Ultra-wideband frequency selective metasurface prediction method based on rapid prediction algorithm

Abstract

The invention relates to an ultra-wideband frequency selective metasurface prediction method based on a rapid prediction algorithm, and belongs to the technical field of electromagnetic engineering. Comprising the following steps: acquiring a single-layer S parameter; phase-amplitude relation modeling is carried out; and constructing a multi-layer structure and optimizing parameters. According to the prediction method provided by the invention, transmission coefficients of units under different unit parameters and different air layer thicknesses can be quickly calculated as long as S parameters of a single-layer structure are obtained; through the innovative technical means, hundreds of hours and even longer time needed by traditional full-wave simulation are greatly shortened to the level of several minutes, and therefore the time expenditure of the simulation process is remarkably reduced. By means of the improvement, the design iteration efficiency is greatly improved, clear structure adjustment guidance is provided for researchers, and resource waste and time loss caused by dependence on blind trial and error and repeated simulation in the past are avoided.

Description

Technical Field

[0001] This invention relates to a method for predicting metasurfaces, belonging to the field of electromagnetic engineering technology. Background Technology

[0002] In recent years, electromagnetic metamaterials and their two-dimensional forms, electromagnetic metasurfaces, have attracted widespread research interest in academic and engineering communities both domestically and internationally as artificial structures capable of flexibly controlling electromagnetic waves. Electromagnetic metamaterials generally refer to artificial composite electromagnetic media formed by arranging subwavelength-scale unit structures in a periodic or aperiodic manner in three-dimensional space; while electromagnetic metasurfaces are their two-dimensional counterparts, achieving precise manipulation of electromagnetic wavefronts and propagation characteristics by arranging subwavelength units on a two-dimensional plane. Compared to three-dimensional metamaterials, electromagnetic metasurfaces offer significant advantages such as relatively simple manufacturing processes, greater freedom in beam control, lower profile, and ease of integration and conformal design. Therefore, they exhibit broader applicability in practical applications and are currently widely used in various electromagnetic engineering fields, including antenna design, radar cross-section control, electromagnetic stealth, and novel lenses and imaging systems.

[0003] In the field of electromagnetic wave manipulation, metasurfaces can be classified into various types based on their mechanism of action on incident electromagnetic waves, including reflective, transmissive, and absorptive types. Transmissive metasurfaces, by controlling the phase of electromagnetic waves passing through their structure, can flexibly generate special beams—such as anomalous refraction beams, focused beams, vortex beams, and multi-beams—with low-profile, easily integrated structures that are difficult or require complex systems to achieve with traditional antennas or antenna arrays, achieving a good balance between cost and performance. Their engineering advantages have translated into a series of concrete applications, including low-profile high-gain antennas, dynamic beam scanning systems, control devices to enhance the capacity and coverage of next-generation wireless communication systems, and efficient directional wireless power transfer systems. When designing transmissive metasurfaces, transmission amplitude and transmission phase are two of the most critical performance parameters. High transmission amplitude means that more incident electromagnetic energy can effectively pass through the metasurface rather than be reflected or lost, which is crucial for ensuring the energy utilization efficiency of the entire system and reducing losses. Simultaneously, achieving precise and continuous control of the transmission phase within a 360° range is fundamental to obtaining sufficient design freedom. Only by achieving full phase coverage can arbitrary phase distributions be introduced in wavefront manipulation, thereby flexibly and accurately realizing a variety of complex electromagnetic functions such as beam deflection, focusing, shaping, and multiplexing.

