Rare earth soft magnetic based ultra-wideband electromagnetic wave absorbing metamaterial and design method thereof

Abstract

The application discloses a rare earth soft magnetic based ultra-wideband electromagnetic wave absorbing metamaterial and a design method thereof, and belongs to the field of electromagnetic functional materials. The rare earth soft magnetic has low loss and planar anisotropy characteristics. The design method comprises the following steps: establishing an equivalent circuit model of a metal-insulator-metal resonator, quantifying the tuning effect of the real magnetic permeability and the real dielectric constant of the insulating layer on the localized surface plasmon resonance frequency; taking the rare earth soft magnetic as an insulating layer filler, adjusting the volume fraction to regulate the electromagnetic parameters of the composite material; designing a geometrically gradient stacked metamaterial unit, tuning the first-order resonance frequency to 2.00-9.00 GHz by scaling the resonator side length, covering high frequencies by using high-order modes, and overlapping multiple-order resonances in 2.00-18.00 GHz to form a continuous absorption spectrum; and optimizing the thickness of the insulating layer to realize wideband impedance matching. The method has predictability and universality, and can systematically design an ultra-wideband absorbing metamaterial covering S to Ku frequency bands.

Description

Technical Field

[0001] This invention belongs to the field of electromagnetic functional materials technology, specifically relating to an ultra-wideband electromagnetic wave absorbing metamaterial based on rare-earth soft magnets and its design method. Background Technology

[0002] Metal-insulator-metal (MIM) metamaterials, due to their unique localized surface plasmon resonance (LSPR) effect, can achieve strong absorption of electromagnetic waves by modulating periodic subwavelength structural units, making them an effective way to construct high-performance microwave absorbers.

[0003] However, the design of traditional metal-insulator-metal metamaterials faces the problem of limited tuning dimensions; existing technologies mainly rely on sharp absorption peaks generated by low-loss non-magnetic dielectrics, or the introduction of high-loss materials that possess a high imaginary part of complex permeability. m r ", Imaginary part of high complex permittivity e r Materials with low complex permittivity (MRP) or resistive films can be used to replace metals to achieve impedance matching and energy dissipation. For example, Chinese patent CN218101705U, "An Ultrawideband Optical Transparent Microwave Absorbing Device Based on Metasurface Structure," uses polyethylene terephthalate (PET) with a low imaginary part of complex permittivity as the insulating layer. It improves the microwave absorption rate of the device by designing metal patterns and adding resistive film patterns, operating in the 8.5~23.42 GHz frequency band, but fails to broaden the effective absorption to lower frequencies such as 2 GHz. Chinese patent CN118054222B, "An Ultralight Wide-Angle Absorbing Metamaterial Based on Inexpensive and Easily Available Carbon-Based Conductive Film for 2-18 GHz Full-Frequency Absorption and Its Manufacturing Method," uses polystyrene foam board with a low imaginary part of complex permittivity as the insulating layer. It achieves 2~18 GHz absorption by adjusting the conductivity of the carbon-based conductive film and iteratively optimizing the unit structure and the shape and size of the conductive film patch. It features GHz ultra-wideband absorption, but its core design lies in geometric design and resistance optimization of the high-loss conductive layer, rather than the effect of the material's electromagnetic parameters on impedance adjustment.

[0004] Existing designs utilizing soft magnetic materials, while taking advantage of the material's electromagnetic parameters to modulate impedance, are limited by the Snoek limit, meaning that soft magnetic materials cannot operate at higher frequencies while maintaining high permeability. This results in soft magnetic materials, already used in metamaterial absorber designs in the 2.00–18.00 GHz frequency band, having a high imaginary part of complex permeability. m r "and lower real permeability mr Therefore, many designs primarily use soft magnetic materials as loss sources, failing to fully utilize their permeability to tune the resonant frequency of local surface plasmon resonances in metal-insulator-metal metamaterials.

[0005] For example, in the 2021 issue of Optics Express, "Hybrid metamaterial absorber for ultra-low and dual-broadband absorption," Zhang C. et al. reported a metamaterial absorber that uses a graphene resistive film as a conductive layer, embeds polymethacrylimide foam, and uses a high-loss carbonyl iron-rubber soft magnetic material as a unit substrate to construct a multi-layer gradient structure, achieving ultra-wideband absorption in the 0.79 ~ 20.9 GHz and 25.1 ~ 40.0 GHz ranges (see Zhang C, et al. Optics Express, 2021, 29(9): 14078). However, this design requires strict control of the sheet resistance of different graphene resistive films, has high requirements for fabrication processes, and its performance is tied to the parameters of specific high-loss soft magnetic materials. Once the soft magnetic material is changed, a redesign is required, which lacks universality.

[0006] In 2021, Zhang J. et al. presented an iterative method for absorption performance based on a computer genetic algorithm in their paper "Genetic Algorithms to Automate the Design of Metasurfaces for Absorption Bandwidth Broadening" published in ACS Applied Materials & Interfaces. This method achieved broadband absorption of 4.5–18 GHz by iteratively optimizing the embedded coded metal patterns in a high-loss carbon-based iron / polyurethane magnetic substrate (see Zhang J, et al. ACS Appl. Mater. Interfaces, 2021, 13(6): 7792). However, this method is time-consuming and computationally resource-intensive.

