Angle-independent wideband metamaterial microwave absorber for C and X band application

Abstract

In this article, an angle-independent wideband metamaterial microwave absorber (MMA) for C (4–8 GHz) and X (8–12 GHz) band frequency is presented. The unit cell of the proposed MMA consists of outer and inner structure associated with lumped resistors. The outer structure consists of rectangular split-ring resonator, whereas the inner structure consists of circular split-ring resonator. The structure is made up of three layers, in which top and bottom layers are made up of copper acting as a conducting material. The middle layer is made up of FR-4 acting as a dielectric substrate. The resonating structure at the top is designed in such a way that wideband absorption is achieved in the range from 6.11 to 13.52 GHz. The wideband absorption within the range approaches almost unity having a bandwidth of 7.41 GHz. Three different peaks are considered in the range of interest having maximum absorption of 0.94, 0.94, and 0.99 at frequencies of 6.76, 11.15, and 13.07 GHz, respectively. The structure is analyzed with respect to the effective parameters, i.e., effective permittivity (${\varepsilon _{{\textrm{eff}}}}$) and effective permeability (${\mu _{{\textrm{eff}}}}$), to prove that the structure acts as a metamaterial. Electric field and current distribution are plotted at three different peaks to prove the mechanism of wideband absorption. Normal and oblique incidence are plotted to determine that the structure is behaving as an angle independent. The simulated structure is fabricated on FR-4 substrate and measured inside an anechoic chamber. Finally, to prove the novelty of the work, the proposed structure is compared with the already reported MMA. The proposed MMA finds practical applications in radar cross section reduction, terrestrial communication, keyless entry system, space communication, radar, and baby monitor.

Introduction

In recent years, there has been a great deal of attention devoted toward metamaterial, and the related research lab moved from being simply a theoretical concept to a field with developed and marketed applications. It is an engineered material having negative permittivity (ε) or permeability (μ) or both negative ε and μ simultaneously [1]. Due to these unique electromagnetic (EM) properties, it supports backward waves [2], inverse Snell’s law [3], opposite group and phase velocity [4], inverse Doppler’s effect [5], etc., which are not found in naturally occurring materials. They are formed by the combination of different materials such as metals and substrate. Different materials are arranged in repeating patterns, at scales that are smaller than the wavelength of the influenced phenomena. Metamaterials achieve their characteristics not from the single material but from the arrangement of repeating pattern structure. Their shape, geometry, size, and arrangement lead to smart properties which are capable of manipulating EM waves: blocking, absorbing, enhancing, or bending waves [6].

For the first time, Jagdish Chander Bose at the end of nineteenth century in the year 1898 performed some experiments that became the seed work for today’s dynamic field of metamaterials [7]. In 1914, Lindell continued the work by embedding artificial chiral elements in a host medium [8]. Thereafter in 1948, Kock tailored the effective medium properties, i.e., effective permittivity (${\varepsilon _{{\textrm{eff}}}}$) and effective permeability (${\mu _{{\textrm{eff}}}}$) by periodically arranging the conducting disks, strips, and spheres [9]. In 1968, Veselago theoretically explained the wave propagation in a double negative (DNG) material and concluded that ${\varepsilon _{{\textrm{eff}}}}$ and ${\mu _{{\textrm{eff}}}}$ and the refractive index (η) are negative with less than zero values [10]. He explored that the direction of phase velocity is opposite to the direction of Poynting vector in a DNG material. However, this extraordinary finding could not be verified until Sir John Pendry et al. in 1999 [11] postulated that the artificially engineered structures such as split-ring resonator (SRR) with negative effective material properties can be constructed. Based on this concept, the existence of first DNG material was experimentally demonstrated by Smith et al., and this type of material is also named as left-handed material [12]. In the demonstration, Smith et al. used a periodic array of SRR and continuous wire, to provide simultaneously negative value of ${\varepsilon _{{\textrm{eff}}}}$ and ${\mu _{{\textrm{eff}}}}$. Since then, these artificially engineered materials, i.e., metamaterials, became the theme of investigation for the researchers worldwide.

