A design method and system for multi-frequency transparent metasurfaces based on backpropagation algorithm

Abstract

This invention relates to a design method and system for multi-frequency transparent metasurfaces based on a backpropagation algorithm. The method includes: S1, modeling the multi-frequency transparent metasurface structure as a cascaded transmission matrix; S2, calculating the theoretical S21 curve based on the cascaded transmission matrix; S3, calculating the loss function between the theoretical S21 curve and the desired transmission coefficient curve; if the loss function meets the convergence condition, proceed to S6; otherwise, proceed to step S4; S4, calculating the difference gradient based on the cascaded transmission matrix, and updating the design optimization parameters in reverse based on the difference gradient; S5, updating the theoretical S21 curve and returning to execute S3; S6, approximating the desired transmission coefficient curve with the theoretical S21 curve to obtain the optimal theoretical parameters, calculating the target S21 curve based on the optimal theoretical parameters, and obtaining the optimal design parameter value for each design optimization parameter based on the target S21 curve. Compared with existing technologies, the metasurface designed in this invention can achieve the dual functions of signal enhancement from outdoors to indoors and signal suppression from indoors to outdoors.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of electromagnetic metasurface structure design, and particularly to a multi-frequency transparent metasurface design method and system based on a back propagation algorithm. BACKGROUND

[0002] With the deployment and development of 5G and 6G wireless communication technology, high-speed and low-latency wireless connection has become a basic requirement for the operation of society. However, the high loss of electromagnetic signals by energy-saving glass such as Low-E glass widely used in modern buildings to improve energy utilization efficiency is increasingly prominent, which greatly deteriorates the signal coverage quality in indoor areas, forming a signal blind area. In addition, the problems of communication security and privacy protection are increasingly prominent. If the wireless signals generated indoors (such as Wi-Fi, Bluetooth, and mobile terminal signals) are not suppressed and leaked outward, they may be intercepted and analyzed by unscrupulous individuals, posing potential data security risks.

[0003] To solve the above problems, a transparent metasurface can be introduced to solve the problems of signal coverage and privacy protection. As a new two-dimensional artificial electromagnetic material, the transparent metasurface has the ability to flexibly regulate electromagnetic waves while maintaining optical transparency. Therefore, there is a need in current engineering practice for a transparent metasurface that can simultaneously achieve outdoor-to-indoor signal transmission enhancement and indoor-to-outdoor signal shielding. However, existing transparent metasurface design methods have significant limitations. In recent years, most research has only focused on the one-way transmission enhancement function of outdoor-to-indoor signals, lacking effective shielding function for indoor-to-outdoor signal leakage, thus failing to meet the dual needs of communication safety and privacy protection. Secondly, to achieve complex electromagnetic regulation functions, metasurfaces often require multi-layer structures; in the face of such multi-layer, multi-parameter complex structures, traditional design methods (such as parameter scanning) are inefficient and difficult to achieve transmission enhancement and shielding functions in multiple frequency bands simultaneously. Therefore, current research often introduces optimization algorithms or machine learning methods to assist metasurface design, such as Chinese Patent Application CN119623134A, which provides a design method for a multi-frequency transparent transmission type surface-pasting metasurface structure. The method uses a cascaded transmission matrix to represent the multi-layer structure of the metasurface and takes the theoretical optimal transmission coefficient as the target. Although the optimization algorithm is used to optimize the transmission signal enhancement design, there are still the following problems: 1) There are deficiencies in the optimization mechanism. The optimization process relies on the initial given structure parameters, and the design parameters of each dielectric layer and metal layer (such as dielectric constant, thickness, equivalent impedance, etc.) cannot be automatically obtained through the target transmission coefficient, limiting the design efficiency; 2) Only signal multi-frequency transmission enhancement is designed, without considering the indoor-to-outdoor signal shielding function, making it difficult to meet the practical application scenarios of communication safety and privacy protection. For example, Chinese Patent Application CN120277916A provides a fast design method for a transmission metasurface. This method achieves design by establishing a multi-port network model and optimizing the internal port load. However, this technology has the following problems: 1) Single function, only transmission enhancement can be achieved, without indoor-to-outdoor signal shielding capability; 2) Structure design is limited, only applicable to metal-dielectric single-layer structures, unable to design multi-layer metasurfaces, making it difficult to achieve complex multi-frequency and multi-function.

[0004] Therefore, providing a transparent metasurface design method that can achieve multi-frequency outdoor-to-indoor wireless communication and indoor-to-outdoor signal shielding is a technical problem to be solved. SUMMARY

[0005] The purpose of the present application is to overcome the defects of the prior art, and provide a multi-frequency transparent metasurface design method and system based on a back propagation algorithm, which constructs a multi-frequency transparent metasurface structure as a cascaded transmission matrix, introduces a back propagation algorithm by using the chain characteristic of the cascaded transmission matrix, reversely propagates the loss function gradient between the theoretical modeling and the expected target to each structure layer parameter, iteratively optimizes the design parameters of the dielectric constant, thickness of the dielectric layer and the equivalent inductance, capacitance of the metal layer, and thus realizes the design of signal transmission enhancement from outdoor to indoor and signal shielding from indoor to outdoor.

