# Towards Mirror-Less Graphene-Based Perfect Absorbers
## 3 Graphene Perfect Absorbers without External Mirror
### 'Degenerate Critical Coupling Absorber' Scheme  
If a mirror-symmetric two-port resonator supports a single resonance, then at most 50% of the incident power can be absorbed when the system is illuminated from a single side. In 2014, however, [PERSON] et al. [80] theoretically demonstrated that the perfect absorption can be achieved through degenerate critical coupling with two resonant modes of opposite symmetry, which are each responsible for 50% absorption (Figure 7a). The proposed resonator consists of a graphene layer placed on top of a photonic crystal slab. When we assume that the loss of graphene does not change the underlying symmetry of the resonator, according to CMT, the total absorption in the system is given by  
\[A(\omega)=\sum_{j=1}^{2}\frac{2\gamma_{\textit{Ieak},j}\gamma_{\textit{loss}, j}}{\left(\omega-\omega_{j}\right)^{2}+\left(\gamma_{\textit{Ieak},j}+\gamma_{\textit{loss},j} \right)^{2}} \tag{2}\]  
where the loss of each mode remains independent and total absorption is the sum of the contribution of each mode. Each of the two terms of in Equation (2) will attain a maximum of 50% when the leakage rate of the mode exactly matches the loss rate of graphene at each resonance (\(\omega=\omega_{j}\), \(\gamma_{\textit{Ieak},j}=\gamma_{\textit{loss},j}\)). If the two modes are degenerate (\(\omega_{1}=\omega_{2}\)), the entire system reaches the so-called degenerate critical coupling, and 100% absorption will be achieved. As shown in Figure 7a, at the point of the mode crossing, the conditions for degenerate critical coupling can be fulfilled, giving rise to the perfect absorption of the structure, thus breaking the limit of 50% absorption. But in reality, it is very difficult to simultaneously satisfy the frequency degeneracy and the critical coupling conditions of dual modes.  
Recently, ultrathin all-dielectric Huygens' metasurfaces have also been proposed for perfect absorption based on degenerate critical coupling [81; 82; 83; 84; 85; 86; 87], although graphene is not used as an absorbing medium. By overlapping two orthogonal Mie resonance (such as one electric dipole (ED) and one magnetic dipole (MD) resonance), perfect absorption can be achieved. In 2018, [PERSON] et al. [83] verified the principle of perfect absorption for all-dielectric metasurfaces based on Ge disks (Figure 7b): the destructive interference between simultaneously excited electric and magnetic dipoles inside each element in the backward direction (known as Kerker condition) in combination with the destructive interference between the scattered field and the incident field in the forward direction. In comparison to photonic crystal slab or grating configurations [80], metasurfaces are more useful for individual tuning of the leakage rates of resonant modes by adjusting the geometrical parameters of each element. In particular, to address the issue of only a moderate quality factor (\(Q\sim 10\)) resulting from the high radiative loss of Mie resonance, [PERSON] et al. also adopted the quasi-bound states in the continuum (quasi-BIC) resonance, thereby achieving high-\(Q\) (\(\sim\)640) near-unity absorption in the near-infrared regime [84]. These all-dielectric Huygens' metasurfaces would offer a new route for mirror-less GPA.