# Polarization Stable Triband Thin Square-Shaped Metamaterial Absorber

Authors: M. L. S. N. S. Lakshmi; S. Prasad Jones Christydass; S. Kannadhasan; K. Anguraj; Jyotir Moy Chatterjee
Journal: International Journal of Antennas and Propagation
 (2023)

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## Abstract

An efficient triband metamaterial absorber is presented for X- and K-band applications. The unit cell is of simple shape. The absorber is fabricated on a thin polyamide, which makes it flexible. The parameters of the designed absorber are optimized. The simulated results show that it has good absorption rate and polarization stability. The stability is exhibited over a wide range in both TE and TE modes of the incident waves. The measured results are on par with the simulated results. The measurement is carried out with the waveguide measurement method.


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## Body

## 1. Introduction

Metamaterials are the artificial manmade periodic structures that are widely used in the design of antennae, frequency selective surfaces, and absorbers. The fact is that it has an unusual property that is not readily available in nature, i.e., negative consecutive parameters, antiparallel group, and phase velocities. In the year 2008 [1], a perfect electromagnetic metamaterial absorber is proposed and it paved the way for many researchers to focus on the design of EM-based metamaterial absorbers in the past two decades. There is a huge demand for the design of EM-based metamaterial absorbers with lighter compact and thinner configurations. A wide variety of structures has been introduced by the researchers by which the performance of the absorbers had been increased. Metamaterial absorbers that are insensitive to polarization are presented [2–4]. The multimode absorbers available are reported [5–7]. In [5], Xu et al. proposed an absorber with a complex shape, but the rate of absorption at the third frequency is very low. In [6], with complex and larger unit cell sizes, an absorber with triband frequency is presented. However, optimizing the performance of the band separately is difficult, even by changing its corresponding physical parameters. In [7], three I-shaped absorbers for THz frequency are reported and it was presented that the peak absorbance of more than 90% was noticed at the largest angle of incidence (60°). Metamaterial absorbers couple E and H fields separately. The absorbance was reported as above 88% at 11.5 GHz. The designers left a valuable suggestion of optimizing the design at the exact resonant frequency by choosing a highly consistent substrate with respect to its dielectric constant. A triband absorber is presented in [1], which uses two resonators. A triangular metamaterial absorber using plasma material is reported in [8]. The developed structure consists of three layers, namely, metal, dielectric, and solid-state plasma (SSP) layers (realized by GaAs), producing the polarization-independent absorption at the rate of absorption greater than 90% across 11.76 GHz–14.43 GHz spectrum. The designers also explored its tuneable performance by exciting the different solid-state plasma resonators.In [9], the absorber with THz range is proposed and a hybrid metamaterial absorber (MA) with high performance with two absorption peaks, which were obtained by electrical and cavity modes of resonance, respectively, in [10]. The method to decrease the operating frequency of the unit cell of an MA (towards 1.35 GHz) was discussed in [11], which was aimed to make the absorber more suitable for practical applications as well as to reduce the sensitivity with respect to the curvature of the structure, leading 88% fractional bandwidth with good absorption for 0°–40° incidence angles. Another miniaturized MA was designed and proposed in [12], which operates in the UHF band (86–960 MHz) for UHF-RFID applications for enhancing the reliability of the RFID system. A THz range MA was demonstrated in [13] with a novel combinatorial approach provided with a nested structure composed of multiple metal-dielectric layers. In [14], a cross-shape unit cell with a flexible substrate is presented, and it was reported that the stretch of 25% was causing a resonant frequency shift of 0.5% for TM polarization. Wide-angle polarization-insensitive characteristics absorbers are presented in [15], and the structure uses a metallic background plane, four groups of pins to connect a metallic ring around which there are four groups of dipoles. Liquid crystal was used in the mesh voids to impart tunability for the F frequency band absorber in [16], in which the variation in the bias voltage causes the frequency tunability of 6.4% and proposed this design for developing the tuneable absorbers and sensors. The tuneable absorption characteristics (claimed to be the biggest in the range of 77.10%) were reported in [17] at 3 μm central wavelength, which was obtained by the reversible phase transition of VO2 between metallic and dielectric states. Two square ring resonators were used of different sizes and fabricated on felt material to prepare a wearable metamaterial absorber in [18]. The deformation effect was also studied claiming that the design provides high absorptivity at 9.475 GHz targeting the indoor radar clear applications. An absorber in [19] is with an active configuration that can be electrically controllable in terms of polarization and frequency. The active nature was implemented by inserting PIN diodes between the circular ring and Jerusalem cross structures of the absorbers. In [20], with metallic incurved structure, an absorber is presented for the UHF-RFID and 4G applications and a relative bandwidth of 108% is reported, and a two-concentric-circular-split-ring-based absorber in the X-band range is presented in [21].In [22], a split-ring-cross resonator (SRCR), metallic ring, and meander line are used to design the absorber. The designers identified that the lowering of operating frequency has decreased the electrical size of the unit cell through the inductance and capacitance generated by the metallic patterns. A quad-band ultrathin MMA was proposed in [23], which uses cross dipoles loaded with split-ring resonators forming the unit cell structure resonating at 3.68/8.58/10.17/14.93 GHz, respectively, showing a high absorption in both TE and TM polarizations. The design proposed in [24] reports the absorber with a two-dimensional metallic structure and operates in two modes, namely, localized surface plasmon (LSP) mode and dielectric loss mode, which contributes to multiband absorption characteristics. Even though a large number of absorbers are reported in the literature, they have a very complex rigid structure with fabrication complexity. Thus, there is a huge demand for the design of metamaterial absorbers with good performance such as multiband, flexible, compact, and low-cost fabrication.In this paper, we propose a metamaterial [25–32] absorber that exhibits three different absorption peaks. A metamaterial-based ultrabroad band absorber is proposed at the THz range. The absorbers are based on the Ti/Ge/Si3N4/Ti. Two types of absorbers are proposed based on the different combinations and both achieved the ultrawide-band response. In [33], a multilayered metamaterial with graphene is proposed for dual-band application. The operating frequency of the proposed absorber is 0.79–20.9 GHz and 25.1–40.0 GHz. The proposed absorber is the combination of the multiple graphene layers and the metamaterial absorber. In [34], the split-disk-based tunable absorber works at THz frequency application; in [35], broadband metamaterial absorber based on CMA is presented for S, C, X, and Ku bands; and in [36–38], metamaterial absorber, which is used for solar energy harvesting, is proposed. The proposed structure is having significant features such as the triple-band, polarization-insensitive, compactness, and simple shape that end in easy fabrication. The flexible nature of the proposed absorber makes it useful for the microbolometer, spectral imaging, and coating material. The absorber is proposed, where the absorptivity is more than 90% at the peak absorption frequencies [39−41].


