CN112615165B - Multi-mode resistor-based multi-layer broadband metamaterial wave absorber and design method thereof - Google Patents
Multi-mode resistor-based multi-layer broadband metamaterial wave absorber and design method thereof Download PDFInfo
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Abstract
The invention belongs to the technical field of metamaterial wave absorption, and particularly relates to a multi-mode resistance-based multi-layer broadband metamaterial wave absorber and a design method thereof. The metamaterial wave absorber is an array formed by periodically extending wave absorber units along the x direction and the y direction, and the period is p; the wave absorbing body unit is formed by stacking a bottom metal floor and three wave absorbing layers-a dielectric plate; the wave absorbing layer is an ITO resistive film printed on the PET film; the top layer of the wave absorber unit is an annular sinuous line ITO structure, the middle layer of the wave absorber unit is a square patch structure, and the bottom layer of the wave absorber unit is a symmetrical four-trapezoid combined patch structure; two adjacent layers of PET films are separated by a dielectric plate; the bottom of the unit is a metal floor; the unit structure is centrosymmetric; the structural parameters of the wave absorber unit are determined through optimized design, so that the metamaterial wave absorber shows excellent broadband wave absorbing performance under excitation of TE and TM polarized waves, and has the characteristic of angle insensitivity under TM polarization; the thickness is less, simple structure, processing is convenient.
Description
Technical Field
The invention belongs to the technical field of metamaterial wave absorption, and particularly relates to a multi-mode resistance-based multi-layer broadband metamaterial wave absorber and a design method thereof.
Background
Modern war environments become more and more complicated, requirements on stealth performance and electromagnetic compatibility of weaponry on battlefields are increasingly improved, and the requirements of thinness, lightness, thinness and strength of traditional radar wave-absorbing materials are difficult to meet. With the development of science and technology, under the application scene of everything interconnection, the problems of multi-antenna interference, electromagnetic radiation, pollution and the like are also getting more serious. The metamaterial wave-absorbing technology can provide a solution for stealth technology and electromagnetic compatibility, can inhibit electromagnetic radiation pollution, and has wide application prospects in various fields such as energy collection, sensing and detection, communication and the like, so that the metamaterial wave-absorbing technology is widely concerned in military and civil fields, and the research of the metamaterial wave-absorbing technology has important strategic significance at home and abroad.
At first, the metamaterial wave absorber adopts a metal resonance working mechanism, although perfect wave absorption can be realized, the metamaterial wave absorber is not easy to popularize and apply due to narrow working frequency band. Although a lot of research attempts to expand the bandwidth by combining multiple units or stacking multiple metal resonant structures, the metal resonant bandwidth is limited, the expected effect cannot be achieved, and the size or thickness of the unit is often large, which is not easy to process. The Indium Tin Oxide (ITO) resistive film has the advantages of both resistance and thin thickness, has weak dispersion characteristic in microwave frequency band, and can effectively realize broadband wave absorption. At present, the wave absorption of the metamaterial mainly comprises the following methods of plane multi-size unit arrangement, vertical space multi-layer unit stacking, loading of lumped elements (such as resistors, capacitors and diodes), loading of resistive films, artificial surface plasmon based and the like, and the bandwidth can be expanded. In the design of the multilayer metamaterial wave absorber, the wave absorbing bandwidth, the absorption rate and the total thickness are three key indexes. It has heretofore been a challenge to achieve a wide bandwidth while maintaining a thin thickness at a high absorption rate. The invention adopts the idea of combining the multilayer structure with the wave absorption of the loading resistive film, and cascades a plurality of modes with complementary wave absorption characteristics, thereby realizing the effect of broadband absorption under thinner thickness.
Disclosure of Invention
The invention aims to provide a multi-layer broadband wave absorber based on multi-mode resistance and a design method thereof, and aims to solve the problem that the thickness is too thick when the multi-layer structure is used for realizing the broadband wave absorber.
The invention provides a multi-layer broadband wave absorber based on multi-mode resistance, which is an array formed by periodically extending wave absorber units along x and y directions, wherein the period is p; the wave absorbing body unit is formed by stacking a bottom metal floor and three pairs of wave absorbing layers-dielectric plates, and the structure of the wave absorbing body unit is shown in figure 1; the wave absorbing layer is an Indium Tin Oxide (ITO) resistance film with a certain structure printed on the continuous PET film; the three-layer ITO structure of unit from top to bottom is respectively: the top layer is an annular meander line ITO structure (1), the middle layer is a square patch structure (2), and the bottom layer is a symmetrical four-trapezoid combined patch structure (3); two adjacent layers of PET films (4) are separated by a dielectric plate (5); the bottom of the unit is a metal floor (6); the unit structure is centrosymmetric.
