Design Method of Oblique Incidence Ultra-Wideband Absorbing Metamaterials Based on Characteristic Mode Theory

Abstract

An ultra-wideband absorbing metamaterial unit with oblique incidence based on the characteristic mode theory, which is composed of upper and lower lossy dielectric plates, metal patches adhered to them, and a bottom metal ground plane. From top to bottom, they are: an upper metal patch, a first dielectric layer, a first air layer, a middle metal patch, a second dielectric layer, a second air layer, and a metal ground. The upper metal patch is adhered to the upper surface of the upper dielectric plate and is a meandering square loop patch; the middle metal patch is adhered to the upper surface of the lower dielectric plate and includes four identical "L"-shaped metal strips placed back to back, presenting a cross shape as a whole; the bottom metal ground plane is a thin metal plate. An ultra-wideband absorbing metamaterial array with oblique incidence is formed by using the above units in an array arrangement. The present invention can achieve the design of an ultra-wideband absorbing metamaterial under oblique incidence without relying on a large number of repeated full-wave simulations, improving the design efficiency.

Description

Technical Field

[0001] The present invention relates to the field of ultra-wideband absorbing metamaterials under oblique incidence, and particularly to a design method of an ultra-wideband absorbing metamaterial based on the characteristic mode theory under oblique incidence. Background Art

[0002] The development of electromagnetic metamaterials has provided broad prospects for regulating the polarization, amplitude, and phase of electromagnetic waves to achieve multifunctionality. Absorbing metamaterials have been widely used in various fields due to their unique properties, such as radar stealth, electromagnetic compatibility, wireless communication, imaging systems, etc. Salisbury screen, Jaumann absorber, and perfect absorber, as early successful practices, although limited by narrow bandwidth and relatively large thickness, have also explored feasible technical routes for the design of metamaterial absorbers. The bandwidth, oblique incidence angle, and profile thickness of absorbing metamaterials are a set of difficult-to-reconcile contradictions. Therefore, a suitable compromise needs to be made to achieve satisfactory performance. The introduction of circuit simulation absorbers is an excellent solution, which largely solves the above limitations. At the same time, the equivalent circuit theory is also a fast and effective method for guiding the design of broadband and low-profile circuit simulation absorbers. In 2020, Zhang et al. proposed that the absorber consists of a lossy layer and four rotationally symmetric curved metal strips embedded with two chip resistors. The metal strips embedded with resistors generate three resonant modes, and the current is consumed through the patch resistors in different modes. The relative bandwidth of the 90% absorption rate under normal incidence is 127.9%. (B. Zhang, C. Jin and Z. Shen, IEEE Trans. Microwave Theory Tech. vol. 68, no. 3, pp. 835-843, 2020.) However, most of the literature studies only focus on the normal incidence angle, and the absorption under oblique incidence urgently requires theoretical insights and practical applications. Recently, Yao et al. proposed a novel absorber, which consists of an array of conductive square loops embedded with lumped resistors and a carefully designed wide-angle impedance matching (WAIM) layer. The equivalent circuit (EC) and rigorous formula derivation are introduced to gain in-depth understanding of the deterioration of absorption performance under oblique incidence and the influence of the WAIM layer. The relative bandwidth of the 10-dB reflection coefficient under normal incidence is 137.1%. When the incidence angle is 45°, the overlapping bandwidth of transverse electric (TE) and transverse magnetic (TM) polarizations is still 110.5%. (Z. Yao, S. Xiao, Y. Li and B. Wang, IEEE Trans. Antennas Propag. DOI: 10.1109 / TAP.2022.3149594.) It is worth mentioning that the equivalent circuit is inadequate for designing complex structures, and more experience is needed for guiding oblique incidence angles. The characteristic mode theory (CMT) of passive analysis defines a series of mutually orthogonal mode currents, providing profound physical insights for analyzing and reshaping fundamental modes and high-order modes. It has been successfully used to guide the design of metasurface antennas and has also been applied in the field of microwave absorption.In 2021, with the help of characteristic modes and characteristic currents, Wu et al. determined the value of the loading resistance, analyzed the equivalent impedance and surface current distribution of the proposed absorber, and obtained a broadband metamaterial absorber with an absorption rate of 90% and a relative bandwidth of 126.88% (Yanjie Wu, Hai Lin, Jie Xiong, Junjie Hou, Rui Zhou, Feng Deng, and Rongxin Tang, J. Appl. Phys. Vol. 129, pp, 134902, 2021.). In terms of the current research status, there are few relevant literatures on designing wave-absorbing metamaterials under oblique incidence with the help of characteristic mode theory. Ultra-wideband and large-angle wave-absorbing metamaterials can be widely used in electromagnetic compatibility, electromagnetic interference, and radar cross-section (RCS) reduction. Therefore, in order to meet the application requirements of wide frequency bands, it is of great research significance to realize a new type of oblique-incidence ultra-wideband wave-absorbing metamaterial. Summary of the Invention

[0003] Aiming at the deficiencies in the design and performance of wave-absorbing metamaterials under oblique incidence in the prior art, the present invention proposes an oblique-incidence ultra-wideband wave-absorbing metamaterial unit, hereinafter referred to as "unit" for short, which is composed of upper and lower lossy dielectric plates, a metal patch attached thereto, and a bottom metal ground plane. From top to bottom, it is in turn: upper metal patch, first dielectric layer, first air layer, middle metal patch, second dielectric layer, second air layer, metal ground; and its characteristics are as follows