[0004] Generally, based on design methods, transmissive metasurfaces can be broadly categorized into multilayer frequency-selective surfaces, Huygens metasurfaces, receiver-transmitter metasurfaces, and polarization-conversion metasurfaces. These types of transmissive surfaces can achieve 360° phase manipulation while maintaining high transmission amplitude. Among them, multilayer frequency-selective surfaces, also known as multilayer resonant metasurfaces, are one of the most effective and simplest forms of metasurfaces. However, multilayer frequency-selective surfaces have some limitations because the transmission phase and transmission amplitude of the multilayer planar conductor are highly bound, and the transmission amplitude is highly correlated with the electromagnetic structure of the planar conductor. Due to the resonant characteristics of the electromagnetic structure, the transmission amplitude of the metasurface changes drastically with the frequency of the incident wave, making it very difficult to maintain both high transmission amplitude and linear phase variation across a wide frequency band. Furthermore, the physical structure design of multilayer frequency-selective surfaces lacks effective theoretical guidance. Currently, the most commonly used method for designing unit structures is continuous modeling, simulation, and trial-and-error processes, which consumes a huge amount of time and effort from researchers. In addition, the equivalent circuit method is a commonly used method for designing metasurface units. It can convert the physical structure into a circuit structure to guide the improvement direction of the unit structure and predict the radiation performance of the unit. However, the equivalent circuit method requires extracting parasitic parameters from the physical structure and building circuit models based on various physical structures. When the physical model of a cell changes, the equivalent circuit needs to be reconstructed. If parameter scanning is performed on the cells, the accuracy of simulation prediction using the equivalent circuit method is difficult to guarantee. Furthermore, the accuracy of the equivalent circuit method depends on the order of the circuit model. Lower-order circuit models are easier to construct but have lower prediction accuracy, while higher-order circuit models have higher prediction accuracy but require more effort. Therefore, while the equivalent circuit method is suitable for guiding the design direction of physical structures, it cannot guarantee the accuracy and time consumption when directly predicting radiation parameters. Machine learning has also been applied to the design of metasurface units in recent years. For example, CN121122519A, entitled "Design Method of a Double-Layer Metasurface Absorber," discloses a method for discretizing the resistive film-air structure of a pixelated unit pattern layer into pixelated structure images, represented by 0-1 matrices. Multiple sets of 0-1 matrices are generated to construct pixelated units, and reflection coefficient curves are obtained. The target reflection coefficient curve and multiple sets of random noise are combined into vectors and input into a generator to generate multiple target pixelated structure images and obtain multiple target pixelated units. The design parameters of the resonant pattern layer are determined, and the target reflection coefficient curve is input into a DNN neural network to output the target design parameters and obtain the target regular topological pattern structure. The target pixelated units and the target regular topological pattern structure are combined to obtain the target double-layer metasurface absorber. This invention enables the rapid design of double-layer metasurface absorbers.However, it not only requires a long training process but also a large dataset for training. Currently, obtaining datasets can only rely on commercial electromagnetic software for simulation, and the machine learning process consumes massive amounts of GPU resources. Moreover, the applicability of machine learning methods is very limited. When any factor such as the target frequency, unit size, or unit thickness changes, the existing training results cannot be applied, and a new simulation and training process is required.

[0005] Therefore, there is an urgent need to propose a prediction method for ultra-wideband frequency-selective metasurfaces based on fast prediction algorithms to solve the above-mentioned technical problems. Summary of the Invention

[0006] To address the aforementioned problems, a prediction method for ultra-wideband frequency-selective metasurfaces based on a fast prediction algorithm is provided. A brief overview of the invention is given below to provide a basic understanding of certain aspects of the invention. It should be understood that this overview is not an exhaustive summary of the invention. It is not intended to identify key or essential parts of the invention, nor is it intended to limit the scope of the invention.

[0007] The technical solution of the present invention: A prediction method for ultra-wideband frequency-selective metasurfaces based on a fast prediction algorithm includes the following steps: Step 1: Obtaining S-parameters for a single layer; Step 2: Phase-amplitude relationship modeling; Step 3: Multi-layer structure construction and parameter optimization.

[0008] Furthermore: In step one, the S-parameters of the single-layer metasurface unit structure in the target frequency band are obtained by combining full-wave simulation and numerical calculation.

[0009] Furthermore: For any single-layer, periodic, all-metal metasurface unit, the S-parameters are calculated as follows: (1) (2) (3) in, and Represents the surface reflectance. and This represents the transmittance of the surface.

[0010] Furthermore, in step two, based on the extracted S-parameters of each metasurface unit and the S-parameters of the air layer, a theoretical relationship model between the transmission coefficient of the overall structure and the local structural parameters is established using the cascade equations of the multilayer electromagnetic structure.