In the invention, the annular serpentine line of the top layer is specifically shaped as follows: the shape of the whole body is enclosed into a big square shape, four corners of the big square shape are enclosed into a small square body, each side of the big square shape is provided with 2 inward square bulges, and the middle part of the big square shape is provided with an outward square bulge; let w be the width of the annular meandering line, c 1Length of a large square, c2Outside length of a small square body having four corners, c3Height of each inwardly square projection in the loop, c4The total length of the annular meandering line is L-4 (c) for the width of each inward square projection in the annular line1+4c3) The sheet resistance value is denoted as R1(ii) a As shown in fig. 2.
In the invention, the square patch of the middle layer is positioned at the central part, b is the length of one side of the square patch, and the square resistance value is R2(ii) a As shown in fig. 3.
In the invention, the bottom layer of the symmetrical four-trapezoid combined patch is specifically shaped into a square body (namely, has quadruple rotational symmetry) formed by four isosceles trapezoids with the same shape and size and bottom angles of 45 degrees, and a gap is formed between every two adjacent isosceles trapezoids; note a1Is the length of the upper base of an isosceles trapezoid a2The length of the lower bottom of the isosceles trapezoid, g is the width of the gap, and the square resistance value is recorded as R3. As shown in fig. 4.
In the invention, the combined patch and the square patch are complementary in structure, namely, the projection of the 2 ITO structures to a plane is basically a complete large square structure.
In the invention, the thickness of three medium plates from top to bottom is recorded as h1、h2、h3T is the thickness of the PET film; as shown in fig. 1.
These parameters are closely related to the performance of the multilayer broadband wave absorber of the present invention, and need to be optimally designed by the present invention.
In the wave absorber unit, the dielectric plate is made of epoxy resin (FR-4) and has a dielectric constant of epsilonr4.3, the electric tangent loss is tan delta 0.025; wave-absorbing materialThe layer is obtained by sputtering an ITO conductive film coating on a PET film substrate by adopting a magnetron sputtering technology and carrying out high-temperature annealing treatment; the PET is polyethylene terephthalate (PET) with a dielectric constant of epsilon r3, the tangent loss is tan delta is 0.018, and the thickness is t is 0.175 mm; the ITO structure is a semiconductor pattern with a certain square resistance value; the metal floor material is copper, and the electrical conductivity thereof is 5.8 multiplied by 107S/m, thickness 0.036 mm.
In the invention, the parameters of the optimized metamaterial unit structure are as follows: p is 12mm, h1＝h2＝h3＝1mm，a1＝4mm， a2＝10mm，g＝0.5mm，b＝4mm，c1＝10.5mm，c2＝3mm，c3＝2mm，c42mm, and 0.6 mm; the square resistance values of the three-layer ITO structure are respectively R1＝200Ω/sq，R2＝100Ω/sq，R3＝40Ω/sq。
The invention provides a design method of a multilayer broadband metamaterial wave absorber, which comprises the following specific steps:
the first step is as follows: preliminarily determining the thickness h and the unit period p of the wave absorber according to the performance requirement and the working frequency of the wave absorber
The wave absorber performance can be measured by the following parameter, the center working frequency f0Relative bandwidth BW, absorption a. By fHAnd fLRespectively, representing the highest and lowest operating frequencies within the operating band. The calculation formula of the relative bandwidth is
The absorption a ═ 1-T (ω) -R (ω), where T and R represent transmission and reflectance, respectively. Generally speaking, the wave absorbing property in a specific frequency band depends on the thickness h and the dielectric constant ε of the mediumrThe initial thickness of the wave absorber can be preliminarily determined according to the empirical formula (2);
it can be seen from equation (2) that the thickness increases with decreasing frequency. According to the effective medium theory, the metamaterial can be integrally characterized by equivalent electromagnetic parameters, epsilon-mu is required to be met for realizing strong absorption, so that the frequency meeting the strongest absorption is determined, namely that the specific frequency has only one optimal period under the given thickness, the optimal period has a certain relation with the frequency and the thickness, and when electromagnetic waves are incident into the metamaterial, the electromagnetic field is supposed to act on the metal floor to generate induced current KEThe equivalent magnetic current excited by the electric field on the surface of the wave absorber is KMThen the two are respectively expressed as:
KE＝H0×n (3)
wherein n is a normal unit vector and is perpendicular to the metal floor. When K isE＝KMWhen for normal incidence there is H0＝E0Thereby, it is possible to obtain:
p≈4h (5)
for all passive wave absorbers based on dielectric loss, the thickness limit can be simplified to the formula (6). Wherein h isminThe minimum theoretical thickness of the wave absorber and the reflection coefficient of R (lambda) can directly influence the minimum design bandwidth of the wave absorber.