[0004] The upper and lower dielectric plates are completely identical thin rectangular parallelepiped structures, and their projections on the horizontal plane coincide. The upper and lower surfaces are both squares with a side length of p;

[0005] The upper metal patch is attached to the upper surface of the upper dielectric plate and adopts a meandering square loop patch with an outer ring length of l1 and a square loop width of w1; lumped resistors R1 are embedded at the right-angle corners of the square loop, and lumped resistors R2 are embedded in the middle of each side of the square loop. Among them, two lumped resistors R1 are embedded at each right-angle corner of the square loop, and these two lumped resistors are respectively located on two mutually perpendicular sides of the corner, and the figure enclosed by these two lumped resistors R1 is exactly the largest square at the corner, and the side length of this square is the square loop width w1. The lumped resistor R2 embedded in the middle of each side of the square loop; each side of the square loop patch is parallel to the edge of the upper dielectric plate and maintains the same distance; the two sections of metal between the lumped resistor R2 on each side of the square loop and the two lumped resistors R1 at both ends of this side are etched into meandering lines, and the meandering lines meander from the lumped resistor R1 to the lumped resistor R2, and there is a certain distance between the two ends of the meandering lines and the lumped resistors R1 and R2;

[0006] The middle-layer metal patch is attached to the upper surface of the lower-layer dielectric substrate. It includes four identical "L"-shaped metal strips placed back-to-back, forming a cross shape as a whole. Each "L"-shaped metal strip occupies two adjacent arms of the cross. Therefore, the adjacent sides of two adjacent "L"-shaped metal strips are parallel to each other and their ends are flush, but there is a same distance between them. The distances between the adjacent sides of the four "L"-shaped metal strips are equal; each arm of the cross-shaped metal patch is parallel to the edge of the lower-layer dielectric substrate respectively, and the ends of the arms are at the same distance from the edge of the lower-layer dielectric substrate; the length of the metal strip is l3, the width of the metal strip is w3, and the distance between the metal strips is w4; two resistors R3 are embedded at each right-angle corner, and their arrangement is the same as that of the two lumped resistors R1 embedded at each right-angle corner of the square ring;

[0007] The bottom-layer metal ground plane is a metal thin plate, and its projection on the horizontal plane coincides with that of the upper and lower-layer dielectric substrates.

[0008] In an embodiment of the present invention, the side length p ranges from 8 to 12 mm; the thicknesses hs1 and hs2 of the two-layer dielectric substrates s are in the range of 0.5 - 1 mm; the two-layer air thicknesses ha1 and ha2 between the two-layer dielectric substrates and between the lower-layer dielectric substrate and the bottom-layer metal ground plane are in the ranges of 3.5 - 4 mm and 1 - 2 mm respectively.

[0009] In a specific embodiment of the present invention, the side length p is 10 mm; the thicknesses hs1 and hs2 of the two-layer dielectric substrates are 0.72 mm and 0.79 mm respectively; the two-layer air thicknesses ha1 and ha2 between the two-layer dielectric substrates and between the lower-layer dielectric substrate and the bottom-layer metal ground plane are 3.87 mm and 1.5 mm respectively; the selected range of the dielectric constant is in the range of 2.2 - 4.0.

[0010] In another embodiment of the present invention,

[0011] The outer ring length l1 of the upper-layer metal patch ranges from 8 to 9 mm; the width w1 of the square ring ranges from 0.8 to 1.2 mm;

[0012] The lumped resistors R1 and R2 range from 75 Ω to 100 Ω;

[0013] The length l2 of the meandering line ranges from 0.8 to 0.9 mm; the width w2 of the meandering line ranges from 0.08 to 0.12 mm.

[0014] In another specific embodiment of the present invention,

[0015] The outer ring length l1 of the upper-layer metal patch is 8.5 mm; the width w1 of the square ring is 1 mm;

[0016] The lumped resistors R1 and R2 are 97.6 Ω;

[0017] The length l2 of the meandering line is 0.85 mm; the width w2 of the meandering line is 0.1 mm.

[0018] In another embodiment of the present invention, for the middle layer metal patch, the length l3 of the metal strip ranges from 3 to 5 mm; the width w3 of the metal strip ranges from 0.8 to 1.2 mm; the spacing w4 between the metal strips ranges from 0.3 to 0.7 mm; the value ranges of the two resistors R3 are from 50 Ω to 100 Ω.

[0019] In another specific embodiment of the present invention, for the middle layer metal patch, the length l3 of the metal strip is 4 mm; the width w3 of the metal strip is 1 mm; the spacing w4 between the metal strips is 0.5 mm; the two resistors R3 are 73.2 Ω.

