Data-driven ultra-wideband achromatic lens hybrid reverse design method

Abstract

The invention discloses a data-driven ultra-wideband achromatic lens hybrid reverse design method, which is characterized in that a data-driven reverse dispersion method is adopted, a reverse dispersion project is executed in a plurality of sub-bands divided by a working band, and spatial multiplexing and global optimization are performed on all unit structures, so that the data-driven ultra-wideband achromatic lens hybrid reverse design is realized. And the ultra-lens overall structure with optimal performance and ultra-wide band continuous achromatism is obtained. Compared with the prior art, the ultra-wideband achromatic lens has end-to-end efficient design capability, can realize excellent ultra-wideband achromatic lens working performance, effectively avoids the dependence of a traditional dispersion engineering method on the dispersion regulation and control capability of the integrated resonance unit, multiplies the working bandwidth on the premise of not sacrificing the performance of the ultra-lens, and improves the working efficiency of the ultra-wideband achromatic lens. And the design precision and efficiency are remarkably improved through a data driving method, a new solution is provided for broadband design of an achromatic device, and the method has good application scenes and prospects.

Description

Technical Field

[0001] The invention relates to the technical field of metasurface beam focusing and metasurface reverse design, in particular to a data-driven ultra-wideband achromatic lens hybrid reverse design method. Background Art

[0002] The metasurface composed of subwavelength units has excellent electromagnetic wavefront control capabilities and can control the amplitude, phase, polarization and other characteristics of the incident electromagnetic wave. It is widely used in the fields of superlens, holographic imaging, stealth, etc. Among them, the superlens designed by the metasurface has shown excellent capabilities in applications such as beam focusing and beam shaping, and has many applications in the fields of imaging, sensing, and antenna performance enhancement. However, due to the phase dispersion of the units used in the metasurface, the traditional superlens based on the metasurface has serious chromatic aberration, which limits its broadband performance. Past studies have proposed various pioneering methods to reduce the chromatic aberration effect of superlenses. The most commonly used method is dispersion engineering, that is, through special resonance design of the unit, the phase dispersion of the unit itself compensates for the focusing chromatic aberration of the lens.

[0003] The existing achromatic method based on dispersion engineering is limited by the dispersion control ability of the unit itself, and it is difficult to broaden the working bandwidth without sacrificing the numerical aperture and focusing efficiency of the lens. At the same time, traditional dispersion engineering solutions rely on complex resonance design, which often requires building a unit library and screening out units that meet the conditions, and then designing the entire lens. This process requires a lot of time and computing power, and relies on the experience of designers, and the design efficiency is relatively low. Summary of the invention

[0004] The purpose of the present invention is to propose a data-driven ultra-wideband achromatic lens hybrid reverse design method in response to the deficiencies of the prior art. The method uses a data-driven reverse dispersion engineering method to divide the operating frequency band into multiple sub-bands, perform dispersion engineering in each sub-band, perform efficient reverse design on the achromatic lens, and use a random spatial multiplexing scheme to perform spatial multiplexing and global optimization on all units to achieve the mapping of the array arrangement and the overall electromagnetic response of the array, and then output the overall structure of the metalens with optimal performance. This method uses reverse dispersion engineering to achieve the mapping of the target electromagnetic response and the metasurface unit structure, avoids a large number of electromagnetic simulations to build a unit library, and efficiently designs the specified dispersion characteristic unit in any working frequency band. Based on an integrated resonant unit with a specific structure, the method can directly reverse design the overall structure of the metalens from the design indicators, realize the efficient design of an end-to-end ultra-wideband achromatic lens, and broaden the achromatic working bandwidth of the metalens as much as possible without sacrificing the numerical aperture, the size of the metalens, and the focusing efficiency, so as to achieve excellent working performance. It can avoid the dependence of traditional dispersion engineering methods on the dispersion control ability of the integrated resonant unit, increase the working bandwidth exponentially without sacrificing the performance of the metalens, and significantly improve the design accuracy and efficiency through a data-driven method, providing a new solution for the broadband design of achromatic devices, and has good application scenarios and prospects.