[0006] The purpose of the present application can be realized by the following technical solutions:

[0007] According to a first aspect of the present application, a multi-frequency transparent metasurface design method based on a back propagation algorithm is provided, comprising:

[0008] S1, modeling a multi-frequency transparent metasurface structure as a cascaded transmission matrix; the multi-frequency transparent metasurface structure comprises an invariable layer and an optimized design layer, the invariable layer is Low-E glass, and the optimized design layer is a metasurface; the metasurface comprises a plurality of dielectric layers and a plurality of metal layers; and when designing initially, a preset equivalent circuit model is constructed for each metal layer;

[0009] S2, calculating a theoretical S21 curve based on the cascaded transmission matrix;

[0010] S3, calculating a loss function of the theoretical S21 curve and an expected transmission coefficient curve, if the loss function meets a convergence condition, executing S6; if not, executing step S4;

[0011] S4, based on the chain multiplication characteristic of the cascaded transmission matrix, calculating a difference gradient of the loss function by using a chain derivation rule, reversely propagating the difference gradient to each layer design optimization parameter of the optimized design layer, and updating each layer design optimization parameter, the design optimization parameter comprising a metasurface dielectric layer parameter and a metal layer parameter;

[0012] S5, updating the theoretical S21 curve based on the updated design optimization parameter, and returning to execute S3 based on the updated theoretical S21 curve;

[0013] S6, approximating the theoretical S21 curve to the expected transmission coefficient curve, obtaining optimal theoretical parameters, calculating a target S21 curve based on the optimal theoretical parameters, taking the target S21 curve as an optimization target, taking each layer parameter of the optimized design layer as an optimization variable, and obtaining an optimal design parameter value of each design optimization parameter.

[0014] As a preferred technical solution, from the outdoor side to the indoor side, the Low-E glass includes a first glass layer, a second coating layer, a third vacuum layer, and a fourth glass layer; and for the metasurface, the metal layers are not directly adjacent to each other.

[0015] As a preferred technical solution, the method for constructing the cascaded transmission matrix is ​​as follows:

[0016] With the first Taking a layered dielectric structure as an example, the corresponding dielectric transport matrix is ​​as follows. The dielectric structure includes a first glass layer, a third vacuum layer, a fourth glass layer, and a dielectric layer:

[0017] ,

[0018] in, Indicates the first Layered dielectric structure transmission matrix; Indicates the first The thickness of the layered dielectric structure, in units of ; Indicates the first The relative permittivity of the layered dielectric structure; The wavelength of an electromagnetic wave is expressed in units of 100 nm. ; Represents the imaginary unit; Represents air wave impedance, in units of ;

[0019] For the The metallic structure has the following metal transport matrix, and the metallic structure includes a metasurface metallic layer and a second coating layer of Low-E glass:

[0020] ,

[0021] Among them, when the first When the metallic structure of the second coating layer is... This represents the sheet resistance of the second coating layer, in units of... , Indicates a dimensionless unit; when the first... The structure of the first layer of metal is When a metal layer is applied, then The equivalent circuit impedance of the metasurface is expressed in units of Ω. The equivalent circuit impedance is calculated based on the equivalent inductance and capacitance, where the unit of equivalent inductance is... The unit of equivalent capacitance is ;

[0022] The chain multiplication form of the cascaded transmission matrix constructed based on the aforementioned medium transmission matrix and metal transmission matrix is ​​as follows: , transformed into And there are or ,in, , ... The transmission matrix of each layer of the structure from the outdoor side to the indoor side is shown in sequence. The layers of the structure from the outdoor side to the indoor side are: the first glass layer, the second coating layer, the third vacuum layer, the fourth glass layer, and the metasurface structure layers. , , as well as This represents the overall equivalent network parameter obtained by multiplying all single-layer transmission matrices together; This represents the transmission matrix of the x-th layer structure; Indicates the total number of structural layers; This represents the transmission matrix of the nth layer structure.

[0023] As a preferred technical solution, the theoretical S21 curve is as follows:

[0024] ,

[0025] in, , , as well as This represents the overall equivalent network parameter obtained by multiplying all single-layer transmission matrices together; Represents air wave impedance, in units of .

[0026] As a preferred technical solution, the desired transmission coefficient curve includes multiple transmission enhancement frequency bands and multiple shielding frequency bands;

[0027] The loss function calculation method is as follows:

[0028] ,

[0029] in, This represents the value of the loss function; For the first The frequency of each frequency band, in units of ; Indicates the total number of frequency bands; Indicates the first The theoretical S21 value corresponding to the frequency of each frequency band; Indicates the first The expected transmission coefficient value corresponding to the frequency of each frequency band.

