A low-cost, reconfigurable metasurface design method with a novel topology

Abstract

The present invention discloses a low-cost reconfigurable metasurface design method with a new topology, including a new topological representation method and a portable separation design architecture, which realizes the design of reconfigurable intelligent metasurfaces with different functions and structures without the need to recollect data sets and retrain models. By utilizing multiple spline control points and pattern mapping, this method can quickly generate and fine-tune continuous patterns, ensure the smooth flow of excitation currents inside the patterns, and reduce the pattern solution space. Based on microwave network theory, the architecture splits the reconfigurable metasurface into active devices, surface pattern layers, dielectric layers, and metal strata. Through pre-incremental learning networks and theoretical calculations, the multi-bit electromagnetic responses of reconfigurable metasurface units can be quickly obtained without the need for numerical simulation. Finally, a continuous-discrete particle swarm optimization algorithm is used to obtain a reconfigurable intelligent metasurface that meets the target function.

Description

Technical Field

[0001] The present invention belongs to the fields of reconfigurable metasurface unit design, metasurface unit physical model analysis and mathematical optimization, and particularly relates to a low-cost reconfigurable metasurface unit design method with a new topology. Background Art

[0002] Reconfigurable metasurfaces precisely control the amplitude, phase, frequency, and polarization of electromagnetic waves in real time. They also feature ease of fabrication, a low profile, and low loss. They have found widespread application in areas such as beam deflection, electromagnetic stealth, and holographic imaging. In wireless communications, reconfigurable metasurfaces are renowned for their remarkable dynamic wireless channel control, making them crucial for fifth-generation (5G) and sixth-generation (6G) research. The evolution from passive metasurfaces to reconfigurable metasurfaces highlights the growing demand for enhanced performance and expanded applications. However, metasurface unit cell structures exhibit variability, and a lack of direct analytical formulas linking them to electromagnetic responses. Traditional designs rely primarily on classical structures and their variants. When these structures prove insufficient to meet design goals, researchers must continuously adjust them, incurring significant costs. Most current machine learning-assisted design methods focus on passive metasurfaces, which is insufficient for reconfigurable metasurfaces with more complex structures and features. First, different active devices exhibit distinct states, making them difficult to quantify and learn within neural networks. Second, different states of active devices correspond to different impedances, resulting in multiple responses of the reconfigurable metasurface, making training more challenging. Finally, conventional random pixelated patterns are often discrete, hindering the smooth flow of excitation current from active devices and the maximum resonance capability of the pattern. Finding a method for designing reconfigurable metasurfaces that is fast and low-cost is crucial. Summary of the Invention

[0003] The present invention provides a low-cost reconfigurable metasurface design method with a new topology to address the design defects existing in the existing methods and the difficulty in quickly solving the problem of reconfigurable unit design according to unit design requirements.

[0004] The specific technical solution of the present invention includes the following four steps:

[0005] Step 1: Establish a separate design architecture for the reconfigurable metasurface unit, separating the reconfigurable metasurface unit into a pattern layer, a dielectric layer, a metal layer, and active devices. The surface pattern layer is a three-port component, connecting the dielectric layer and active devices; the dielectric layer is further connected to the metal layer. It is important to note that in this method, the dielectric layer and active devices are not internally connected. These sub-components are combined to form the complete reconfigurable metasurface unit.

[0006] Step 2: Non-uniform rational B-spline topology representation method and surface pattern layer dataset generation. Based on the properties of the non-uniform rational B-spline curve, n groups of control points are generated in the (M+1, N+1) area of ​​the pattern layer. According to the curve expression:

[0007]

[0008] Generate a non-uniform rational B-spline curve; discretize the curve and downsample it into coordinate points, and then mirror it to the surface pattern layer area; use Python to control the simulation software to automatically model and obtain the electromagnetic response curve of the corresponding surface pattern layer, and create a pattern layer-scattering electromagnetic response dataset.

[0009] Step 3: Train the pre-incremental learning network based on the pattern layer-scattered electromagnetic response dataset in step 2; in the first stage of network training, the network learns the regular influence of the dielectric constant of the medium layer on the scattered electromagnetic response of the pattern layer; in the second stage of network training, the network learns the joint influence of the pattern and dielectric constant on the scattered electromagnetic response of the pattern layer, and realizes the prediction of the scattered electromagnetic response of the pattern layer.

