Design of the structure

The proposed metamaterial absorber (MA) is composed of periodic unit cells. The unit cell structure of MA consists of seven layers, of which first and fourth surface layer designs are identical; second and fifth surface layer designs are identical; third and sixth surface layer designs are identical. The overall optimized dimension of the proposed unit cell is 31.5 mm × 31.5 mm × 10.805 mm. The first and fourth surface layer design is a resonating structure, consisting of three consecutive resonating circular rings of diameter “r1,” “r2,” and “r3,” made of metallic copper (Cu, conductivity = 5 × 107 S/m, thickness = 0.035 mm) separated from each other with an equal radial gap, “r”. Passive elements are introduced into the resonators to achieve a wider absorption along with miniaturizing the structure, as discussed in [Reference Barde, Gupta, Ranjan, Roy and Sinha22]. Each resonating circular ring consists of four lumped resistors of resistances “res1,” “res2,” and “res3,” inserted by cutting an equal dimension (size = 1 mm × 1 mm) in x and y directions on four sides of the ring. The first and fourth surface layer are adhered to the second and fifth surface layer, respectively, which are made up of Duroid (dielectric constant = 2.2, dielectric loss tangent = 0.0009, and thickness = 1.6 mm) substrate. The third and sixth surface design layers are air spacers (thickness = 3.75 mm) used for achieving a flat absorption above 90% in the region of interest. The seventh surface layer design (bottommost layer) is made up of resonating structure, copper (thickness = 0.035 mm), which completely covers the bottom surface of the design. Figures 1 and 2 show the side view and the schematic diagram of the proposed unit cell structure, respectively. Figure 3 shows the front view of the proposed unit cell structure.

Figure 1.

The frontage of the suggested MMA unit cell.

Figure 2.

A graphic representation of the suggested MMA.

Figure 3.

The front view of the proposed unit cell structure.

Numerical simulations and analysis

The design of the proposed unit cell structure of MA was simulated in the commercially available Finite Element Method solver, ANSYS HFSS. To achieve the desired bandwidth of the proposed MA, the optimized dimensions of the unit cell structure are as follows: a = 31.5 mm, r1 = 12 mm, r2 = 7 mm, r3 = 2 mm, r = 4 mm, res1 = res2 = 220 ohm, and res3 = 150 ohm, where res1, res2, and res3 are the resistances of four resistors placed in the outer circle, middle circle, and the inner circle, respectively. Materials found in nature comprise micro-atoms that have magnetization and polarization attributes to determine their electromagnetic (EM) response. However, in metamaterials, EM wave traverse through the electric field and magnetic field, which helps in actuating the electrons present in the atoms. These transmission properties help to modify the consuming energy of incident waves. Permittivity, ε = ε′ + iε″, and permeability, μ = μ′ + iμ″, indicate the degree of motion. The real components of ε and μ specify the polarization and magnetization degree, respectively. However, the imaginary components of ε and μ specify the basic characterization parameters that help in determining the losses in a medium. We have computed wideband absorptivity, A(ω), using equations (1) and (2).

(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 computed value of A(ω) depends upon reflected (S ₁₁) and transmitted (S ₂₁) power. As the bottommost layer of the unit cell structure is completely covered with a resonating material, copper, there is no transmission of waves; hence, the transmitted power in equation (1) is zero and the absorptivity becomes completely dependent on reflected power as shown in equation (2). The absorptivity of the unit cell structure can be controlled by manipulating the reflected power from the surface, i.e., lower the value of reflected power, the higher will be the transmitted power and vice versa.

The proposed unit cell structure shows wide bandwidth of 7.62 GHz (2.8–10.42 GHz) along with 99.99% (∼100%) absorption at two distinct peaks, 3.41 GHz and 9.75 GHz, as depicted in Fig. 4.

Figure 4.

The simulated absorption of the proposed MA structure.

Theory of absorption

The MA is considered to be a homogeneous medium in order to define the absorption properties. The normalized impedance is evaluated using equation (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}

As the bottom layer is completely covered with copper and the transmitted power becomes zero, the normalized impedance does not give efficient solution. Hence, the transmitted power plays an important role while computing the normalized impedance.

In order to compute the transmitted power, four small portions of dimension 0.5 × 0.5 mm² from the bottommost layer are cut from four corners each in such a manner that the absorption frequency does not get altered. Figure 5 depicts the normalized impedance, in which it is observed that in the range of interest (2.8–10.42 GHz), the real and imaginary components approached toward unity and zero, respectively, which clearly indicates the achievement of perfect impedance resulting into maximum absorption.

Figure 5.

The normalized impedance.

The real component that approaches toward unity as shown in Fig. 5 occurs due to rapid change in variables of permittivity (ε _eff) and permeability (μ _eff) at the absorption frequency, eventually satisfying the electric and magnetic resonance conditions, respectively. This is demonstrated in Figs. 6 and 7.

Figure 6.

The simulated real components of permittivity and permeability.

Figure 7.

The simulated imaginary components of permittivity and permeability.

