# Towards Mirror-Less Graphene-Based Perfect Absorbers
## 2 Graphene Perfect Absorbers with External Mirror
### 'Single-Resonance/Mirror Absorber' Scheme
#### 2.1.1 Absorption Control by Oblique Incidence  
In 2017, [PERSON] et al. [18] experimentally showed angle-selective giant light absorption by placing large-area unpatterned graphene on a structure consisting of a dielectric layer atop a gold mirror (Figure 2a). The doped graphene has metallic property due to _lf_ < 2E\({}_{f}\). Such a simple structure supports a resonance mode with light trapped in the dielectric layer owing to the reflections at its top and bottom surfaces. The loss rate is insensitive to incident angle, whereas the leakage rate reaches zero at 90 degrees. Thus, the critical coupling condition can be always satisfied by adjusting the incident angle, even though the critical angle is a considerably high value. In ref. [19], the proposed structure can lead to perfect THz absorption because of strong light localization in the defect layer of the heterostructure using two Si/SiO\({}_{2}\) DBR (Figure 2b). When the incident angle increases, the resonant peak shifts toward higher frequencies due to the correlation between the resonance frequency and the incident angle. In 2016, [PERSON] et al. [20] proposed a multi-layer photonic configuration, which consists of an ultrathin metal film coated on a DBR and a graphene sheet in a silica spacer. The monolayer graphene exhibits an impressive absolute absorption of light, which can reach up to 80% (34.8-fold enhancement compared to the intrinsic value of 2.3%), due to the strong field confinement of Tamm plasmon in the silica spacer. The Tamm plasmon originates from the appropriate combination of a metal film (not a dielectric graphene) and a DBR. Changing the incident angle is a straightforward method to efficiently adjust the operating wavelength of graphene absorption. In detail, the absorption peak wavelength experiences a blueshift as the incident angle increases.  
Figure 1: Schematic of a lossy one-port resonant system with an external mirror on the backside (that is, output port). \(a\) denotes the mode amplitude of the resonator. \(S_{1+}\), \(S_{1-}\), and \(S_{2-}\) are the incident, reflected, and transmitted field amplitudes, respectively. \(\gamma_{1}\) (=\(\gamma_{\textit{1 eak}}\)) and \(\gamma_{2}\) (=0) denote the mode leakage rate to the front side and back side of the resonator, respectively. \(\gamma_{\textit{loss}}\) denotes the loss rate of the resonator. The green dashed lines are reference planes for the field amplitudes in the ports.  
In 2013, [PERSON] et al. [41] proposed a prism-coupling absorber in which a gap layer of an intermediate index value was embedded, and graphene was located at the interface between the gap layer and the substrate. They demonstrated broadband enhanced absorption with practically available materials by using five or ten layers of graphene. However, it is difficult to achieve perfect absorption for monolayer graphene due to the limitation on material index choice. In 2017, [PERSON] et al. [42] proposed a modified absorber structure in which monolayer graphene is embedded in the middle of the gap layer, enabling practical perfect absorption in monolayer graphene with naturally available materials. The perfect absorption is attributed to enhanced light-graphene interaction through the creation of a cavity mode within the gap layer when a proper gap thickness and a graphene position are chosen. In 2019, the excellent performance of the proposed absorber was also experimentally demonstrated [43] (Figure 2c). The absorption peak is enhanced up to \(\sim\)86% at \(\lambda\) = 650 nm with bandwidth of 314 nm (from 542 nm to 856 nm); this absorption performance is the best experimental result for monolayer graphene in the visible range, to the best of our knowledge.