Taking the working frequency range of 6-22GHz as an example, the center frequency f0H ≈ 5mm can be obtained at 14GHz, and | S is obtained according to the thickness limit formula11H is a minimum thickness of 0.1, | 10dB, R (λ)min2.2mm, h is 3mm and p is 12 mm.
The second step is that: determining unit structure, layer number and multiple working modes (ITO structure in different layers) operating in different frequency bands according to unit period, thickness and bandwidth
After the thickness and the period of the unit are determined, a plurality of wave-absorbing modes are cascaded in a multilayer structure overlapping mode according to the bandwidth requirement to expand the wave-absorbing bandwidth. The wave-absorbing mode is determined by the structure type and the square resistance value, and the ITO structure can be roughly divided into three types according to the wave-absorbing characteristic of the resistance film type wave absorber, namely a single mode, a double mode and a multi-mode working mode.
The single-mode working mode refers to that only one working mode is in a working frequency range, namely the working mode works in a single frequency range; the dual-mode working mode is characterized in that two working modes are provided, and dual-peak wave absorption can be realized in two discrete frequency bands; the multimode working mode means that three or more than three working modes exist, and cascade connection of a plurality of absorption peaks can be realized. The magnitude of the square resistance value plays an important role in the working mode, the double-mode working mode is adopted when the square resistance value is small, and the single-mode working mode is gradually changed after a certain critical value is reached. In order to further expand the working bandwidth, a multi-mode cascade method with complementary wave-absorbing characteristics can be adopted, three structural types of a circular line, a square patch and a combined patch are taken as examples, so three wave-absorbing layers are selected, the middle of each wave-absorbing layer is separated by a medium plate with the thickness of 1mm, and the working frequency band of 6-22GHz is divided into three parts: the low frequency is 6-11GHz, the intermediate frequency is 11-16GHz and the main frequency is 6-22GHz, and three resonance frequencies are respectively set to be 8GHz, 14GHz and 18 GHz; the perimeter L of the ring structure is close to the resonance wavelength, so that the length of each side c of the four-side ring structure 1Can be approximated as:
when f is0When equal to 8GHz, c1Approximately 9.4mm, the annular structure can be expanded into a winding line structure in order to prolong the current path, and an additional bending part length c is introduced3The annular line width w affects the absorption rate, which increases with increasing width w; according to the standing wave theory, the side length b of the square patch structure is generally lambdao/2：
When f is0Dielectric constant of FR-4 at 14GHzrB can be calculated to be about 5mm under 4.3; for the combined patch structure, the center frequencies are respectively 8GHz and 18GHz, and the initial value is a1＝4.1mm，a2A trapezoidal patch structure with two bases can be selected, and the designed structure should have four-fold rotational symmetry in view of polarization and angular insensitivity.
The third step: determining the working mechanisms of different wave-absorbing layers through contrast research, determining the layer arrangement sequence of the multilayer ITO structure, and forming a preliminary model
The working mechanisms of different layer structures are known by adopting a control variable method to carry out comparative analysis, for example, the change of the reflection coefficient of the wave absorber unit is observed by only changing one layer structure every time, and the function of the layer structure can be known through comparative research; in addition, the arrangement sequence of the space structure layers also influences the wave absorption performance, the three-layer ITO structure is taken as an example, the arrangement sequence is totally 6, the optimal arrangement sequence can be obtained by comparing the wave absorption performance in different sequences, and the multi-layer broadband wave absorber preliminary model is realized.
The fourth step: carrying out parameter scanning on each layer structure, determining the structure of the whole multilayer broadband wave absorber, and realizing the final multilayer broadband wave absorber
The adjustable parameters of each layer structure comprise ITO sheet resistance value of each layer and ITO structure geometric parameters, in particular to three-layer ITO sheet resistance value R1、R2And R3Side length c of ring line structure1And line width w, side length b of the square patch structure, etc. And simulating the reflection coefficient by adopting a frequency domain solver of CST Microwave Studio of electromagnetic simulation software, finding out parameters with the widest-10 dB absorption bandwidth and high absorption rate, and determining the final multilayer broadband wave absorber.
The multilayer broadband metamaterial wave absorber designed by the invention has excellent broadband wave absorbing performance under the excitation of TE and TM polarized waves, has the characteristic of angle insensitivity under TM polarization, and has the advantages of thin thickness, simple structure, easiness in processing and the like.