[0020] In addition, in an embodiment of the present invention, the combination of the upper layer metal patch and the upper layer dielectric plate in the unit is named as unit 1, and the combination of the middle layer metal patch and the lower layer dielectric plate is named as unit 2; the equivalent circuit along the electric field polarization direction is as follows:

[0021] In unit 1, the first coupling capacitor C u1 is the coupling capacitor between adjacent metal patches in unit 1; the first equivalent inductor L A1 is the equivalent inductor on the metal strip parallel to the polarization direction; C p1 is the parasitic capacitor on the meandering line; the first equivalent resistor R A1 is the equivalent resistor of R1 and R2 inserted into the metal strip; in unit 2, the second coupling capacitor C u2 is the coupling capacitor between adjacent metal patches in unit 2; the second equivalent inductor L A2 is the equivalent inductor on the metal strip parallel to the polarization direction; the third equivalent inductor L A3 is the equivalent inductor on the metal strip perpendicular to the polarization direction; the third coupling capacitor C A1 and the fourth coupling capacitor C A2 are the coupling capacitors between adjacent parallel metal strips in unit 2; the second equivalent resistor R A2 is the equivalent resistor of the resistor R3 inserted into the lower layer metal patch;

[0022] In the equivalent circuit of unit 1: the parasitic capacitor C p1 of the meandering line is in parallel with the first equivalent inductor L A1 to form the first inductance-capacitance circuit; one end of the first coupling capacitor C u1 is connected to the plane wave port, and the other end is connected to one end of the first inductance-capacitance circuit; the other end of the inductance-capacitance circuit is grounded through the first equivalent resistor R A1 ;

[0023] In the equivalent circuit of unit 2: the second coupling capacitor C u2 and the second equivalent inductor LA2 2. The second equivalent resistor R A2 3. The third coupling capacitor C A1 are connected in series in sequence to form a first series circuit. The third coupling capacitor C in the first series circuit A1 is grounded downward via the second dielectric layer and the second air layer. The second coupling capacitor C in the first series circuit u2 is connected to the plane wave port upward in sequence via the first air layer and the first dielectric layer, and is grounded downward via the second dielectric layer and the second air layer; The third equivalent inductor L A3 is connected in series with the fourth coupling capacitor C A2 to form a second inductance-capacitance circuit. The third equivalent inductor L in this circuit A3 is connected to the connection point of the second coupling capacitor C u2 and the second equivalent inductor L A2 . The fourth coupling capacitor C in this circuit A2 is grounded downward via the second dielectric layer and the second air layer.

[0024] There is also provided an oblique-incidence ultra-wideband absorbing metamaterial array based on the characteristic mode theory, which is based on the above-mentioned oblique-incidence ultra-wideband absorbing metamaterial unit based on the characteristic mode theory, and is characterized in that a plurality of units are arranged in an array.

[0025] In an embodiment of the present invention, a 12*12 array is adopted.

[0026] The unit and the array of the oblique-incidence ultra-wideband absorbing metamaterial based on the characteristic mode theory of the present invention have the following advantages:

[0027] 1. The present invention designs an oblique-incidence ultra-wideband absorbing metamaterial based on the characteristic mode theory. Through characteristic mode analysis and equivalent circuit theory derivation, the working mode and mechanism of the designed ultra-wideband absorbing metamaterial can be clearly revealed.

[0028] 2. The present invention provides a general design idea for ultra-wideband absorbing metamaterials. This method can realize the design of oblique-incidence ultra-wideband absorbing metamaterials without relying on a large number of repeated full-wave simulations, improving the design efficiency.

[0029] 3. The oblique-incidence ultra-wideband absorbing metamaterial proposed by the present invention has the characteristics of easy processing, low cost, and broad application prospects. Description of the Drawings

[0030] The above and / or additional aspects and advantages of the present invention will become obvious and easy to understand in conjunction with the description of the embodiments with the following drawings, where:

[0031] Figure 1 is a schematic diagram of the unit of the ultra-wideband absorbing metamaterial of the present invention, where Figure 1(a) Three-dimensional schematic diagram of the microwave absorbing metamaterial, Figure 1 (b) Schematic diagram of the metal meandering square loop with an embedded resistor on the top layer, Figure 1 (c) Symmetrically bent metal strip with an embedded resistor in the middle layer, and the bottom layer is a metal ground plane;

[0032] Figure 2 are the modal currents and modal direction patterns of the metal structure without embedded lumped resistors for two cells, where Figure 2 (a) are the four modal currents of one cell 1 (Element 1, E1), where Figure 2 (b) are the four modal direction patterns of one cell 1 (Element 1, E1), where Figure 2 (c) are the four modal currents of two cells 2 (Element 2, E2), where Figure 2 (d) are the four modal direction patterns of two cells 2 (Element 2, E2);

[0033] Figure 3 are the modal significance coefficients (Modal significances, MS) of the two cells with and without embedded lumped resistors, where Figure 3 (a) is the modal significance coefficient of one cell 1 without an embedded lumped resistor, Figure 3 (b) is the modal significance coefficient of two cells 2 without an embedded lumped resistor, Figure 3 (c) is the modal significance coefficient of one cell 1 with an embedded lumped resistor, Figure 3 (d) is the modal significance coefficient of two cells 2 with an embedded lumped resistor;

[0034] Figure 4 are the modal weighting coefficients (Modalweighting coefficient, MWC) of the two cells without embedded lumped resistors under TE and TM polarized incident waves, where Figure 4 (a) is the MWC of one cell 1 under TE polarized incident wave, Figure 4 (b) is the MWC of two cells 2 under TE polarized incident wave, Figure 4 (c) is the MWC of one cell 1 under TM polarized incident wave, Figure 4 (d) is the MWC of two cells 2 under TM polarized incident wave;