[0030] As a preferred technical solution, the chain-like differentiation rule is as follows:

[0031] Using the cascaded transmission matrix as a partial transmission matrix For example, this matrix and the aforementioned cascaded transmission matrix The relationship is:

[0032] ,

[0033] Then, during the backpropagation process, the design optimization parameters... Calculate the cascaded transmission matrix. For the transmission matrix about The gradient is then multiplied by the transfer matrix. right about The gradient is multiplied step by step along the reverse path of the multiplication chain until... right about The gradient;

[0034] in, Indicates the total number of structural layers; Indicates the layer number of the transmission matrix, and ; , , as well as Indicates the first Equivalent network parameters of the layer; Indicates the first Partial transmission matrix of the layer; , , as well as Indicates the first Equivalent network parameters of the layer; , , as well as Indicates the first Equivalent network parameters of the layer.

[0035] As a preferred technical solution, the method for calculating the difference gradient is as follows:

[0036] ,

[0037] in, This represents the value of the loss function; This represents the design optimization parameters of the m-th layer structure in the optimization design layer; For the first The frequency of each frequency band; Indicates the total number of frequency bands; Indicates the first The theoretical S21 value corresponding to the frequency of each frequency band; Indicates the first The expected transmission coefficient value corresponding to the frequency of each frequency band; This indicates that the matrix is ​​expanded into column vectors in column order; express Cascaded transmission matrix at a given frequency, and let ,have:

[0038] ,

[0039] Let m be the transmission matrix of the m-th layer; Denotes a constant matrix, and Indicates air wave impedance; express . conjugate.

[0040] As a preferred technical solution, the method for updating the design optimization parameters is as follows:

[0041] For the aforementioned dielectric layer, the design optimization parameters This includes dielectric constant and dielectric thickness; for the aforementioned metal layer, the design optimization parameters... Including the equivalent inductance and metasurface equivalent capacitance in the equivalent circuit model, the update takes the following form:

[0042] ,

[0043] in, Indicates design optimization parameters The learning rate; Represents the loss function Regarding design optimization parameters The difference gradient; This indicates the updated design optimization parameters.

[0044] As a preferred technical solution, the method for obtaining the optimal design parameter values ​​is as follows:

[0045] Based on the optimization objective and optimization variables, a quasi-Newton optimization algorithm is used to iteratively optimize the optimization variables in the full-wave electromagnetic simulation. After each optimization iteration, the transmission coefficient of the current optimization variable under the current value is calculated. If the deviation from the optimization target is less than a preset threshold, the iteration stops, and the current value of the optimization variable is taken as the optimal design parameter value.

[0046] According to a second aspect of the present invention, a multi-frequency transparent metasurface design system based on a backpropagation algorithm is provided for implementing the above-described method.

[0047] Compared with the prior art, the present application has the following beneficial effects:

[0048] 1) The present application models the multilayer glass-hyper surface structure as a transmission matrix chain, sets the desired transmission coefficient curves of multiple transmission enhancement frequency bands and multiple shielding frequency bands as optimization targets, constructs loss functions consistent with the targets for the transmission frequency bands and the shielding frequency bands respectively, introduces a back propagation algorithm based on the chain rule, back propagates the deviation gradient between the theoretical S21 curve and the desired transmission coefficient curve to the parameters of each structure layer, combines the multi-frequency point loss function and the negative gradient update strategy, to simultaneously realize transmission enhancement in the transmission frequency bands and transmission suppression in the shielding frequency bands. Specifically, in the transmission frequency bands, the desired S21 curve has a higher value at each frequency point, and the optimization aims to reduce the loss function value , so as to drive the actual S21 curve to approach the high-transmission target; in the shielding frequency bands, the desired S21 curve has a lower value at each frequency point, and the optimization target is also to reduce the loss function value , so as to drive the actual S21 curve to approach the shielding target, and through this strategy, the transmission coefficient in the transmission frequency bands can be optimized in the enhancement direction, and the transmission coefficient in the shielding frequency bands can be optimized in the shielding direction. Compared with the prior art which can only realize transmission enhancement optimization design, the method provided by the present application can realize impedance matching (i.e. transmission enhancement) and impedance mismatching (i.e. shielding effect) in specific frequency bands respectively, thereby realizing the dual functions of signal enhancement from outdoor to indoor and signal suppression from indoor to outdoor.

[0049] 2) The present application uses transmission matrix chain modeling to model each layer in the multi-frequency transparent hyper surface structure as an independent transmission matrix, and constructs the transmission matrix of the overall structure through cascading, and simultaneously utilizes the chain multiplication characteristics of the transmission matrix chain to back propagate the deviation between the theoretical performance index and the desired target to the design optimization parameters of each layer; based on the chain cascaded transmission matrix constructed, the chain derivation is performed, which can accurately calculate the contribution of each design optimization parameter in the multi-layer coupled structure to the loss function, thereby realizing directional and collaborative optimization of the dielectric constant, thickness of the dielectric layer and equivalent impedance parameters of the metal layer of the hyper surface, effectively overcoming the parameter optimization difficulty caused by the mutual coupling of the multi-layer structure in the traditional design, and effectively solving the optimization problem caused by the coupling of the multi-layer structure.