[0005] The specific technical scheme for achieving the purpose of the present invention is: a data-driven hybrid inverse design method for ultra-wideband achromatic lenses, which is characterized by dividing the operating frequency band into multiple sub-bands, performing dispersion engineering in each sub-band, and spatially multiplexing and globally optimizing the units of each sub-band through an optimal random spatial multiplexing scheme, thereby realizing efficient reverse design of achromatic lenses and transforming the design process from a time-consuming trial-and-error process to a parallel, end-to-end efficient automated process.

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

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

[0008] 2) Using the sub-band decomposition method, the target working frequency band is divided into k sub-bands;

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

[0010] 4) Use the optimal random spatial multiplexing method to spatially multiplex and globally optimize the units of each sub-band obtained by inverse design, and finally obtain the overall structure of the superlens.

[0011] Specifically, the hybrid inverse design first adopts data-driven inverse dispersion engineering according to the sub-band division method, and uses a neural network to perform parallel inverse design on the required units in each sub-band according to the calculated target phase dispersion distribution, and quickly predicts the geometric structure of all units that meet the conditions. Subsequently, the units in each sub-band are randomly sampled, and the sampled units are reorganized and reused into a complete superlens overall structure, and the sampling matrix is ​​iterated using a genetic algorithm to capture the nonlinear relationship between the superlens structure and the achromatic focusing effect corresponding to different sampling matrices, and finally output the sampling matrix with the optimal achromatic focusing performance and its corresponding complete superlens structure. This step is called the optimal random space multiplexing method. Different from the traditional random space multiplexing method, this method can learn the nonlinear relationship between the random meta-atom arrangement and the corresponding electromagnetic response through intelligent pattern generation, and then output the optimal random multiplexing scheme, realizing global optimization while realizing the reuse of sub-band units. Through the above steps, the hybrid inverse design framework can realize the end-to-end design of the achromatic lens, that is, directly give the optimal achromatic lens structure based on the design requirements, and give the superlens ultra-wideband working characteristics through sub-band decomposition.

[0012] The sub-band decomposition method is to divide the working band into multiple sub-bands, and perform dispersion engineering in each sub-band to avoid the performance limitation of the broadband operation of the achromatic lens due to the phase dispersion control capability of the integrated resonant unit in the traditional method. Based on the sub-band decomposition scheme, hybrid inverse design is introduced to perform efficient inverse design of the achromatic lens, avoiding the complex resonant structure design and the construction of the meta-atom library, and transforming the design process from a time-consuming trial and error process to a parallel, end-to-end efficient 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 is adopted, which effectively avoids the constraints of the unit dispersion control capability on the working bandwidth, numerical aperture and lens size of the achromatic lens in the traditional dispersion engineering scheme, and the complex resonance design of the integrated resonance unit. It can also multiply the working bandwidth of the lens 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 solution is adopted, which effectively avoids the design process of traditional dispersion engineering solutions that consumes a lot of time and computing power to build a unit library and screen out units that meet the conditions. Instead, neural networks and optimization algorithms are used to quickly predict and retrieve units that meet the conditions, which can achieve efficient reverse design. Combined with the sub-band decomposition solution, the parallel unit structure design of multiple sub-bands can be completed, which significantly improves the design efficiency. The designed unit can approach the performance limit of the unit itself.

[0016] 3) An optimal random spatial multiplexing scheme is adopted. Compared with the traditional spatial multiplexing scheme, the proposed scheme can effectively alleviate the sidelobe effect in the traditional shared aperture method. At the same time, for the general random spatial multiplexing scheme, the sampling of sub-regions is completely random. Although it is effective in some cases, it still has certain deficiencies in sidelobe suppression, coupling reduction and interpretability. Therefore, completely random sampling is not enough to optimize the performance of the metasurface. By embedding global optimization into the traditional random spatial multiplexing scheme, the nonlinear relationship between the meta-atom arrangement and the electromagnetic response is captured, thereby effectively alleviating the efficiency deterioration and focal spot offset in the phase distribution after random interleaving. BRIEF DESCRIPTION OF THE DRAWINGS

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

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

[0019] Figure 3 Schematic diagram of the achromatic lens and integrated resonance unit designed for Example 1;

[0020] Figure 4 The phase and dispersion distribution diagram of the achromatic lens of Example 1;