[0011] Furthermore, the formula for the S-parameter of the air layer is as follows: (4) in, Let the wave number be in free space. The thickness of the air layer; The cascade equations for the multilayer electromagnetic structure are as follows: (5).

[0012] Furthermore: In step three, the metasurface unit is composed of three or more layers of metal electrical conductor patterns stacked together, with each metal structure printed on a dielectric substrate and the layers separated by air layers.

[0013] Furthermore, the S-parameters of the dielectric layer are as follows: (6) in: (7) In the formula, It is the relative permittivity of the dielectric substrate; the S-parameters of the metasurface metal layer, dielectric layer, and air layer are repeatedly substituted into the system cascade equations to iterate through the theoretical relationships between the overall structure's transmission coefficient and the single-layer metasurface unit structure, air layer thickness, and dielectric layer thickness in step two, in order to find a multilayer metasurface unit structure that can achieve high transmission amplitude, wide phase coverage, and wide bandwidth operation; the transmission response under different interlayer spacing and structural parameters is predicted by theoretical model, and the parameter combination with the largest phase modulation range and the best phase linearity under amplitude limitation is selected; the final selection results show.

[0014] Furthermore, it also includes step four: verification and array design.

[0015] Further: In step four, full-wave simulation verification is carried out on the optimized parameters to obtain a metasurface. This metasurface can achieve a transmission amplitude of not less than a specified threshold in the corresponding frequency band, and the transmission phase can be continuously controlled periodically. This metasurface is arranged in phase based on the generalized Snell's theorem. Several metasurface units are arranged according to the designed phase gradient to form a transmission array, which is used to realize the focusing of electromagnetic waves in a wide frequency band.

[0016] The present invention has the following beneficial effects: (1) Based on the actual electromagnetic properties and cascade equations of electric conductors in space, this invention can predict the radiation coefficient and Huygens resonant frequency of the cascaded electric conductors after broadband processing and calculation of the S-parameters of a single-layer electric conductor. This can provide a theoretical basis for the design of metasurface units and guide the design direction of metasurface units.

[0017] (2) The prediction method proposed in this invention has the same process for extracting S-parameters for different unit structures. It does not require the establishment of a separate model based on the specific electromagnetic physical structure. It has low complexity and is easy to implement.

[0018] (3) The prediction method proposed in this invention can quickly calculate the transmission coefficient of the unit under different unit parameters and different air layer thicknesses as long as the S-parameters of the single-layer structure are obtained. This invention shortens the calculation time of hundreds of hours or even longer that rely on full-wave simulation to a few minutes, which can greatly reduce the time spent on simulation and provide researchers with a direction for adjusting the unit structure, rather than blindly trying and repeating simulations. Attached Figure Description

[0019] Figure 1 This is a flowchart illustrating a specific embodiment of the present invention.

[0020] Figure 2 This is a schematic diagram of a single-layer metal metasurface layer under electromagnetic wave incidence.

[0021] Figure 3 This is a schematic diagram of a system in which electromagnetic waves are incident on a single-layer electrical conductor.

[0022] Figure 4 Diagram of the optimized three-layer metasurface unit structure Figure 5 This is a diagram of the metasurface array actually processed according to the present invention.

[0023] Figure 6 A comparison diagram of energy intensity at the focal point after beam focusing of the metasurface of the present invention.

[0024] The labels in the attached diagram are: Jerusalem cross-ring metasurface unit structure: P=20 mm, C=17 mm, L=10 mm, W=0.5 mm; incident wave at port 1. Port 2 incident wave Metasurface reflected waves Transmitted waves of metasurface . Detailed Implementation

[0025] To make the objectives, technical solutions, and advantages of this invention clearer, the invention is described below with reference to specific embodiments shown in the accompanying drawings. However, it should be understood that these descriptions are merely exemplary and not intended to limit the scope of the invention. Furthermore, descriptions of well-known structures and technologies are omitted in the following description to avoid unnecessarily obscuring the concept of the invention.