[0050] 3), The application is based on a preset equivalent circuit model, and the equivalent circuit model is an equivalent circuit model corresponding to an existing metasurface pattern. In the optimization process of designing and optimizing parameters, optimal theoretical parameters of inductance and capacitance in the equivalent circuit are obtained through a back propagation algorithm, and because the physical pattern of the metasurface has a certain mapping relationship with the equivalent circuit parameters, the optimal circuit parameter values after optimization can correspond to a type of geometric pattern structure that can be realized, thereby providing a clear optimization target for physical geometric pattern optimization in full-wave simulation, shortening the time required for design from performance expectation to a manufacturable metasurface, and improving the overall design efficiency. BRIEF DESCRIPTION OF DRAWINGS

[0051] Figure 1 A method flowchart of the application;

[0052] Figure 2 An unoptimized multi-frequency transparent metasurface structure in an embodiment of the application;

[0053] Figure 3 A circuit schematic diagram of metasurface modeling as a transmission matrix chain in an embodiment of the application;

[0054] Figure 4 A desired transmittance coefficient curve and an S21 curve of the optimized multi-frequency transparent metasurface structure in an embodiment of the application;

[0055] Figure 5 An initial design structure form schematic diagram of a ring of metal rings in an embodiment of the application;

[0056] Figure 6 An initial design structure form schematic diagram of two rings of metal rings in an embodiment of the application;

[0057] Figure 7 A theoretical S21 curve and a simulation S21 curve after optimization by the quasi-Newton algorithm in an embodiment of the application;

[0058] Figure 8 An optimized multi-frequency transparent metasurface structure in an embodiment of the application. DETAILED DESCRIPTION

[0059] The technical solutions in the embodiments of the application will be described clearly and completely below with reference to the drawings in the embodiments of the application. Obviously, the described embodiments are part of the embodiments of the application, rather than all the embodiments. Based on the embodiments in the application, all other embodiments obtained by those skilled in the art without creative labor should fall within the scope of protection of the application.

[0060] In order to solve the problems in the prior art, the present application provides a multi-frequency transparent metasurface design method based on a back propagation algorithm, and the flow of the method is as shown in Figure 1 , which comprises the following steps:

[0061] S1, model the multi-frequency transparent metasurface structure as a cascaded transmission matrix.

[0062] In this embodiment, the multi-frequency transparent metasurface structure as shown in Figure 2 needs to be optimized and designed. First, model the multi-frequency transparent metasurface structure which has not been optimized in Figure 2 as a cascaded transmission matrix chain, which comprises, from the outdoor side to the indoor side, Low-E glass and a metasurface, a multi-layer dielectric layer and a multi-layer metal layer of the metasurface, and the metal layers are not directly adjacent to each other; and the specific layer structure is as follows: a first glass layer, a second coating layer, a third vacuum layer, a fourth glass layer, a fifth dielectric layer, a sixth metasurface metal layer, a seventh dielectric layer, an eighth metasurface metal layer, a ninth dielectric layer, a tenth metasurface metal layer and an eleventh dielectric layer. By modeling each layer as a transmission matrix, the complexity of the model is reduced.

[0063] In this embodiment, the Low-E glass is set as an unchangeable layer, and the structure parameters thereof remain fixed during the optimization process, and specifically include: the first glass layer is a dielectric structure, the thickness of the glass is , and the relative dielectric constant of the glass is 6.98; the second coating layer is a metallic structure, and the equivalent impedance ; the third vacuum layer is a dielectric structure, and the thickness of the vacuum layer is , and the relative dielectric constant is 1; the fourth glass layer is a dielectric structure, and the thickness thereof is .

[0064] The metasurface is set as an optimization design layer, and the design optimization parameters in the layer need to be iteratively optimized and updated, including: the dielectric constant , the dielectric thickness , the equivalent inductance of the metasurface , and the equivalent capacitance of the metasurface . And at the beginning of the design, a preset equivalent circuit model is constructed for each metal layer, and the preset equivalent circuit model should be the equivalent circuit model of the existing metasurface pattern, which is conducive to redesigning the circuit model as a metasurface pattern later. Specifically, the fifth dielectric layer is a dielectric structure, and the thickness thereof is set as , and the relative dielectric constant is ; the sixth metasurface metal layer is a metallic structure, and at the beginning, the equivalent circuit thereof is set as a series connection of an inductance and a capacitance , and then the series connection is connected in parallel with another inductance Composition; the seventh layer is a dielectric layer, which is a dielectric structure, and its thickness is set to be... The relative permittivity is The eighth metasurface metal layer is a metallic structure, and its equivalent circuit is initially set to consist of an inductor. With a capacitor After being connected in series, it is then connected in parallel with another inductor. Composition; the ninth dielectric layer, a dielectric structure, with a thickness of The relative permittivity is The tenth metasurface metal layer is a metallic structure, and its equivalent circuit is initially set to be an inductor. With a capacitor The structure is connected in series; the eleventh dielectric layer has a thickness of The relative permittivity is .