[0021] Figure 5 Schematic diagram of the deep neural network structure;

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

[0023] Figure 7 It is a flow chart of the reverse dispersion engineering method;

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

[0025] Fig. 9 A diagram showing simulation results of the achromatic lens designed for Example 1;

[0026] Fig.101 is a performance curve diagram of the actual focal length, half maximum full width and relative focusing efficiency of the achromatic lens in Example 1. DETAILED DESCRIPTION

[0027] See also Figure 1 , the present invention specifically includes:

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

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

[0030] 3) According to the working frequency band range, focal length, incident surface aperture, and integrated resonant unit structure, a sub-band decomposition scheme is used to decompose the working frequency band, including the number of sub-bands and the range of each sub-band.

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

[0032]

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

[0034] 5) Determine the phase dispersion distribution that the metalens needs to satisfy to achieve achromatic dispersion compensation in each sub-band according to the following formula:

[0035]

[0036] Among them, ω0 represents the starting frequency of the corresponding working frequency band, It indicates that the additional phase shift introduced to better compensate for the initial phase of the unit can shift the hyperbolic phase distribution of the metalens upward or downward as a whole without affecting the focal length and achromatic focusing effect.

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

[0038] The present invention uses the optimal random spatial multiplexing scheme to perform global design and optimization based on the units of each sub-band obtained by reverse dispersion engineering, and performs random spatial multiplexing in the optimal arrangement mode on the units obtained based on the reverse dispersion engineering design, optimizes the overall performance of the metalens, and obtains the final metalens layout and the overall structure of the metalens. The above-mentioned reverse dispersion engineering is combined with the optimal random multiplexing scheme to finally form a hybrid design framework for end-to-end design of ultra-wideband achromatic lenses. The method avoids the constraints of the dispersion control capability of the integrated resonant unit on the overall performance of the achromatic lens through sub-band decomposition, and optimizes the performance of the metalens through a data-driven scheme, and improves the design efficiency.

[0039] The present invention divides the total working frequency band into multiple sub-bands according to the overall working frequency band required by the design target and the specific phase dispersion control range that can be achieved by the integrated resonant unit used, so that the integrated resonant unit can achieve the phase dispersion value and reflection amplitude required for achromatic focusing under the target focal length and lens size in each sub-band, thereby avoiding the limitation of the dispersion control ability of the integrated resonant unit itself on the working bandwidth and numerical aperture of the achromatic lens. Specifically, for the achromatic lens, its lens diameter R max , numerical aperture NA, operating frequency band Δω, and the phase dispersion control range that can be achieved by the integrated resonant unit Satisfies the following relationship:

[0040]

[0041] For the target working frequency band Δω, the sub-band decomposition method used first divides it into N consecutive sub-bands Δω n For each sub-band Δω n , the dispersion control range of the integrated resonant unit The above inequality is also satisfied, as shown in the following formula:

[0042]

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

[0044]

[0045] By reasonably dividing the sub-band range, it is possible to avoid complex resonance design of the unit and alleviate the constraints on bandwidth and numerical aperture in the design of the achromatic lens.

[0046] The reverse dispersion engineering method comprises a neural network for forward prediction and an adaptive differential evolution algorithm for reverse retrieval. The method uses full-wave simulation to obtain a data set including unit structure parameters and reflection coefficients according to the integrated resonant unit structure used, and trains a neural network based on the data set to quickly predict the electromagnetic response of different structural units, including the real and imaginary parts of the reflection coefficient. Then, the amplitude and phase dispersion values ​​of different structural units are calculated based on the real and imaginary parts of the reflection coefficient, and then the adaptive differential evolution algorithm is used to quickly reverse design a unit that works in a specific frequency band and meets specific phase dispersion and amplitude requirements.

[0047] The specific process of the reverse design includes:

[0048] 1) Use Latin hypercube sampling to generate the initial population;

[0049] 2) Use neural network to predict the phase dispersion and amplitude of the initial population in the target working frequency band;

[0050] 3) Calculate the difference between each individual's phase dispersion curve and the target phase dispersion curve and the individual's amplitude score based on the prediction results;

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

[0052] 5) Execute selection, crossover and mutation of differential evolution algorithm;

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

[0054] 7) Output the optimal unit structure.