Metamaterials have a wide range of potential applications in EM (ranging from low microwave to optical frequencies), including controllable “smart” surfaces [13], miniaturized cavity resonators [14], novel wave-guiding structures [15], angular-independent surfaces [16], biomedical devices [17], terahertz switches [15], fluid-tunable frequency-agile materials [14], radar cross section (RCS) reduction [18], EM compatibility in electronic devices [19], antennas [20], chip-less RFID [21], solar cells [22], cloaking [23], phase modulators [23], thermal emitters [24], power imaging [25], bolometers [26], photo-detectors [27], artificial magnetic conductors [28], and metamaterial absorber (MA) [29].

This article presents an angle-independent wideband metamaterial microwave absorber (MMA). The proposed structure consists of outer (rectangular SRR [RSSR]) and inner (circular SSR [CSRR]) geometry. The structure is a three-layer design in which top and bottom surfaces are made up of copper, and middle layer consists of FR-4 substrate. The resonate surface is designed to achieve maximum absorption in the range of 6.11–13.52 GHz. The bandwidth of absorption achieved is 7.41 GHz. In the range of interest, three different peaks are considered having maximum absorption with respect to other points. At three different peaks, electric and current distribution are plotted to show the absorption phenomenon. The metamaterial behavior is satisfied by using effective parameters ${\varepsilon _{{\textrm{eff}}}}$ and ${\mu _{{\textrm{eff}}}}$. Normal and oblique incidence are plotted to verify angle-independent phenomenon. The simulation of the proposed structure is carried out using commercially available ANSYS HFSS 19.1v. The simulated structure is fabricated and measured inside the anechoic chamber. Finally, the proposed and already reported MMA are compared to find the novelty of the structure [30–36]. It is observed that the proposed structure is novel in terms of uniquely used resistors in congestion with two circular slotted rings, which is compact in size and has larger bandwidth. The proposed MMA finds practical applications in RCS reduction, terrestrial communication, keyless entry system, space communication, radar, and baby monitor.

Structure design

The unit cell of the proposed MMA consists of outer and inner structures. The outer structure is an RSRR, and the inner structure is CSRR. The lumped resistors are connected to the outer and inner structures. The geometry of the structure is made up of three layers. The top and bottom layers are made up of copper (Cu, conductivity σ = 5 × 10⁷ S/m, thickness = 0.035 mm). The middle layer is made up of FR-4 (ε _r = 4.4, loss tangent δ = 0.02, thickness = 3.2 mm) substrate acting as a dielectric medium. The three-layer geometry is portrayed in Fig. 1. The overall dimension of the structure is 14 mm × 14 mm × 3.2 mm, as shown in Fig. 2. The top resonating structure is designed in such a way that maximum absorption and angle independence are achieved for C and X band frequency applications.

Figure 1. Schematic diagram of proposed MA.

Figure 2. Front view of proposed MA unit cell.

Simulation and parametric analysis

The MMA proposed in this article is simulated using commercially available ANSYS HFSS 19.1 v. The maximum absorption is achieved by optimizing the geometry with respect to height of substrate, inner resistance, and outer resistance. The height of the substrate varies from 0.8 to 4.8 mm in the step size of 0.8 mm, and for substrate height equal to 3.2 mm maximum absorption is achieved as shown in Fig. 3. Second, the outer value of resistance varies from 50 to 150 Ω in the step size of 20 Ω, and for 110 Ω maximum absorption is achieved as shown in Fig. 4. Finally, the inner value of resistance varies from 105 to 185 Ω in the step size of 20 Ω, and for 145 Ω maximum absorption is achieved as shown in Fig. 5.

Figure 3. Absorptivity for different cases—height of the substrate.

Figure 4. Absorptivity for different cases—outer resistance.

Figure 5. Absorptivity for different cases—inner resistance.

After varying the parameters, i.e., height of substrate, outer resistance, and inner resistance, the wideband absorptivity A(ω) is obtained when height of substrate equals 3.2 mm, outer resistance equals 110 Ω, and inner resistance equals 145 Ω.