[0035] Figure 5 are the equivalent circuit and admittance Smith chart, where Figure 5 (a) is the equivalent circuit model of the designed double-layer microwave absorbing metamaterial, Figure 5 (b) is the reflection coefficient of the equivalent circuit calculated value and full-wave simulation, Figure 5 (c) is the admittance Smith chart of the designed microwave absorbing metamaterial and the separate two-layer microwave absorption;

[0036] Figure 6 For the chromatograms of the simulated electromagnetic wave absorption rate and RCS reduction value, where Figure 6 (a) is the chromatogram of the electromagnetic wave absorption rate versus frequency and angle under TE-polarized incident waves, Figure 6 (b) is the chromatogram of the electromagnetic wave absorption rate versus frequency and angle under TM-polarized incident waves, Figure 6 (c) is the chromatogram of the RCS (Radar cross section) reduction value versus frequency and angle under TE-polarized incident waves, Figure 6 (d) is the chromatogram of the RCS reduction value versus frequency and angle under TM-polarized incident waves;

[0037] Figure 7 For the processed physical object and test environment, where Figure 7 (a) is the schematic diagram of the designed microwave absorbing metamaterial, Figure 7 (b) is the test environment, Figure 7 (c) is the microwave absorption composed of one unit 1, Figure 7 (d) is the microwave absorption composed of two units 2;

[0038] Figure 8 For the simulation and test results, where Figure 8 (a) is the absorption rate under TE-polarized incident waves, Figure 8 (b) is the absorption rate under TM-polarized incident waves. Detailed implementation manners

[0039] The present invention proposes a design method for an oblique-incidence ultra-wideband microwave absorbing metamaterial based on the characteristic mode theory. The schematic diagram of the structure of the microwave absorbing metamaterial unit (hereinafter referred to as "unit") is as shown in Figure 1 (a)-(c). The unit consists of upper and lower lossy dielectric plates, a metal patch attached thereto, and a bottom metal ground plane, where R1, R2, and R3 are lumped resistors embedded in the metal patch. As can be seen from Figure 1 (a), from top to bottom, the unit is successively: upper metal patch, first dielectric layer, first air layer, middle metal patch, second dielectric layer, second air layer, and metal ground.

[0040] Consisting of Figure 1(a) It can be seen that the upper and lower dielectric plates are identical thin rectangular parallelepiped structures and their projections on the horizontal plane coincide. Both the upper and lower surfaces are square with a side length of p, where the range of the side length p is 8 - 12 mm, and the preferred value is 10 mm. The thicknesses hs1 and hs2 of the two dielectric plates are in the range of 0.5 - 1 mm, and the preferred values are 0.72 mm and 0.79 mm respectively. The thicknesses ha1 and ha2 of the two air layers between the two dielectric plates and between the lower dielectric plate and the bottom metal ground plate are in the ranges of 3.5 - 4 mm and 1 - 2 mm respectively, and the preferred values are 3.87 mm and 1.5 mm respectively. The dielectric constant is selected in the range of 2.2 - 4.0, and the preferred value is 2.65. The tangent of the loss angle is in the range of 0.01 - 0.03, and the preferred value is 0.02.

[0041] The upper metal patch is attached to the upper surface of the upper dielectric plate and is a meandering square loop patch. The length l1 of the outer loop ranges from 8 - 9 mm, and the preferred value is 8.5 mm. The width w1 of the square loop ranges from 0.8 - 1.2 mm, and the preferred value is 1 mm. Lumped resistors R1 are embedded at the right-angle corners of the square loop, and lumped resistors R2 are embedded in the middle of each side of the square loop. Among them, two lumped resistors R1 are embedded at each right-angle corner of the square loop, and these two lumped resistors are located on two mutually perpendicular sides of the corner respectively, and the figure enclosed by these two lumped resistors R1 is exactly the largest square at the corner, and the side length of this square is the width w1 of the square loop. The position of the lumped resistor R2 embedded in the middle of each side of the square loop is well-known to those skilled in the art and will not be elaborated here. Each side of the square loop patch is parallel to the edge of the upper dielectric plate and maintains the same distance. The values of the lumped resistors R1 and R2 range from 75 Ω - 100 Ω, and the preferred value for both is 97.6 Ω. The two sections of metal between the lumped resistor R2 on each side of the square loop and the two lumped resistors R1 at both ends of this side are etched into meandering lines. The meandering lines extend from the lumped resistor R1 towards the lumped resistor R2, and there is a certain spacing between the two ends of the meandering lines and the lumped resistors R1 and R2. In the figure, it is shown that one end of the meandering line (the end adjacent to the lumped resistor R2) has a relatively wide spacing from the lumped resistor R2 for the convenience of soldering the resistor. The length and width values of the meandering lines are obtained through optimization, and the method is known to those skilled in the art and will not be elaborated here. The length l2 of the meandering line ranges from 0.8 - 0.9 mm, and the preferred value is 0.85 mm. The width w2 of the meandering line ranges from 0.08 - 0.12 mm, and the preferred value is 0.1 mm.