[0010] Step 4: Based on the multi-port microwave network theory and the pre-incremental learning network trained in step 3, a two-step scattering matrix cascade calculation is used to obtain the overall electromagnetic response of the reconfigurable unit; the scattering matrix of the active device is replaced to obtain the multi-bit electromagnetic response of the reconfigurable metasurface unit; the scattering matrix of any split part in the separated design architecture is replaced to obtain the electromagnetic response of the optimized reconfigurable unit; without the need for time-consuming numerical simulation.

[0011] Step 5: Use the improved discrete-continuous particle swarm optimization algorithm to optimize the reconfigurable metasurface unit to meet the design goals.

[0012] Furthermore, step 1 specifically includes the following: splitting the reconfigurable metasurface unit into pattern layer A, dielectric layer B, active device C, and metal ground; considering these subcomponents as distributed components in a microwave circuit, port 1 represents the excitation port for the incident electromagnetic wave, and ports 4-7 represent the interconnection ports between A, B, and C. Ports 2 and 3 are the ground side and can be simplified as short circuits.

[0013] Furthermore, step 2 specifically includes the following: generating n groups of control points B i (i=1,…,n), the coordinates of a single control point are (x i ,y i ), the corresponding weight is R i ; Basis function N i,m (K) is expressed as:

[0014]

[0015] Among them, K defines the nodes in the non-uniform rational B-spline curve, K={K1,K2,…,K P}, m represents the order of the curve, p = n + m + 1. Among the n groups of control points, the starting point B1 represents the starting position of the non-uniform rational B-spline curve and the welding position of the active device, and its position coordinates are fixed. Other control points are randomly selected in the pattern layer (M+1, N+1) area. According to formula 1, the order of the curve is set to 3, the weight of each control point is set to 1, and the curve is generated according to the coordinates of the control points; the generated curve is discretized and sampled, and the coordinates of each sampling point are sorted into integer coordinates P(x i ,y i ); Divide the pattern layer area (M, N) into a 10*5 grid, with a pixel matrix of 1 side length per grid, and calculate the pixel matrix according to P(x i ,y i ) coordinates, marking the corresponding positions in the pixel matrix with "1" and the rest with "0", thus obtaining a 10*5 0 / 1 matrix, and mirroring it to obtain a 10*10 0 / 1 matrix; in the simulation software, the corresponding metal pattern is generated according to the 10*10 matrix. In step 1, the pattern layer is associated with the dielectric layer, active device, and incident wave port respectively. There are three external ports, and their scattering matrix can be expressed as:

[0016]

[0017] Where b = [b1, b4, b6] T The vector representing the normalized output waves of the three ports, a=[a1,a4,a6] T The vectors representing the normalized incident waves of the three ports. When acquiring the scattered electromagnetic response data of the pattern layer, the dielectric constant of the space between the metal patch and the output port is set to the dielectric constant of the dielectric layer, and the thickness of the dielectric layer is set to zero.

[0018] Furthermore, step 3 specifically includes the following: the pre-incremental learning network is responsible for the forward prediction of the scattered electromagnetic response of the pattern layer. After the 50-bit pattern layer 01 encoding input, three 100-dimensional deconvolution layers are set to collect information of the pattern layer. The information of the 300-dimensional deconvolution layer and the 20-bit binary code converted by the dielectric constant together constitute the input of the subsequent fully connected layer. The fully connected layers are 600 dimensions, 900 dimensions, and 1200 dimensions respectively. Batch normalization is performed after each deconvolution and fully connected layer, and the final output is 2 sets of 701-dimensional real and imaginary curves of the scattered electromagnetic response. LeakyReLU is used as the activation function:

[0019]

[0020] The mean square error between the simulation curve and the prediction curve is used as the loss function.

[0021]

[0022] Among them, f P_i and f S_i Represents the i-th sampling point of the scattered electromagnetic response prediction curve and the simulation curve respectively. The final loss of the pre-incremental learning network is the sum of the mean square error of the real part curve and the mean square error of the imaginary part curve with the same weight, which is defined as:

[0023] Final_Loss=0.5*L re +0.5*L im (13)

[0024] Among them, L re and L im Representing the independent losses of the two outputs, respectively. The pre-incremental learning network consists of two training steps: first, pre-training is performed using a 2000×10 dataset, encompassing all dielectric constants in the F4B substrate range of 2 to 3, to learn the effect of dielectric constant on the electromagnetic response of the patterned layer. The second training step consists of the dataset from the first step, augmented with 8,000 different patterns, for a total of 50,000 datasets of patterned layers and scattered electromagnetic responses. After the first training step, the neural network parameters are fixed, and training continues using the full 50,000 datasets to learn the connection between the patterned layer and the scattered electromagnetic response. The two training steps last for 50 and 100 epochs, respectively.

