. Then, the designed sub-band units are optimally multiplexed using random space to ultimately obtain a complete achromatic superlens structure, thereby achieving ultra-wideband continuous achromaticity. This invention consists of two parts: a data-driven inverse dispersion engineering method and an optimal random space multiplexing method. It enables efficient design of ultra-wideband achromatic lenses and maximizes the achromatic operating bandwidth of the superlens without sacrificing numerical aperture, superlens size, or focusing efficiency, achieving excellent performance. Compared with existing technologies, this invention overcomes the dependence of existing technologies on the dispersion control capability of metasurface units and significantly improves design efficiency, demonstrating promising application scenarios and prospects.

[0065] The following example, using an achromatic lens operating at 8-16 GHz, with a focal length of 215 mm and an aperture diameter of 310 m, demonstrates the process and design effect of constructing a hybrid reverse design framework according to the present invention, and provides a more detailed explanation of the technical solution of the present invention and its effects.

[0066] Example 1

[0067] See Figure 2 The specific process of the hybrid reverse engineering is as follows:

[0068] 1) Determine the operating frequency band, focal length, numerical aperture, and integrated resonant unit structure of the achromatic lens.

[0069] See Figure 3 b) An integrated resonant unit structure is adopted, consisting of two stacked dielectric substrates. A rectangular metal resonant patch is placed on top of each dielectric substrate layer, and a metal reflector is placed at the bottom of the unit. The metal layer is made of copper, and the dielectric substrate is made of F4B-265 with a dielectric constant of 2.65. The specific fixed dimensional parameters of each part are as follows: unit period p = 12 mm, gold plating thickness t = 0.035 mm, and the thickness of the lower dielectric substrate is... =2 mm, thickness of upper dielectric substrate =2 mm, width of the lower metal resonant patch =1 mm, width of upper metal patch =1 mm. The symbols for the variable dimension parameters of each part of the unit are as follows: Length of the lower metal resonant patch. Length of the upper metal resonant patch The angle between the two metal resonant patches The two metal patches rotate together by an angle β.

[0070] See Figure 3 The integrated resonant unit structure, under the illumination of a normally incident circularly polarized wave, can generate cross-polarized reflected waves within a specific frequency range. This can be achieved by adjusting the parameters. , This allows adjustment of the unit's resonant point, thereby enabling control over the dispersion of the operating frequency band, reflection amplitude, and reflection phase. By changing... Furthermore, the phase dispersion of the unit can be adjusted. By rotating the two metal patches together by β degrees, the phase of the reflected wave can be further controlled through the Pancharatnam-Berry phase, achieving 2π phase coverage. Therefore, by precisely designing the dimensional parameters of the unit structure, precise control can be achieved in four dimensions: reflected wave phase dispersion, amplitude, operating frequency band, and reflection phase.

[0071] 2) After determining the operating frequency band, focal length, numerical aperture, and integrated resonant unit structure of the achromatic lens, the target frequency band is divided into multiple sub-bands based on the dispersion control capability of the unit, so that the unit can meet the required phase dispersion value in each sub-band.

[0072] In this embodiment, the 8-16 GHz band is divided into two sub-bands: 8-13 GHz and 13-16 GHz. The phase distribution required for the superlens to achieve focusing at the starting frequency of each sub-band is determined according to the following formula:

[0073] .

[0074] Where F is the focal length of the lens, and r is the radial position along the aperture surface of the superlens. For the target operating frequency, This represents the additional phase constant.

[0075] The phase dispersion distribution required for the superlens to achieve achromatic dispersion compensation within each sub-band is determined using the following formula:

[0076] .

[0077] in, This indicates the starting frequency of the corresponding operating frequency band. This indicates the introduction of an additional phase shift to better compensate for the initial phase of the unit, enabling the hyperbolic phase distribution of the superlens to be shifted upwards or downwards as a whole without affecting the focal length and achromatic focusing effect.