The effective ε _eff and μ _eff are computed using electric susceptibility (E _s) and magnetic susceptibility (M _s) as seen in equations (4–7).

(4)\begin{equation}{E_{\textrm{s}}} = {{2j{S_{11}} - 1} \over {k{S_{11}} + 1}},\end{equation}

(5)\begin{equation}{E_{\textrm{s}}} = {{2j{S_{11}} + 1} \over {k{S_{11}} - 1}},\end{equation}

(6)\begin{equation}{\varepsilon _{{\textrm{eff}}}} = 1 + {{{E_{\textrm{s}}}} \over d},\end{equation}

(7)\begin{equation}{\mu _{{\textrm{eff}}}} = 1 + {{{M_{\textrm{s}}}} \over d}.\end{equation}

In the above formulae, k demonstrates the wave number and d is the distance traveled by the incident EM wave. The value of refractive index (η) is computed using equation (8) and is shown in Fig. 8.

(8)\begin{equation}\eta = {1 \over {kd}}{\cos ^{ - 1}}\left[ {{1 \over {2{S_{21}}}}\left( {1 - S_{21}^2 - S_{11}^2} \right)} \right].\end{equation}

Figure 8.

Refractive index.

To explain the mechanism of absorption, field distributions are computed at 3.66 GHz and 9.54 GHz. It is observed that the current distributions of the top and bottom surfaces are anti-parallel with reference to each other, as depicted in Fig. 9. As a consequence of the circulating current, magnetic excitation is generated perpendicular to the magnetic field. Also, electric field is induced through electric excitation, as depicted in Fig. 10. As a result, strong EM resonance transpires that maximizes the absorption.

Figure 9.

The electric field distribution of the proposed MA. (a) Top surface at 3.66 GHz, (b) top surface at 9.54 GHz, (c) bottom surface at 3.66 GHz, and (d) bottom surface at 9.54 GHz.

Figure 10.

The current distribution of the proposed MA. (a) Top surface at 3.66 GHz, (b) top surface at 9.54 GHz, (c) bottom surface at 3.66 GHz, and (d) bottom surface at 9.54 GHz.

It is observed from Figs. 6 and 7 that ε _eff and μ _eff show a huge deviation near two absorptivity peaks. This proves that the magnetic excitation and the electric excitation occur simultaneously.

Analysis of metamaterial under normal and oblique incidence

To understand the sensitivity of polarization, the proposed MA is examined under normal incident of wave for transverse electric (TE) mode and transverse magnetic (TM) mode, which is further examined under oblique incident for TE and TM mode. For analyzing the absorption, the direction of electric field is kept constant, and the wave vector and direction of magnetic field are varied.

Under normal incident of wave, the reflection coefficient of the proposed MA is measured by rotating the MA from horizontal degree of polarization (ϕ = 0°) to vertical degree of polarization (ϕ = 90°) at every 15° increments. It is spotted that with every increasing angle of polarization, the absorptivity remains the same as depicted in Fig. 11. Hence, it can be said that the proposed MA is polarization insensitive.

Figure 11.

The simulated absorptivity curve under normal incidence.

The proposed MA is further inspected under oblique incident of wave to study the polarization properties for TE and TM mode, where the reflection coefficient of the structure is measured by rotating the MA from horizontal degree of polarization (ϕ = 0°) to vertical degree of polarization (ϕ = 90°) at every 15° increments. It is spotted from Figs. 12 and 13 that the absorptivity decreases with an increase in the angle of incidence.

Figure 12.

The simulated absorptivity curve under oblique incidence for TE polarization.

Figure 13.

The simulated absorptivity curve under oblique incidence for TM polarization.

Measurement setup

The MA presented in this article was fabricated on a Duroid sheet of 31.5 cm × 31.5 cm containing 10 × 10 unit cells. A copper sheet is used to cover the bottommost layer of the proposed MA. The entire setup is placed inside the anechoic chamber. The VNA is used to calculate the absorption of the proposed MA under normal incidence. This experimental setup consists of two horn antennas, among which one acts as a transmitting antenna and the other acts as a receiving antenna, as depicted in Fig. 14. Figure 15 portrays the simulated and the measured results of the proposed MA; it is perceived from the graph that the results are in compliance with each other.

Figure 14.

The experimental setup inside anechoic chamber. (a) Metamaterial absorber, (b) transmitting horn antenna, (c) receiving horn antenna, and (d) vector network analyzer.

Figure 15.

The absorption plot for simulated and measured results.

Table 1 shows the comparison between our proposed MA and the MAs investigated in the literature. The comparison concerns with the resonance frequencies, bandwidth, and the absorption of the unit cell structures. It is observed that the proposed MA achieves a better bandwidth as compared to the other MAs.

Table 1.

Comparison between the proposed work and MAs investigated in literature

The tested and simulation plots are measured and shown in Fig. 16. From the plot, it is observed that the tested and simulated results are close in the agreement.

Figure 16.

Arrangement inside anechoic chamber.