[0042] The middle-layer metal patch is attached to the upper surface of the lower-layer dielectric substrate, and includes four identical "L"-shaped metal strips placed back-to-back, presenting a cross shape as a whole. Each "L"-shaped metal strip occupies two adjacent arms of the cross. Therefore, the adjacent sides of two adjacent "L"-shaped metal strips are parallel to each other and flush at both ends, but there is a same distance between them, and the distances between the adjacent sides of the four "L"-shaped metal strips are equal; each arm of the cross-shaped metal patch is parallel to the edge of the lower-layer dielectric substrate respectively, and the wall ends are at the same distance from the edge of the lower-layer dielectric substrate; the length l3 of the metal strip ranges from 3 to 5 mm, and the preferred value is 4 mm; the width w3 of the metal strip ranges from 0.8 to 1.2 mm, and the preferred value is 1 mm; the distance w4 between the metal strips ranges from 0.3 to 0.7 mm, and the preferred value is 0.5 mm. Similar to the upper-layer metal patch, two resistors R3 are embedded at each right-angle corner, and their arrangement is the same as that of the two lumped resistors R1 embedded at each right-angle corner of the square ring, with a value range of 50 Ω - 100 Ω, and the preferred value is 73.2 Ω.

[0043] The bottom-layer metal ground plane is a thin metal plate, and its projection on the horizontal plane coincides with that of the upper-layer and lower-layer dielectric substrates.

[0044] The numerical operations of the present invention are realized by simulation with the electromagnetic simulation software CST Studio Suite 2020. The eigenmode analysis is performed on the upper-layer structural unit 1 (E1) without resistors and meandering curves. Figure 3 (a) It can be seen that there are 4 main resonance modes within 5 - 20 GHz. Figure 2 (a) and (b) are the mode current and mode pattern of a unit 1. J a1 and J a2 are a pair of orthogonal modes, and the maximum values of the mode patterns are all along the normal direction. J a3 The mode current of is the strongest in the middle of each side, J a4 the mode current of is reversed on each side and is rotationally symmetric. J a3 and J a4 the mode patterns of are both zero points in the normal direction. J a1 , J a2 and J a4 the mode current of is the strongest at the right-angle corners. As Figure 4 (a) and (c) show that under the normal incident wave, only J a1 and J a2 are excited. According to the reciprocity theorem, the radiation and absorption modes are consistent. Therefore, the mode pattern radiating along the normal direction has the strongest ability to absorb the vertically incident wave. For the TE-polarized incident wave, J a1 , J a2 (not drawn, with the same magnitude as J a1 ) and J a3It can be seen that as the incident angle increases, the excitation degree of J a1 becomes smaller, and the excitation of J a3 shifts to higher frequencies. For TM-polarized incidence, J a1 and J a2 are still the main excitation modes. In addition, J a4 is also excited. As the incident angle increases, the excitation amplitude increases and shifts to higher frequencies. To improve the absorption ability of electromagnetic waves under normal incidence and oblique incidence, lumped resistors are loaded at the strongest positions of the four mode currents, that is, eight resistors R1 are loaded at the four corners, and four resistors R2 are loaded in the middle of each side. Taking R1 = 100 Ω and R2 = 100 Ω, a mode analysis is performed on a unit 1 with loaded resistors. The mode currents and mode patterns of the four basic modes do not change, but the MS is significantly broadened, as shown in Figure 3 (c).

[0045] The same operation as that for unit 1 is performed on unit 2. A characteristic mode analysis is performed on unit 2 without resistors to obtain the MS. It can be seen that there are mainly four mode resonances within 13 - 16 GHz. J b1 and J b2 are a pair of orthogonal modes, and the mode patterns both radiate along the normal direction. Undoubtedly, under the incidence of a vertical plane wave, J b1 and J b2 are mainly excited. The mode current of J b3 is axisymmetric, while the mode current of J b4 is rotationally symmetric, and the mode patterns of J b3 and J b4 are both zero at the normal direction. For TE-polarized incident waves, as the incident angle increases, the excitation of J b1 and J b2 (not drawn, with the same magnitude as J b1 ) becomes smaller, and the excitation of J b4 increases, but relatively speaking, the excitation is still smaller. For TM-polarized incident waves, as the incident angle increases, the excitation of J b3 increases, the excitation of J b1 first increases and then decreases. When θ = 60°, the excitation of J b3 is larger than that of J b1 . According to the reciprocity theorem, under oblique incidence, J b1 and J b3 play the main wave absorption role. The strongest positions of the four mode currents are all located at the corners of the curved metal strips. To expand the bandwidth of the MS and enhance the wave absorption ability under oblique incident waves, lumped resistors are embedded at the strongest positions of the mode currents. A characteristic mode analysis is performed again, and neither the mode currents nor the mode patterns change. The MS of the four modes all become wider, as shown in Figure 3(d). Under normal incidence waves and oblique incidence waves, a strong wave absorption ability is obtained.