[0078] See Figure 4 Based on the radial required phase and phase dispersion distribution calculated above, the superlens is a circular array with a maximum of 25 units arranged radially.

[0079] 3) The reverse dispersion engineering method is used to quickly predict the size parameters of the cells required for each sub-band, which specifically includes:

[0080] 3-1: Using the simulation software CST Microwave Studio, the following was performed... , , A relatively sparse parameter scan is performed on the three size parameters to obtain the training dataset;

[0081] 3-2: Train two deep neural networks (DNNs) based on the training dataset, which are used to predict the real and imaginary parts of the reflection coefficients based on the unit structure parameters.

[0082] See Figure 5 The input layer of the deep neural network (DNN) contains three dimensions, namely... , , The output layer contains 101 dimensions, corresponding to the real or imaginary parts of the reflection coefficients at 101 frequency points. This DNN contains 13 fully connected hidden layers, with 32, 64, 128, 256, 512, 1024, 1024, 1024, 512, 256, 128, and 128 neurons respectively. Dropout layers are added in the seventh and ninth hidden layers to help the model better suppress noise and accelerate model convergence.

[0083] See Figure 6 A trained deep neural network (DNN) can accurately predict the real and imaginary parts of the reflection coefficient corresponding to a cell with a specific size parameter.

[0084] 4) After training the neural networks used for forward prediction, they are embedded into the Adaptive Differential Evolution Algorithm (SADEA). The reverse retrieval of size parameters is achieved through SADEA, ultimately forming a complete reverse dispersion engineering method.

[0085] See Figure 7 The inverse dispersion engineering generates an initial population through Latin hypercube sampling, and then calculates the fitness function of each individual based on the prediction results of the neural network using the following formula:

[0086] .

[0087] in, and These represent the weights of the phase error and reflection amplitude scores, respectively, and N represents the number of frequency points within the target frequency range. and Indicates based on the corresponding frequency point The real part of the place and the virtual part The calculated amplitude and phase values, This represents the target phase response value of the cell generated based on the calculated achromatic dispersion and group delay requirements.

[0088] The Adaptive Differential Evolutionary Algorithm (SADEA) iterates through the calculated fitness, performs screening, mutation, and crossover using a genetic algorithm, and updates the population until convergence is met. As the algorithm iterates, the inverse dispersion engineering method comprehensively considers the errors in amplitude mean and phase response, thereby quickly retrieving and outputting the optimal unit structure that meets the design objectives within each sub-band.

[0089] See Figure 4 b. Based on the calculated target dispersion profile, predict the phase dispersion values ​​of the radial elements within each sub-band (e.g., ...). Figure 4 (Scattered points in b).

[0090] See Figure 2 After obtaining the parameter matrix output by the reverse dispersion engineering, i.e. the optimal unit structure of each sub-band, the second stage of the hybrid reverse design framework is entered, namely optimal random space reuse, the specific steps of which are as follows:

[0091] 4-1: Define the sampling matrix , , where element 0 indicates that there is no cell at the corresponding coordinate position of the array; element 1 indicates that the corresponding coordinate position of the array is a cell operating in sub-band 1 (8-13 GHz); element 2 indicates that the corresponding coordinate position of the array is a cell operating in sub-band 2 (13-16 GHz).

[0092] 4-2: Based on the sampling matrix, generate the corresponding sampling mask to sample the units of each sub-frequency band, and reuse and reassemble the sampled units into the complete structure of the superlens. Based on the array parameter matrix, use the previously trained neural network to predict its amplitude and phase response matrices.

[0093] 4-3: Based on the predicted amplitude and phase response matrices, the reflected wave of the superlens is approximated and normalized using the point source estimation method to obtain the normalized reflected electric field intensity distribution of the superlens in the 8-16 GHz range. The fitness of the superlens is then calculated using the following formula to evaluate its achromatic focusing effect:

[0094] .

