Design of broadband metamaterial absorber utilized by ﬂ ower-shaped unit loaded with lumped-resistor

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Introduction
With the continuous development of information technology, wireless equipment, such as mobile phones and laptops, has been greatly convenient for people's lives.However, it has also been accompanied by serious electromagnetic interference and pollution issues, which may affect the stability of communication signals, as well as impair human health [1][2][3][4][5][6][7].Therefore, it is of great significance to study efficient electromagnetic (EM) wave absorption materials.During the past decades, various kinds of material have been investigated for EM wave absorption, such as ferrites, carbon nanotubes, graphene, amorphous metal, etc. [8][9][10][11][12][13][14][15].In 2008, Landy and co-workers first proposed the concept of a 'perfect absorber' based on metamaterials, which could achieve 99% absorption at the designed frequency [16].Unlike the traditional absorbing material, excellent absorption performance could be obtained and precisely controlled through the design of artificial periodic structures in metamaterial absorber.
In traditional absorbing materials, the absorption mechanism usually can be attributed to interface polarization, dipole polarization, multiple reflection, current loss, and magnetic loss.In metamaterial, however, the absorption of the EM wave comes from electromagnetic resonance, which is strongly dependent on the size and shape of the metamaterial unit.In this case, the bandwidth of the metamaterial absorber is usually limited to a quite narrow frequency range.Broadening the effective absorption bandwidth (EAB) of metamaterial absorbers has already become one of the most challenging research topics in this field.Ali and co-workers used resonance rings of different size in metamaterial absorbers to generate electromagnetic coupling, which broadened the effective absorption bandwidth [17].Xiong et al. combined metal resonance rings with a dielectric layer to build up a multiple-layer structure, in which the effective absorption bandwidth can reach up to 12.63 GHz [18].Although using different size units or multiple-layer designs in metamaterial absorbers can increase the EAB, the relatively large thickness, as well as the complex unit structure, has greatly limited the practical application [19,20].
Compared with the above methods, using lumped resistors in metamaterial unit can improve the impedance matching property, leading to a broadband EM wave absorption performance [21][22][23][24][25][26][27][28][29].In this paper, a broadband metamaterial absorber was designed using a flower-shaped unit loaded with lumped resistor.By optimizing the resistance and structural parameters of the absorber, the maximum EAB can reach up to 9.1 GHz (8.3-17.4GHz) with 3 mm thickness.Besides, the angle stability of the absorber is also improved (EAB is 3.7 GHz @ 60°incident angle) by adding vertical metal through holes.In the metamaterial absorber loaded with lumped resistance, the dissipation of electromagnetic waves is achieved by ohmic loss caused by resistance elements, as well as the magnetic resonance caused by induced circle current, which will not be affected by temperature or other factors.

Experiment
The unit structure of the metamaterial absorber consists of a top dielectric layer, a metal pattern layer, an intermediate dielectric layer and a metal backplane, as shown in panel (a) of Figure 1.The top layer (blue part) is Arlon AD 250C with the relative dielectric constant e r = 2.5 and loss tangent tan u = 0.0013.Copper has been used as the metal The geometric parameters of the unit are as follows, the periodicity of the unit p = 10 mm, and the thickness of Arlon AD 250C layer h 1 = 0.5 mm, while the FR-4 dielectric layer thickness h 2 = 2.5 mm.To build up the flower-shaped unit in the metal pattern layer, a parametric equation has been used, which is shown in panel (a) of Figure 1.The radius of the hollow circle r in the center of the flowershaped pattern was set to 1 mm, and the same lumped resistors (z = 100 V) were been used as the connecting parts between the 'petal'.During the simulation, both x and y directions are set as unit cell boundary conditions that can be considered as an infinite plate.The positive direction of the Z axis is set as 'open' to simulate the free space, in which the electromagnetic wave is perpendicular incident to the model surface.The frequency domain solver is used for calculation.Finally, the 30 cm Â 30 cm sample was fabricated and measured by using the NRL arch method.