[0065] The transfer matrix is ​​constructed separately for each dielectric and metallic structure, and the detailed steps include:

[0066] With the first Taking a layered dielectric structure as an example, as mentioned above, a dielectric structure includes a first glass layer, a third vacuum layer, a fourth glass layer, and all the dielectric layers of the metasurface. The corresponding dielectric transport matrix is ​​as follows:

[0067] ,

[0068] in, Indicates the first Layered dielectric structure transmission matrix; Indicates the first The thickness of the layered dielectric structure, in units of ; Indicates the first The relative permittivity of the layered dielectric structure; The wavelength of an electromagnetic wave is expressed in units of 100 nm. ; Represents the imaginary unit; Represents air wave impedance, in units of The value is ;and .

[0069] For the The structure exhibits metallic properties, and as mentioned earlier, it includes a metasurface metallic layer and a second coating layer of Low-E glass. The corresponding metallic transport matrix is ​​as follows:

[0070] ,

[0071] Among them, when the first when the layer metallic property structure is the second coating layer, representing the sheet resistance of the second coating layer, unit is , representing the dimensionless unit; when the first layer metallic property structure is the first metallic layer, then representing the equivalent circuit impedance of the metasurface, unit is , and the equivalent circuit impedance is calculated based on the equivalent inductance and the equivalent capacitance, wherein the unit of the equivalent inductance is , and the unit of the equivalent capacitance is , and .

[0072] Finally, the chain multiplication form of the cascaded transmission matrix is constructed based on the dielectric transmission matrix and the metal transmission matrix: , and , and or , wherein, , , representing the transmission matrix of each layer structure from the outdoor side to the indoor side, and the layer structure from the outdoor side to the indoor side is: the first layer glass layer, the second layer coating layer, the third layer vacuum layer, the fourth layer glass layer and the metasurface structure layer in turn; , , and represent the overall equivalent network parameters obtained by multiplying all single-layer transmission matrices; representing the transmission matrix of the xth layer structure; representing the total number of structure layers; representing the transmission matrix of the nth layer structure. Finally, the modeling structure is shown in the equivalent circuit shown in Figure 3 .

[0073] S2, calculate the S21 curve based on the cascaded transmission matrix calculation theory.

[0074] Using the calculation relationship between the transmission matrix and the scattering matrix , the theoretical transmission coefficient theoretical S21 curve is:

[0075] ,

[0076] wherein, , , and represent the overall equivalent network parameters obtained by multiplying all single-layer transmission matrices; representing the air wave impedance, unit is ; , , as well as All of these represent scattering matrix parameters.

[0077] S3. Calculate the loss function between the theoretical S21 curve and the expected transmission coefficient curve. If the loss function meets the convergence condition, i.e. If the condition is met, proceed to step S6; otherwise, proceed to step S4.

[0078] In the method used in this invention, the desired transmission coefficient curve includes multiple transmission enhancement frequency bands and multiple shielding frequency bands. In this embodiment, the outdoor to indoor transmission enhancement frequency bands are selected as 5G-A / 6G communication frequency bands, namely 3.5GHz, 4.9GHz and 6.2GHz; the indoor to outdoor shielding frequency bands are selected as commonly used Wi-Fi operating frequency bands, namely 2.4GHz, 5.2GHz and 7GHz. The specific parameters of the desired transmission coefficient curves are shown in Table 1 and Table 2.

[0079] Table 1. Parameters of the expected transmission coefficient curve for the transmission frequency band.

[0080]

[0081] Table 2 Parameter Table of Expected Transmission Coefficient Curve for Shielded Frequency Bands

[0082]

[0083] The loss function calculation method provided by this invention is as follows:

[0084] ,

[0085] in, This represents the value of the loss function; For the first The frequency of each frequency band, in this embodiment ; Indicates the total number of frequency bands; Indicates the first The theoretical S21 value corresponding to the frequency of each frequency band; Indicates the first The expected transmission coefficient value corresponding to the frequency of each frequency band.

[0086] S4. Based on the chain multiplication property of the cascaded transfer matrix, the differential gradient of the loss function is calculated using the chain rule of differentiation. The differential gradient is then backpropagated to the design optimization parameters of each layer of the optimization design layer, and the design optimization parameters of each layer are updated. The design optimization parameters include the parameters of the metasurface dielectric layer and the parameters of the metal layer.

[0087] The implementation of this step is based on the chain multiplication characteristics of the transmission matrix chain, which is represented by the equivalent transmission matrix of the Low-E glass and the overall structure of the metasurface The transmission matrix of each sub-layer 、 、 is sequentially multiplied to form a fixed-order transmission matrix chain, which is Based on this structure, the gradient of the loss function with respect to any layer parameter can be calculated using the chain rule. Specifically, the chain rule is:

[0088] Taking part of the transmission matrix in the cascade transmission matrix as an example, the relationship between this matrix and the cascade transmission matrix is:

[0089] ,

[0090] Then, during the backpropagation process, the design optimization parameter is calculated as follows: the cascade transmission matrix is calculated based on the transmission matrix The gradient of is multiplied by the transmission matrix to obtain the gradient of The gradient of is multiplied by the transmission matrix to obtain the gradient of The gradient of .