[0095] in, , , and N represent the calculated actual focal length, target focal length, and number of frequency points considered within the working frequency band, respectively.

[0096] 4-4: Evaluate whether the calculated fitness satisfies the algorithm's convergence condition. If not, proceed to the genetic algorithm for iterative update. During the iteration process The elements in the algorithm are crossovered and mutated, and the above calculation process is repeated until the convergence condition is met or the maximum number of iterations is reached.

[0097] See Figure 8 This embodiment compares the theoretical calculation results of the electric field intensity distribution of the achromatic lens array obtained by the optimal random space scheme design with the calculation results of the traditional random space multiplexing scheme, and also compares the calculation results of the traditional chromatic lens. It can be seen that the superlens designed based on the above scheme can significantly reduce grating lobes and clutter, and reduce the shift of the focused spot, exhibiting superior achromatic focusing performance.

[0098] See Figure 9To verify the design of the achromatic lens, the reflected electric field of the designed superlens in the 8-16 GHz range was calculated by full-wave simulation. It can be seen that the designed achromatic lens significantly suppresses the shift of the focused spot and achieves a good achromatic focusing effect in the ultra-wideband range.

[0099] See Figure 10 Based on the simulated electric field results, the actual focal length, full width at half maximum (FWHM), and relative focusing efficiency of the designed achromatic lens were calculated. It can be seen that the achromatic lens designed using this invention achieves good achromatic focusing performance in the 8-16 GHz range, significantly suppressing focal length shift compared to lenses without ultra-wideband achromatic design. The simulated relative focusing efficiency ranges from 12.02% to 69.12% in the 8-16 GHz range, with an average focusing efficiency of 52.91%, exhibiting significantly wider bandwidth and higher efficiency compared to similar devices. The results verify that this invention can achieve achromatic focusing in an ultra-wideband range using a resonant unit with a simple structure, while ensuring numerical aperture and focusing efficiency as much as possible.

[0100] The above description is only a specific embodiment of this application, but the protection scope of this application is not limited thereto. Any modifications, equivalent substitutions and improvements made by those skilled in the art within the scope of the technology disclosed in this application should be included within the protection scope of this invention.