[0007] In 2024, Liu J. et al. presented a design method in the *Journal of Materials Science & Technology*, titled "Cut-wire metasurface embedded in magnetic mediums for ultra-wideband polarization-insensitive absorber with environmental adaptability." This method involves embedding a pattern of resistive metal strips into a high-loss soft magnetic material, optimizing the effective absorption bandwidth to 2.9–18 GHz by precisely adjusting the resistance value (see Liu J, et al. J. Mater. Sci. Technol., 2024, 178: 162). The core of this design is based on precisely controlling the equivalent circuit of external passive components using defined material electromagnetic parameters, rather than directly tuning the local surface plasmon resonance frequency using the material's own electromagnetic parameters.

[0008] In recent years, 2:17 type rare earth alloys with planar magnetocrystalline anisotropy (such as Nd2Co) have been studied. 17 Y2Co 17 Pr2Fe 17 ) and its alloys doped with interstitial atoms (such as Sm 1.5 Y 0.5 Fe 15.5 Si 1.5 Y2Fe 16 SiN y This demonstrates the ability to push the Snoek limit. Such materials also exhibit high real permeability in the microwave band. m r ′, real permittivity e rThe extremely low imaginary part provides an ideal material platform for tuning the local surface plasmon resonance frequency by magnetic and electrical parameters under low-loss conditions (related material properties can be found in Chen N, et al. J. Alloys Compd., 2023, 947: 169554; Ma J, et al. Adv. Funct. Mater., 2024, 34(27): 2316715; Yuan M, et al. J. Mater. Sci.: Mater. Electron., 2021, 32(10): 13108; Yang W, et al. Acta Mater., 2018, 145:331; Lin Z, et al. Acta Mater., 2024, 264: 119575).

[0009] However, how to establish a precise and quantitative design model to incorporate the electromagnetic parameters of such materials, especially... m r 'and e r There is still a lack of clear and universal technical solutions for integrating '' as an independent variable into the metamaterial design process and systematically exciting and arranging multi-order local surface plasmon resonance modes to cover ultra-wideband frequencies.

[0010] In summary, the existing technology has not yet provided a method that can fully utilize the real permeability of low-loss soft magnetic materials. m r ′ and real permittivity e r As two independent yet coordinated tuning dimensions, and based on this, a quantifiable equivalent circuit model is established for systematic gradient structure design, in order to achieve a universal method covering ultra-wideband absorption of 2.00 ~ 18.00 GHz. Summary of the Invention

[0011] This invention aims to overcome the shortcomings of existing technologies and provide a design method for ultra-wideband microwave absorbing metamaterials based on rare-earth soft magnets. This invention is applicable to fields such as radar stealth, electromagnetic compatibility, and high-performance microwave anechoic chambers, where high requirements are placed on absorption bandwidth, incident angle stability, and design predictability.

[0012] To achieve the above objectives, the present invention provides the following technical solution:

[0013] The present invention proposes an ultra-wideband microwave absorbing metamaterial based on rare-earth soft magnets, comprising several metamaterial units arranged periodically along a two-dimensional plane. Each metamaterial unit includes multiple metal-insulator-metal layered resonators arranged in a geometric gradient on a continuous metal backplate. Each layered resonator has a square horizontal cross-section and a certain thickness. The layered resonator includes, from top to bottom, a square metal patch layer, an insulating layer, and another square metal patch layer, wherein the insulating layer is a composite material containing rare-earth soft magnets. The rare-earth soft magnets have a complex permeability ratio of less than 0.75 to less than 0.25 to less than 0.25 in the 2.00–18.00 GHz frequency band (complex permeability). Complex permittivity The rare earth soft magnet is selected from Ce2Fe. 17 N 3-δ 、Nd2Co 17 、Sm 1.5 Y 0.5 Fe 15.5 Si 1.5 Y2Co 17 Pr2Fe 17 Y2Fe 16 SiN y One or more of the following; the minimum side length of the plurality of layered resonators l min with the longest side length l max satisfy: l min / l max Between 0.2 and 0.4, and with the multi-order localized surface plasmon resonance modes of all layered resonators overlapping in the 2.00 to 18.00 GHz band, a continuous absorption spectrum with a reflection loss of less than -10 dB is formed.

[0014] According to a preferred embodiment of the present invention, the geometric gradient arrangement is preferably as follows: multiple metal-insulator-metal layered resonators are stacked vertically, and adjacent layered resonators share overlapping square metal patch layers to form a multilayer structure of metal-insulator-metal-insulator-…-insulator-metal; and the centers of each layered resonator are located on the same vertical line, and the side length difference between adjacent layered resonators is 1 mm to 2 mm.

[0015] More preferably, the plurality of layered resonators are stacked vertically to form a pyramid structure, with the side length of each layered resonator increasing from the top to the bottom, the top layer being the layered resonator with the smallest side length and the bottom layer being the layered resonator with the largest side length. Taking a single layered resonator as an example, the areas of the two square metal patch layers are different; for the aforementioned pyramid structure, the area of ​​the upper square metal patch layer is smaller than that of the lower one. The size of the insulating layer is the same as the size of the smaller square metal patch layer.

[0016] According to a preferred embodiment of the present invention, the composite material is composed of rare earth soft magnets and an insulating matrix; the volume fraction of rare earth soft magnets in the composite material is 7.5 vol% to 30.0 vol%; the insulating matrix is ​​selected from one or more of paraffin wax, epoxy resin or polyurethane.