[0055] The present invention adopts a random interleaving scheme to spatially multiplex the metasurface units, and the specific random multiplexing mode is given by the sampling matrix. By loading the deep learning method and the global optimization algorithm, the nonlinear relationship between the metasurface arrangement scheme and the electromagnetic field response is adaptively learned, and then the optimal random spatial multiplexing scheme is obtained, so that the multiplexed metasurface has the best performance. The specific process is as follows:

[0056] 1) generating a sampling matrix M with k different elements according to k groups of hypersurface units that are reused as needed;

[0057] 2) Generate a sampling mask according to the sampling matrix, sample the structural parameter tensor of each group of metasurface units, and obtain the structural parameter tensor of all units after multiplexing based on the tensor containing the structural parameters of the unit in each channel after sampling;

[0058] 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] 4) According to the amplitude and phase distribution of the metasurface, the point source approximation scheme is used to calculate the electric field intensity distribution of the metasurface in the target plane;

[0060] 5) According to the design goal, the fitness function is calculated based on the calculated field strength distribution to evaluate the performance of the multiplexing metasurface obtained based on the current sampling matrix M;

[0061] 6) Use genetic algorithm to update M and repeat steps 2) to 5) until the convergence condition is met or the maximum number of iterations is reached;

[0062] 7) Output the optimal M, and obtain the final layout and overall structure of the metasurface based on M.

[0063] The hybrid design and a double-layer integrated resonant unit design result in a microwave frequency band reflective ultra-wideband achromatic lens, whose operating frequency band is: 8-16GHz, bandwidth is 66.7%, focal length is 215mm, effective aperture size is 310mm, and numerical aperture is 0.58. The achromatic lens can achieve achromatic focusing of the reflected beam within the ultra-wideband range of 8-16GHz, and the average relative focusing efficiency within the working bandwidth is 52.91%.

[0064] Based on the design goal, the present invention divides the target working frequency band into multiple sub-bands, performs reverse dispersion engineering in each sub-band, automatically designs the metasurface unit according to the theoretical dispersion compensation value, and then performs optimal random spatial multiplexing on each sub-band unit designed, and finally obtains a complete achromatic metalens structure, thereby realizing ultra-wideband continuous achromatism. The present invention consists of two parts: a data-driven reverse dispersion engineering method and an optimal random spatial multiplexing method, which realizes the efficient design of ultra-wideband achromatic lenses, and broadens the achromatic working bandwidth of the metalens as much as possible without sacrificing the numerical aperture, the size of the metalens, and the focusing efficiency, so as to achieve excellent working performance. Compared with the prior art, the present invention can overcome the reliance of the prior art on the dispersion control capability of the metasurface unit, and can significantly improve the design efficiency, and has good application scenarios and prospects.

[0065] The following is a specific implementation of an achromatic lens operating at 8-16GHz, with a focal length of 215mm and an aperture diameter of 310m as an example of the design target, which is used to demonstrate the process and design effect of constructing a hybrid inverse design framework of the present invention, and further explain in detail the technical solution of the present invention and the effect achieved.

[0066] Example 1

[0067] See also Figure 2, the specific process of the hybrid reverse design is as follows:

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

[0069] See also Figure 3 b, adopts an integrated resonant unit structure composed of two layers of dielectric substrates stacked together, with a rectangular metal resonant patch placed on the upper layer of each dielectric substrate, and the bottom layer of the unit is a metal reflector. Among them, the material of the metal layer is copper, and the material of the dielectric substrate is F4B-265, with a dielectric constant of 2.65. The fixed size parameters of each part are as follows: unit period p = 12mm, gold plating thickness t = 0.035mm, lower dielectric substrate thickness t1 = 2mm, upper dielectric substrate thickness t2 = 2mm, lower metal resonant patch width w1 = 1mm, upper metal patch width w2 = 1mm. The symbols of the variable size parameters of each part of the unit are as follows: length of the lower metal resonant patch l1; length of the upper metal resonant patch l2; angle α between the two metal resonant patches; common rotation angle β of the two metal patches.