Drawings
Fig. 1 is a schematic structural diagram of a multi-layer broadband metamaterial wave absorber unit.
FIG. 2 is a top layer circular serpentine line structure.
Fig. 3 is a diagram of a middle square patch.
Fig. 4 is a structure diagram of a bottom layer symmetrical four-trapezoid combined patch.
Fig. 5 shows the influence of (a) thickness and (b) period change of the symmetrical four-trapezoid combined patch structure on the reflection coefficient of the wave-absorbing layer.
FIG. 6 is the influence of the structural parameters of the symmetrical four-trapezoid combined patch on the reflection coefficient of the wave-absorbing layer. Wherein, (a) the trapezoid is at the upper bottom, (b) the trapezoid is at the lower bottom, (c) the gap width and (d) the ITO square resistance value.
Fig. 7 is an equivalent circuit diagram of the absorber unit.
Fig. 8 is an absorptance contrast diagram of theoretical simulation of equivalent circuit of a wave absorber unit and calculation of FDTD value.
FIG. 9 is a comparison graph of reflection coefficients of different wave-absorbing layer structures. Wherein, (a) is a comparison graph of all structures and only one layer of structure; and (b) is a comparison graph of the total structure and the two-layer structure.
FIG. 10 is the electric field distribution diagram of each wave-absorbing layer at the resonant frequency (8, 14, 17GHz) under TE polarization at normal incidence.
FIG. 11 is a current distribution diagram of each wave-absorbing layer at resonant frequency (8, 14, 17GHz) under TE polarization at normal incidence.
FIG. 12 is a graph showing reflection coefficients of six types of arrangement of the multilayer absorber units (see Table 1).
FIG. 13 shows the influence of structural parameters of the absorbing layer on the reflection coefficient. Wherein (a) is the top layer annular meandering line width w, and (b) is the sheet resistance value of the top layer ITO; (c) the side length b of the middle layer square patch, and the (d) is the square resistance value of the middle layer ITO.
FIG. 14 shows the absorptance of a absorber under (a) TE and (b) TM polarizations at different oblique incidence angles.
FIG. 15 is a graph comparing the simulation and experimental structure of a multilayer absorber. Wherein (a) is the reflection coefficient and (b) is the absorption coefficient.
Detailed Description
The technical scheme of the invention is further explained in detail by combining the attached drawings;
1. single-layer ITO structure design
In order to explain the wave absorbing mechanism based on the multi-mode resistance wave absorber and lay a foundation for selecting the later ITO structure type, the wave absorbing characteristic of the single-layer ITO structure is represented based on the simulation software CST Microwave Studio.
Taking the symmetric four-trapezoid combined patch ITO structure in FIG. 4 as an example, the influence of the thickness and the period on the wave absorption performance is firstly determined to be distinguished from the final multilayer wave absorber unit structure, which is denoted by t1And p1Respectively representing the thickness and period of the single-layer ITO structure. As shown in FIG. 5(a), the thickness t is varied1Gradually moves towards lower frequencies, t in general1The bandwidth is widest at 2.5mm, the working frequency band range is 7.3-14.8GHz, and the relative bandwidth is 67.8%. As in FIG. 5(b), with p1Increasing from 11mm to 14mm, gradually moving the low-frequency resonance point to high frequency, gradually reducing the absorption peak value in the high-frequency band, comprehensively considering the working bandwidth and the absorption rate, and finally selecting p1＝12mm。
The structural parameters are then scanned, and the upper bases a of the isosceles trapezoids are shown in FIGS. 6(a-c), respectively1Lower base a2And the influence of the change of the gap width g on the reflection coefficient of the wave absorber; wherein the absorption peak is along with a 1Gradually increases from low frequency to high frequency, and the working frequency band follows a2Increase the shift to low frequencies due to the lower base a2The size of the structure is determined by the upper bottom a1The ITO structure area can be indirectly changed, the gap width g mainly influences the low-frequency resonance point, gradually moves towards high frequency along with the increase of g, and the absorption bandwidth and the peak value are comprehensively considered, and g is 0.5mm as the best choice. The influence of the sheet resistance on the wave absorption performance is shown in fig. 6(d), four sheet resistance values of 6, 40, 100 and 200 Ω/sq are selected in combination with the commercial ITO specification for research, and it can be seen that the working mode is a dual mode when the sheet resistance value is small, and is converted into a single mode when a certain critical value is reached. Size of widest wave-absorbing bandwidth can be realized by single-layer symmetrical four-trapezoid combined patch structureThe parameters are as follows: ITO sheet resistance R of 40 Ω/sq, g of 0.5mm, a1＝4mm，a2＝10mm。
The initial value for the annular and square patch structures may be in terms of the center frequency f0Designed, the circumference of the annular structure is approximate to
Taking a quadrilateral ring as an example, the side length is
While the square patch structure is typically sized 1/2 at the resonant wavelength. The designed structure has four-fold rotational symmetry in view of polarization and angular insensitivity.