[0017] According to a preferred embodiment of the present invention, the rare-earth soft magnet is Ce2Fe. 17 N 3-δ Furthermore, the electromagnetic parameters of the composite material in the range of 2.00 to 18.00 GHz satisfy... e r Between 6.12 and 7.70, e r " / e r < 0.07; m r The value is between 1.04 and 1.78. m r " / m r ′ < 0.67, where e r ′ is the real part of the complex permittivity of the composite material. e r "The imaginary part of the complex permittivity describes the dielectric loss." m r ′ represents the real part of the complex permeability of the composite material. m r "This is the imaginary part of the complex permeability that describes magnetic loss."

[0018] According to a preferred embodiment of the present invention, the thickness of the insulating layer of the layered resonator is... h The diameter ranges from 0.5 mm to 6.0 mm.

[0019] This invention also provides a method for designing the aforementioned ultrawideband microwave absorbing metamaterial based on rare-earth soft magnetism, which includes the following steps:

[0020] 1) Establish an equivalent circuit model for the metal-insulator-metal layered resonator: For the metal-insulator-metal layered resonator, its localized surface plasmon resonance excited in the microwave band is equivalent to a resistor-insulator-metal layered resonator. R ,inductance L ,capacitance C The RLC circuit consists of:

[0021] The inductor L Free electron kinetic energy inductor containing metal L k and the real permeability of the insulating layer m r Mutual Intuition of Contribution L ms ;

[0022] The capacitor C Includes the real dielectric constant of the insulating layer e r Contribution of parallel plate capacitance C cs ;

[0023] Will n The second-order localized surface plasmon resonance mode is equivalent to a 2-order localized surface plasmon resonance mode segmented along the antiparallel current directions of the upper and lower metal surfaces. n - One sub-resonator, and the contributions of metal ohmic loss, insulating layer magnetic loss and dielectric loss are quantified by the total impedance expression;

[0024] 2) Selection and control of rare-earth soft magnetic materials: Select materials that meet the following requirements within the 2.00 ~ 18.00 GHz frequency band. m r " / m r ′ < 0.75 and e r " / e r Low-loss, planar anisotropic rare-earth soft magnets with a dielectric constant < 0.25 were obtained. These were then combined with an insulating matrix, and the real permittivity of the composite material in the target frequency band was controlled by adjusting the volume fraction of the rare-earth soft magnets between 7.5 vol% and 30.0 vol%. e r ′ and real permeability m r ′;

[0025] 3) Achieving multi-order localized surface plasmon resonance coverage of the target spectrum based on geometric gradient structure: Based on the model described in step 1) and the material selected in step 2), a metamaterial unit composed of multiple metal-insulator-metal layered resonators with different side lengths arranged according to a geometric gradient is designed; by scaling the side length of the resonators... lThis allows the first-order localized surface plasmon resonance frequencies of resonators with different layered structures to be continuously distributed in the range of 2.00 GHz to 9.00 GHz, and utilizes higher-order localized surface plasmon resonance modes to cover even higher frequency bands; among which, the maximum side length l max The corresponding first-order resonant frequency is designed to be between 2.00 and 3.50 GHz, with a minimum side length of... l min The first-order resonance frequency is designed to be between 7.00 and 9.00 GHz, so that the multi-order localized surface plasmon resonance modes generated by all layered resonators are interleaved and overlapped in the frequency band of 2.00 to 18.00 GHz, forming a continuous absorption spectrum;

[0026] 4) Optimize impedance matching conditions: After fixing the geometric gradient structure in step 3), optimize the insulation layer thickness. h The metamaterial is made such that the real part of the normalized impedance in the 2.00 ~ 18.00 GHz band is between 0.6 and 1.7 and the imaginary part is between -0.6 and 0.6, so as to achieve a reflection loss of less than -10 dB, thus obtaining the ultra-wideband electromagnetic wave absorbing metamaterial.

[0027] Compared with the prior art, the present invention has the following beneficial effects:

[0028] (1) Ultra-wideband effective absorption is achieved; through the aforementioned systematic design, this invention can achieve metamaterials with an effective absorption bandwidth (RL < -10 dB) covering 2.00 ~ 18.00 GHz, fully covering the S, C, X, and Ku bands;

[0029] (2) It has wide incident angle stability; the metamaterial designed based on the method of this invention can still maintain an effective absorption bandwidth of more than 15.00 GHz when the incident angle of electromagnetic waves is as high as 40°.

[0030] (3) It has high design predictability and universality; the equivalent circuit model established by the present invention has clear physical meaning and can quantitatively predict the local surface plasmon resonance frequency.

[0031] (4) This invention proposes a physical mechanism for multi-order localized surface plasmon resonance based on the synergistic tuning of permeability and dielectric constant of low-loss rare-earth soft magnets; the real permeability of the insulating layer is... m r Increased to the real permittivity e r Equally important independent tuning dimensions;

[0032] (5) This invention provides a clear physical picture; it clarifies that the overlap of multi-order local surface plasmon resonance modes in the spectrum is the fundamental physical mechanism for realizing ultra-wideband absorption;

[0033] (6) The general design framework provided by this invention is applicable to a range of low-loss rare earth soft magnets. Attached Figure Description

[0034] Figure 1 This is a schematic diagram of the metamaterial unit and equivalent circuit in an embodiment of the present invention; the z-axis of the spatial rectangular coordinate system is the vertical direction, and the x and y-axis are parallel to the horizontal plane, which are also the lattice vector directions of the metamaterial unit with lattice periodic translational symmetry: (a) is the structure of a metamaterial unit composed of a single square metal-insulator-metal layered resonator; (b) is the equivalent RLC circuit corresponding to the unit in (a); (c) is an example of a metamaterial unit composed of various metal-insulator-metal layered resonators of different sizes stacked according to geometric gradient (taking a pyramid structure as an example); (d) is the equivalent parallel LC circuit corresponding to the stacked structure unit in (c).