[0025] Furthermore, step 4 specifically includes the following: According to step 1, the reconfigurable metasurface unit is split into four parts, and the sub-parts are regarded as distributed components in the microwave circuit. The transmission matrix of dielectric layer B can be expressed as:

[0026]

[0027] Where ω is the angular frequency, C0 is the speed of light, is the refractive index, h is the dielectric layer thickness, and η is the dielectric wave impedance. The scattering matrix of active device C is obtained by the product company or through measurement. Since there is no direct connection between dielectric layer B and active device C, the electromagnetic response of the reconfigurable unit requires a two-step cascade calculation: first, the pattern layer A and dielectric layer B are cascaded using Equation 9:

[0028] S(f)=S pp (f)+S pc (Γ-S cc (f)) -1 S cp (f) (15)

[0029] Among them, S pprepresents the scattering matrix between internal ports, S cc represents the scattering matrix between external ports, S pc represents the scattering matrix from the external port to the internal port, S cp represents the scattering matrix from the internal port to the external port. Based on the matrix cascade operation in the first step, the metal layer associated with the dielectric layer is short-circuited to calculate the two-port scattering matrix of the passive portion of the reconfigurable unit. This two-port scattering matrix of the passive portion is further cascaded with the scattering matrix of the active device C to calculate the overall electromagnetic response of the reconfigurable unit. By replacing the scattering matrix of the active device C, the multi-bit electromagnetic response of the unit can be obtained without the need for a second simulation.

[0030] Furthermore, step 5 specifically includes the following: taking the coordinates of the control points, the dielectric constant and thickness of the dielectric layer, and the number of active devices as the input of the continuous-discrete particle swarm optimization algorithm, the optimal design of the reconfigurable metasurface unit is achieved by updating the velocity and coordinates of the particles. On the basis of the conventional particle swarm optimization algorithm, a discrete coordinate processing operation is introduced, namely

[0031]

[0032] Among them, X k+1 represents the updated discrete coordinates, X k represents the updated coordinates after non-discretization, X variable represents all possible values ​​of a discrete variable. Compare X k With X variable The mean square error of all values ​​in X k+1 Locate the nearest discrete variable value to achieve the update and optimization of discrete variables.

[0033] The above steps can achieve rapid design of the target unit.

[0034] This paper is dedicated to developing an efficient and universal design paradigm for rapidly designing reconfigurable metasurface units with various functions and structures. It has the following advantages:

[0035] 1. This invention introduces a new topological representation method, which realizes the equivalent mapping of the surface metal pattern of the metasurface unit from high-dimensional coding to low-dimensional control points, ensuring the smooth flow of the excitation current of the active device under the continuous pattern and maximizing the resonance ability of the pattern layer.

[0036] 2. This paper proposes a separate design architecture to rapidly obtain the multi-bit electromagnetic response of reconfigurable metasurface units; at the same time, this independent design architecture only needs to capture the response of the pattern layer, reducing the dataset cost by 62.5%, marking a strategic shift towards minimizing dataset costs, promoting data reuse, and liberating design freedom.

[0037] Additional aspects and advantages of the present invention will be set forth in part in the description which follows and, in part, will be obvious from the description which follows, or may be learned through practice of the present invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0038] The above and / or additional aspects and advantages of the present invention will become apparent and readily understood from the following description of the embodiments in conjunction with the accompanying drawings, in which:

[0039] Figure 1 Designing architectures for reconfigurable metasurface unit separation;

[0040] Figure 2 A flowchart for the topological representation of continuous patterns based on non-uniform rational B-splines;

[0041] Figure 3 A diagram of the neural network structure for pre-incremental learning;

[0042] Figure 4 The figure is the amplitude diagram of S11 changing with the dielectric constant, and the sub-figure is the simulation setting diagram of the pattern layer;