[0046] The combination of the upper metal patch and the upper dielectric plate in the unit is named Unit 1, and the combination of the middle metal patch and the lower dielectric plate is named Unit 2. Considering the equivalent circuit along the direction of electric field polarization, the equivalent R-L-C of Unit 1 and Unit 2 are respectively as Figure 1 (b) and (c) shown. In Unit 1, the first coupling capacitor C u1 is the coupling capacitor between adjacent metal patches in Unit 1 (i.e., two adjacent sides of the square ring patch in Unit 1); the first equivalent inductor L A1 is the equivalent inductor on the metal strip parallel to the polarization direction, and all metal strips parallel to the polarization direction have the equivalent inductor L A1 ; C p1 is the parasitic capacitor on the meander line, and a meander line with a miniaturized structure is adopted to facilitate broadening the wave absorption bandwidth. The first equivalent resistance R A1 is the equivalent resistance of R1 and R2 inserted into the metal strip (R1 and R2 are the resistors welded in actual processing and actually exist. As Figure 5 (b) shown, one full-wave simulation value and one equivalent circuit model value, and the two values should be equal. In the equivalent circuit, R1 and R2 are equivalent to R A1 , with different values and different concepts. R A1 is the simulation value that satisfies the curve in the equivalent circuit). In Unit 2, the second coupling capacitor C u2 is the coupling capacitor between adjacent metal patches in Unit 2 (i.e., two adjacent sides of the square ring patch in Unit 2); the second equivalent inductor L A2 is the equivalent inductor on the metal strip parallel to the polarization direction, and all metal strips parallel to the polarization direction have the second equivalent inductor L A2 ; the third equivalent inductor L A3 is the equivalent inductor on the metal strip perpendicular to the polarization direction, and all metal strips perpendicular to the polarization direction have the third equivalent inductor L A3 ; the third coupling capacitor C A1 and the fourth coupling capacitor C A2 are the coupling capacitors between adjacent parallel metal strips in Unit 2 (the same point is that both are the coupling capacitors in Unit 2, different from the coupling capacitors C u1 and C u2 between units; from Figure 1 (c), it can be seen that C A1 and C A2 are the coupling capacitors at different positions, C A1 is the coupling capacitor between adjacent metal strips in Unit 2 along the polarization direction, C A2is the coupling capacitance between adjacent metal strips in the second unit 2 along the direction perpendicular to the polarization direction); the second equivalent resistance R A2 is the equivalent resistance of the resistor R3 inserted in the lower metal patch (R3 is the resistor soldered in actual processing and actually exists. As Figure 5 (b) shows, one full-wave simulation value and one equivalent circuit model value, and the two values should be equal. In the equivalent circuit, R3 is equivalent to the second equivalent resistance R A2 , with different values and different concepts. The second equivalent resistance R A2 is the simulation value that satisfies the curve in the equivalent circuit).

[0047] As Figure 5 (a) shows, the equivalent circuits of unit 1 and unit 2 are marked with dashed boxes. The left side is the equivalent circuit of unit 1, and the right side is the equivalent circuit of unit 2. The equivalent circuit of unit 1 consists of an R-L-C series circuit, forming two resonance points at low frequencies to absorb electromagnetic waves. In the equivalent circuit of unit 1: the serpentine parasitic capacitance C p1 is in parallel with the first equivalent inductance L A1 to form the first inductance-capacitance circuit; one end of the first coupling capacitance C u1 is connected to the plane wave port, and the other end is connected to one end of the first inductance-capacitance circuit; the other end of the inductance-capacitance circuit is grounded through the first equivalent resistance R A1 . In the equivalent circuit of unit 2: the second coupling capacitance C u2 , the second equivalent inductance L A2 , the second equivalent resistance R A2 , and the third coupling capacitance C A1 are connected in series in sequence to form the first series circuit. The third coupling capacitance C A1 in the first series circuit is grounded downward through the second dielectric layer and the second air layer. The second coupling capacitance C u2 in the first series circuit is connected to the plane wave port upward through the first air layer and the first dielectric layer and grounded downward through the second dielectric layer and the second air layer; the third equivalent inductance L A3 is in series with the fourth coupling capacitance C A2 to form the second inductance-capacitance circuit. The third equivalent inductance L A3 in this circuit is connected to the connection point of the second coupling capacitance C u2 and the second equivalent inductance L A2 . The fourth coupling capacitance C A2 in this circuit is grounded downward through the second dielectric layer and the second air layer. In the equivalent circuit of unit 2, the series resonance circuits L A2 R A2 C A1 and the series resonance circuits L A3 C A2Connected in parallel, two resonance points are formed at high frequencies to absorb electromagnetic waves. The two dielectric plates and the air layer play an impedance matching role, and the equivalent circuits of the two units work together to achieve ultra-wideband absorption of electromagnetic waves.

[0048] Multiple units form an array arrangement. In a specific embodiment of the present invention, a 12*12 array is adopted. A circuit model is established in Advanced Design System (ADS), fitted, and the R-L-C values are optimized. The good agreement between the equivalent circuit model and the full-wave simulation proves the reliability of the equivalent circuit model, as Figure 5 (b) shows. Y1 and Y2 are the admittances of the single layers E1 and E2 in the best matching state under normal incident waves, respectively. The shaded part is the -10dB reflection coefficient. From Figure 5 (c), it can be seen that the proposed double-layer wave absorption has a wider wave absorption bandwidth than the single-layer wave absorption.