[0035] Figure 2 This is a schematic diagram verifying the principle of localized surface plasmon resonance synergistically tuned by permeability and dielectric constant: (a) shows Ce2Fe with different volume fractions. 17 N 3-δ Complex permittivity of paraffin composites in the range of 2.00 ~ 18.00 GHz ( e r 'and e r ") and complex permeability ( m r 'and m r (b) is to adopt Figure 2 (a) shows the simulated reflection loss (RL) curves of a fixed-size metal-insulator-metal resonator when different composite materials are used as the insulating layer. (c) shows the normalized impedance of the resonator corresponding to (b). Z / Z (0) Curve, solid line is its real part, dashed line is its imaginary part; (d) Power loss density and magnetic field distribution of composite material resonators of different compositions at different orders of local surface plasmon resonance frequencies; (e) Local surface plasmon resonance frequency of metal-insulator-metal resonator with side length when material composition is fixed. l A comparison chart of the changing simulation results and the RLC model prediction results.

[0036] Figure 3 Based on Ce2Fe 17 N 3-δSimulation results of the geometric gradient structure metamaterial designed for materials: (a) shows the simulated reflection loss curves of the optimized pyramidal gradient structure metamaterial at different insulation layer thicknesses from 2.00 to 18.00 GHz; (b) shows the normalized impedance corresponding to the structure in (a). Z / Z 0 (real part) Z ′ and imaginary part Z (c) is a curve; (d) is a profile of the power loss density distribution within the metamaterial unit at the key local surface plasmon resonance frequency point.

[0037] Figure 4 It is Ce2Fe 17 N 3-δ Experimental verification results of the pyramid-shaped gradient structure metamaterial: (a) Comparison of measured reflection loss and simulation results of the prepared sample, with the lower left showing a schematic diagram of the incident angle of the arched antenna and the lower right showing the actual sample; (b) The sample under different electromagnetic wave incident angles ( i The measured reflection loss curve is shown below.

[0038] Figure 5 The simulated reflection loss diagrams were obtained after replacing the insulating layer in the pyramid-shaped gradient metamaterial with five other rare-earth soft magnetic materials. Detailed Implementation

[0039] The present invention will be further described below with reference to specific embodiments.

[0040] Example 1

[0041] This embodiment details the establishment of the equivalent circuit model, determination of key parameters, and verification process described in step one of this invention, and demonstrates how the design method described in this invention can be applied to complete a Ce2Fe with 15.0 vol% Ce2Fe 17 N 3-δ The entire process from design, simulation to experimental verification of an ultrawideband microwave absorbing metamaterial with (CFN) / paraffin composite material as the insulating layer and a geometric gradient structure.

[0042] Step 1: Establish an equivalent circuit model of the metal-insulator-metal structure.

[0043] (1) Model construction and parameter definition:

[0044] Consider a basic metamaterial unit composed of a square metal-insulator-metal layered resonant structure, the structure of which is as follows: Figure 1 As shown in (a), it contains a square copper patch (side length...) l ,thickness t ), insulating layer (with Ce2Fe) 17 N 3-δ Taking paraffin composites as an example, Ce2Fe17 N 3-δ Abbreviated as CFN, thickness h ) and continuous metallic backplate, metamaterial unit lattice period p Adhesive thickness h a A constant of 0.1 mm is used. To describe its local surface plasmon resonance, a model is established as follows: Figure 1 The lumped circuit shown in (b) is illustrated. The components in the model are defined as follows:

[0045] inductance L Including free electron kinetic energy inductance of metals Mutual inductance between upper and lower metal layers ;in e m 'and e m "The complex permittivity of metals as defined by the Drude model," d It is the skin depth of the metal. oh It is angular frequency. e 0 is the vacuum permittivity. m 0 represents the permeability of free space;

[0046] capacitance C Including capacitors on the upper and lower parallel plates. ; α The geometric fitting coefficients represent the non-uniform distribution of the electric field;

[0047] resistance R Including metal ohmic loss resistors Insulation layer magnetic loss resistance and dielectric loss resistance (when );

[0048] for n Localized surface plasmon resonance mode ( n (where the integer is positive), its equivalent circuit can be considered as divided along the current path (2). n - 1) A sub-resonator, whose total impedance is:

[0049] ;

[0050] Setting the imaginary part of the total impedance to zero, we obtain the resonance condition: ,in ;

[0051] Figure 1 In the diagram, (c) represents a geometrically gradient metamaterial unit composed of multiple resonators stacked together. Its resonance condition can be satisfied by any one of the resonators, and the entire unit can be used. Figure 1The parallel LC circuit with stacked structure shown in (d) represents the normalized imaginary part of the impedance of the resonators of each side length. Z 1 to Z 9 and air resistance Z air Matching. Geometric gradient structures can be... Figure 1 The pyramid-shaped stacking structure shown in (c) or other three-dimensional structures that can achieve a gradient arrangement of resonator side lengths.

[0052] (2) Validation of the model's predictions for electromagnetic parameter tuning:

[0053] To determine the geometric fitting coefficients representing the non-uniform distribution of the electric field α CFN powder was selected and combined with a paraffin matrix to prepare composite materials with volume fractions of 7.5 vol%, 15.0 vol%, and 30.0 vol%, and their electromagnetic parameters were measured. e r ′、 e r "、 m r ′、 m r "),like Figure 2 As shown in (a) in the figure.

