# Implementation of Atomically Thick Graphene and Its Derivatives in Electromagnetic Absorbers
## 2 Graphene-Based Quarter-Wavelength Absorbers
### Graphene and Its Derivatives-Based Dallenbach Absorbers
as well as the wave cancellation at the material/air interface, excellent microwave absorption performance is achieved. For a thickness of 1.8 mm, the material demonstrates a minimum RL (RL\({}_{\min}\)) of \(-\)38.8 dB at 16.4 GHz with more than 4.1 GHz effective absorption bandwidth (13.9-18+ GHz). In 2012, the microwave absorption of composites consist of rGO and nitrile butadiene rubber (NBR) were conducted by [PERSON] et al. [45]. The non-magnetic rGO/NBR Dallenbach absorber exhibits a RL\({}_{\min}\) as low as \(-\)57 dB and 4.5 GHz effective absorption bandwidth with a thickness of 3 mm. The authors believe the multiple reflections inside the rGO/NBR composites as well as the ionic conduction and dipolar relaxation caused by microwave/material interaction are the possible reasons behind the enhanced peak absorption. In 2013, [PERSON] et al. synthesized the non-magnetic polypyrrole (PPy)/rGO/Co\({}_{3}\)O\({}_{4}\) nanocomposites with a three-step approach [46]. They explored the complex permittivity and permeability of the synthesized PPy/rGO/Co\({}_{3}\)O\({}_{4}\) nanocomposites and revealed that dielectric loss plays an important role in microwave absorption. With a thickness of 2.5 mm, the Dallenbach absorber exhibits a broad effective absorption bandwidth of more than 6.7 GHz (11.6-18+ GHz) and a RL\({}_{\min}\) of \(-\)33.5 dB at 13.8 GHz. In 2015, [PERSON] et al. investigated the microwave absorbing performance of a Dallenbach absorber with ultralight compressible graphene foam (GF) [48]. Figure 3a-d illustrate the cross-sectional SEM images of uncompressed GF and GF under 30% (GF-30), 60% (GF-60) and 90% (GF-90) compressive strains. Figure 3e depicts the schematic of corresponding Dallenbach absorber. The measured real permittivity and loss tangent are shown in Figure 3f,g. Although the unstrained GF with 10 mm thickness is required and the RL\({}_{\min}\) achieved is only \(-\)28 dB at 12.2 GHz, the material demonstrates excellent broadband absorption over three different frequency bands, as shown in Figure 3h-j. In 2016, [PERSON] et al. combined the magnetic NiFe\({}_{2}\)O\({}_{4}\) nanoparticles and nanohybrids with non-magnetic rGO sheets to realize a Dallenbach layer operating at low microwave frequencies [47]. The calculated RL demonstrates two absorption peaks within 1 MHz to 3 GHz (RL\({}_{\min}=68\) dB at 1.11 GHz) and an effective operation bandwidth of 3 GHz or more under a thickness of 2 mm only. In the same year, [PERSON] et al. reported their exploration results on rGO/Silicon oxycarbide (SiOC) based EM absorbing material [49]. Figure 4a-f present the SEM images of the rGO/SiOC ceramic. A remarkable RL\({}_{\min}=-69.3\) dB is achieved at 10.55 GHz for a Dallenbach absorber with thickness of 2.35 mm, as shown in Figure 4g. In addition, they also explore the temperature-dependent complex permittivity of the rGO/SiOC composites from 293-673 K. It is noted that both \(\epsilon^{\prime}\) and \(\epsilon^{\prime\prime}\) increase when the temperature rises, as shown in Figure 4h,i, resulting in smaller RL\({}_{\min}\) and thinner absorber thickness. In 2017, a double-layer Dallenbach absorber consists of a matching layer (i.e., Co\({}_{0.2}\)Ni\({}_{0.4}\)Zn\({}_{0.4}\)Fe\({}_{2}\)O\({}_{4}\)) on the top and a absorption layer (i.e., rGO) underneath was investigated [50]. The input impedance is calculated as  
\[Z_{in}=\frac{\sqrt{\frac{\mu_{2}}{\epsilon_{2}}}\left(\sqrt{\frac{\mu_{1}}{ \epsilon_{1}}}\tanh\left[j\left(\frac{2\pi fd_{1}}{c}\right)\sqrt{\mu_{1} \epsilon_{1}}\right]+\sqrt{\frac{\mu_{2}}{\epsilon_{2}}}\tanh\left[j\left( \frac{2\pi fd_{2}}{c}\right)\sqrt{\mu_{2}\epsilon_{2}}\right]\right)}{\sqrt{ \frac{\mu_{2}}{\epsilon_{2}}}+\sqrt{\frac{\mu_{1}}{\epsilon_{1}}}\tanh\left[ j\left(\frac{2\pi fd_{1}}{c}\right)\sqrt{\mu_{1}\epsilon_{1}}\right]\tanh\left[j\left( \frac{2\pi fd_{2}}{c}\right)\sqrt{\mu_{2}\epsilon_{2}}\right]}, \tag{14}\]  
Figure 3: The cross-sectional SEM images of (**a**) graphene foam (GF) and GF under (**b**) 30%; (**c**) 60%; and (**d**) 90% compressive strains.