2. Design and analysis of multi-layer ITO structure metamaterial wave absorber
After the selected ITO structure is determined, the broadband wave absorber can be realized in a multilayer space stacking mode. According to the equivalent circuit theory, the metamaterial absorber with the multilayer ITO structure can be represented by an equivalent circuit as shown in FIG. 7, and the metamaterial absorber mainly consists of a series RLC circuit and a transmission line which are connected in parallel. The ITO structure is equivalent to an RLC circuit, the PET film and the FR-4 dielectric plate are equivalent to a transmission line, and the metal floor is equivalent to a terminal short-circuit line. According to the transmission line theory, the input impedance at the interface of the air and the metamaterial absorber can be calculated according to the following equation:
wherein Z is0377 Ω represents the wave impedance in air, and ZLThe load impedance needs to be calculated and inversely deduced according to the equivalent circuit in fig. 7 to obtain: firstly, the impedance calculation in the equivalent circuit is divided into two parts, one part is the equivalent characteristic impedance Z of the transmission linediThe other part is the characteristic impedance Z of the RLC equivalent circuitpiWhere i is 1,2, 3. As shown in fig. 7, the input impedance corresponding to each transmission line can be obtained from right to left, and the input impedance can be regarded as the load of the front transmission lineZLiThen the input impedance of the adjacent left transmission line can be calculated by equation (10), i.e.
Wherein ZcAnd Z LiRespectively representing the characteristic impedance and the load impedance of the transmission line, diIs the thickness of the medium, and has a value of d for PET filmsiFor FR-4 dielectric sheets di＝hiWith a transmission constant of
Wherein epsilonriAnd muriRespectively the dielectric constant and the magnetic permeability of the dielectric material,
omega being the corresponding angular frequency, e.g. short-circuited line ZL3When h is 0, then h is adjacent3Input impedance Z of transmission lined3＝jZc tan(β3h3)。
For an RLC series circuit, its characteristic impedance is calculated by equation (11), i.e.
Wherein R isi、Li、CiRespectively representing the equivalent resistance, the equivalent inductance and the equivalent capacitance of the ith layer structure by SunitAnd SpatchRespectively representing the areas of the absorber unit and the ITO structure, the equivalent resistance can be obtained by the formula (13),
the smaller the area occupied by the ITO structure is, the larger the equivalent resistance is, and if the pattern is a square ring, S ispatchTo the area of the current flowing, etcThe effective inductance and the equivalent capacitance can be obtained according to the ITO structure parameters, and the empirical formula is as follows:
wherein,
l is the size of the pattern, and if the pattern is a square patch pattern, l is the side length of the square patch. Equivalent to a capacitance C-B/ω,
equivalent to L ═ X/ω, then take
The reflection coefficient at the interface of the air and the metamaterial wave absorber is represented by R (omega), and the final absorption rate can be obtained by the following formula
According to the theory, the upper layer annular line, the middle layer square patch and the bottom layer combined patch structure can be respectively equivalent to R1-L1-C1、 R2-L2-C2And R3-L3-C3The initial model is simulated by adopting CST Microwave Studio, the unit is set as periodic boundary conditions in the x and y directions, and the electrical boundary conditions are set in the z direction and the upper boundary conditions are open by adopting a metal floor, so that the solution is carried out by a frequency domain solver. The FDTD numerical simulation result and the equivalent circuit theoretical calculation result are shown in fig. 8, which are more ideal than the theoretical calculationBoth generally remain in agreement with trends.