[0054] Fixed resonator geometry parameters ( l = 14 mm, h = 2 mm, t = 0.08 mm, p = 15.5 mm), and the electromagnetic parameters of the above different composite materials were imported into the simulation model. Through analysis Figure 2 (b) The minimum point of reflection loss in the middle. Figure 2 The real maxima and imaginary zeros of the normalized impedance in (c) are used to extract its first-order impedance. n = 1), Second order (2nd order) n = 2) and third order, n = 3) Simulated resonance frequency of local surface plasmon resonance, and through Figure 2 The power loss density (PL) or magnetic field distribution map (|H|) in (d) confirms the mode order.

[0055] Then, the electromagnetic parameters of these materials ( m r ′, e r Substituting into the formula for the local surface plasmon resonance frequency The theoretical values ​​were calculated and linearly regressed to fit the simulated values. The fitting results show that the model can accurately predict the local surface plasmon resonance frequency as a function of the material's electromagnetic parameters (…). m r ′, e r The change of (′) determines the coefficient of determination R 2 The values ​​are greater than 0.91 (first order) and 0.85 (second order), respectively; the third-order resonance is not obvious here. The corresponding geometric fitting coefficients are obtained through fitting inversion. α The values ​​are 0.229 (first order) and 0.208 (second order), respectively, which quantifies the electromagnetic parameters of the material. m r ′, e r ′)The tuning effect on the local surface plasmon resonance frequency.

[0056] (3) Validation of model predictions for geometric parameter tuning

[0057] The insulating layer material is fixed as a 15.0 vol% CFN / paraffin composite material. The resonator side length... l The local surface plasmon resonance frequency was simulated and read as a variable, varying from 7 mm to 21 mm. An RLC equivalent circuit model was used to simulate the local surface plasmon resonance frequency (…). Figure 2 The model is fitted to the black hexagonal legend of the data points in (e), and the model prediction results are ( Figure 2 The red diamond-shaped plot of the data points in (e) in the diagram closely matches the pattern, and the coefficients of determination for the three patterns are highly consistent. R 2 They reached 0.994, 0.950, and 0.783 respectively, corresponding to α The values ​​were 0.206, 0.248, and 0.254, respectively. This verifies that the model is effective in predicting geometric parameters. l Effectiveness of local surface plasmon resonance frequency tuning.

[0058] Step 2: Select and adjust low-loss rare-earth soft magnetic materials

[0059] Based on the above model, a 15.0 vol% CFN / paraffin composite material was selected as the insulating layer. This material exhibits a real permeability of [missing value] in the 2.00–18.00 GHz frequency band. m r The real permittivity is between 1.04 and 1.78. e r The value is between 6.12 and 7.70, while the magnetic and electrical losses are relatively low. m r " / mr ′ < 0.67, e r " / e r (< 0.07), which meets the material requirements for low-loss magnetoelectric co-tuning.

[0060] Step 3: Implement multi-order LSPR coverage of the target spectrum based on geometric gradient structure

[0061] Based on the validated RLC model and the selected material (15.0 vol% CFN / paraffin), a geometric gradient structure was designed to cover the 2.00–18.00 GHz frequency band. The goal was to achieve a reasonable distribution of the first-order localized surface plasmon resonance frequencies of different resonators within the 2.00–9.00 GHz range. Through model calculations, a set of resonator side length values ​​was selected. l ={7.00, 8.75, 10.50, ..., 21.00} mm (a total of 9 values, forming an arithmetic sequence with a tolerance of 1.75 mm). These 9 resonators with different side lengths are stacked vertically in increasing order of side length (the z-direction is vertical), forming a pyramid-shaped gradient structure unit, as shown below. Figure 1 As shown in (c) of the diagram. The minimum side length of the top layer is... l min = 7.00 mm, maximum side length of the bottom layer l max = 21.00 mm, side length ratio l min / l max ≈ 0.33. (Setting) t = 0.08 mm, h a = 0.1 mm, setting the unit lattice period p = 22.5 mm (i.e.) l max + 1.5 mm, where 1.5 mm is the horizontal spacing of the bottom layer of the unit.

[0062] Step 4: Optimize geometry to achieve impedance matching

[0063] The pyramid structure was simulated to optimize the common thickness of each insulating layer. h Simulation results show that, Figure 3 As shown in (a) in the figure, when h Within the 2.0 mm to 6.0 mm range, the structure exhibits a reflection loss of less than -10 dB in the 2.00 ~ 18.00 GHz frequency band. (Selection...) h = 2.0 mm as the optimized value, such as Figure 3 As shown in (b) above, the normalized impedance of the structure at this time ( Z In most frequency bands, the real part is close to 1 and the imaginary part is close to 0, indicating that good broadband impedance matching has been achieved. Figure 3 As shown in (a) above, the optimized h The simulated reflection loss curve is 2.0 mm, with an effective absorption bandwidth of 16.00 GHz, and the curve has 12 resonance peaks. Figure 3 (c) in the paper reveals that the mechanism of ultrawideband absorption is one or more of the first-order, second-order, and third-order local surface plasmon resonances that overlap in the spectrum and couple in space.