[0070] See also Figure 3 , the integrated resonant unit structure can generate a cross-polarized reflected wave within a specific frequency range under the irradiation of a normally incident circularly polarized wave. By adjusting the parameters l1 and l2, the resonance point of the unit can be adjusted, thereby achieving regulation of the dispersion of the operating frequency band, reflection amplitude, and reflection phase. By changing α, the phase dispersion of the unit can be further adjusted. By rotating the two metal patches together by β degrees, the phase of the reflected wave can be further regulated by the Pancharatnam–Berry phase, and 2π phase coverage can be achieved. Therefore, by precisely designing the size parameters of the unit structure, precise regulation of the four dimensions of reflected wave phase dispersion, amplitude, operating frequency band, and reflection phase can be achieved.

[0071] 2) After determining the operating frequency band range, focal length, numerical aperture, and integrated resonant unit structure of the achromatic lens, the target frequency band is divided into multiple sub-bands according to 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, 8-16 GHz is divided into two sub-bands, 8-13 GHz and 13-16 GHz. The phase distribution required for the metalens to achieve focusing at the starting frequency of the sub-band in each sub-band is determined according to the following formula:

[0073]

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

[0075] The phase dispersion distribution that the metalens needs to satisfy to achieve achromatic dispersion compensation in each sub-band is determined according to the following formula:

[0076]

[0077] Among them, ω0 represents the starting frequency of the corresponding working frequency band, It indicates that the additional phase shift introduced to better compensate for the initial phase of the unit can shift the hyperbolic phase distribution of the metalens upward or downward as a whole without affecting the focal length and achromatic focusing effect.

[0078] See also Figure 4 ,According to the radial required phase and phase dispersion distribution obtained by the above calculation, the superlens is a circular array with a maximum of 25 units arranged along the radial direction.

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

[0080] 3-1: Using the simulation software CST Microwave Studio, a relatively sparse parameter scan is performed on the three size parameters l1, l2, and α to obtain a training data set;

[0081] 3-2: Two deep neural networks (DNNs) are trained based on the training data set, which are used to predict the real and imaginary parts of the reflection coefficient based on the unit structure parameters.

[0082] See also Figure 5 The input layer of the deep neural network (DNN) contains three dimensions, namely l1, l2, and α, and the output layer contains 101 dimensions, corresponding to the real or imaginary values ​​of the reflection coefficient at 101 frequency points. The DNN contains 13 fully connected hidden layers, containing 32, 64, 128, 256, 512, 1024, 1024, 1024, 1024, 512, 256, 128 and 128 neurons respectively, and dropout layers are added in the seventh and ninth hidden layers to facilitate the model to better suppress noise and accelerate model convergence.

[0083] See also Figure 6 , the trained deep neural network (DNN) can accurately predict the real and imaginary parts of the reflection coefficient corresponding to the unit with specific size parameters.

[0084] 4) After training the neural networks for forward prediction, they are embedded in the self-adaptive differential evolution algorithm (SADEA) to achieve reverse retrieval of size parameters through SADEA, ultimately forming a complete reverse dispersion engineering method.

[0085] See also Figure 7 , the reverse dispersion engineering generates an initial population through Latin hypercube sampling, and then calculates the fitness function of each individual according to the prediction result of the neural network by the following formula:

[0086]

[0087] in, and α R They represent the weights of phase error and reflection amplitude scores respectively, N represents the number of frequency points in the target frequency range, and Indicates that according to the corresponding frequency f m The real part of and the imaginary part The calculated amplitude and phase values ​​are Represents the target phase response value of the unit generated based on the calculated achromatic dispersion and group delay requirements.

[0088] The adaptive differential evolution algorithm (SADEA) iterates the calculated fitness, performs genetic algorithm screening, mutation and crossover, and updates the population until the convergence condition is met. With the algorithm's iterative process, the reverse dispersion engineering method can comprehensively consider the error of the amplitude mean and phase response, so as to quickly retrieve and output the optimal unit structure that meets the conditions according to the design goals in each sub-band.

[0089] See also Figure 4 b, based on the calculated target dispersion profile, the predicted phase dispersion value of the radial unit in each sub-band is predicted (such as Figure 4 (shown as scattered points in b).