Wideband absorptivity A(ω) is calculated from Eq. (1), which depends upon reflected (${S_{11}}$) and transmitted (${S_{21}}$) power, but as the lower layer is completely covered with copper, the transmitted power in Eq. (1) is zero and absorptivity completely depends upon reflected power given by Eq. (2). The absorptivity of the structure can be increased by minimizing the reflected power from the surface.

(1)\begin{equation}A\left( \omega \right) = 1 - {\left| {{S_{11}}\left( \omega \right)} \right|^2} - {\left| {{S_{21}}\left( \omega \right)} \right|^2}\end{equation}

(2)\begin{equation} A\left( \omega \right) = 1 - {\left| {{S_{11}}\left( \omega \right)} \right|^2}\end{equation}

The proposed geometry obtains wideband absorption of 7.41 GHz ranging from 6.11 GHz to 13.52 GHz above 0.9 absorptivity with three absorption peaks at 6.76, 11.15, and 13.07 GHz as shown in Fig. 6.

Figure 6. Absorptivity vs frequency plot.

Absorption mechanism

The unit cell of the proposed MMA is considered a homogeneous medium for the absorption mechanism process. The normalized impedance can be evaluated by Eq. (3).

(3)\begin{equation}Z = \sqrt {{{{{\left( {1 + {S_{11}}} \right)}^2} - S_{21}^2} \over {{{\left( {1 - {S_{11}}} \right)}^2} - S_{21}^2}}} \end{equation}

In Eq. (3), transmitted power (${S_{21}}$) is absent because the bottom layer is completely covered with conducting material; due to this, no incident wave will be transmitted from the structure. Therefore, Eq. (3) is now modified as Eq. (4).

(4)\begin{equation}Z = {{\left( {1 + {S_{11}}} \right)} \over {\left( {1 - {S_{11}}} \right)}}\end{equation}

For analysis purpose and to calculate the exact normalized impedance, transmitted power (${S_{21}}$) plays an important role. To calculate ${S_{21}}$ the small portion from the bottom conducting layer is etched from all the four corner in such a way that absorption curve remains the same. The normalized impedance curve obtained after the process of etching is portrayed in Fig. 7. From Fig. 7 it is observed that in the range of interest real part is approaching toward unity while imaginary part is approaching toward zero, which confirms that proper impedance matching is achieved for the proposed structure.

Figure 7. Simulated normal impedance.

The real and imaginary parts approach toward 1 and 0, respectively, as shown in Fig. 7, which is due to the fact that effective parameters, i.e., ${\varepsilon _{{\textrm{eff}}}}$ and ${\mu _{{\textrm{eff}}}}$ are changing very rapidly at the wide range of absorption frequency, which is the region of interest. This can be proven by the observation from Figs. 8 and 9, respectively.

Figure 8. Simulated real part of permittivity and permeability.

Figure 9. Simulated imaginary part of permittivity and permeability.

The refractive index ($\eta $) is calculated using Eq. (5) and plotted in Fig. 10. The $\eta $ changes abruptly due to resonance conditions at a particular value or range of $\varepsilon $ and $ \mu $.

(5)\begin{equation}\eta = {1 \over {kd}}{\textrm{co}}{{\textrm{s}}^{ - 1}}\left[ {{1 \over {2{S_{21}}}}\left( {1 - S_{21}^2 - S_{11}^2} \right)} \right]\end{equation}

Figure 10. Refractive index vs frequency.

The absorption mechanism can be properly explained from the electric field and current distribution at the top and bottom surface of the proposed structure. To simulate the plot fields, three different frequencies are considered in the region of interest. The three different frequencies are 6.76, 11.15, and 13.07 GHz with absorptivities of 0.94, 0.94, and 0.99, respectively.

The current distribution plot shows that the current flowing at top and bottom surface is anti-parallel to each other, as shown in Fig. 11. Due to circulating current, magnetic excitation is created perpendicular to magnetic field. Electric field is induced due to electric excitation, as shown in Fig. 12; due to this strong EM, resonance occurs which maximizes the absorption.