## 2. Unit Cell Design

The geometry of the absorber unit cell is shown in Figure1. The design consists of the patch, ground, and substrate, where its patch consists of a block line border, which is spaced by a 0.5 mm, at the center of the unit cell, cross having a rhombic-shaped patch element with a spacing value of 0.5 mm and four rectangular strips with triangular pointing structures looking outwards from the center towards corners of the unit cell.Figure 1
Structure of the proposed unit cell: (a) unit cell geometry; (b) Floquet port simulation; (c) schematic representation of incident field; (d) geometrical parameters:L = 10, L1 = 2.25, L2 = 0.5, L3 = 1, L4 = 1.5, L5 = 0.5, L6 = 0.5, L7 = 4.6, L8 = 2.75, L9 = 3.75, L10 = 1, L11 = 0.5, S = 0.7, S1 = 0.5, S2 = 0.35, and T = 0.1 (all dimensions are in mm).
(a)(b)(c)(d)The proposed geometrical structure of the unit cell is designed on the polyimide substrate with a thickness of 0.1 mm, which imparts compactness in terms of the overall volume of the absorber. The absorber’s absorption is characterized by A = 1-R-T, where the background will be made up of the metals, which makes the transmissivity zero. The parameters of the unit cell are optimized properly such that the incident wave is properly coupled. The simulation of the proposed absorbers is carried out using Ansoft HFSS with PBC as its boundary condition.