Claims

1. A data-driven hybrid reverse engineering method for ultrawideband achromatic lenses, characterized in that, The data-driven reverse dispersion engineering method is adopted to perform hybrid reverse design on the achromatic lens in multiple sub-bands divided by the working frequency band, and spatial multiplexing and global optimization are performed on all unit structures to obtain the overall structure of the superlens with optimal performance, and the specific steps of the hybrid reverse design of the achromatic lens include: 1) determining the working frequency band range, focal length, entrance aperture and numerical aperture of the target achromatic superlens, and the integrated resonant unit structure used; 2) the working frequency band is divided into k sub-bands by using the sub-band decomposition method, and the range of each sub-band is determined; 3) the phase distribution required by the superlens to achieve focusing at the starting frequency point of the sub-band is determined according to the following formula: ； Wherein, F is the focal length of the lens; r is the radial position along the superlens aperture surface; is the target operating frequency point; is the phase constant; The phase dispersion distribution required by the superlens to achieve achromatic dispersion compensation in each sub-band is determined according to the following formula: ； wherein, is a starting frequency point of a corresponding working frequency band; is an introduced additional phase shift; 4) according to the determined integrated resonant unit structure and the calculated target phase dispersion, the unit structure in each sub-band is automatically reverse designed by using reverse dispersion engineering, and all unit structures meeting the phase dispersion, working frequency band and amplitude requirements are obtained; 5) the unit structures obtained in step 4) are spatially multiplexed and globally optimized by using the optimal random spatial multiplexing method to obtain the design scheme of the overall structure of the superlens; wherein: The sub-band decomposition of step 2) includes: dividing the number of sub-bands and the range of each sub-band, the sub-band decomposition method according to the working frequency range required by the design target and the phase dispersion regulation range of the integrated resonant unit, the target working frequency range Cutting into N continuous sub-bands The phase dispersion value and reflection amplitude required by the integrated resonant unit to achieve achromatic lens focusing under the target focal length and lens size in each sub-band, and the diameter of the achromatic lens Numerical aperture NA, working frequency range And the phase dispersion regulation range that the integrated resonant unit can achieve Satisfy the following inequalities: ； The working frequency band is represented by the following formula: ； wherein, is the nth sub-band; N is the number of sub-bands; By analogy, for each sub-band whose dispersion control range of integrated resonant units Also satisfies the following inequality: ； The phase dispersion regulation range of the integrated resonant unit structure after sub-band decomposition is reduced, and is represented by the following formula: 。 2.The data-driven inverse design method of an ultra-wideband achromatic lens according to claim 1, wherein, The step 4) uses a forward prediction neural network and a reverse search adaptive differential evolution algorithm, the forward prediction neural network uses a full-wave simulation to obtain a dataset of integrated resonant unit structure parameters and reflection coefficients, and a neural network trained with the dataset is used to predict the electromagnetic response of different structure units; the electromagnetic response includes the real part and the imaginary part of the reflection coefficient, and the amplitude and phase dispersion values of different structure units are calculated based on the real part and the imaginary part of the reflection coefficient; the adaptive differential evolution algorithm inversely designs the unit structure parameters of the unit structure working in a specific frequency band and meeting specific phase dispersion and amplitude requirements according to the amplitude and phase dispersion values of different structure units; the reverse design specifically includes: 4-1) generate an initial population by using Latin hypercube sampling; 4-2) predict the phase dispersion and amplitude of the initial population in the target working frequency band by using a neural network; 4-3) calculate the difference between the phase dispersion curve of each individual and the target phase dispersion curve and the amplitude score of the individual according to the prediction results; 4-4) evaluate the fitness of each individual according to the calculated phase error and amplitude score, and determine whether the condition is met; 4-5) perform selection, crossover and mutation of the differential evolution algorithm; 4-6) update the population and repeat steps 4-2) to 4-6) until the convergence condition is met; 4-7) output the optimal unit structure. 3.The data-driven inverse design method of an ultra-wideband achromatic lens according to claim 1, wherein, The step 5) uses a random multiplexing mode given by a sampling matrix to spatially multiplex the super surface unit, and adaptively learns the nonlinear relationship between the super surface arrangement and the electromagnetic field response by loading a deep learning method and a global optimization algorithm to obtain an optimal random spatial multiplexing scheme, and the specific process is as follows: 5-1) generating a sampling matrix with k different elements from k groups of metasurface units according to the required multiplexing ; 5-2) generating a sampling mask according to the sampling matrix, sampling the structure parameter tensor of each group of metasurface units, and obtaining the structure parameter tensor of all units after multiplexing according to the tensor containing the structure parameter of each channel after sampling; 5-3) inputting the structure parameter tensor of all units after multiplexing into a neural network to predict the amplitude and phase distribution of the metasurface; 5-4) calculating the electric field intensity distribution of the metasurface in the target plane by using a point source approximation method according to the amplitude and phase distribution of the metasurface; 5-5) According to the design target, the fitness function is calculated on the basis of the field intensity distribution, and the current sampling matrix is evaluated based on the current sampling matrix The performance of the obtained multiplexed metasurface; 5-6) updating using genetic algorithm repeating steps 5-2) to 5-5) until a convergence condition is met or a maximum number of iterations is reached; 5-7) output optimal , resulting in the final layout and overall structure of the super surface. 4.The data-driven inverse design method of an ultra-wideband achromatic lens according to claim 3, wherein, The fitness function is calculated by the following formula: ； wherein, , and N are the actual focal length, the target focal length and the number of frequencies considered in the operating frequency band, respectively.

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