The absorption mechanism of the proposed design is described by taking MMA into consideration as a homogeneous medium. The normalized impedance can be evaluated by Eq. 3.

$$Z=\sqrt{\frac{{(1+{S}_{11})}^{2}-{S}_{21}^{2}}{{(1-{S}_{11})}^{2}-{S}_{21}^{2}}}$$

3

As, the bottom layer of the proposed design is fully covered with copper, the transmitted power (\({S}_{21}\)) is zero.

$$Z=\frac{{(1+{S}_{11})}^{2}}{{(1-{S}_{11})}^{2}}$$

4

But to evaluate the normalized impedance transmitted power (\({S}_{21}\)) play an important role. In order to calculate \({S}_{21}\) the bottom layer is cut from all the four corners such that absorption frequency does not swerve. The normalized impedance obtained is shown in Fig. 8 and it is observed that at absorption peaks (2.46 and 5.68 GHz), the real and imaginary parts approaches towards the values of unity and zero respectively, which indicates perfect impedance is achieved which leads to the maximum absorption.

Real part approaching towards unity in Fig. 8 occurs due to speedy change in valuesof \({\epsilon }_{eff }\)and \({\mu }_{eff}\) at frequency of absorption, that satisfies the conditions of electric and magnetic resonance. This is obvious from \({\epsilon }_{eff}\) and \({\mu }_{eff}\) plots shown in Figs. 9 and 10.

The effective \({\epsilon }_{eff}\) and \({\mu }_{eff}\) are calculated using electric susceptibility (Es) and magnetic susceptibility (Ms), mention in equations 5, 6, 7 and 8. Where K is a wave numberand d is the distance travelled by the incident EM wave.

$${E}_{s}=\frac{2j{S}_{11}-1}{k{S}_{11}+1}$$

5

$${E}_{s}=\frac{2j{S}_{11}+1}{k{S}_{11}-1}$$

6

$${\epsilon }_{eff}=1+\frac{{E}_{s}}{d}$$

7

$${\mu }_{eff}=1+\frac{{M}_{s}}{d}$$

8

The value of refractive index (\(\eta\)) is computed by using Eq. 9 and represented further in Fig. 11. The value of \(\eta\) changes abruptly because of the resonance conditions at a given value or at the range of \(\epsilon\) and\(\mu\).

$$\eta =\frac{1}{kd}{cos}^{-1}\left[\frac{1}{2{S}_{21}}(1-{S}_{21}^{2}-{S}_{11}^{2})\right]$$

9

For explaining the absorption mechanism, calculation of field distributions is done at two distinct absorptivity peaks (2.46 and 5.68 GHz). The current distributions of the proposed design’s top and bottom surfaces are anti-parallel with respect to each other as shown in Fig. 12. The magnetic excitation is generated perpendicular to the magnetic field because of the circulating current. Because of the electric excitation, electric field is induced which has been shown in Fig. 13. Owing to the given fact, strong EM resonance occur that maximizes the absorption.

Magnetic excitation as well as the electric excitation occurs simultaneously, which has been proved by observing Figs. 9 and 10 in which \({\epsilon }_{eff}\)and \({\mu }_{eff}\) gets a huge deviation near all the two absorptivity peaks.