[0043] Figure 5 Schematic diagram of the two-part scattering matrix cascade calculation based on multi-port microwave network theory

[0044] Figure 6 A 1-bit phase control unit and an optimization curve diagram designed according to an embodiment of the present invention;

[0045] Figure 7 A comparison chart of the calculated and simulated electromagnetic responses of a 1-bit phase control unit designed according to an embodiment of the present invention, including amplitude and phase;

[0046] Figure 8 A 3-bit phase control unit and an optimization curve diagram designed according to an embodiment of the present invention;

[0047] Figure 9 This is a comparison chart of the calculated and simulated electromagnetic responses of a 3-bit phase control unit designed according to an embodiment of the present invention, including amplitude and phase. DETAILED DESCRIPTION

[0048] To better understand the purpose, structure, and function of the present invention, the following, in conjunction with the accompanying drawings, further describes in detail a low-cost, reconfigurable metasurface design method with a novel topology. The embodiments described below with reference to the accompanying drawings are exemplary and intended to explain the present invention, and are not to be construed as limiting the present invention.

[0049] Metasurfaces are two-dimensional metamaterials that are easy to manufacture, low-cost, and have a powerful ability to control electromagnetic waves. To address this, the present invention proposes a low-cost, reconfigurable metasurface design method with a new topology. First, a separation design architecture is established, utilizing microwave network theory to separate the reconfigurable metasurface units into a pattern layer, a dielectric layer, a metal stratum, and active devices. In the separation design architecture, the subsections of each unit are parameterized as inputs to a continuous-discrete particle swarm optimization algorithm. The scattering electromagnetic response matrix of each subsection is predicted or calculated based on its parameters, and a multi-port scattering matrix cascade operation is performed to rapidly obtain the multi-bit electromagnetic response of the reconfigurable metasurface unit.

[0050] Step 1: Create a separation design architecture.

[0051] Based on the multi-port microwave network theory, the reconfigurable metasurface unit is separated into pattern layer, dielectric layer, metal layer and active device. The internal connection relationship of each sub-part of the split unit is as follows: Figure 1 As shown, these subsections can be considered as distributed components in a microwave circuit, where the surface pattern layer is directly connected to the dielectric layer and active devices. Port 1 represents the excitation port for the incident electromagnetic wave, and ports 4-7 represent the interconnection ports between A, B, and C. Ports 2 and 3 are grounded and can be simplified as short circuits.

[0052] Step 2: Topological representation of the pattern layer and generation of surface pattern layer dataset.

[0053] Based on the properties of non-uniform rational B-spline curves, n groups of control points B are generated in the pattern layer (M+1, N+1) area. i (i=1,…,n), the coordinates of a single control point are (x i ,y i ), the corresponding weight is R i , a continuous curve is generated according to Formula 1:

[0054]

[0055] Generate continuous curve, basis function N i,m (K) is expressed as:

[0056]

[0057] Among them, K defines the nodes in the non-uniform rational B-spline curve, K={K1,K2,…,K P}, m represents the order of the curve, p = n + m + 1; among the n groups of control points, the starting point B1 represents the starting position of the non-uniform rational B-spline curve and the welding position of the active device, and its position coordinates are fixed. Other control points are randomly selected in the pattern layer (M+1, N+1) area. According to formula 1, the order of the curve is set to 3, the weight of each control point is set to 1, and the curve is generated according to the coordinates of the control points; the generated curve is discretized and sampled, and the coordinates of each sampling point are sorted into integer coordinates P(x i ,y i );like Figure 2 As shown, the pattern layer area (M, N) is divided into 10*5 grids, each with a side length of 1 pixel matrix, and according to P(x i ,y i ) coordinates mark the corresponding positions of the pixel matrix with "1" and the rest with "0", thereby obtaining a 10*5 0 / 1 matrix, and a 10*10 0 / 1 matrix is ​​obtained by mirror symmetry; the corresponding metal pattern is generated in the simulation software according to the 10*10 matrix. It should be noted that this topological representation method is not limited to a fixed pixel division. In the present invention, 10*5 is used for clarity of description. In fact, this topological representation method can be divided into any combination of pixel grids. In step 1, the pattern layer is respectively associated with the dielectric layer, the active device and the incident wave port. There are three external ports, and their scattering matrix can be expressed as:

[0058]

[0059] Where b = [b1, b4, b6] T The vector representing the normalized output waves of the three ports, a=[a1,a4,a6] T The vectors representing the normalized incident waves of the three ports. When acquiring the scattered electromagnetic response data of the pattern layer, the dielectric constant of the space between the metal patch and the output port is set to the dielectric constant of the dielectric layer, and the thickness of the dielectric layer is set to zero. Figure 3 The amplitude change curve of the scattering parameter S11 of the pattern layer under this simulation setting is shown, in which the dielectric constant has a regular effect on the scattering characteristics of the pattern layer, which is consistent with the design of the pre-incremental learning network in the next step.