[0049] The proposed oblique-incidence ultra-wideband absorbing metamaterial verifies the feasibility of the invention through simulation and processing measurement. As Figure 6 (a) and (b) show, the proposed wave absorption has polarization insensitivity and angular stability. For TE polarization, the absorption rate is almost above 90% within 4-20GHz, except for some frequency bands. For TM polarization, as the incident angle increases, the 90% bandwidth of the absorption rate shifts to higher frequencies and can still reach four times the frequency. At the same time, the proposed wave absorption also shows excellent performance in absorbing electromagnetic waves and reducing RCS. Figure 6 (c) and (d) show that compared with a metal ground plane of the same area, whether it is TE polarization or TM polarization, the proposed wave absorption can almost reduce by 10dB within 0-60°. To verify the ultra-wideband and polarization-insensitive characteristics of the proposed wave absorption, the wave absorption array consists of 12*12 units. Considering the pads, the adjacent resistance space distance at the corner is relatively close. Therefore, one of the resistors is placed on the back of the dielectric plate and connected through a metallized via, as Figure 7 (c) and (d) show. Under normal incidence, there is no impact on the absorption bandwidth, and under oblique incidence, except that the absorption bandwidth shifts to lower frequencies, the wave absorption bandwidth is also not affected at all. Figure 8 The good agreement between the measured and simulated results shown under TE and TM polarizations fully proves the reliability and effectiveness of the designed absorbing metamaterial.

[0050] The present invention proposes a novel ultra-wideband and polarization-insensitive metamaterial absorber. The absorber consists of conductive square loops, symmetrically bent metal strips, and a lossy layer. By analyzing the mode fields and mode parameters, lumped resistors are loaded at the locations where the mode currents of the conductive meandering square loops and the bent metal strips are maximum. Meanwhile, the equivalent circuit model is analyzed to further understand the ultra-wideband absorption mechanism. Simulations and measurements show that for the proposed metamaterial absorber structure, under normal incidence, the bandwidth with an absorption rate of 90% is 4.3 - 26.5 GHz (143.3%). When the oblique incidence angle is 45°, the absorption bandwidths under TE polarization and TM polarization are 5.1 - 21.3 GHz (122.72%) and 6.8 - 29.5 GHz (125.07%), respectively. The proposed method can be extended to other frequency domains and advanced metamaterial absorber designs.

Claims

1. A slant-incidence ultra-wideband absorbing metamaterial unit based on the characteristic mode theory, hereinafter referred to as "unit", which is composed of upper and lower lossy dielectric plates, a metal patch attached thereto, and a bottom metal ground plane. From top to bottom, it is successively: an upper metal patch, a first dielectric layer, a first air layer, an intermediate metal patch, a second dielectric layer, a second air layer, and a metal ground; characterized in that The upper and lower dielectric plates are identical thin rectangular parallelepiped structures, and their projections on the horizontal plane coincide. The upper and lower surfaces are both squares with a side length of p; The upper metal patch is attached to the upper surface of the upper dielectric plate and adopts a meandering square loop patch with an outer ring length of l1 and a square loop width of w1; Lumped resistors R1 are embedded at the right-angle corners of the square loop, and lumped resistors R2 are embedded in the middle of each side of the square loop. Among them, two lumped resistors R1 are embedded at each right-angle corner of the square loop. These two lumped resistors are respectively located on two mutually perpendicular sides of the corner, and the figure enclosed by these two lumped resistors R1 is exactly the largest square at the corner, with a side length of the square loop width w1. The lumped resistor R2 is embedded in the middle of each side of the square loop; Each side of the square loop patch is parallel to the edge of the upper dielectric plate and maintains the same distance; The two sections of metal between the lumped resistor R2 on each side of the square loop and the two lumped resistors R1 at both ends of this side are etched into meandering lines, which meander from the lumped resistor R1 to the lumped resistor R2, and there is a certain spacing between the two ends of the meandering line and the lumped resistors R1 and R2; The intermediate metal patch is attached to the upper surface of the lower dielectric plate and includes four identical "L"-shaped metal strips placed back to back, forming a cross shape as a whole. Each "L"-shaped metal strip occupies two adjacent arms of the cross shape. Therefore, the adjacent sides of two adjacent "L"-shaped metal strips are parallel to each other and the two ends are flush, but there is the same distance between them. The distances between the adjacent sides of the four "L"-shaped metal strips are equal; Each arm of the cross-shaped metal patch is parallel to the edge of the lower dielectric plate, and the wall ends are both at the same distance from the edge of the lower dielectric plate; The length of the metal strip is l3, the width of the metal strip is w3, and the distance between the metal strips is w4; Two resistors R3 are embedded at each right-angle corner, and their arrangement method is the same as that of the two lumped resistors R1 embedded at each right-angle corner of the square loop; The bottom metal ground plane is a thin metal plate, and its projection on the horizontal plane coincides with that of the upper and lower dielectric plates.

2. The ultra-wideband absorbing metamaterial unit with oblique incidence based on the characteristic mode theory according to claim 1, characterized in that, The range of the side length p is 8 - 12 mm; The thicknesses hs1 and hs2 of the two dielectric plates are in the range of 0.5 - 1 mm; The thicknesses ha1 and ha2 of the two air layers between the two dielectric plates and between the lower dielectric plate and the bottom metal ground plane are in the ranges of 3.5 - 4 mm and 1 - 2 mm respectively.