## 3. Results and Discussion

### 3.1. Absorptivity Characteristics

It undergoes master-slave periodic boundary conditions. Mathematically, it can be obtained by the equation A (ɷ) = 1−R (ɷ)−T (ɷ), which can be rewritten as follows:To analyze the absorptivity of the absorber unit cell,(1)A=A−S11ϖ2−S21ϖ2,where as Rϖ=S11ϖ2 and Tϖ=S21ϖ2 are the reflected power and transmitted power, respectively. But the ground plane is covered fully, so the ground plane acts as an obstacle for the incident wave and gives a zero transmission as a result. So, the equation can be written as(2)A=1−S11ϖ2.Figure2 shows the simulated absorptivity values of the absorber, the absorber has two absorptivity peaks where the absorption is above 90%, and it is created at 11.4 GHz and 19.2 GHz frequencies where the absorption values at those peaks are 0.9753 and 0.9652, respectively. The absorption peaks are created one in the X-band and other in the K-band. There are many variations in the absorptivity by varying the incident angles.Figure 2
Absorptive characteristics.Figure3 represents the absorptivity values of the absorber by varying the incident angles for TE polarization, where the incident angle ranges from 10 degrees to 90 degrees by a varying factor of 10 degrees. The absorption values are higher at incident angle phi 90 degrees, where the values are greater than 0.9 at two different frequencies and at different frequency bands. Figure 4 represents the absorption values of the absorber achieved by varying the incident angles for TM polarization, which is same as TE polarization, but the absorption peaks are achieved at theta 0 degrees.Figure 3
Absorptivity simulated for multiple angles of phi.Figure 4
Absorptive simulated for multiple angles of theta.Conduction current (on the top and bottom conductors) and displacement current are created when the top and bottom layers’ dominant current densities are antiparallel to one another (in between the top and bottom layer conductors through dielectric). At each of the peak absorption frequencies, a current loop is created by the conduction and displacement currents. This circulating current loop, which is centered on the incident magnetic field, causes magnetic excitation. The incident electric field at the top metallic surface causes electric excitation. Consequently, simultaneous electric and magnetic excitations take place.


### 3.2. Return Loss Characteristics

The return loss graphs are used to estimate the working of the structure, where the absorber achieved two resonance peaks one in x-band and the other in k-band where the return losses at those peaks are greater than −10 dB. The return losses with respect to the theta and phi are also simulated to know the relation between the graphs achieved and the achieved bands, where the theta0 and phi90 achieved the same values, as the absorption is achieved based on the values of the return loss; if the return loss is achieved for a particular structure, we can assume that the achieved working band in the return loss is also the same band for absorptivity is shown in Figure5.Figure 5
Reflection coefficient.The reflection coefficient values are also achieved by varying the incident angles of TE polarization and TM polarization, where the results are good at theta0 and phi90, the peaks are achieved with respect to both the absorptivity and return loss where the simulated results TE and TM polarization are shown in Figures6 and 7, respectively.Figure 6
Return loss simulated for multiple angles of phi.Figure 7
Return loss simulated for multiple angles of theta.At oblique incidences, there is a slight difference between TE and TM. For TE polarization, the electric field is parallel to the top of the absorber, so most of the energy losses will be concentrated on the top layer. So, the absorptivity is more similar to the normal incidence. But in the case of TM polarization, the absorptivity is insensitive only if the dielectric loss is very high. At a low dielectric loss, the absorptivity loss is reduced with the increase in incident angle. This is due to the reason part which is depleted by the top layer and remailing is consumed by the dielectric substrate.


### 3.3. Fabricated Model

Here, the unit cells arranged into a group to achieve the absorbing characteristics in a wide area are shown in Figure8(a). The structure designed is a 5 × 5 cell structure sheet where the spacing between each cell is 0.5 mm; an array of cells formed is shown in Figure 8(b). The measurement setup is shown in Figure 8(c).Figure 8
(a) Proposed absorber on thin substrate; (b) fabricated prototype; (c) measurement setup; (d) equivalent circuit.
(a)(b)(c)(d)In Figure8(d), the equivalent circuit of the proposed absorber is presented. The capacitance c1 to c8 correspond to the rectangular and triangular slots in the proposed structure. The inductance L1 corresponds to the conductor ring between the slots, and the capacitor c9 denotes the diamond-shaped slot at the center. The inductance L2 and L3 correspond to the conductor length. The capacitance C10 and C11 denote the horizontal coupling between the unit cells, while the capacitors c12 and c13 denote the vertical coupling between the metal ring and the ground plane.


