Design and equivalent circuit model

The metamaterial absorber design considered for the wide bandwidth consists of an array of circular ring structure that has split gaps and dielectric substrate that is grounded to block the transmission of electromagnetic waves as shown in Fig. 1(a).

Fig. 1.

Unit cell structure: (a) 3D view of the absorber unit cell, (b) the dimensions from the front view of the absorber, and (c) the dimensions from a side view.

The dielectric substrate used is the commercially available FR-4 (ε_r = 4.3 and tan δ = 0.02) having a thickness of 1.6 mm. A top metallic patch having a circular ring structure and the bottom ground plane is constructed with copper having conductivity σ = 5.8 × 10⁷ S/m and thickness of 0.035 mm. Figure 1(a) shows the 3D view of the unit cell structure indicating the placement of the ground, substrate, and the patch for maximum absorption. Figure 1(b) indicates the detailed optimized dimensions of the patch on the top of the substrate. The spacing between the unit cells is given as S = 6.8 mm, the outer radius of a ring is given as R1 = 2.5 mm, and the inner radius R2 = 1.7 mm which indicates the ring width is 0.8 mm. The two split gaps given in the ring structure are denoted by G = 0.4 mm. Considering the inner floret patch the outer radius is R3 = 1.5 mm and the inner radius R4 = 0.7 mm. The eight split gaps of equal dimensions are given as P = 0.2 mm. Figure 1(c) shows the side view of the absorber structure which indicates the thickness of ground and patch as t = 0.035 mm and thickness of the substrate as h = 1.6 mm.

The absorption offered by an absorber A(ω) at various frequencies can be obtained by equation (1)

(1)$$A( \omega ) = 1-R( \omega ) -T( \omega ) $$

where R(ω) is the reflection coefficient and T(ω) is the transmission coefficient, and the copper ground plane ensures that there is no transmission through the absorber so the effective absorption offered is now obtained using equation (2)

(2)$$A( \omega ) = 1-\vert {S_{11}} \vert ^2$$

Simulations performed in CST-microwave studio provide the S-parameter values in the desired frequency sweep. The reflection coefficient includes both co-polarization and cross-polarization for transverse electric (TE) and transverse magnetic (TM) given in equation (3)

(3)$$\vert {S_{11}} \vert ^2 = \vert {S_{11TE, TE}} \vert ^2 + \vert {S_{11TE, TM}} \vert ^2 = \vert {S_{11TM, TM}} \vert ^2 + \vert {S_{11TM, TE}} \vert ^2$$

where for TE as the incident wave S _{11TE, TE} is co-polarization reflection coefficient and S _{11TE, TM} indicates the cross-polarization reflection coefficient of the proposed design respectively. To confirm that the designed structure is not a polarization converter, the cross-polarization reflectivity is calculated.

The series equivalent circuit is approximated based on the resonator structure having R, L & C as the approximate values of resistance, inductance, and capacitance respectively. Z_in is the input impedance of the absorber, Z_m equivalent impedance of top layer of the proposed metasurface absorber, and Z_t is the input impedance of dielectric metal surface or ground as given by equations (4)–(6) (Fig. 2):

(4)$$\displaystyle{1 \over {Z_{in}}} = \displaystyle{1 \over {Z_m}} + \displaystyle{1 \over {Z_t}}$$

(5)$$Z_m = R + j\left({2\pi fL-\displaystyle{1 \over {2\pi fC}}} \right)$$

(6)$$Z_t = j\displaystyle{{Z_0} \over {\sqrt {\varepsilon _r} }}{\rm tan}\left({\displaystyle{{2{\rm \pi }f\sqrt {\varepsilon_r} \, h} \over c}} \right)$$

Fig. 2.

Equivalent circuit for the absorber circuit for Resistance (R), Inductance (L) & Capacitance (C).