[0090] See also Figure 2 After obtaining the parameter matrix output by the reverse dispersion engineering, that is, the optimal unit structure of each sub-band, the second stage of the hybrid reverse design framework, that is, optimal random spatial multiplexing, is entered. The specific steps are as follows:

[0091] 4-1: Define the sampling matrix M, M s ∈{0,1,2} 25×25 , where element 0 indicates that there is no unit at the corresponding coordinate position of the array; element 1 indicates that the corresponding coordinate position of the array is a unit operating in sub-band 1 (8-13 GHz); element 2 indicates that the corresponding coordinate position of the array is a unit 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-band, and reuse the sampled units to reorganize into the complete structure of the superlens. According to the array parameter matrix, use the previously trained neural network to predict its amplitude and phase response matrix.

[0093] 4-3: Based on the predicted amplitude and phase response matrix, the point source estimation method is used to approximate and normalize the reflected wave of the metalens, and the normalized reflected electric field intensity distribution of the metalens in the range of 8-16GHz is obtained. The fitness of the metalens is calculated by the following formula to evaluate its achromatic focusing effect:

[0094]

[0095] Among them, F i ,F design , and N represent the calculated actual focal length, target focal length and the number of frequencies considered in the working frequency band respectively.

[0096] 4-4: The calculated fitness is evaluated to see if it meets the algorithm convergence conditions. If not, the genetic algorithm is entered to iteratively update M. During the iteration, the elements in M ​​are crossovered and mutated, and the above calculation process is repeated until the convergence conditions are met or the maximum number of iterations is reached.

[0097] See also 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 compares the calculation results of the traditional chromatic lens. It can be seen that the superlens designed based on the scheme can significantly reduce grating lobes and clutter, and reduce the deviation of the focused light spot, and has a more excellent achromatic focusing performance.

[0098] See also Fig. 9 In order to verify the design content of the above-mentioned achromatic lens, the reflected electric field of the designed superlens in the range of 8-16GHz was calculated through full-wave simulation. It can be seen that the designed achromatic lens significantly suppresses the deviation of the focused spot and achieves a relatively good achromatic focusing effect in the ultra-wideband range.

[0099] See also Fig.10According to the electric field results obtained by simulation, the actual focal length, half-maximum full width and relative focusing efficiency of the designed achromatic lens are calculated. It can be seen that the achromatic lens designed by the present invention achieves a good achromatic focusing effect in the range of 8-16GHz, and significantly suppresses the focal length deviation compared with the lens without ultra-wideband achromatic design. The relative focusing efficiency obtained by simulation is 12.02% to 69.12% in the range of 8-16GHz, and the average focusing efficiency is 52.91%, which has a significantly broadened bandwidth and higher efficiency compared with similar devices. The results verify that the present invention can achieve achromatic focusing in an ultra-wideband range by using a resonant unit with a simple structure while ensuring the numerical aperture and focusing efficiency as much as possible.

[0100] The above description is only a specific implementation manner of the present application, but the protection scope of the present application is not limited thereto. Any modifications, equivalent substitutions and improvements made by any technician familiar with the technical field within the technical scope disclosed in the present application should be included in the protection scope of the present invention.

Claims

1. A data-driven hybrid inverse design method for ultra-wideband achromatic lenses, characterized in that: A data-driven reverse dispersion engineering method is used to perform hybrid reverse design on an 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 an overall structure of a metalens with optimal performance. The specific steps of hybrid reverse design of the achromatic lens include: 1) Determine the operating frequency band range, focal length, incident surface aperture and numerical aperture of the target achromatic metalens, as well as the integrated resonant unit structure used; 2) Using the sub-band decomposition method to divide the working frequency band into k sub-bands and determine the range of each sub-band; 3) Determine the phase distribution required for the metalens to achieve focusing at the starting frequency of the sub-band in each sub-band according to the following formula: Wherein, F is the focal length of the lens; r is the radial position along the aperture surface of the superlens; ω is the target operating frequency; is the phase constant. The phase dispersion distribution that the metalens needs to satisfy to achieve achromatic dispersion compensation in each sub-band is determined according to the following formula: Among them, ω0 is the starting frequency of the corresponding working frequency band; is the additional phase shift introduced; 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 to obtain all unit structures that meet the phase dispersion, working frequency band and amplitude requirements; 5) For each unit structure obtained in step 4), the optimal random spatial multiplexing method is used to perform spatial multiplexing and global optimization to obtain a design scheme for the overall structure of the metalens.