[0060] Step 3: Train the pre-incremental learning network based on the pattern layer-scattered electromagnetic response dataset in step 2.

[0061] The pre-incremental learning network is responsible for the forward prediction of the scattered electromagnetic response of the pattern layer. In the first stage of network training, the network learns the regular influence of the dielectric constant of the medium layer on the scattered electromagnetic response of the pattern layer; in the second stage of network training, the network learns the joint influence of the pattern and dielectric constant on the scattered electromagnetic response of the pattern layer, and realizes the prediction of the scattered electromagnetic response of the pattern layer. Figure 4 As shown in the figure, after the 50-bit pattern layer 01 encoding input, three 100-dimensional deconvolution layers are set up to collect information from the pattern layer. The information from the 300-dimensional deconvolution layer and the 20-bit binary code converted from the dielectric constant together form the input to the subsequent fully connected layer. The fully connected layers are 600-dimensional, 900-dimensional, and 1200-dimensional, respectively. Batch normalization is performed after each deconvolution and fully connected layer, and the final output is two sets of 701-dimensional real and imaginary curves of the scattered electromagnetic response. LeakyReLU is used as the activation function:

[0062]

[0063] The mean square error between the simulation curve and the prediction curve is used as the loss function.

[0064]

[0065] Among them, f P_i and f S_i Represents the i-th sampling point of the scattered electromagnetic response prediction curve and the simulation curve respectively. The final loss of the pre-incremental learning network is the sum of the mean square error of the real part curve and the mean square error of the imaginary part curve with the same weight, which is defined as:

[0066] Final_Loss=0.5*L re +0.5*L im (7)

[0067] Among them, L re and L im Representing the independent losses of the two outputs, respectively. The pre-incremental learning network consists of two training steps: first, pre-training is performed using a 2000×10 dataset, encompassing all dielectric constants in the F4B substrate range of 2 to 3, to learn the effect of dielectric constant on the electromagnetic response of the patterned layer. The second training step consists of the dataset from the first step, augmented with 8,000 different patterns, for a total of 50,000 datasets of patterned layers and scattered electromagnetic responses. After the first training step, the neural network parameters are fixed, and training continues using the full 50,000 datasets to learn the connection between the patterned layer and the scattered electromagnetic response. The two training steps last for 50 and 100 epochs, respectively.

[0068] Step 4: Two-step scattering matrix cascade calculation to obtain the electromagnetic response of the metasurface unit.

[0069] Based on multi-port microwave network theory and the pre-incremental learning network trained in step 3, a two-step scattering matrix cascade calculation is used to obtain the electromagnetic response of the entire reconfigurable unit; the scattering matrix of the active device is replaced to obtain the multi-bit electromagnetic response of the reconfigurable metasurface unit; the scattering matrix of any split part in the separation design architecture is replaced to obtain the optimized electromagnetic response of the reconfigurable unit; without the need for time-consuming numerical simulation. According to step 1, the reconfigurable metasurface unit is split into four parts, and the sub-parts are regarded as distributed components in the microwave circuit. The transmission matrix of dielectric layer B can be expressed as:

[0070]

[0071] Where ω is the angular frequency, C0 is the speed of light, is the refractive index, h is the dielectric layer thickness, and η is the dielectric wave impedance. The scattering matrix of the active device C is obtained by the product company or by measurement. Since there is no direct connection between the dielectric layer B and the active device C, the electromagnetic response of the reconfigurable unit requires a two-step cascade calculation, as shown in Figure 5 First, use formula 9 to cascade the pattern layer A and the dielectric layer B:

[0072] S(f)=S pp (f)+S pc (Γ-S cc (f)) -1 S cp (f) (9)

[0073] Among them, S pp represents the scattering matrix between internal ports, S cc represents the scattering matrix between external ports, S pc represents the scattering matrix from the external port to the internal port, S cp represents the scattering matrix from the internal port to the external port. Based on the matrix cascade operation in the first step, the metal layer associated with the dielectric layer is short-circuited to calculate the two-port scattering matrix of the passive portion of the reconfigurable unit. This two-port scattering matrix of the passive portion is further cascaded with the scattering matrix of the active device C to calculate the overall electromagnetic response of the reconfigurable unit. By replacing the scattering matrix of the active device C, the multi-bit electromagnetic response of the unit can be obtained without the need for a second simulation.