Results and discussion
The absorption ratio effected by the geometric parameters of the model has been shown in panels (b)À(e) of Figure 1.It can be clearly observed that absorption bandwidth increases as the r value increases from 0.5 mm to 1 mm.When r = 0.5 mm, the bandwidth is approximately 4 GHz (14-18 GHz), while at r = 1.0 mm, the bandwidth reaches nearly 7 GHz (11.4-18.3GHz).If further increasing the value of r, the bandwidth decreases to only 3 GHz @ 2 mm (15-18 GHz).The resistance value of the loaded lumped resistance also has a decisive impact on the absorption ratio.As shown in panel (c) of Figure 1, the absorption bandwidth increases with the increase of resistance value.However, when z = 150 V, the effective absorption frequency band is transformed into dual-band of 11-16.1 GHz and 17-18.85GHz, making it more difficult in practical military applications.The further increase of the resistance value causes the EAB to decrease rapidly.Besides, the thickness of the dielectric layer is another key factor affecting the absorption performance.The effect of the thickness is shown in panels (d) and (e) of Figure 1.It can be found that, compared with the thickness of the upper layer, the thickness of the bottom layer can greatly affect the effective absorption bandwidth and the maximum absorption intensity.When the thickness of the bottom layer is equal to 2.5 mm, the EAB can get up to 8.13 GHz (from 8.22 to 16.35 GHz).The thickness of the upper layer does not affect the EAB obviously, but changing the maximum absorption peak position.Based on the simulation results above, the optimal parameters of the unit are r = 1 mm, z = 100 V, h 1 = 0.5 mm and h 2 = 2.5 mm.This optimized model is used for the following investigation and discussion.
It is worth noting that for practical applications, the angle stability and polarization insensitivity are also extremely important in the performance evaluation of the metamaterial absorber.The microwave absorption performance of the designed unit under TE and TM polarization modes, as well as different incident angles, are shown in Figure 2. As can be seen from panel (a) of Figure 2, there is no difference in the absorption ratio between TE and TM modes, indicating an excellent polarization insensitivity of the designed metamaterial absorber.However, it can be found that in TE mode, with the increase of incident angles, the resonance peak moves to high frequency.The absorption bandwidth has no obvious change from 0°to 30°, while the absorption ratio decreases slightly.Nevertheless, as the further increases of incident angle, the EAB began to drop down continuously.When the incident angle gets up to 60°, the absorption rate is less than 90% in the whole frequency range.Therefore, the angle stability of the unit under TE mode is about 40°.When the polarization changes to TM mode, the EAB decreases rapidly with the incident angle changing from 0°t o 60°, indicating a relatively low angle stability.
To elucidate the mechanism of the metamaterial absorber, the field monitor was added during the simulation process to analyze the surface current, electric field, magnetic field, and energy flow distribution at 10.65 GHz and 16 GHz, respectively.As shown in Figure 3, the surface current direction on the metal pattern layer is opposite to the backplane at 10.65 GHz, resulting the formation of a ring electric current between the metal pattern layer and the backplane, thereby inducing magnetic resonance.Meanwhile, by the introducing a lumped resistance at the center of the metal pattern, the current flows through the resistance, the ohmic loss converts EM wave energy into heat energy and dissipate it.Therefore, both the magnetic and ohmic losses contribute to the enhanced absorption efficiency.This inference can be confirmed by the field distribution results.Notably, the power loss density distribution is closely consistent with the electric and magnetic field distribution, mainly concentrated along the edge of the petal-shaped pattern, indicating that the absorption mechanism at 10.65 GHz is attribute to the electric and magnetic losses.At 16 GHz, however, the situation is slightly different.The surface current on the metal pattern aligns generally with the direction of the backplane current, so there is no magnetic current and magnetic loss.Instead, the main loss forms are electrical resonance and ohmic heat.The field distribution results reveal that the power loss density distribution is only consistent with the electric field distribution.The magnetic field distribution only partially overlaps with the power loss density, indicating that the absorption at 16 GHz mainly comes from the electric loss.
In order to further improve the angle stability under TM polarization mode, the model has been modified by adding four through-holes in the FR-4 dielectric layer.Figure 4 displays the new model of the metamaterial unit and its microwave absorption performance under TE, TM polarization mode, and different incident angles in TM mode.It can be found that, compared with the original model without metal vias, the angle stability has been significantly improved.The EAB could maintained at 4.15 GHz bandwidth (from 9.6 to 13.75 GHz) with the  incident angle reaching up to 50°.Even at an incident angle of 60°, the unit still exhibits relatively acceptable EAB (3.72 GHz, from 9.53 to 13.25 GHz).Particularly, the EAB further expands to 9.1 GHz (8.3-17.4GHz), and the comparison of absorption properties is listed in Table 1.
Besides, there is no significant difference in the absorption ratio between TE and TM polarization modes.
The surface current at different incident angles has been investigated to find out the reason for the angle stability improvement by adding though-hole, as depicted in Figure 5.When the incident angle is 0°, the presence of a circle electric current before and after adding the throughhole indicates magnetic resonance behavior, demonstrating excellent absorption performance.As the incident angle increases to 60°, the unit with added through-hole still exhibits a circle electric current flowing from the metal pattern layer to the backplane, resulting in enhanced absorption performance through induced magnetic resonance.Nevertheless, in the unit without through-hole, although a circle electric current still exists, there is a current in the backplane that aligns with the direction of the surface current, leading to a weakened circle current and magnetic resonance, showing a decrease in absorption performance.Therefore, the addition of through-hole improves the angle stability of the metamaterial absorber.Additionally, it is evident from Figure 5 that the current intensity is significantly enhanced with the addition of through-hole, further enhancing the absorption performance.
In order to verify the real performance of the designed metamaterial absorber, a 30 cm Â 30 cm sample was fabricated, and the reflection coefficient was measured by the NRL arch frame test method.The image of the sample and testing result are shown in Figure 6, in which the tendency of the experimental curves is in close agreement with that of the simulation results.Particularly, stable broadband absorption performance with excellent angular stability is observed under the TE polarization.Under the TM polarization, absorption band with absorptivity higher than 90% are still present at an angle incidence of 60°.

Conclusion
Utilizing the metal pattern layer and lumped resistance, a broadband absorber is designed with a double-layer dielectric plate sandwich structure.Copper is employed for both the metal pattern layer and backplane, while the middle dielectric layer is FR-4 glass fiber epoxy resin plate, and the top dielectric layer utilizes the Rogers AD250C high frequency circuit plate, which is a composite of PTFE

Fig. 2 .
Fig. 2. (a) The absorption ratio under TE and TM mode, (b) reflection coefficient and absorptivity curve under TE mode.The absorption ratio with different incident angle under (c) TE mode and (d) TM mode.

Fig. 3 .
Fig. 3. Surface current, electric field, magnetic field and energy flow distribution at 10.65 GHz (left row) and 16 GHz (right row).

Fig. 4 .
Fig. 4. (a) Modified unit structure, (b) absorption rate of different polarization modes, (c) absorption ratio of the new structure at different incident angles for TM polarization.

Fig. 5 .
Fig. 5. Surface current on the metal pattern and backplane of the original and modified unit at different incident angles.

Table 1 .
Comparison of existing literature work.