2. The data-driven ultra-wideband achromatic lens hybrid inverse design method according to claim 1, characterized in that: The sub-band decomposition of step 2) includes: dividing the number of sub-bands and the range of each sub-band, and the sub-band decomposition method cuts the target working frequency band Δω into N continuous sub-bands Δω according to the working frequency band required by the design target and the phase dispersion control range of the integrated resonant unit. n , so that the integrated resonant unit can achieve the phase dispersion value and reflection amplitude required for the achromatic lens focusing under the target focal length and lens size in each sub-band, and the diameter R of the achromatic lens max , numerical aperture NA, operating frequency band Δω, and the phase dispersion control range that can be achieved by the integrated resonant unit The following inequality is satisfied: The working frequency band Δω is expressed by the following formula: Among them, Δω n is the nth sub-band; N is the number of sub-bands; Similarly, for each sub-band Δω n , the dispersion control range of its integrated resonant unit is The following inequality is also satisfied: The phase dispersion control range satisfied by the integrated resonant unit structure after sub-band decomposition is reduced and is expressed by the following formula:

3. The data-driven ultra-wideband achromatic lens hybrid inverse design method according to claim 1, characterized in that: The step 4) uses a forward prediction neural network and a reverse retrieval adaptive differential evolution algorithm, wherein the forward prediction neural network uses a full-wave simulation to obtain a data set of integrated resonant unit structural parameters and reflection coefficients for training, and the neural network trained with the data set is used to predict the electromagnetic response of different structural 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 structural units are calculated based on the real part and the imaginary part of the reflection coefficient; the adaptive differential evolution algorithm reversely designs the unit structural parameters that work in a specific frequency band and meet specific phase dispersion and amplitude requirements according to the amplitude and phase dispersion values ​​of different structural units; the reverse design specifically includes: 1) Use Latin hypercube sampling to generate the initial population; 2) Use neural network to predict the phase dispersion and amplitude of the initial population in the target working frequency band; 3) Calculate the difference between each individual's phase dispersion curve and the target phase dispersion curve and the individual's amplitude score based on the prediction results; 4) Based on the calculated phase error and amplitude score, evaluate the fitness of each individual and determine whether the conditions are met; 5) Execute selection, crossover and mutation of differential evolution algorithm; 6) Update the population and repeat steps 2) to 6) until the convergence condition is met; 7) Output the optimal unit structure.

4. The data-driven ultra-wideband achromatic lens hybrid inverse design method according to claim 1, characterized in that: The step 5) adopts the random multiplexing mode given by the sampling matrix to spatially multiplex the metasurface units, and adaptively learns the nonlinear relationship between the metasurface arrangement and the electromagnetic field response by loading the deep learning method and the global optimization algorithm to obtain the optimal random spatial multiplexing scheme. The specific process is as follows: 1) Generate a sampling matrix M with k different elements according to the k groups of hypersurface units that need to be reused; 2) Generate a sampling mask according to the sampling matrix, sample the structural parameter tensor of each group of hypersurface units, and obtain the structural parameter tensor of all units after multiplexing based on the tensor of the structural parameters of the unit in each channel after sampling; 3) Input the structural parameter tensors of all the multiplexed units into the neural network to predict the amplitude and phase distribution of the metasurface; 4) According to the amplitude and phase distribution of the metasurface, the point source approximation method is used to calculate the electric field intensity distribution of the metasurface in the target plane; 5) According to the design goal, the fitness function is calculated based on the field strength distribution to evaluate the performance of the multiplexing metasurface obtained based on the current sampling matrix M; 6) Use genetic algorithm to update M and repeat steps 2) to 5) until the convergence condition is met or the maximum number of iterations is reached; 7) Output the optimal M and obtain the final layout and overall structure of the metasurface.

5. The data-driven ultra-wideband achromatic lens hybrid inverse design method according to claim 4, characterized in that: The fitness function is calculated by the following formula: Among them, F i 、F design and N are the actual focal length, target focal length and the number of frequencies considered in the working frequency band, respectively.

Images