As shown in FIG. 9(a), the wave absorber with the three-layer ITO structure operates at 6.8-20.8GHz, and has an operating bandwidth of 14GHz, i.e. a relative bandwidth of 101.4%. By using the controlled variable method, in which the reflection coefficient of the absorber is shown in fig. 9(a) when only a single layer structure is included, and the reflection coefficient is shown in fig. 9(b) in comparison with the reflection coefficient when only a single layer structure is absent, the different effects of each layer structure can be understood by comparing fig. 9(a) and (b). The trend of the reflection coefficient curve is approximately the same as that of the whole wave absorber only when the bottom layer structure is adopted, and the main effect of the wave absorber in the main frequency band can be inferred; the middle layer structure is double-model, which provides good supplement for the frequency band with poor wave-absorbing performance originally, and the effect is most obvious especially near 14 GHz; and the top layer acts to resonate at around 6.8GHz to broaden the low band. For a deeper understanding of the working mechanism, fig. 10 and 11 show the electric field and current distribution diagram of the absorber at three resonant frequencies (8, 14, 17GHz) respectively under the normal incidence of the TE polarized wave. In general, the electric field near the bottom layer structure is always strong, especially the gap structure plays a great role in the whole absorption frequency band, and the low frequency band is mainly contributed by the top layer annular serpentine line structure, because the annular serpentine line structure prolongs the current path to enhance the equivalent inductance, so the frequency is shifted to the low frequency. From the side view of the electric field distribution, it can be seen that at 14GHz the electric field is mainly due to interlayer coupling, since the absorption strength is enhanced by the local absorption of the middle square patch ITO structure. While the induced current caused by the change of the electric field distribution changes the current distribution pattern, as shown in fig. 11, the current is mainly concentrated on the top layer circular line structure along the electric field direction (y direction) at low frequency, the current on the square patch structure is most concentrated at 14GHz, and the induced current is excited by the portion close to the square patch structure in the y direction in the top layer and the bottom layer structure due to interlayer coupling. While at 17GHz the current is concentrated primarily in the bottom y-direction trapezoidal structure.
To illustrate the influence of the arrangement on the absorber, table 1 shows six combinations of three-layer structures, and the simulation result of the corresponding reflection coefficient is shown in fig. 12. The wave absorbers in the two cases II and IV have similar wave absorbing characteristics (including resonance frequency band and absorption peak value), and in the two cases, the symmetrical four-trapezoid combined patch ITO is in the middle layer; similarly, under two conditions of V and VI, the symmetrical four-trapezoid combined patch structure is positioned on the top layer, both the two conditions show the characteristic of low-frequency narrow-band wave absorption, the main function of the symmetrical four-trapezoid combined patch structure in the multilayer wave absorber is further explained, and the condition I is selected as the arrangement mode.
TABLE 1 arrangement of the multi-layer wave absorber units
| Combination of | Bottom layer | Middle layer | Top layer |
| I | 3 | 2 | 1 |
| |
2 | 3 | 1 |
| |
3 | 1 | 2 |
| |
1 | 3 | 2 |
| |
2 | 1 | 3 |
| |
1 | 2 | 3 |
3. Simulation and experiment of multilayer metamaterial wave absorber
Next, simulation study is performed on structural parameters and ITO sheet resistance values of the multilayer metamaterial wave absorber, as shown in fig. 13(a), as the top-layer annular meandering line width w increases, the absorption peak gradually increases but shifts to a high frequency, and w is 0.6mm in consideration of the bandwidth and the absorptivity. As can be seen from fig. 13(c), for the middle layer square patch ITO structure, the wave-absorbing bandwidth is gradually widened as the side length b increases, but the reflection coefficient is gradually deteriorated, and b is selected to be 4mm as the optimal size in comprehensive consideration. Fig. 13(b) and (d) show the influence of different sheet resistances on the reflection coefficient, and the optimal sheet resistances of the three layers of ITO obtained by parameter scanning are: r 1＝200Ω/sq，R2＝100Ω/sq，R3＝40Ω/sq。
The final structural parameters are listed in table 2.
TABLE 2 wave absorber unit construction parameters (mm)
Further researching polarization and angle wave-absorbing characteristics of the multilayer broadband metamaterial wave absorber, respectively simulating oblique incidence angles under TE polarization and TM polarization, wherein the direction of an electric field is perpendicular to an incidence plane to form the TE polarization, TE polarization electromagnetic waves are arranged to be incident along an xz plane, and the electric field of the TE polarization electromagnetic waves is arranged to be along a y direction, and as shown in a graph 14, as shown in a simulation result, when the incidence angle is changed from 0 degrees to 60 degrees, the absorption rate of the wave absorber under the TE polarization is gradually reduced, and the absorption rate under the TM polarization gradually becomes better along with the increase of the angle in a high-frequency band, and can be kept above 80%. In general, no matter TE wave or TM wave, the designed wave absorber has good wave absorbing performance under wide-angle incidence.
FIGS. 15(a) and (b) are graphs comparing the reflection coefficient and absorption coefficient of the absorber, respectively, and it can be seen from the graphs that the reflection coefficient is less than-10 dB in the 6.68-21.8GHz band, the equivalent bandwidth is 104.1%, the absorption coefficient from 7.15-18GHz is higher than 90%, and the lowest frequency absorption coefficient can reach 86%. The simulation and experiment results are well matched. The total thickness of the final wave absorber is only 3.5mm, and compared with the existing multilayer wave absorber, the thickness of the final wave absorber is thinner, and effective broadband wave absorption can be realized.