[0091] wherein represents the total number of layers; represents the number of transmission matrix layers, and ; 、 、 and represent the equivalent network parameters of the first layer; represents the partial transmission matrix of the first layer; 、 、 and represent the equivalent network parameters of the first layer; 、 、 and represent the equivalent network parameters of the first layer. 、 、 and represent the equivalent network parameters of the first layer.

[0092] In this embodiment, the difference gradient and the gradient are calculated in the same way,

[0093] ,

[0094] Definition Then we have: ,

[0095] Thus we can get:

[0096] ,

[0097] Finally, according to the chain multiplication feature we can get:

[0098] ,

[0099] wherein, represents the loss function value; represents the design optimization parameter of the mth structure in the optimization design layer; is the frequency of the mth frequency band; represents the total number of frequency bands; represents the frequency of the mth frequency band; represents the theoretical S21 value corresponding to the frequency of the mth frequency band; represents the expected transmittance value corresponding to the frequency of the mth frequency band in the expected transmittance curve; represents the expected transmittance value corresponding to the frequency of the mth frequency band in the expected transmittance curve; represents the expansion of the matrix into a column vector in column priority order; represents the cascaded transmission matrix at the frequency, and let ,

[0100] ,

[0101] is the transmission matrix of the mth layer; represents a constant matrix, and represents the air wave impedance; represents the conjugate of

[0102] Through the above chain derivation process, the bias gradient is back-propagated to each layer parameter, so that the optimization process can effectively handle the multi-layer structure coupling problem,

[0103] In detail, in this step, the method for updating the design optimization parameter is: for the dielectric layer, the design optimization parameter includes the dielectric constant and the dielectric thickness; for the metal layer, the design optimization parameter includes the equivalent inductance in the equivalent circuit model and the equivalent capacitance of the metasurface, and the update form is:

[0104] , ​

[0105] in, Indicates design optimization parameters The learning rate; Represents the loss function Regarding design optimization parameters The difference gradient; This indicates the updated design optimization parameters.

[0106] Meanwhile, the actual design needs to be considered during the optimization process; therefore, the range of values ​​for the design optimization parameters in this embodiment is as follows: , , , .

[0107] Using this update strategy, the parameters are updated along the negative gradient direction of the loss function to gradually reduce the value of the loss function. Since this loss function incorporates the S21 characteristics of multiple frequencies, through the above iterative optimization, the actual S21 responses of multiple frequencies can continuously approach the desired target.

[0108] This loss is minimized by constructing loss functions consistent with the target for both the transparent and shielded frequency bands, and uniformly employing a strategy of updating along their negative gradient direction. In the transparent frequency band, it is desirable that the S21 curve has a high value at each frequency point; the optimization aims to reduce the value of the loss function. This drives the actual S21 curve to approximate the high-transmission target; in the shielded frequency band, it is desirable for the S21 curve to have a lower value at each frequency point, and optimization also aims to reduce the value of the loss function. This drives the actual S21 curve to approach the near-shielded target. Therefore, this optimization framework can simultaneously enhance the transmission coefficient in the transmittance frequency band and suppress the transmission coefficient in the shielded frequency band, satisfying the dual requirements of transmission and shielding over a wide frequency range.

[0109] S5. Update the theoretical S21 curve based on the updated design optimization parameters, and return to execute S3 based on the updated theoretical S21 curve.

[0110] Specifically, the updated design optimization parameters from step S4 are substituted into the theoretical S21 curve to achieve the update; steps S3 through S5 are repeated until the loss function meets the convergence condition. After optimization, from... Figure 4 As can be seen, the theoretical S21 curve approximates the desired transmission coefficient curve, with the black dots representing the desired transmission coefficient curve. This verifies the effectiveness of the proposed backpropagation algorithm in achieving complex multi-band responses. After optimization, the obtained parameters need to be selected within a practically feasible range to ultimately obtain a set of optimal theoretical parameters for each layer, including the thickness of each dielectric layer. Dielectric constant and the equivalent inductance of each metal layer and capacitor .

[0111] S6, the theoretical S21 curve is approximated to the desired transmittance coefficient curve, the optimal theoretical parameter is obtained, the target S21 curve is calculated based on the optimal theoretical parameter, the target S21 curve is taken as an optimization target, and each layer parameter of the optimization design layer is taken as an optimization variable to obtain an optimal design parameter value of each design optimization parameter.

[0112] Based on the optimization target and the optimization variable, in the full-wave electromagnetic simulation, the quasi-Newton optimization algorithm is used to iteratively optimize the optimization variable, and the transmittance coefficient of the current optimization variable under the current value is calculated after each optimization iteration The deviation of the optimization target (the deviation calculation method is the same as the difference gradient calculation method in the foregoing), if the deviation is less than a preset threshold Stop iteration, and take the current optimization variable value as the optimal design parameter value.

