Basically, permittivity (ε) and permeability (µ) are the materials properties which are used in absorption of the EM wave. The absorption of the wave can be modified by altering those properties. The permittivity of the any material [16–17] is a measurement of its dielectric polarization and it occurs on the application of electric field and specifies as complex quantity as Eq. (1),
\({\epsilon }= {{\epsilon }}^{{\prime }}-{\text{j}{\epsilon }}^{{\prime }{\prime }}\) , (1),
Where εʹ component, also known as dielectric constant and is, what stores the electromagnetic energy. The εʺ component which is also known as dielectric loss factor, describes how the constantly shifting field cause electric energy to be lost as heat from the movement of molecules and ions. It should also be noted that both components depend on the frequency of the field variation. The loss tangent is yet another aspect that influences how well dielectrics convert microwave energy into thermal energy [16–17] and is given by
The wave is more attenuated as the loss tangent is higher. A dielectric material becomes polarized when an electric field passes through it. In a dielectric, electronic polarization and dipole polarization are two polarization mechanisms causing energy dissipation in dielectrics termed as dielectric loss. The parameters used to calculate the loss factor are conductivity and conduction loss. The material's conductivity is listed as follows [16–17]:
\({\sigma }^{{\prime }}=\omega {\epsilon }_{0}{\epsilon }^{"}=2\pi f{\epsilon }_{0}{\epsilon }^{"}=2\pi f{\epsilon }_{0}{\epsilon }^{{\prime }}tan\delta\) , (3),
$${\sigma }^{"}= \omega {\epsilon }_{0}{\epsilon }^{{\prime }}=2\pi f{\epsilon }_{0}{\epsilon }^{{\prime }}$$
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where\(\omega =2\pi f \left(Hz\right)\), f is the frequency of incident wave, is permittivity of free space.
Figure 1 illustrates the EM wave absorption mechanism. The electromagnetic waves' initial power Pi into the material is subjected to absorption Pa, transmission Pt, and reflection Pr. This study attempted to reduce the power of the reflection and transmission parts by supporting a metal plate in order to increase the loss of the electromagnetic waves within the material. The following is the material's absorption profile:
$$AR\left(\omega \right)= 1-\left|{s}_{11}^{2}\right|+\left|{s}_{21}^{2}\right|$$
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S11 and S21 are reflection coefficient and transmission coefficient of the EM wave. An electromagnetic wave degrade exponentially through a material by the factor\({ e}^{-\alpha x}\), and attenuation factor \(\alpha\) of the wave in the absorber depends on the dielectric loss and is denoted by [16–17] :
$$\alpha =\frac{2\pi \left(8.686\right)}{{\lambda }_{0}}\sqrt{\frac{{\mu }^{{\prime }}{\epsilon }^{{\prime }}}{2}}\times \left(\sqrt{\left(1+{tan}^{2}\delta \right)}-1\right)$$
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This equation relates the attenuation factor of EM wave for a microwave absorber depending upon\({ \epsilon }^{{\prime }}\), \(tan\delta\) and\(\left({\mu }^{{\prime }}=1\right).\)