[0064] Experimental verification:

[0065] Based on the above design, an 8 × 8 periodic array metamaterial sample with an area of ​​180 mm × 180 mm was prepared. Selected square copper patches and CFN / paraffin composite materials were bonded together to form a pyramid-structured metamaterial unit. Sixty-four essentially identical metamaterial units were then bonded to a 180 mm × 180 mm metal plate according to the unit lattice period, with a 1.5 mm spacing between the bottom layers of units, thus obtaining the metamaterial sample. Its reflection loss was measured in the 2.00–18.00 GHz frequency band using an arched frame testing system. Experimental results are as follows: Figure 4 As shown in (a), the measured effective absorption bandwidth (RL < -10 dB) is 2.10 ~ 18.00 GHz (15.90 GHz), which is basically consistent with the simulation results. Figure 4 As shown in (b), the sample at the electromagnetic wave incident angle ( i Even at a temperature as high as 40°, it can still maintain an effective absorption bandwidth of over 15.00 GHz.

[0066] Example 2

[0067] This embodiment aims to demonstrate that the design method proposed in this invention is also universally applicable to other rare-earth soft magnetic materials with low loss and high planar anisotropy.

[0068] (1) Selection of verification materials:

[0069] Taking a rare-earth soft magnetic material with low loss and high planar anisotropy that has been disclosed in the prior art as an example, Nd2Co... 17 For example, the electromagnetic parameters of its composite material in the 2.00 ~ 18.00 GHz frequency band satisfy: m r Between 0.8 and 1.4 m r " / m r< 0.25; e r Between 8.0 and 10.0 e r " / e r ′ < 0.15.

[0070] (2) Application of a unified design process:

[0071] For Nd2Co 17 The composite material was redesigned strictly following the four-step design method described in this invention:

[0072] Application of RLC equivalent circuit model: The same RLC model framework and geometric fitting coefficients as in Example 1 are adopted. α = 0.229), based on the electromagnetic parameters of this material, the first-order localized surface plasmon resonance frequency of its single resonator is predicted ( l =14 mm, h = 2 mm, t = 0.08 mm, p = 15.5 mm, h a = 0 mm);

[0073] Screening by characteristics: Confirm that the selected materials meet the low-loss condition. m r " / m r ′ < 0.75, e r " / e r < 0.25;

[0074] Tuned Localized Surface Plasmon Resonance: Based on RLC Equivalent Circuit Model and Material Target Frequency m r 'and e r ′, recalculate the resonator side length gradient sequence required to achieve a first-order localized surface plasmon resonance frequency coverage of 2.00 ~ 9.00 GHz (i.e., determine l max and l min Based on this, geometric gradient structure units are constructed, taking a pyramid-shaped gradient structure as an example. For example, based on Nd2Co... 17 This unit needs l max = 21 mm, l min = 7 mm; setting t= 0.08 mm, h a = 0 mm, p = l max + 1.5 mm.

[0075] Impedance optimization: Optionally, for each material's corresponding geometric gradient structure, optimize its insulating layer thickness. h To achieve optimal impedance matching. Based on Nd2Co 17 This unit h = 2.0 mm.

[0076] (3) Performance comparison and conclusion:

[0077] For Nd2Co-based 17 The absorption performance of the pyramid-shaped gradient structure metamaterial obtained by the composite material design was simulated and compared as follows: Figure 5 As shown, this metamaterial successfully achieved ultra-wideband absorption with an effective absorption bandwidth (RL < -10 dB) of 15.61 GHz.

[0078] Example 3

[0079] Select Sm 1.5 Y 0.5 Fe 15.5 Si 1.5 For example, the same design process as in Examples 1 and 2 is followed. Based on the electromagnetic parameters of its composite material in the 2.00 ~ 18.00 GHz frequency band ( m r Between 1.0 and 1.6, m r " / m r ′ < 0.50; e r Between 19.0 and 24.0 e r " / e r (where ′ < 0.20), apply the equivalent circuit model from step one (taking the geometric fit coefficients). α = (0.229) Recalculate.

[0080] To achieve a first-order LSPR frequency coverage of 2.00 ~ 9.00 GHz, the required resonator side length gradient sequence was determined, and a geometric gradient structure unit was constructed accordingly, taking a pyramid-shaped gradient structure as an example. The minimum side length of the top layer of this unit was calculated. l min = 5 mm, maximum side length of the bottom layer l max= 13 mm. Set the thickness of the metal patch. t = 0.08 mm, unit lattice period p = l max + 1.5 mm = 14.5 mm. The insulation layer thickness was determined through optimization. h = 2.0 mm.

[0081] Simulations were performed on the metamaterial designed based on this material, and the results are shown in [the table below]. Figure 5 Its effective absorption bandwidth (RL < -10 dB) is 15.79 GHz, successfully achieving ultra-wideband absorption.

[0082] Example 4

[0083] Select Y2Co 17 For example, the same design process as in Examples 1 and 2 is followed. Based on the electromagnetic parameters of its composite material in the 2.00~18.00 GHz frequency band (… m r Between 1.0 and 1.6, m r " / m r < 0.75; e r Between 8.0 and 9.0 e r " / e r (where ′ < 0.10), apply the equivalent circuit model from step one (taking the geometric fit coefficients). α = (0.229) Recalculate.

[0084] To achieve a first-order LSPR frequency coverage of 2.00 ~ 9.00 GHz, the required resonator side length gradient sequence was determined, and a geometric gradient structure unit was constructed accordingly, taking a pyramid-shaped gradient structure as an example. The minimum side length of the top layer of this unit was calculated. l min = 5 mm, maximum side length of the bottom layer l max = 19 mm. Set the thickness of the metal patch. t = 0.08 mm, unit lattice period p = l max + 1.5 mm = 20.5 mm. The insulation layer thickness was determined through optimization. h = 2.0 mm.