[0074] Step 5: Optimize the reconfigurable metasurface units using the discrete-continuous particle swarm optimization algorithm.

[0075] The coordinates of the control points, the dielectric constant and thickness of the dielectric layer, and the number of active devices are used as inputs to the continuous-discrete particle swarm optimization algorithm. The optimal design of the reconfigurable metasurface unit is achieved by updating the velocity and coordinates of the particles. Based on the conventional particle swarm optimization algorithm, a one-step discrete coordinate processing operation is introduced, namely

[0076]

[0077] Among them, X k+1 represents the updated discrete coordinates, X k represents the updated coordinates after non-discretization, X variable represents all possible values ​​of a discrete variable. Compare X k With X variable The mean square error of all values ​​in X k+1 The nearest discrete variable value is located, thereby updating and optimizing the discrete variable. By completing the above steps, the target unit can be quickly designed.

[0078] The following are specific implementation cases:

[0079] The design objectives are a 1-bit phase-controlled metasurface unit operating in the 9-15 GHz frequency band and a 3-bit phase-controlled metasurface unit operating in the 4-5 GHz frequency band. The initial population consists of 500 particles, each containing the coordinates of the control points, the thickness and dielectric constant of the dielectric layer, and the number of active devices. The number of optimization iterations is set to 50. After the initial particles are generated, the control point coordinates are first transformed into a continuous pattern using a non-uniform rational topology representation. Together with the dielectric constant of the dielectric layer in the particles, the pattern layer is formed. The electromagnetic scattering response matrix of the pattern layer is predicted using a trained pre-incremental learning network, while the electromagnetic scattering matrix of the dielectric layer is calculated according to Equation 8. The three-port scattering matrix of the cascaded pattern layer and dielectric layer is then calculated using Equation 9. The metal layer is short-circuited to convert it into a two-port scattering matrix of the passive component. Furthermore, this two-port matrix of the passive component is cascaded with the two-port matrix of the active device to obtain the electromagnetic response of the entire metasurface unit, enabling replacement of numerical simulations. The electromagnetic response of all particles in the initial population is calculated and evaluated using a fitness function. The initial velocity of random particles is then updated and the position of particles is iteratively updated. The above steps are repeated in the subsequent iteration process to finally achieve the optimal design of the target unit.

[0080] Under the requirements of the first design goal, the fitness function is:

[0081] Fitness=-I / M (11)

[0082]

[0083] Where M is the total number of frequency points sampled at 200MHz intervals in the range of 9-15GHz. If the condition is met, the indicator function χ{condition} is 1, otherwise it is 0. Where I represents the total number of frequency points that meet the condition, where f i represents the i-th frequency point, and a represent the phase and amplitude respectively when the unit S11 is in the “on” state. and a0 represent the phase and amplitude of S11 in the “off” state, respectively. The final designed unit uses MADP-000907-14020x as the load and achieves 9-15GHz 1-Bit phase control. The fitness curve of the optimization process is shown in Figure 6 shown. Figure 7 The predicted and simulated results for the medium cell agree well, strongly validating the designed cell and our paradigm. The device performs well even compared to handcrafted devices, achieving a rapid design in just 8 hours, significantly reducing the time cost compared to manual or general optimization.

[0084] Under the requirements of the second design goal, the fitness function is:

[0085]

[0086] Different voltages allow for continuous variation of the reverse bias junction capacitance of the varactor, and the active device is designated SMV1405-040lf. and a are the phase and amplitude of S11 under -30V voltage load, respectively. and a0 represent the phase and amplitude of S11 in the “off” state, respectively. Consistent with the design process of the 1-bit phase modulation unit, the optimal unit achieves 3-bit phase modulation in the range of 4.06-4.38GHz. The optimization curve is shown in Figure 8 shown. Figure 9 The 8-bit electromagnetic response of the designed cell is demonstrated.

