# Towards Mirror-Less Graphene-Based Perfect Absorbers
## 2 Graphene Perfect Absorbers with External Mirror  
Before we get started the main issue, the optical properties of graphene need to be addressed. In the mid-IR to THz regime (strictly, \(hf<2E_{f}\), where \(h,f\), and \(E_{f}\) are the Plank constant, the frequency of incident light, and the Fermi level of graphene, respectively), the optical conductivity of graphene is dominated by the intraband transition, and thus, it can be treated as a metallic material [6; 7; 8; 9; 10]. This indicates that doped graphene supports plasmon resonances, which are collective oscillations of free electrons. Unlike noble metals, free carriers in doped graphene can easily be tuned by electrostatic gating or chemical doping. Additionally, graphene plasmons have lower loss and stronger field confinement compared to plasmons in noble metals in the mid-IR to THz regime [7]. On the other hand, in the near-IR to visible regime (strictly, \(hf>2E_{f}\)), absorption is nearly wavelength independent because its optical conductivity is dominated by the interband transition [6; 7; 8; 9; 10]. In particular, undoped monolayer graphene is treated as a lossy dielectric material that has an absorption efficiency of \(\sim\)2.3% over a wideband wavelength range. Under single-sided illumination, the most straightforward approach for achieving perfect absorption is to use a one-port resonant system that has a 100% reflective external mirror on the backside, as shown in Figure 1. In general, DBRs (distributed Bragg reflectors) and noble metals can be used as typical external mirrors for achieving zero transmission. According to the coupled mode theory (CMT), absorption efficiency in a lossy one-port resonant system can be described using the following equation [24; 33; 49]  
\[A(\omega)=\frac{4\gamma_{\textit{Ieak}}\gamma_{\textit{loss}}}{\left(\omega- \omega_{o}\right)^{2}+\left(\gamma_{\textit{Ieak}}+\gamma_{\textit{loss}} \right)^{2}} \tag{1}\]  
where \(\omega_{o}\), \(\gamma_{\textit{Ieak}}\), and \(\gamma_{\textit{loss}}\) are the resonant frequency, leakage rate, and loss rate, respectively. When \(\gamma_{\textit{Ieak}}=\gamma_{\textit{loss}}\), \(A=1\) at resonance (\(\omega=\omega_{o}\)). This means that perfect absorption is achieved by balancing the internal loss rate and the external leakage (or coupling) rate of the resonator, commonly referred to as the '_critical coupling_' condition. While \(\gamma_{\textit{Ieak}}\) is controlled by the quality factor (\(Q\)-factor) of the resonator, \(\gamma_{\textit{loss}}\) is controlled by the absorption coefficient and the electric field intensity in the graphene layer. The graphene absorption coefficient is determined by the doping level and the quality of the graphene, which can be generally described by the Kubo formula [6; 7; 8; 9; 10]. In this review, we mainly consider a CVD-grown graphene because it has moderate carrier mobility [50; 51]. Due to the straightforward critical coupling concept, most previous perfect absorbers, including GPAs, have employed an external mirror [1; 2; 3; 4; 5; 6; 7; 8; 9; 10]. When these GPAs support only single-resonance at wavelength range of interest, as shown in Figure 1 or Equation (1), they are dubbed as the'single-resonance/mirror absorber'. In the case of dual-band [52; 53; 54; 55; 56] or multi-band [57; 58; 59; 60; 61; 62] absorption, the absorption efficiency can be described through the superposition of absorption in single-resonance/mirror absorbers with different resonances. In particular, ultra-broadband absorption [63; 64; 65; 66; 67; 68] can be attributed to the overlapping of multiple resonance absorption bands which exhibit a significantly wider bandwidth. An alternative approach for implementing a one-port resonant system is 'Prism-coupling absorber' scheme [41; 42; 43; 44], which utilizes total internal reflection (TIR) to achieve zero transmission. This implies that the prism functions as an external mirror at above critical incident angles.