[0085] Simulations were performed on the metamaterial designed based on this material, and the results are shown in [the table below]. Figure 5Its effective absorption bandwidth (RL < -10 dB) is 16.00 GHz, successfully achieving ultra-wideband absorption.

[0086] Example 5

[0087] Select Pr2Fe 17 For example, the same design process as in Examples 1 and 2 is followed. Based on the electromagnetic parameters of its composite material in the 2.00~18.00 GHz frequency band (… m r Between 1.0 and 1.6, m r " / m r < 0.25; e r Between 13.0 and 18.0 e r " / e r (′ < 0.25), apply the equivalent circuit model from step one (taking the geometric fit coefficients). α = (0.229) Recalculate.

[0088] To achieve a first-order LSPR frequency coverage of 2.00 ~ 9.00 GHz, the required resonator side length gradient sequence was determined, and a geometric gradient structure unit was constructed accordingly, taking a pyramid-shaped gradient structure as an example. The minimum side length of the top layer of this unit was calculated. l min = 5 mm, maximum side length of the bottom layer l max = 15 mm. Set the thickness of the metal patch. t = 0.08 mm, unit lattice period p = l max + 1.5 mm = 16.5 mm. The insulation layer thickness was determined through optimization. h = 2.0 mm.

[0089] Simulations were performed on the metamaterial designed based on this material, and the results are shown in [the table below]. Figure 5 Its effective absorption bandwidth (RL < -10 dB) is 16.00 GHz, successfully achieving ultra-wideband absorption.

[0090] Example 6

[0091] Select Y2Fe 16 SiN y For example, the same design process as in Examples 1 and 2 is followed. Based on the electromagnetic parameters of its composite material in the 2.00~18.00 GHz frequency band (… mr Between 1.1 and 1.9, m r " / m r < 0.45; e r Between 13.0 and 15.0 e r " / e r (where ′ < 0.10), apply the equivalent circuit model from step one (taking the geometric fit coefficients). α = (0.229) Recalculate.

[0092] To achieve a first-order LSPR frequency coverage of 2.00 ~ 9.00 GHz, the required resonator side length gradient sequence was determined, and a geometric gradient structure unit was constructed accordingly, taking a pyramid-shaped gradient structure as an example. The minimum side length of the top layer of this unit was calculated. l min = 5 mm, maximum side length of the bottom layer l max = 14 mm. Set the thickness of the metal patch. t = 0.08 mm, unit lattice period p = l max + 1.5 mm = 15.5 mm. The insulation layer thickness was determined through optimization. h = 2.0 mm.

[0093] Simulations were performed on the metamaterial designed based on this material, and the results are shown in [the table below]. Figure 5 Its effective absorption bandwidth (RL < -10 dB) is 16.00 GHz, successfully achieving ultra-wideband absorption.

[0094] The embodiments described above are merely illustrative of several implementations of the present invention, and while the descriptions are specific and detailed, they should not be construed as limiting the scope of the present invention. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of the present invention, and these modifications and improvements all fall within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the appended claims.

Claims

1. A broadband electromagnetic wave absorbing metamaterial based on rare-earth soft magnetism, characterized in that, The device comprises several metamaterial units arranged periodically along a two-dimensional plane. Each metamaterial unit includes multiple metal-insulator-metal layered resonators arranged in a geometric gradient on a continuous metal backplate. Each layered resonator has a square horizontal cross-section and a certain thickness. The layered resonator includes, from top to bottom, a square metal patch layer, an insulating layer, and another square metal patch layer. The insulating layer is a composite material containing rare-earth soft magnets. The rare-earth soft magnets have a complex permeability ratio of less than 0.75 to less than 0.25 between 2.00 and 18.00 GHz, and the rare-earth soft magnets are selected from Ce₂Fe₂. 17 N 3-δ 、Nd2Co 17 、Sm 1.5 Y 0.5 Fe 15.5 Si 1.5 Y2Co 17 Pr2Fe 17 Y2Fe 16 SiN y One or more of the following; the minimum side length l of the plurality of layered resonators min With the maximum side length l max Satisfy: l min / l max Between 0.2 and 0.4, and the multi-order localized surface plasmon resonance modes of all layered resonators overlap in the 2.00 ~ 18.00 GHz frequency band, forming a continuous absorption spectrum with a reflection loss of less than -10 dB; The geometric gradient arrangement is as follows: multiple metal-insulator-metal layered resonators are stacked vertically, and adjacent layered resonators share overlapping square metal patch layers, and the centers of each layered resonator are located on the same vertical line, with the side length difference between adjacent layered resonators being 1 mm to 2 mm. The multiple layered resonators are stacked vertically to form a pyramid structure. The side length of each layered resonator increases from the top to the bottom, with the top layer being the layered resonator with the smallest side length and the bottom layer being the layered resonator with the largest side length.

2. The ultra-wideband electromagnetic wave absorbing metamaterial based on rare-earth soft magnetism according to claim 1, characterized in that, The composite material is composed of rare earth soft magnets and an insulating matrix; the volume fraction of rare earth soft magnets in the composite material is 7.5 vol% to 30.0 vol%; the insulating matrix is ​​selected from one or more of paraffin wax, epoxy resin or polyurethane.