The circuit and equations thus analyzed for the maximum power transfer, where the impedance of free space shall be equal to the absorber impedance, gives the approximate values of R, L & C as given in equations (7)–(9):

(7)$$R = \displaystyle{{Z_0{\rm ta}{\rm n}^2\left({2{\rm \pi }f\sqrt {\varepsilon_r} h/c} \right)} \over {\varepsilon _r + {\rm ta}{\rm n}^2\left({2{\rm \pi }f\sqrt {\varepsilon_r} h/c} \right)}}$$

(8)$$\left({2{\rm \pi }fL-\displaystyle{1 \over {2{\rm \pi }fC}}} \right) = \displaystyle{{\sqrt {\varepsilon _r} Z_0{\rm tan}\left({2{\rm \pi }f\sqrt {\varepsilon_r} h/c} \right)} \over {\varepsilon _r + Z_0{\rm ta}{\rm n}^2\left({2{\rm \pi }f\sqrt {\varepsilon_r} h/c} \right)}}\;\;$$

(9)$$L = 0.0002 \times {\rm l} \times \left({2.303 \times {\rm lo}{\rm g}_{10}\left({\displaystyle{{{\rm 4 \times l}} \over t}} \right)-\alpha } \right)\,\,{\rm \mu H}$$

where the perimeter of circular ring l = 2πR4, conductor thickness t = 0.035 mm, and for circular-shaped ring structure value of α is 2.451.

Absorber structure and parametric analysis

To analyze the structure for the design parameters, first, the basic structure design criteria are explained. Figure 3(a) indicates the various steps of designing the absorber structure and the absorptivity response in accordance. The initial structure is approximated from the L and C values calculated in Table 1 at the center frequency. The closed-loop structure shown in Fig. 3(a) in the desired bandwidth has absorptivity below 20%. The structure is improved fairly by introducing the split gaps that increase the effective capacitance of the circuit. A floret-shaped structure is introduced in the absorber to increase the overall bandwidth of the structure through the multimode resonance mechanism. When a floret-shaped structure is merged with a split-ring resonator structure, the bandwidth variation is quite large when compared to the previous two cases. The bandwidth of the absorber is 7.4 GHz at 90% absorptivity as shown in Fig 3(b). Fig. 3(c) and 3(d) indicate the results obtained for the reflectivity for co-polarization and cross-polarization. From equation (2) the corresponding absorptivity is calculated.

Fig. 3.

Design phases of the absorber structure and absorptivity response of (a) a closed-loop ring, ring structure with split gaps i.e. split ring and split ring loaded with a patch, (b) absorptivity at normal incidence having a bandwidth of 7.4 GHz at 90% absorptivity (c) Reflection coefficient of co-polarization and (d) cross-polarization of TE and TM wave at normal incident.

Table 1.

Estimated values of R, L & C

The optimized structure is achieved from the parametric iteration for the desired results. Different parameters are varied one at a time while keeping the other parameters fixed as shown in Fig. 4. The unit cell spacing “S” is a critical parameter that responds to the achievement of desired bandwidth without compromising the absorption. In Fig. 4(a) it can be observed that there is a partial absorptivity drop throughout the desired bandwidth of the absorber until the optimum spacing S = 6.8 mm. If the spacing is increased beyond 6.8 mm the bandwidth of the absorber reduces to a large extent along with the absorption level. Furthermore, the iterations done on the outer ring radius R1 as indicated in Fig. 4(b) indicate that the absorptivity and bandwidth are affected by these variations.

Fig. 4.

Parametric analysis of proposed absorber (a) absorptivity response in variance with unit cell spacing “S” (b) absorptivity response in variance with outer ring radius “R1” (c) absorptivity variation due to split-gap in the outer ring “G” at normal incident.

It is also clear that the optimum ring radius for the absorber structure is R1 = 2.5 mm having absorptivity above 90% throughout the bandwidth. Split gaps are very significant as they contribute to the effective capacitance of the absorber resonance and thus can be used for the tuning of the resonator. Figure 4(c) indicates the iterations of a split gap that is optimized to keep the entire bandwidth above 90% absorptivity. It can be observed that if the gap is reduced the performance of the absorber reduces and if the gap is increased the bandwidth of the absorber is affected. So, to maintain the performance as well as the bandwidth of the absorber the optimum gap width is G = 0.4 mm.