[0113] According to the different equivalent circuit models of each layer of the metasurface, the initial pattern structure of the metasurface is set to one circle or two circles.

[0114] For a single circle structure, as shown in Figure 5 , the circle is divided into eight independent metal segments (1a~8a), wherein the optimization parameters include the radius of the circle (unit: m), and the width of each metal segment (unit: m). For a double circle structure, as shown in Figure 6 , it is composed of two concentric circles, and the two circles are composed of an outer circle and an inner circle. The outer circle is divided into eight metal segments (1a~8a), and the inner circle is also divided into eight metal segments (1b~8b), wherein the optimization parameters include the radius of the circle and , and the width of each metal segment. Using these two basic pattern structures, the equivalent circuit structure required by the metasurface metal layer is realized.

[0115] The quasi-Newton optimization algorithm is used to dynamically adjust the radius of each circle, the width of each metal segment, and other geometric parameters, so that the transmittance coefficient obtained by simulation is consistent with the theoretical curve, as shown in Figure 7 , and the final metasurface structure that satisfies all design expectations is as shown in Figure 8 .

[0116] Specifically, Figure 8 , the structure diagram of the multi-frequency transparent metasurface structure designed and optimized by the present application is shown in Figure 2 . According to the foregoing description, Figure 8The structure shown is composed of two parts of an unchangeable layer and an optimization design layer, wherein: the unchangeable layer comprises, from the outdoor side to the indoor side, a first layer of glass layer, a second layer of film-coated layer, a third layer of vacuum layer, and a fourth layer of glass layer; the optimization design layer comprises, from the outdoor side to the indoor side, a fifth layer of dielectric layer, a sixth layer of metasurface metal layer, a seventh layer of dielectric layer, an eighth layer of metasurface metal layer, a ninth layer of dielectric layer, a tenth layer of metasurface metal layer, and an eleventh layer of dielectric layer. The optimization range of the embodiment is limited to the optimization design layer, the dielectric constant and the dielectric thickness parameters of the fifth layer, the seventh layer, the ninth layer and the eleventh layer of dielectric layer are optimized; for the sixth layer, the eighth layer and the tenth layer of metasurface metal layer, the metal layers in the embodiment all adopt double circular ring structure, and the radius parameters and the metal segment width parameters of the double circular rings of each layer are optimized. After optimization, as shown in the figure, Figure 8 As shown in the figure, the double circular ring radius and the metal segment width of the three layers of metasurface metal layer are designed differently, that is, the method provided by the application is implementable.

[0117] In addition, the application also provides a multi-frequency transparent metasurface design system based on a back propagation algorithm, which is used to realize the above-mentioned method, and those skilled in the art can clearly understand that, for the convenience and brevity of description, the specific working process of the described modules can refer to the corresponding process in the foregoing method embodiment, which will not be repeated here.

[0118] The above is only a specific embodiment of the application, but the protection scope of the application is not limited thereto, any person skilled in the art can easily think of various equivalent modifications or replacements within the technical range disclosed by the application, and these modifications or replacements should be covered in the protection scope of the application. Therefore, the protection scope of the application should be subject to the protection scope of the claims.

Claims

1. A method for designing a multi-frequency transparent metasurface based on a back propagation algorithm, characterized in that, The application relates to a system and a method for designing a multi-frequency transparent metasurface structure. The application comprises the following steps: S1, modeling the multi-frequency transparent metasurface structure as a cascaded transfer matrix; The multi-frequency transparent metasurface structure comprises an invariable layer and an optimized design layer, the invariable layer is Low-E glass, the optimized design layer is a metasurface, the metasurface comprises a plurality of dielectric layers and a plurality of metal layers, and a preset equivalent circuit model is constructed for each metal layer at the initial design stage; S2, calculating a theoretical S21 curve based on the cascaded transfer matrix; S3, calculating a loss function of the theoretical S21 curve and an expected transmittance coefficient curve, if the loss function meets a convergence condition, executing S6, and if the loss function does not meet the convergence condition, executing step S4; with the partial transmission matrix For example, the matrix has the following relationship with the cascade transmission matrix ​ ， then in the process of back propagation for design optimization parameters there are: calculating the cascade transfer matrix the transfer matrix about the gradient, multiply the transfer matrix about the gradient, multiply step by step according to the reverse path of the multiplication chain to about the gradient; wherein, total structure layer number; transfer matrix layer number, and ; , , , , and the equivalent network parameters of the first layer; the partial transfer matrix of the first layer; , , and the equivalent network parameters of the first layer; , , and the equivalent network parameters of the first layer; S4, calculating a differential gradient of the loss function by using a chain derivation method based on a chain multiplication characteristic of the cascaded transfer matrix, back-propagating the differential gradient to each layer of the optimized design layer to update design optimization parameters of each layer, the design optimization parameters comprising metasurface dielectric layer parameters and metal layer parameters, and the chain derivation method being: S5, updating the theoretical S21 curve based on the updated design optimization parameters, and returning to execute S3 based on the updated theoretical S21 curve; 2. The method of claim 1, wherein, S6, approximating the theoretical S21 curve to the expected transmittance coefficient curve to obtain optimal theoretical parameters, calculating a target S21 curve based on the optimal theoretical parameters, taking the target S21 curve as an optimization target, taking each layer parameter of the optimized design layer as an optimization variable, and obtaining an optimal design parameter value of each design optimization parameter.

