# Towards Mirror-Less Graphene-Based Perfect Absorbers
## 2 Graphene Perfect Absorbers with External Mirror
### 'Single-Resonance/Mirror Absorber' Scheme
#### 2.1.2 Absorption Control by Patterned Structures  
In the mid-IR to THz regime (strictly, _lift_\(<\) 2_E_), due to the metallic property of doped graphene, tunable graphene plasmons can be utilized by periodically patterning graphene itself. In 2012, [PERSON] et al. [21] reported that 100% light absorption can take place in the graphene disk arrays supported on a dielectric-coated gold surface, provided that the critical coupling condition is satisfied by properly choosing the dielectric coating layer thickness. [PERSON] et al. [22] incorporated an air nano-slit into a similar structure, positioned at a specific displacement distance from its center, as illustrated in Figure 3a. The air nano-slit can not only exhibit an efficient asymmetrical characteristic for the graphene disk but also proposes a viable approach for realizing a high-\(Q\) resonant spectrum. Also, there have been many reports based on different metamaterials, such as graphene ribbon arrays [34; 35], square metal patches [36], cross-shaped resonators [36; 37], and split-ring resonators [36; 38], as shown in Figure 3b-d. Most importantly, plasmon resonances in patterned graphene also  
Figure 2: GPAs with angle-selective absorption. (**a**) Top: Schematic of a GPA consisting of monolayer graphene, separated from a gold mirror (light gray) by a dielectric spacer layer (dark gray). Bottom: leakage rate (blue line) and loss rate (red line) as a function of incident angle [18]. (**b**) Top: schematic of a GPA based on the strong light localization in the defect layer of heterostructure. Bottom: absorption spectra as a function of incident angle [19]. (**c**) Top: schematic of a GPA based on prism coupling, where monolayer graphene is embedded in the middle of dielectric cavity and a substrate is replaced with air. Bottom: measured absorption spectra by fundamental mode as a function of incident angle [43]. Reproduced with permission from [18; 19; 43], © 2023 Springer Nature; © 2023 Optical Society of America; © 2023 Elsevier Ltd.  
exhibit good absorption stability over a wide-angle range [34; 35], as shown in Figure 3b, similarly to plasmon resonance in noble metals [31]. In near-IR to visible regime (strictly, _lf_ > 2_E_), there is no plasmonic response in undoped graphene, so the critical coupling is entirely controlled by the resonance properties of the patterned structures excluding the graphene layer. To greatly enhance graphene absorption, a quite low \(\gamma_{\textit{Los}}\) resonant structure is required to be balanced with quite low \(\gamma_{\textit{Los}}\). In many reports, unpatterned graphene is coupled with periodically patterned dielectric resonant structures of a high-\(Q\). [PERSON] et al. [24] and [PERSON] et al. [25] numerically demonstrated that by using guided resonance in a photonic crystal slab backed by a DBR or a metal reflector, the absorption of monolayer graphene located on the top of a photonic crystal slab can reach perfect absorption (Figure 4a). By properly adjusting structural parameters such as period, thickness, and hole radius of photonic crystal slab, the system is critically coupled (\(\gamma_{\textit{Los}}=\gamma_{\textit{loss}}\)). [PERSON] et al. [26] and [PERSON] et al. [27] demonstrated experimentally close to total absorption in monolayer graphene absorbers based on critical coupling with guided resonances in transfer printed photonic crystal Fano resonance filters at near-IR. In 2018, [PERSON] et al. [39] introduced an asymmetric metasurface for an ultra-narrowband GPA. In the proposed absorber, in which monolayer graphene is on top of the dielectric metasurface backed by a silver substrate, the high angle tolerance and \(Q\) (\(\sim\)2600) are due to the magnetic dipole resonance based on two asymmetric silicon rings placed over a silica slab. [PERSON] et al. [29] reported that peak absorptions over 99% with FWHM about 20 nm in the near-IR were measured for monolayer graphene coupled with subwavelength gratings on top of a back gold mirror (Figure 4b).