Absorber performance and structure analysis

After designing the absorber and ensuring the absorptivity, it is very much required to quantify the absorber performance based on the orientation of the absorber as well as the angle at which the absorber receives the electromagnetic waves. The orientation of the absorber termed as the polarization angle is given by ϕ, which agrees that if the absorber orientation changes and there is no variation in absorptivity, the absorber is polarization insensitive. Furthermore, the direction from which the electromagnetic waves are incident is denoted with angle θ, such that θ = 0°, when a wave is an incident normal to the absorber plane. In this section, polarization angle and incident angle are demonstrated with the Floquet ports considered for both TE and TM waves. Figure 5 shows the variation of absorption bandwidth and performance due to the variation in polarization angle (ϕ) and incident angle (θ). It is clear from Fig. 5(a) that the structure holds good reliability when electromagnetic waves are incident at different angles. Incident angle θ is varied from 0 to 45°. It has been observed from the results that more than 80% of the absorptivity is maintained throughout a bandwidth of 12.6–18.7 GHz for an incident angle of 45°. This indicates at the incident angle of 45°, 77% of total bandwidth is maintained for the proposed absorber. Therefore, the absorber is insensitive to the angle of incidence of the approaching electromagnetic wave. Figure 5(b) shows the variation of the polarization angle. The structure is studied for different polarization angles in a range of 0–90° with a step size of 15°, at the normal incidence in order to inspect its polarization sensitivity. Figure 5(b) shows that absorption decreases gradually with an increase in the polarization angle due to the non-symmetrical geometry of the proposed structure. It is also observed that the absorptivity gradually decreases with an increase in the polarization angles and the minimum value is at 45°. It again increases gradually and reached maximum absorption at 90° polarization angle, showing that the proposed structure is two-fold symmetric. Therefore, the absorptivity is the same at polarization angles ϕ = 0 and 90°. It can be stated from the results that the proposed absorber is insensitive to incident angle variations and sensitive to polarization angle variations.

Fig. 5.

Absorber Performance (a) shows the variation in the incident angle “θ” with polarization angle ϕ = 0°, (b) shows the variation of polarization angle “ϕ” with normal incidence.

The structure of the absorber design comprises a split-ring and is floret-shaped. Figure 6 shows the structure behavior with the approaching electromagnetic wave indicating the electric and magnetic fields. The fields are analyzed using the field monitors in the CST-microwave studio. Figures 6(a) and 6(b) show that at a lower frequency of the entire spectrum i.e. 12.23 GHz, the electric and magnetic fields are majorly contributed by the ring structure. Further moving to the higher frequencies i.e. 15.4 and 18.25 GHz it is observed that the inner floret structure has a significant contribution.

Fig. 6.

Electric field distribution at (a) 12.23 GHz, (b) 15.14 GHz & (c) 18.25 GHz. Magnetic field distribution at (d) 12.23 GHz, (e) 15.14 GHz & (f) 18.25 GHz respectively at normal incidence.

Measurements and results

To validate the designed absorber, the setup has been prepared by placing the horn antenna in front of the fabricated prototype absorber at a distance of 1 m. The fabricated prototype and a large view of the unit cell structure of the designed absorber are shown in Fig. 7(a). The prototype is prepared using a photolithography process with copper-clad laminate. The absorber has been backed by a wedge-shaped conventional absorber to mitigate undesirable reflections as already shown in Fig. 7(b).

Fig. 7.

Measurements: (a) fabricated metasurface absorber sheet and unit cell structure of the prototype absorber (b) Simulated and measured results of metasurface at normal incidence (c) Measurement setup.

The prototype of the absorber consisting of an array of 20 × 20 unit cells fabricated on a 1.6 mm thick FR-4 substrate using a photolithography technique and the measurement setup in the laboratory is shown in Fig. 7(c).

Measurement of the reflection coefficient is taken by connecting the setup shown with the vector network analyzer-VNA (Agilent Technologies-N5222A) having a frequency range of 10 MHz to 50 GHz. Figure 7(b) shows the simulated and measured results are in good agreement. Minor deviations are due to fabrication errors or manual errors during measurements [Reference Saxena, Awasthi and Jain21–Reference Saxena, Yadava, Jain and Awasthi23].