[0026] Specific implementation method one: Combining Figure 1-6This embodiment describes a prediction method for ultra-wideband frequency-selective metasurfaces based on a fast prediction algorithm. This method is used for predicting the performance of metasurface units based on S-parameter (scattering parameter) cascades, and includes the following steps: Step 1: Obtaining S-parameters for a single layer; Step 2: Phase-amplitude relationship modeling; Step 3: Multi-layer structure construction and parameter optimization; This invention presents a novel method for designing multilayer frequency-selective surfaces. First, based on the cascade equations of multilayer electrical conductors, we extend these equations to the frequency axis to predict the S-parameters of the cascaded electrical conductor units in space. This method can also predict the Huygens resonant frequency generated by the multilayer metasurface, and the prediction results are highly consistent with full-wave simulation results. Compared to traditional simulation-trial-and-error and machine learning processes, this method provides necessary theoretical guidance, making the construction of metasurface units no longer an unexplainable black box. In this invention, by obtaining a set of S-parameters of a single-layer electrical conductor through electromagnetic simulation, the radiation coefficient of multilayer metasurfaces with different air layer thicknesses and structures can be predicted. Only a small amount of full-wave simulation and numerical calculation is required to determine the... This invention addresses the issues of high complexity and low accuracy in equivalent circuit design methods by optimizing the spacing between unit layers, the optimal operating frequency band of the unit, and the optimal structural parameters of the unit. Furthermore, the full-wave simulation and numerical computation time required by this method is significantly lower than that of machine learning methods, maximizing the saving of GPU resources and time consumed during the design process. Through innovative technical means, this invention drastically reduces the hundreds of hours or even longer required for traditional full-wave simulation to the level of minutes, thereby significantly reducing the time cost of the simulation process. This improvement not only greatly enhances the efficiency of design iteration but also provides researchers with clear guidance for structural adjustments, avoiding the resource waste and time consumption caused by relying on blind trial and error and repeated simulations in the past.

[0027] Specific Implementation Method Two: Combining Figure 1-6 This embodiment describes a prediction method for ultra-wideband frequency-selective metasurfaces based on a fast prediction algorithm. In step one, the S-parameters of a single-layer metasurface unit structure within the target frequency band are obtained by combining full-wave simulation and numerical calculation. A symmetrical ultrathin planar metal structure is designed on a dielectric substrate. (See...) Figure 2 The substrate needs to be as thin as possible to minimize its impact on the calculation results; parameterization is performed by scanning all possible parameters of the designed single-layer structure through full-wave simulation.

[0028] Specific implementation method three: Combining Figure 1-6This embodiment describes a prediction method for ultra-wideband frequency-selective metasurfaces based on a fast prediction algorithm. In step one, each metasurface layer is an ultra-thin and symmetrical periodic metal patch, which can employ a Jerusalem cross-ring structure. The metal patch is placed on a substrate, which needs to be as thin as possible to minimize its impact on the calculation results. Figure 2 As shown; for any single-layer, periodic, all-metal metasurface unit, the S-parameter calculation formula is as follows: (1) (2) (3) in, and Represents the surface reflectance. and Represents the transmittance of the surface. e For natural index, j For imaginary numbers, the input-output relationship of spatial electromagnetic waves in the system is shown in the figure. Figure 3 The electromagnetic scattering model of a two-port network describes the transmission and reflection process of electromagnetic waves incident on a metasurface metal unit.

[0029] Specific implementation method four: Combination Figure 1-6 This embodiment describes the prediction method for ultra-wideband frequency-selective metasurfaces based on a fast prediction algorithm. In step two, based on the extracted S-parameters of each metasurface unit and the S-parameters of the air layer, a theoretical relationship model between the transmission coefficient of the overall structure and the local structural parameters is established using the cascade equations of the multilayer electromagnetic structure. Extract the values ​​of each frequency point under all structural parameter variations to generate a two-dimensional database indexed by frequency and structural parameters; evaluate whether the designed structure can cover the phase range of -90° to 90° at a given frequency; if the structure can cover most of the target phase range, proceed to the next step; otherwise, it indicates that its phase modulation capability is limited and the structure needs to be redesigned; perform three-dimensional numerical calculations using frequency, electrical conductor structural parameters, and air layer thickness as variables and cascade equations as calculation formulas; if different layer units use different air layer thicknesses or structural designs, more complex calculations are required.