Figure 11. Current distribution: (a) top and (b) bottom surfaces at 6.76, 11.15, and 13.07 GHz of proposed MA.

Figure 12. Electric field distribution: (a) top and (b) bottom surfaces at 6.76, 11.15, and 13.07 GHz of proposed MA.

Metasurface analysis under normal and oblique incidence

The angle independence of MMA is observed by analyzing the structure under normal and oblique (TE and TM) incidence. The electric field direction is fixed, and the wave vector and magnetic field direction are changed to analyze the absorption. Under normal incidence, the structure is rotated from horizontal polarization ($\phi = 0^\circ $) to a vertical polarization ($\phi = {90^ \circ }$), and the reflection coefficient is measured at every $15^\circ $ increments. When the polarization angle changes the absorptivity remains the same. Therefore, the proposed MMA is angle independent as shown in Fig. 13 as simulated and Fig. 14 as measured.

Figure 13. Simulated absorptivity curve under normal incidence.

Figure 14. Measured absorptivity curve under normal incidence.

The structure is further examined under oblique incidence of wave. The proposed structure is investigated at different angles from 0° to 90° at each 15° increments for both TE and TM polarization, and the absorptivity curves are plotted in Figs. 15 and 16, respectively. It is observed that absorptivity response degrades as angle of incidence increases.

Figure 15. Absorptivity curve under oblique incidence for TE polarization.

Figure 16. Absorptivity curve under oblique incidence for TM polarization.

The proposed and already reported MMA are compared with respect to size of unit cell, bandwidth, and thickness in Table 1. It is observed from the table that the proposed structure is compact in terms of size and has larger bandwidth.

Table 1. Comparison between proposed and already published metamaterial absorber articles

Measurement setup

The proposed MMA was fabricated on FR-4 substrate having an overall dimension of 140 cm × 140 cm, containing 10 × 10 unit cells as depicted in Fig. 17. The backside of FR-4 sheet has been covered with copper. The measurement of absorptivity under normal incidence is carried out inside an anechoic chamber with the help of vector network analyzer. The setup consists of two horn antennas acting as a transmitter and receiver. The complete setup for measurement is replicated in Fig. 18. The simulation and measurement results for absorptivity are shown in Fig. 19. and a close agreement between the simulation and measured results is observed.

Figure 17. Fabricated 140 cm × 140 cm sheet.

Figure 18. Experimental setup inside anechoic chamber.

Figure 19. Simulated and measured absorptivity plot.

Conclusion

The MMA reported in this article is angle-independent wideband absorber. The structure is simulated on FR-4 substrate having overall dimension of 14 mm × 14 mm × 3.2 mm. The unit cell of proposed MMA consists of outer and inner structure associated with lumped resistors. The outer structure consists of RSRR, whereas inner structure consists of CSRR. The structure is made up of three layers, in which top and bottom layer is made up of copper acting as a conducting material. The middle layer is made up of FR-4 acting as a dielectric substrate. The resonating structure at the top is design in such a way so that wideband absorption is achieved in the range from 6.11 to 13.52 GHz. The wideband absorption within the range is approaching almost toward unity having bandwidth of 7.41 GHz. Three different peaks are considered in the range of interest having maximum absorption of 0.94, 0.94, and 0.99 at frequencies of 6.76, 11.15, and 13.07 GHz, respectively. The structure is analyzed using the effective parameters, i.e., effective permittivity (${\varepsilon _{{\textrm{eff}}}}$) and effective permeability (${\mu _{{\textrm{eff}}}}$), to satisfy that structure is acting as a metamaterial. Electric field and current distribution are plotted at three different peaks to prove the mechanism of wideband absorption. Normal and oblique incidence are plotted to satisfy that structure is behaving as an angle independent. The simulated structure is fabricated on FR-4 substrate and measured inside an anechoic chamber. Finally, to prove the novelty of the work, the proposed structure is compared with the already reported MMA. The proposed MMA finds practical applications in RCS reduction, terrestrial communication, keyless entry system, space communication, radar, and baby monitor.