# Implementation of Atomically Thick Graphene and Its Derivatives in Electromagnetic Absorbers
## 2 Graphene-Based Quarter-Wavelength Absorbers
### Graphene-Based Salisbury and Jaumann Absorbers  
In the 1940s, [PERSON] invented an absorbent structure, known as Salisbury screen, to reduce the radar cross section of EM waves. However, the work was not patented until 1952 due to the security requirements in World War II [32]. The EM absorber consists of a thin resistive layer, a low loss/lossless dielectric spacer and a metallic ground [32]. The resistive layer splits the incidence into reflected and transmitted signals. The metallic ground acts as a perfect reflector that fully reflects the transmitted signal. The thickness of spacer is carefully selected so that destructive wave interference can be achieved between the reflections from resistive sheet and metallic ground. For a spacer with thickness \(d=M\cdot\lambda/4\) where \(M\) is a positive odd integer, the reflected waves exhibit a phase difference of \(M\cdot\lambda/2\) and cancel each other when their amplitude matches. This configuration is also known as a Fabry-Perot resonator, which operates within a narrow frequency range near the resonant frequency. According to the transmission line theory, the input admittance (\(Y_{1,in}\)) of Salisbury screen under normal incidence for both transverse electric (TE) and transverse magnetic (TM) polarized waves is [35]:  
\[Y_{1,in}=Y_{s}-jY_{d}\cot\left(\beta_{d}d\right), \tag{4}\]  
where \(Y_{s}=1/\sigma_{s}\), \(\beta_{d}=\omega\sqrt{\epsilon_{r}}/c\), \(e_{r}\) is the relative permittivity of the dielectric spacer, \(c\) is speed light, \(Y_{d}=\sqrt{\epsilon_{r}}/Z_{0}\) and \(Z_{0}=\sqrt{\mu_{0}/\epsilon_{0}}\) is the free space impedance. To enhance the operation bandwidth of Salisbury screen, a few resistive layer/spacer pairs can also be stacked on the top of each other to realize the Jaumann absorber, as shown in Figure 1a,b. For a Jaumann screen consisting of \(N\) quarter-wavelength-thick layers, the corresponding input admittance can be calculated as [35]  
\[Y_{i,in}=Y_{s}+Y_{d}\frac{Y_{i-1,in}+jY_{d}\tan{(\beta_{d}d)}}{Y_{d}+jY_{i-1,in} \tan{(\beta_{d}d)}}(i=1,2,...,N). \tag{5}\]  
Thus, the reflection coefficient (\(\Gamma_{r}\)) can be achieved as  
\[\Gamma_{r}=\frac{Z_{\rm in}-Z_{0}}{Z_{\rm in}+Z_{0}}, \tag{6}\]  
and the reflectance (\(R\)) can be represented as \(R=\Gamma_{r}^{2}\). Hence, the absorption (\(A\)) is  
\[A=1-R-T, \tag{7}\]  
where \(T\) is the transmittance. Since the metallic ground fully reflects the signal through the resistive layer(s) and results in zero transmittance (i.e., \(T=0\)), Equation (7) can be rewritten as  
\[A=1-R. \tag{8}\]  
That means the wave is either absorbed or reflected in the Salisbury screen and Jaumann absorbers. For \(Z_{\rm in}=Z_{0}\), perfect absorption is achieved as \(R=0\) and \(A=1\). Hence, in practice, engineers always would like to reduce the value of \(R\) for absorbers with metallic ground. At microwave frequencies, the return loss (dB), defined as  
\[\mathrm{RL}=-20\log{|\Gamma_{r}|}, \tag{9}\]  
is often preferred over \(R\) to describe the reflection of a device. For absorbers with metallic ground, the effective wave absorption is frequently defined as \(\mathrm{RL}\leq-10\) dB, which means that more than 90% of the signal energy is absorbed. In 2013, theoretical exploration results on the graphene-based tunable Salisbury screen [36] and Jaumann [37] absorbers operating at THz frequencies were reported. The next year, experimental results of graphene-based transparent Salisbury screen and Jaumann absorbers operating at millimeter wave frequency were presented by [PERSON] et al. [35]. As shown in Figure 1c, their graphene is synthesized on the Cu/SiO\({}_{2}\)/Si wafers with over 90% monolayer coverage utilizing chemical vapour deposition (CVD) approach. This is followed by coating a layer of poly (methyl methacrylate) (PMMA) on the top of graphene. Then, the substrate is etched away in the aqueous ammonium persulfate solution, leaving only floating graphene-PMMA films that can be washed in de-ionized water and transferred onto arbitrary substrate.