[0030] Specific Implementation Method Five: Combining Figure 1-6 This embodiment describes the prediction method for ultra-wideband frequency-selective metasurfaces based on a fast prediction algorithm. In step two, the formula for the S-parameters of the air layer is as follows: (4) in, Let the wave number be in free space. The thickness of the air layer; The cascade equations for the multilayer electromagnetic structure are as follows: (5) in, The reflection coefficient of port 1, The transmission coefficient from port 2 to port 1, The transmission coefficient from port 1 to port 2, Let be the reflection coefficient of port 2, and a, c, and s be the identifiers on the corresponding structures.

[0031] Specific Implementation Method Six: Combination Figure 1-6 This embodiment describes the prediction method for ultra-wideband frequency-selective metasurfaces based on a fast prediction algorithm. In step three, the metasurface unit is composed of three or more layers of stacked metal conductor patterns, with each metal structure printed on a dielectric substrate and separated by air layers. The required parameter values ​​and frequency bands are determined using transmission amplitude limitation and transmission phase range as indicators. If the frequency band meets the design requirements, proceed to the next step; otherwise, the structure needs to be redesigned.

[0032] Specific implementation method seven: Combination Figure 1-6 This embodiment describes the prediction method for ultra-wideband frequency-selective metasurfaces based on a fast prediction algorithm. In step three, the S-parameters of the dielectric layer are as follows: (6) in: (7) In the formula, It is the relative permittivity of the dielectric substrate. It is the wavelength; by repeatedly substituting the S-parameters of the metasurface metal layer, dielectric layer, and air layer into the system cascade equations, the theoretical relationships between the overall structure's transmission coefficient and the single-layer metasurface unit structure, air layer thickness, and dielectric layer thickness in step two are calculated to quickly find multilayer metasurface unit structures that can achieve high transmission amplitude, wide phase coverage, and wide bandwidth operation; the transmission response under different interlayer spacings and structural parameters is predicted through theoretical models, and the best multilayer metasurface unit structures with high transmission amplitude, wide phase coverage, and wide bandwidth operation are selected. The parameter combination that maximizes the phase modulation range and achieves the optimal phase linearity under a 3dB amplitude limit; the optimized metasurface unit structure is shown below. Figure 4 .

[0033] Specific implementation method eight: Combination Figure 1-6 This embodiment describes a prediction method for ultra-wideband frequency-selective metasurfaces based on a fast prediction algorithm, which further includes step four: verification and array design.

[0034] Specific Implementation Method Nine: Combining Figure 1-6 This embodiment describes a prediction method for an ultra-wideband frequency-selective metasurface based on a fast prediction algorithm. In step four, full-wave simulation is performed on the optimized parameters to obtain the metasurface. This metasurface can achieve a transmission amplitude of not less than a specified threshold within the corresponding frequency band, and the transmission phase can be continuously controlled periodically. The phase arrangement of this metasurface is based on the generalized Snell's theorem, and several metasurface units are arranged according to the designed phase gradient to form a transmission array, which is used to focus electromagnetic waves in a wide frequency band. Full-wave simulation is performed on the selected unit structure to verify the accuracy of the calculation results. If there is a significant deviation between the calculation results and the simulation results, it is necessary to increase the air layer thickness or decrease the dielectric layer thickness. Specifically, the invention performs full-wave simulation verification on the optimized parameters, and the resulting metasurface achieves a transmission amplitude of not less than [value missing] within the operating frequency band. 3dB, and the transmission phase can be continuously adjusted to nearly 360°; based on the generalized Snell's theorem, the phase arrangement is designed, using 17×17 metasurface units arranged according to the designed phase gradient to form a transmission array, used to achieve electromagnetic wave focusing in a wide frequency band. The metasurface array arrangement is shown in the figure; experiments show that the metasurface array can achieve focusing of electromagnetic waves in the operating frequency band (e.g., 6000 GHz). Stable beam focusing can be achieved at 8 GHz, with the energy at the focal point increased by at least 9.8 dB compared to when there is no metasurface; the improvement effect is shown in Figure 6.