### 3.4. Measured Results

The proposed metamaterial absorber has achieved a good correlation between simulated and measured values of absorptivity, where the graph represents the simulated and measured values of the absorber. The proposed metamaterial absorber has achieved good correlation as shown in Figure9.Figure 9
Measured vs simulated absorptivity.Further to understand the radiation mechanism of the proposed structure, the surface current distribution of the proposed structure is studied. The performance analysis of the proposed absorber is shown in Table1. Figure 10 shows the surface current distribution of the proposed structure at various resonating bands. It is observed that the current is centered around the metal strips and on the gaps in the structure. From Figure 10, it is observed that the current is around the outer square ring at 11.4 GHz. The absorption peak at 17.1 GHz is due to the X-shaped slots in the center of the square plate since the maximum surface current is higher around it at 17.1 GHz. The absorption peak at 19.2 GHz is due to the triangular slot in the square plate. The surface current flows strongly around the discontinuities leading to a strong electric and magnetic field in the opposite direction. Hence, the proposed structure simulates an equivalent LC, and its resonance can be adjusted by controlling the parameters.Table 1
Performance analysis of the proposed absorber.
[Ref]Configuration of the absorberOperation center frequency/band (GHz)Size of the unit cell (in mm)No. of bands getting absorbedPercentage of absorption (%)[2]Metamaterial resonators11.512 × 4.2 × 0.21>88[4]Metamaterial resonators11.76–14.4372 × 72 × 31>90[5]Hybrid dielectric layer absorber1.35–3.520 × 20 × 1.61>90[6]Square loop loaded lumped resistor MMA0.86–0.9620 × 19.2 × 1.61>90[1]Stretchable metamaterial absorber11–11.48 × 8 × 31>90[8]Ultrathin metamaterial absorber3.25, 9.45, 10.911 × 11 × 1.033>90[11]Wearable MMA9, 9.8530 × 30 × 12>90[12]Active MMA4.3, 5.913.8 × 13.8 × 12>90[13]Ultrawide-band MMA0.8–2.720 × 20 × 1.61>90ProposedMMA11.4, 17.1, and 19.210 × 10 × 0.12>90MMA = metamaterial-based absorber.Figure 10
Surface current distribution at various resonating frequencies: (a) 11.4 GHz. (b) 17.1 GHz. (c) 19.2 GHz.


## 3.1. Absorptivity Characteristics

It undergoes master-slave periodic boundary conditions. Mathematically, it can be obtained by the equation A (ɷ) = 1−R (ɷ)−T (ɷ), which can be rewritten as follows:To analyze the absorptivity of the absorber unit cell,(1)A=A−S11ϖ2−S21ϖ2,where as Rϖ=S11ϖ2 and Tϖ=S21ϖ2 are the reflected power and transmitted power, respectively. But the ground plane is covered fully, so the ground plane acts as an obstacle for the incident wave and gives a zero transmission as a result. So, the equation can be written as(2)A=1−S11ϖ2.Figure2 shows the simulated absorptivity values of the absorber, the absorber has two absorptivity peaks where the absorption is above 90%, and it is created at 11.4 GHz and 19.2 GHz frequencies where the absorption values at those peaks are 0.9753 and 0.9652, respectively. The absorption peaks are created one in the X-band and other in the K-band. There are many variations in the absorptivity by varying the incident angles.Figure 2
Absorptive characteristics.Figure3 represents the absorptivity values of the absorber by varying the incident angles for TE polarization, where the incident angle ranges from 10 degrees to 90 degrees by a varying factor of 10 degrees. The absorption values are higher at incident angle phi 90 degrees, where the values are greater than 0.9 at two different frequencies and at different frequency bands. Figure 4 represents the absorption values of the absorber achieved by varying the incident angles for TM polarization, which is same as TE polarization, but the absorption peaks are achieved at theta 0 degrees.Figure 3
Absorptivity simulated for multiple angles of phi.Figure 4
Absorptive simulated for multiple angles of theta.Conduction current (on the top and bottom conductors) and displacement current are created when the top and bottom layers’ dominant current densities are antiparallel to one another (in between the top and bottom layer conductors through dielectric). At each of the peak absorption frequencies, a current loop is created by the conduction and displacement currents. This circulating current loop, which is centered on the incident magnetic field, causes magnetic excitation. The incident electric field at the top metallic surface causes electric excitation. Consequently, simultaneous electric and magnetic excitations take place.