3. The method of claim 1, wherein, From an outdoor side to an indoor side, the Low-E glass comprises a first glass layer, a second coating layer, a third vacuum layer and a fourth glass layer, and for the metasurface, the metal layers are not directly adjacent to each other. In the first embodiment, the first layer is a glass layer, the second layer is a vacuum layer, the third layer is a glass layer, and the fourth layer is a glass layer. For example, the medium transmission matrix of a medium structure including a first glass layer, a third vacuum layer, a fourth glass layer, and a medium layer is as follows: ， wherein, represents the first layer dielectric structure transmission matrix; represents the first layer dielectric structure thickness, in units of ; represents the first layer dielectric structure relative permittivity; represents the electromagnetic wave wavelength, in units of ; j represents the imaginary unit; represents the air wave impedance, in units of ; For the first The corresponding metal transfer matrix of the metallic property structure is as follows, and the metallic property structure comprises a super surface metal layer and a second coated layer of Low-E glass: ， wherein, when the first metal layer is the second metal layer, when the layer metal property structure is the second coating layer, represents the square resistance of the second coating layer, and the unit is , represents a dimensionless unit; when the first metal layer is the second metal layer, when the layer metal property structure is the first metal layer, represents the square resistance of the first metal layer, and the unit is represents the equivalent circuit impedance of the super surface, and the unit is , and the equivalent circuit impedance is calculated based on the equivalent inductance and the equivalent capacitance, wherein the unit of the equivalent inductance is , and the unit of the equivalent capacitance is ; Based on the medium transmission matrix and the metal transmission matrix, a chain multiplication form of the cascade transmission matrix is constructed as follows: , conversion is obtained , and has or , wherein , ,..., indicate the transmission matrix of each layer structure from the outdoor side to the indoor side, and the layer structures from the outdoor side to the indoor side are in turn: the first layer of glass layer, the second layer of coated layer, the third layer of vacuum layer, the fourth layer of glass layer, and the structure layer of metasurface; , , and indicate the overall equivalent network parameters obtained by multiplying all single-layer transmission matrices; indicates the transmission matrix of the xth layer structure; indicates the total number of structures; indicates the transmission matrix of the nth layer structure.

4. The method of claim 1, wherein, The method for constructing the cascaded transfer matrix is: ， wherein, , , and represent the overall equivalent network parameters obtained by multiplying all the single-layer transmission matrices; represents the air wave impedance, with units of .

5. The method of claim 1, wherein, The theoretical S21 curve is: The expected transmittance coefficient curve comprises a plurality of transmittance enhancement frequency bands and a plurality of shielding frequency bands; ， wherein, represents a loss function value; is the frequency of the th frequency band, in units of ; represents the total number of frequency bands; represents the theoretical S21 value corresponding to the frequency of the th frequency band; represents the expected transmission coefficient value corresponding to the frequency of the th frequency band.

6. The method of claim 1, wherein, The loss function calculation method is: ， in, This represents the value of the loss function; This represents the design optimization parameters of the m-th layer structure in the optimization design layer; For the first The frequency of each frequency band; Indicates the total number of frequency bands; Indicates the first The theoretical S21 value corresponding to the frequency of each frequency band; Indicates the first The expected transmission coefficient value corresponding to the frequency of each frequency band; This indicates that the matrix is ​​expanded into column vectors in column order; express Cascaded transmission matrix at a given frequency, and let ,have: ， the transmission matrix for the mth layer; denotes a constant matrix, and denotes the air wave impedance; denotes the conjugate of 7. The method of claim 1, wherein, The differential gradient calculation method is: For the dielectric layer, the design optimization parameters including the dielectric constant and the dielectric thickness; for the metal layer, the design optimization parameters including the equivalent inductance in the equivalent circuit model and the metasurface equivalent capacitance, the updated form is: ， wherein, denotes a learning rate of the design optimization parameter ; denotes a loss function ; denotes a difference gradient with respect to the design optimization parameter ; denotes an updated design optimization parameter.

8. The method of claim 1, wherein, The method for updating the design optimization parameters is: Based on the optimization target and the optimization variable, in the full-wave electromagnetic simulation, a quasi-Newton optimization algorithm is used to iteratively optimize the optimization variable, and the transmission coefficient of the current optimization variable at the current value is calculated after each optimization iteration The deviation from the optimization target, if the deviation is less than a preset threshold, the iteration is stopped, and the current optimization variable value is taken as the optimal design parameter value.

9. A multi-frequency transparent metasurface design system based on back propagation algorithm, characterized in that, The method for obtaining the optimal design parameter value is: The system is used for realizing the method as claimed in any one of claims 1-8.

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