[0035] It should be noted that in the above embodiments, as long as the technical solutions are not contradictory, they can be permuted and combined. Those skilled in the art can exhaust all possibilities based on the mathematical knowledge of permutation and combination. Therefore, the present invention will not describe the technical solutions after permutation and combination one by one, but it should be understood that the technical solutions after permutation and combination have been disclosed by the present invention.

[0036] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A prediction method for ultra-wideband frequency-selective metasurfaces based on a fast prediction algorithm, characterized in that: Includes the following steps: Step 1: Obtaining S-parameters for a single layer; Step 2: Phase-amplitude relationship modeling; Step 3: Multi-layer structure construction and parameter optimization.

2. The prediction method for ultra-wideband frequency-selective metasurfaces based on a fast prediction algorithm according to claim 1, characterized in that: In step one, the S-parameters of the single-layer metasurface unit structure in the target frequency band are obtained by combining full-wave simulation and numerical calculation.

3. The prediction method for ultra-wideband frequency-selective metasurfaces based on a fast prediction algorithm according to claim 2, characterized in that: For any single-layer, periodic, all-metal metasurface unit, the S-parameters are calculated as follows: （1） （2） （3） in, and Represents the surface reflectance. and This represents the transmittance of the surface.

4. The prediction method for ultra-wideband frequency-selective metasurfaces based on a fast prediction algorithm according to claim 2, characterized in that: In step two, based on the extracted S-parameters of each metasurface unit and the S-parameters of the air layer, a theoretical relationship model between the transmission coefficient of the overall structure and the local structural parameters is established using the cascade equations of the multilayer electromagnetic structure.

5. The prediction method for ultra-wideband frequency-selective metasurfaces based on a fast prediction algorithm according to claim 4, characterized in that: The formula for the S-parameter of the air layer is as follows: （4） in, Let be the wave number in free space. The thickness of the air layer; The cascade equations for the multilayer electromagnetic structure are as follows: （5）。 6. The prediction method for ultra-wideband frequency-selective metasurfaces based on a fast prediction algorithm according to claim 4, characterized in that: In step three, the metasurface unit is composed of three or more layers of metal conductor patterns stacked together. Each metal structure is printed on a dielectric substrate, and the layers are separated by air layers.

7. The prediction method for ultra-wideband frequency-selective metasurfaces based on a fast prediction algorithm according to claim 6, characterized in that: The S-parameters of the dielectric layer are as follows: （6） in: （7） In the formula, It is the relative permittivity of the dielectric substrate; the S-parameters of the metasurface metal layer, dielectric layer, and air layer are repeatedly substituted into the system cascade equations to iterate through the theoretical relationships between the overall structure's transmission coefficient and the single-layer metasurface unit structure, air layer thickness, and dielectric layer thickness in step two, in order to find a multilayer metasurface unit structure that can achieve high transmission amplitude, wide phase coverage, and wide bandwidth operation; the transmission response under different interlayer spacing and structural parameters is predicted by theoretical model, and the parameter combination with the largest phase modulation range and the best phase linearity under amplitude limitation is selected; the final selection results show.

8. The prediction method for ultra-wideband frequency-selective metasurfaces based on a fast prediction algorithm according to any one of claims 1-7, characterized in that: It also includes step four: verification and array design.

9. The prediction method for ultra-wideband frequency-selective metasurfaces based on a fast prediction algorithm according to claim 8, characterized in that: In step four, full-wave simulation verification is carried out on the optimized parameters to obtain a metasurface. This metasurface can achieve a transmission amplitude of not less than a specified threshold in the corresponding frequency band, and the transmission phase can be continuously controlled periodically. This metasurface is arranged in phase based on the generalized Snell's theorem. Several metasurface units are arranged according to the designed phase gradient to form a transmission array, which is used to realize the focusing of electromagnetic waves in a wide frequency band.

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