[0087] In summary, the reconfigurable metasurface unit optimization design method of the present invention is a very fast, effective and low-cost design method. The effectiveness of this optimization method has been strongly demonstrated from full-wave simulation and physical testing, and it has great practical significance for the research on the rapid design of metasurface units.

[0088] It is understood that the present invention is described through some embodiments, and those skilled in the art will appreciate that various changes or equivalent substitutions may be made to these features and embodiments without departing from the spirit and scope of the present invention, including but not limited to multi-layer, multi-polarization, and transmissive metasurface units. In addition, under the guidance of the present invention, these features and embodiments may be modified to adapt to specific design goals without departing from the spirit and scope of the present invention. Therefore, the present invention is not limited to the specific embodiments disclosed herein, and all embodiments that fall within the scope of the claims of this application fall within the scope of protection of the present invention.

Claims

1. A low-cost reconfigurable metasurface design method with a new topology, characterized by: The steps include: Step 1: Establish a reconfigurable metasurface unit separation design architecture, splitting the reconfigurable metasurface unit into a surface pattern layer, a dielectric layer, a metal layer, and an active device; the surface pattern layer is a three-port component, connecting the dielectric layer, the active device, and the incident wave port respectively; the dielectric layer is connected to the metal layer; Step 2: Generate multiple sets of control points in the surface pattern layer area, and generate a non-uniform rational B-spline curve according to the non-uniform rational B-spline formula; discretize the generated curve into integer sampling coordinate points, and map the generated curve to the surface pattern layer area; Generate the electromagnetic response curve of the surface pattern layer and make a pattern layer-scattered electromagnetic response data set; the specific steps include: generating n groups of control points B i , i=1,…,n, the coordinates of a single control point are (x i ,y i ), the corresponding weight is R i ; According to the non-uniform rational B-spline formula: Generate continuous curve, basis function N i,m (K) is expressed as: Among them, K defines the nodes in the non-uniform rational B-spline curve, K={K1,K2,…,K P }, m represents the order of the curve, p = n + m + 1; the generated curve is discretized into integer sampling coordinate points and mapped to the surface pattern area of ​​the metasurface according to 01 coding to achieve the generation of continuous metal patterns; Step 3: Train a pre-incremental learning network based on the pattern layer-scattered electromagnetic response dataset. In the first phase of network training, the network learns the regular influence of the dielectric constant of the dielectric layer on the scattered electromagnetic response of the pattern layer. In the second phase of network training, the network learns the combined influence of the pattern and dielectric constant on the scattered electromagnetic response of the pattern layer, thereby achieving prediction of the scattered electromagnetic response of the pattern layer. Step 4: Based on multi-port microwave network theory and the trained pre-incremental learning network, a two-step scattering matrix cascade calculation is used to obtain the electromagnetic response of the entire reconfigurable unit. The scattering matrix of the active device is replaced to obtain the multi-bit electromagnetic response of the reconfigurable metasurface unit. The scattering matrix of any split part in the separation design architecture is replaced to obtain the electromagnetic response of the optimized reconfigurable unit. Step 5: The coordinates of the control points, the dielectric constant and thickness of the dielectric layer, and the number of active devices are used as inputs to the continuous-discrete particle swarm optimization algorithm. The optimal design of the reconfigurable metasurface unit is achieved by updating the velocity and coordinates of the particles.

2. A low-cost reconfigurable metasurface design method with a new topology according to claim 1, characterized in that: The surface pattern area mapped to the metasurface according to the 01 coding specifically includes: in the XY two-dimensional plane coordinate system, the metal pattern area (M, N) generated for the target, and the range of the control point coordinates is (M+1, N+1); the metal area is divided into H*J blocks, and the blocks passed by the generated non-uniform rational B-spline curve are marked as "1", indicating that the block space is a metal block; the blocks not passed are marked as "0", indicating that there is no metal block in the block space.

3. The method for designing a low-cost reconfigurable metasurface with a new topology according to claim 1, characterized in that: Among the n groups of control points, the starting point B1 represents the starting position of the non-uniform rational B-spline curve and the welding position of the active device, and its position coordinates are fixed; the other control points are randomly selected in the (M+1, N+1) area of ​​the pattern layer.