## 3.2. Return Loss Characteristics

The return loss graphs are used to estimate the working of the structure, where the absorber achieved two resonance peaks one in x-band and the other in k-band where the return losses at those peaks are greater than −10 dB. The return losses with respect to the theta and phi are also simulated to know the relation between the graphs achieved and the achieved bands, where the theta0 and phi90 achieved the same values, as the absorption is achieved based on the values of the return loss; if the return loss is achieved for a particular structure, we can assume that the achieved working band in the return loss is also the same band for absorptivity is shown in Figure5.Figure 5
Reflection coefficient.The reflection coefficient values are also achieved by varying the incident angles of TE polarization and TM polarization, where the results are good at theta0 and phi90, the peaks are achieved with respect to both the absorptivity and return loss where the simulated results TE and TM polarization are shown in Figures6 and 7, respectively.Figure 6
Return loss simulated for multiple angles of phi.Figure 7
Return loss simulated for multiple angles of theta.At oblique incidences, there is a slight difference between TE and TM. For TE polarization, the electric field is parallel to the top of the absorber, so most of the energy losses will be concentrated on the top layer. So, the absorptivity is more similar to the normal incidence. But in the case of TM polarization, the absorptivity is insensitive only if the dielectric loss is very high. At a low dielectric loss, the absorptivity loss is reduced with the increase in incident angle. This is due to the reason part which is depleted by the top layer and remailing is consumed by the dielectric substrate.


## 3.3. Fabricated Model

Here, the unit cells arranged into a group to achieve the absorbing characteristics in a wide area are shown in Figure8(a). The structure designed is a 5 × 5 cell structure sheet where the spacing between each cell is 0.5 mm; an array of cells formed is shown in Figure 8(b). The measurement setup is shown in Figure 8(c).Figure 8
(a) Proposed absorber on thin substrate; (b) fabricated prototype; (c) measurement setup; (d) equivalent circuit.
(a)(b)(c)(d)In Figure8(d), the equivalent circuit of the proposed absorber is presented. The capacitance c1 to c8 correspond to the rectangular and triangular slots in the proposed structure. The inductance L1 corresponds to the conductor ring between the slots, and the capacitor c9 denotes the diamond-shaped slot at the center. The inductance L2 and L3 correspond to the conductor length. The capacitance C10 and C11 denote the horizontal coupling between the unit cells, while the capacitors c12 and c13 denote the vertical coupling between the metal ring and the ground plane.


## 3.4. Measured Results

The proposed metamaterial absorber has achieved a good correlation between simulated and measured values of absorptivity, where the graph represents the simulated and measured values of the absorber. The proposed metamaterial absorber has achieved good correlation as shown in Figure9.Figure 9
Measured vs simulated absorptivity.Further to understand the radiation mechanism of the proposed structure, the surface current distribution of the proposed structure is studied. The performance analysis of the proposed absorber is shown in Table1. Figure 10 shows the surface current distribution of the proposed structure at various resonating bands. It is observed that the current is centered around the metal strips and on the gaps in the structure. From Figure 10, it is observed that the current is around the outer square ring at 11.4 GHz. The absorption peak at 17.1 GHz is due to the X-shaped slots in the center of the square plate since the maximum surface current is higher around it at 17.1 GHz. The absorption peak at 19.2 GHz is due to the triangular slot in the square plate. The surface current flows strongly around the discontinuities leading to a strong electric and magnetic field in the opposite direction. Hence, the proposed structure simulates an equivalent LC, and its resonance can be adjusted by controlling the parameters.Table 1
Performance analysis of the proposed absorber.
[Ref]Configuration of the absorberOperation center frequency/band (GHz)Size of the unit cell (in mm)No. of bands getting absorbedPercentage of absorption (%)[2]Metamaterial resonators11.512 × 4.2 × 0.21>88[4]Metamaterial resonators11.76–14.4372 × 72 × 31>90[5]Hybrid dielectric layer absorber1.35–3.520 × 20 × 1.61>90[6]Square loop loaded lumped resistor MMA0.86–0.9620 × 19.2 × 1.61>90[1]Stretchable metamaterial absorber11–11.48 × 8 × 31>90[8]Ultrathin metamaterial absorber3.25, 9.45, 10.911 × 11 × 1.033>90[11]Wearable MMA9, 9.8530 × 30 × 12>90[12]Active MMA4.3, 5.913.8 × 13.8 × 12>90[13]Ultrawide-band MMA0.8–2.720 × 20 × 1.61>90ProposedMMA11.4, 17.1, and 19.210 × 10 × 0.12>90MMA = metamaterial-based absorber.Figure 10
Surface current distribution at various resonating frequencies: (a) 11.4 GHz. (b) 17.1 GHz. (c) 19.2 GHz.


## 4. Conclusion

In this article, a new design is proposed to achieve a triband metamaterial-based ultrathin polarization-insensitive absorber. The absorber is flexible in nature. The bands are achieved by optimizing the parameters. The proposed absorbers exhibit absorption above 90% in the bands for the incident wave both in TE and TM. It also exhibits high polarization insensitivity over wide angles, making it suitable for the multimode metamaterial absorbers.



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*Source: 6065300-2023-01-14.xml*