Claims (5)
1. The multi-mode resistance-based multi-layer broadband metamaterial wave absorber is characterized in that the wave absorber is an array formed by periodically extending wave absorber units along x and y directions, wherein the period is p; the wave absorbing body unit is formed by stacking a bottom metal floor and three wave absorbing layers, namely a dielectric plate; the wave absorbing layer is an ITO resistive film with a certain structure printed on the continuous PET film; the wave absorber unit comprises three layers: the top layer is of an annular meander line ITO structure, the middle layer is of a square patch structure, and the bottom layer is of a symmetrical four-trapezoid combined patch structure; two adjacent layers of PET films are separated by a dielectric plate; the bottom of the unit is a metal floor; the unit structure is centrosymmetric; wherein:
the specific shape of the annular meander line of the top layer is as follows: the shape of the whole body is enclosed into a big square shape, four corners of the big square shape are enclosed into a small square body, each side of the big square shape is provided with 2 inward square bulges, and the middle part of the big square shape is provided with an outward square bulge; let w be the width of the annular meandering line, c1Length of a large square, c2Outside length of a small square body having four corners, c3Height of each inward square projection in the loop, c4Is the width of each inward square bulge in the loopAnd the total length of the annular winding line is L-4 (c) 1+4c3) The sheet resistance value is denoted as R1；
The square patch in the middle layer is positioned in the center, b is the length of one side of the square patch, and the square resistance value is R2；
The bottom layer of the symmetrical four-trapezoid combined patch is specifically shaped as a square body formed by four isosceles trapezoids with the same shape and size and 45-degree bottom angles, and a gap is formed between every two adjacent isosceles trapezoids; note a1Is the length of the upper base of an isosceles trapezoid a2The length of the lower bottom of the isosceles trapezoid, g is the width of the gap, and the square resistance value is recorded as R3；
The combined patch and the square patch are complementary in structure, namely, the projection of the 2 ITO structures to a plane is basically a complete large square structure;
the thickness of the three medium plates from top to bottom is recorded as h1、h2、h3And t is the thickness of the PET film.
2. The multi-mode-resistor-based multi-layer broadband metamaterial wave absorber as claimed in claim 1, wherein the dielectric plate is FR-4 epoxy resin and has a dielectric constant of er4.3, the electric tangent loss is tan delta 0.025; the wave-absorbing layer is obtained by adopting a magnetron sputtering technology, sputtering an ITO conductive film coating on a PET film substrate and carrying out high-temperature annealing treatment, wherein the PET is polyethylene terephthalate, and the dielectric constant is epsilonr3, the tangent loss is tan delta is 0.018, and the thickness is t is 0.175 mm; the metal floor material is copper, and the electrical conductivity thereof is 5.8 multiplied by 10 7S/m, thickness 0.036 mm.
3. The multimode-resistance-based multilayer broadband metamaterial absorber of claim 1, wherein the optimized structure has the following parameters: p is 12mm, h1＝h2＝h3＝1mm，a1＝4mm，a2＝10mm，g＝0.5mm，b＝4mm，c1＝10.5mm，c2＝3mm，c3＝2mm，c42mm, and 0.6 mm; the square resistance values of the three-layer ITO structure are respectively R1＝200Ω/sq，R2＝100Ω/sq，R3＝40Ω/sq。
4. The method for designing the multilayer broadband metamaterial wave absorber according to claim 1, comprising the following steps:
the first step is as follows: preliminarily determining the thickness h and the unit period p of the wave absorber according to the performance requirement and the working frequency of the wave absorber;
the wave absorber performance is characterized by the following parameters, the center working frequency f0Relative bandwidth BW and absorption a; by fHAnd fLRespectively representing the highest and lowest operating frequencies within the operating band; the calculation formula of the relative bandwidth is as follows:
the absorption a ═ 1-T (ω) -R (ω), where T and R represent transmission and reflectance, respectively; wave absorber thickness h and working frequency f0And a dielectric constant of ∈ given thatrThe absorber thickness h and the cell period p are preliminarily determined from empirical formulas (2) and (3):
p≈4h(3)
for all passive wave absorbers based on dielectric loss, the thickness limit can be simplified to the formula (4):
wherein h isminFor the minimum theoretical thickness of the absorber, R (λ) is the reflection coefficient:
When the working frequency range is 6-22GHz, the center frequency f0Taking S according to a thickness limit formula at 14GHz11|＝-10dB, R (lambda) is 0.1, and the minimum thickness is hmin2.2mm, taking h as 3mm and p as 12mm in comprehensive consideration;
the second step is that: determining a unit structure, a layer number and a plurality of working modes working in different frequency bands according to the period, the thickness and the bandwidth of the unit;