4. The method for designing a low-cost reconfigurable metasurface with a new topology according to claim 1, wherein: The scattering matrix of the surface pattern layer is expressed as: Among them, S *A (f) represents the scattering coefficient of the port, b = [b1, b4, b6] T The vector representing the normalized output waves of the three ports, a=[a1,a4,a6] T The vectors representing the normalized incident waves of the three ports; when obtaining the scattered electromagnetic response data of the pattern layer, the dielectric constant of the space between the metal patch and the output port is set to the dielectric constant of the dielectric layer, and the thickness of the dielectric layer is set to zero.

5. The method for designing a low-cost reconfigurable metasurface with a new topology according to claim 1, wherein: The pre-incremental learning network includes two training steps. The first training data set is 20,000 sets of electromagnetic response data sets consisting of 2,000 patterns and 10 sets of F4B substrates with all dielectric constants ranging from 2 to 3, to learn the influence of dielectric constant on the electromagnetic response of the pattern layer; the second training data set includes the data set of the first step, and is expanded with 8,000 different patterns, making a total of 50,000 sets of pattern layer-scattering electromagnetic response data sets; the pre-incremental learning network contains 50-bit pattern code and binary 20-bit dielectric constant input, which is sent to a 600-dimensional fully connected network layer through three identical 100-dimensional convolutional network layers in the same layer, and then passed through 900 and 1200-dimensional fully connected network layers respectively, and finally output is two sets of 702-dimensional real and imaginary scattering parameter curves.

6. A low-cost reconfigurable metasurface design method with a new topology according to claim 1, characterized in that: During the two-step training process of the pre-incremental learning network, the dielectric constant and the metal pattern generated by the non-uniform rational B-spline together constitute the surface pattern layer; the electromagnetic response data of the surface pattern layer is automatically collected through Python.

7. A low-cost reconfigurable metasurface design method with a new topology according to claim 1, characterized in that: The multi-port calculation in step 4 is divided into two steps; the first step is to combine the surface pattern layer and the dielectric layer as the passive part of the metasurface unit, where the surface pattern layer is a three-port scattering matrix and the dielectric layer is a two-port scattering matrix, and the electromagnetic response of the passive part is obtained through cascade calculation; the second step is to combine the passive part and the active device, where the passive part is a two-port scattering matrix and the active device is a two-port scattering matrix, and the overall response of the unit is obtained through cascade calculation; during the calculation process, the port scattering matrix of the active device can be replaced to realize the multi-bit electromagnetic response calculation of the reconfigurable metasurface unit.

8. A low-cost reconfigurable metasurface design method with a new topology according to claim 7, characterized in that: The transmission matrix of the dielectric layer is expressed as: Where ω is the angular frequency, C0 is the speed of light, is the refractive index, h is the dielectric layer thickness, and η is the dielectric wave impedance. The scattering matrix of the active device is obtained by the product company or by measurement. Since there is no direct connection between the dielectric layer and the active device, the electromagnetic response of the reconfigurable unit requires a two-step cascade calculation: first, the pattern layer and the dielectric layer are cascaded using the following formula: S(f)=S pp (f)+S pc (Γ-S cc (f)) -1 S cp (f) (6) Among them, S pp represents the scattering matrix between internal ports, S cc represents the scattering matrix between external ports, S pc represents the scattering matrix from the external port to the internal port, S cp Represents the scattering matrix from the internal port to the external port; based on the first step of matrix cascade operation, the metal layer associated with the dielectric layer is short-circuited to realize the calculation of the two-port scattering matrix of the passive part of the reconfigurable unit; the two-port scattering matrix of the passive part is further cascaded with the scattering matrix of the active device to realize the calculation of the overall electromagnetic response of the reconfigurable unit; by replacing the scattering matrix of the active device, the multi-bit electromagnetic response of the unit can be obtained without the need for secondary simulation.

9. A low-cost reconfigurable metasurface design method with a new topology according to claim 1, characterized in that: In step 5, the control points of the pattern layer are continuous variables, and the thickness and dielectric constant of the dielectric layer and the type of active device are discrete variables. When the particle position is updated, the discrete variables need to add an additional operation, that is, based on the current discrete variable position and the mean square error of each discrete point in the discrete variable list, the nearest discrete point is selected and replaced.

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