3. The obliquely incident ultra-wideband absorbing metamaterial unit based on the characteristic mode theory according to claim 2, characterized in that, The side length p is 10 mm; The thicknesses hs1 and hs2 of the two dielectric plates are 0.72 mm and 0.79 mm respectively; The thicknesses ha1 and ha2 of the two air layers between the two dielectric plates and between the lower dielectric plate and the bottom metal ground plane are 3.87 mm and 1.5 mm respectively; The selected range of the dielectric constant is within 2.2 - 4.

0.

4. The obliquely incident ultra-wideband absorbing metamaterial unit based on the characteristic mode theory according to claim 1, wherein the length l1 of the outer ring of the upper metal patch ranges from 8 to 9 mm; the width w1 of the square ring ranges from 0.8 to 1.2 mm; the values of the lumped resistors R1 and R2 range from 75 Ω to 100 Ω; the length l2 of the meandering line ranges from 0.8 to 0.9 mm; the width w2 of the meandering line ranges from 0.08 to 0.12 mm.

5. The obliquely incident ultra-wideband absorbing metamaterial unit based on the characteristic mode theory according to claim 4, wherein the length l1 of the outer ring of the upper metal patch is 8.5 mm; the width w1 of the square ring is 1 mm; the lumped resistors R1 and R2 are 97.6 Ω; the length l2 of the meandering line is 0.85 mm; the width w2 of the meandering line is 0.1 mm.

6. The ultra-wideband absorbing metamaterial unit with oblique incidence based on the characteristic mode theory according to claim 1, wherein For the middle layer metal patch, the length l3 of the metal strip ranges from 3 to 5 mm; the width w3 of the metal strip ranges from 0.8 to 1.2 mm; the spacing w4 between the metal strips ranges from 0.3 to 0.7 mm; the values of the two resistors R3 range from 50 Ω to 100 Ω.

7. The obliquely incident ultra-wideband absorbing metamaterial unit based on the characteristic mode theory according to claim 6, characterized in that, The length l3 of the metal strip of the middle layer metal patch is 4 mm; the width w3 of the metal strip is 1 mm; the spacing w4 between the metal strips is 0.5 mm; the two resistors R3 are 73.2 Ω.

8. The ultra-wideband absorbing metamaterial unit with oblique incidence based on the characteristic mode theory according to claim 1, wherein The combination of the upper metal patch and the upper dielectric plate in the unit is named as unit (1), and the combination of the middle layer metal patch and the lower dielectric plate is named as unit (2); the equivalent circuit along the direction of electric field polarization is: In a unit (1), the first coupling capacitor C u1 is the coupling capacitor between adjacent metal patches of the unit (1); the first equivalent inductor L A1 is the equivalent inductor on the metal strip parallel to the polarization direction; C p1 is the parasitic capacitor on the meander line; the first equivalent resistor R A1 is the equivalent resistance of R1 and R2 inserted into the metal strip; in a unit (2), the second coupling capacitor C u2 is the coupling capacitor between adjacent metal patches of the unit (2); the second equivalent inductor L A2 is the equivalent inductor on the metal strip parallel to the polarization direction; the third equivalent inductor L A3 is the equivalent inductor on the metal strip perpendicular to the polarization direction; the third coupling capacitor C A1 and the fourth coupling capacitor C A2 are the coupling capacitors between adjacent parallel metal strips in the unit (2); the second equivalent resistor R A2 is the equivalent resistance of the resistor R3 inserted into the lower metal patch; In the equivalent circuit of a unit (1): the parasitic capacitance C of the meander line p1 is connected in parallel with the first equivalent inductance L A1 to form a first inductance-capacitance circuit; one end of the first coupling capacitance C u1 is connected to the plane wave port, and the other end is connected to one end of the first inductance-capacitance circuit; the other end of the inductance-capacitance circuit is grounded through the first equivalent resistance R A1 ; In the equivalent circuit of the second unit (2): the second coupling capacitor C u2 , the second equivalent inductor L A2 , the second equivalent resistor R A2 , and the third coupling capacitor C A1 are connected in series in sequence to form a first series circuit. The terminal of the third coupling capacitor C A1 in the first series circuit is grounded downward via the second dielectric layer and the second air layer. The terminal of the second coupling capacitor C u2 in the first series circuit is connected to the plane wave port upward via the first air layer and the first dielectric layer, and is grounded downward via the second dielectric layer and the second air layer. The third equivalent inductor L A3 is connected in series with the fourth coupling capacitor C A2 to form a second inductor-capacitor circuit. The terminal of the third equivalent inductor L A3 in this circuit is connected to the connection point of the second coupling capacitor C u2 , the second equivalent inductor L A2 . The terminal of the fourth coupling capacitor C A2 in this circuit is grounded downward via the second dielectric layer and the second air layer.

9. An inclined-incidence ultra-wideband absorbing metamaterial array based on the characteristic mode theory, which is based on the inclined-incidence ultra-wideband absorbing metamaterial unit according to any one of claims 1 to 7, and is characterized in that Multiple units are arranged in an array.

10. The oblique-incidence ultra-wideband absorbing metamaterial array based on the characteristic mode theory according to claim 9, characterized in that, A 12*12 array is adopted.

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