after the thickness and the period of the unit are determined, a plurality of wave-absorbing modes are cascaded to expand wave-absorbing bandwidth in a multilayer structure overlapping mode according to bandwidth requirements; the wave-absorbing mode is determined by the structure type and the square resistance value together, and the ITO structure is roughly divided into three types according to the wave-absorbing characteristic of the resistance film type wave absorber, namely a single mode, a double mode and a multi-mode working type:
the single-mode working mode refers to that only one working mode is in a working frequency range, namely the working mode works in a single frequency range; the dual-mode working mode is characterized in that two working modes are provided, and dual-peak wave absorption can be realized in two discrete frequency bands; the multimode working type means that three or more than three working modes exist, and cascade connection of a plurality of absorption peaks can be realized; the square resistance value plays an important role in the working mode, when the square resistance value is smaller, the working mode is a dual-mode working mode, and when the square resistance value reaches a certain critical value, the working mode is gradually changed into a single-mode working mode; in order to further expand the working bandwidth, a multi-mode cascade method with complementary wave-absorbing characteristics is adopted; for three structural types of a circular line, a square patch and a combined patch, three wave-absorbing layers are selected, the middle of each wave-absorbing layer is separated by a dielectric plate with the thickness of 1mm, and the working frequency band of 6-22GHz is firstly divided into three parts: the low frequency is 6-11GHz, the intermediate frequency is 11-16GHz and the main frequency is 16-22GHz, and three resonance frequencies are respectively set to be 8GHz, 14GHz and 18 GHz; the perimeter L of the annular structure is close to the resonance wavelength; for each side length c of the four-sided ring structure 1The approximation is:
wherein c is the speed of light, when f0When equal to 8GHz, c1≈9.4mm；
To extend the current path to expand the ring structure into a meandering structure, an additional meandering section length c is introduced3If the circumference length L is 4 (c)1+4c3) The annular line width w affects the absorption rate, which increases with increasing width w; according to the standing wave theory, the side length b of the square patch structure is lambdao/2，λoAs the central operating wavelength:
when f is0Dielectric constant ε of FR-4 epoxy resin (14 GHz)rSolving b is approximately equal to 5mm when the value is 4.3; for the combined patch structure, the center frequencies are respectively 8GHz and 18GHz, and the initial value is a1＝4.1mm，a2When the thickness is 9.4mm, a trapezoidal patch structure with two bases is selected, and the designed structure has four-fold rotational symmetry in consideration of polarization and angle insensitivity;
the third step: determining the action and the working mechanism of different layer structures through comparative research, determining the layer arrangement sequence of the multilayer ITO structure, and forming a preliminary model;
analyzing the working mechanisms of different layer structures by adopting a control variable method to carry out comparative analysis; specifically, the change of the reflection coefficient of the wave absorber unit is observed by changing only one layer of structure each time, and the effect of the layer of structure can be known through comparative research; in addition, the arrangement sequence of the space structure layers also influences the wave absorption performance; for the three-layer ITO structure, the arrangement sequence is 6, the optimal arrangement sequence is obtained by comparing the wave-absorbing performance under different sequences, and a multi-layer broadband wave absorber preliminary model is realized;
The fourth step: carrying out parameter scanning on each layer structure, determining wave absorber structure parameters, and realizing a final multilayer broadband wave absorber;
the scannable parameters of each layer structure comprise the square resistance value of each layer of ITO and the geometric parameters of the ITO structure, in particular to the three-layer ITO square resistance value R1、R2And R3C of ring line structure1、c2、c3、c4And w, b of a square patch structure, a of a composite patch structure1，a2G; using electromagnetic simulation softwareAnd (3) simulating the reflection coefficient by a frequency domain solver of the CST Microwave Studio, finding out parameters with the widest-10 dB absorption bandwidth and high absorption rate, and determining the final multilayer broadband wave absorber.
5. The method as claimed in claim 4, wherein the metamaterial unit structure has the following parameters: p is 12mm, h1＝h2＝h3＝1mm，a1＝4mm，a2＝10mm，g＝0.5mm，b＝4mm，c1＝10.5mm，c2＝3mm，c3＝2mm，c42mm, and 0.6 mm; the square resistance values of the three-layer ITO structure are R respectively1＝200Ω/sq，R2＝100Ω/sq，R3＝40Ω/sq。
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