3. The ultra-wideband electromagnetic wave absorbing metamaterial based on rare-earth soft magnetism according to claim 1, characterized in that, The rare earth soft magnetic material is Ce2Fe. 17 N 3-δ Furthermore, the electromagnetic parameters of the composite material in the range of 2.00 ~ 18.00 GHz satisfy ε. r ′ is between 6.12 and 7.70, ε r " / ε r ′ < 0.07; μ r μ' is between 1.04 and 1.

78. r " / μ r ′ < 0.67, where ε r ε' is the real part of the complex permittivity of the composite material, and ε' is the real part of the complex permittivity of the composite material. r "μ is the imaginary part of the complex permittivity describing dielectric loss." r ′ represents the real part of the complex permeability of the composite material, μ r "This is the imaginary part of the complex permeability that describes magnetic loss." 4. The ultra-wideband electromagnetic wave absorbing metamaterial based on rare-earth soft magnetism according to claim 1, characterized in that, The thickness h of the insulating layer of the layered resonator is from 0.5 mm to 6.0 mm.

5. A method for designing an ultra-wideband electromagnetic wave absorbing metamaterial based on rare-earth soft magnetism as described in claim 1, characterized in that, Includes the following steps: 1) Establishing an equivalent circuit model for the metal-insulator-metal layered resonator: For the metal-insulator-metal layered resonator, its localized surface plasmon resonance excited in the microwave band is equivalent to an RLC circuit composed of a resistor R, an inductor L, and a capacitor C, where: The inductor L comprises a metal free electron kinetic energy inductor L. k and the real permeability μ of the insulating layer r Mutual intuition of contribution L ms ; The capacitor C contains the real dielectric constant ε of the insulating layer. r The parallel plate capacitance component contributed by ′ cs ; The nth-order local surface plasmon resonance mode is equivalent to 2n-1 sub-resonators divided along the opposite parallel current directions of the upper and lower metal surfaces, and the contributions of metal ohmic loss, insulating layer magnetic loss and dielectric loss are quantified by the total impedance expression. 2) Selection and control of rare-earth soft magnetic materials: Select materials that meet the μ requirements within the 2.00 ~ 18.00 GHz frequency band. r " / μ r ′ < 0.75 and ε r " / ε r Low-loss, planar anisotropic rare-earth soft magnets with a density of ε' < 0.25 were obtained. These were then combined with an insulating matrix, and the real permittivity ε of the composite material in the target frequency band was controlled by adjusting the volume fraction of the rare-earth soft magnets between 7.5 vol% and 30.0 vol%. r ′ and real permeability μ r ′; 3) Achieving multi-order local surface plasmon resonance coverage of the target spectrum based on geometric gradient structure: Based on the model described in step 1) and the material selected in step 2), a metamaterial unit is designed, consisting of multiple metal-insulator-metal layered resonators with different side lengths arranged according to a geometric gradient. By scaling the side length l of the resonators, the first-order local surface plasmon resonance frequencies of different layered resonators are continuously distributed in the range of 2.00 GHz to 9.00 GHz, and higher-order local surface plasmon resonance modes are used to cover higher frequency bands; wherein, the maximum side length l max The corresponding first-order resonant frequency is designed to be between 2.00 and 3.50 GHz, with a minimum side length l. min The first-order resonance frequency is designed to be between 7.00 and 9.00 GHz, so that the multi-order localized surface plasmon resonance modes generated by all layered resonators are interleaved and overlapped in the frequency band of 2.00 to 18.00 GHz, forming a continuous absorption spectrum; 4) Optimize impedance matching conditions: After fixing the geometric gradient structure in step 3), optimize the insulation layer thickness h between 0.5 mm and 6.0 mm so that the real part of the normalized impedance of the metamaterial in the 2.00 ~ 18.00 GHz frequency band is between 0.6 and 1.7, and the imaginary part is between -0.6 and 0.6, so as to achieve a reflection loss of less than -10 dB, and obtain the ultra-wideband electromagnetic wave absorbing metamaterial.

6. The method according to claim 5, characterized in that, Includes the following steps: The mutual inductance L ms Through formula Calculate, where μ0 is the vacuum permeability and h is the thickness of the insulating layer; Capacitor C cs Through formula The calculations are performed, where ε0 is the vacuum permittivity, l is the side length of the square of the layered resonator, and α is the geometric fitting coefficient representing the non-uniform distribution of the electric field. Its value is determined by the resonant frequency obtained from fitting simulation and model calculation. The fitting determination coefficient R0 is... 2 Greater than 0.78; Total impedance Z tot (n) Represented as: ; Where n is a positive integer, R k R is a metal ohmic loss resistor. ms For the imaginary part μ of the complex permeability of the insulating layer r "Contributing resistance, ε is the imaginary part of the complex permittivity of the insulating layer. r "The resistance contributed, ω is the angular frequency." 7. The method according to claim 6, characterized in that, In step 1), the geometric fitting coefficient α is determined as follows: for the metal-insulator-metal geometry based on rare-earth soft magnetism, the simulated values ​​of its first-order, second-order, and third-order local surface plasmon resonance frequencies are obtained; the material parameter μ is... r ′, ε r Substituting the structural parameter l into the resonant frequency formula Calculate the theoretical value, fit the simulated value and the theoretical value through linear regression, and make the coefficient of determination R... 2 If the value is greater than 0.78, the corresponding α value is obtained, where the value of α ranges from 0.15 to 0.26.

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