## 2 Principle  
Let us explain the principle of SCCPA, considering the system as shown in Figure 1. Here, \(n_{0},\ n_{1},\ \text{and}\ n_{2}\) are the refractive indices of the substrate, the thin film (thickness \(d\)), and the surrounding medium, respectively. It is assumed that \(n_{0}\) and \(n_{2}\) are real while \(n_{1}=n+i\kappa\) is complex, with \(\kappa\) being the extinction coefficient. When the angle of incidence to each layer is \(\theta_{i}\), the wavenumber of the incident light in vacuum is \(k\), and the phase change due to one-way propagation in the thin film is \(\phi=kn_{1}d\cos\theta_{1}=p+iq\), the complex-amplitude reflection coefficient considering multiple reflections in the monolayer film is expressed by [19]  
\[r=\frac{r_{01}+r_{12}e^{2i\phi}}{1+r_{01}r_{12}e^{2i\phi}}. \tag{1}\]  
Therefore, the required condition of CPA is \(r_{01}+r_{12}e^{2i\phi}=0\). When the incidence angle is greater than the critical angle of TIR (\(n_{1}\sin\theta_{1}\geq n_{2}\)) from \(n_{1}\) layer to \(n_{2}\) layer and \(\kappa=0,\ r_{12}=e^{i\Omega_{\chi}}\) with \(\Omega_{\chi}\) being the phase shift by TIR for X (p or s) polarization. Then, \(r=\frac{r_{01}+e^{i\Omega_{\chi}}e^{2i\phi}}{1+r_{01}e^{i\Omega_{\chi}}e^{2i \phi}}\) and \(r_{01},\Omega_{\chi}\) and \(\phi\) are real, so \(\left|r\right|^{2}=1\) and no reflection dip occurs. It is thus necessary for CPA to occur so that the thin film has even a small amount of absorption (\(\kappa\
eq 0\)) [17]. In this case (\(n_{1}=n+i\kappa\)), \(r_{01}\) is complex and \(r_{12}\) is not only complex (as usual for TIR) but also \(\left|r_{12}\right|<1\). For CPA (\(r_{01}+r_{12}e^{2i\phi}=0\)), therefore, the following two equations of real and imaginary parts (or magnitude and phase) should be simultaneously satisfied [7]:  
\[\left|r_{01}\right|=\left|r_{12}\right|e^{-2q} \tag{2}\]  
and  
\[\phi_{01}=\phi_{12}+2p+(2m+1)\pi \tag{3}\]  
with \(r_{ij}=\left|r_{ij}\right|e^{i\phi_{ij}}\). If Equations (2) and (3) are satisfied with \(\phi=p+iq\), then \(r_{01}+r_{12}e^{2i\phi}=|r_{01}|e^{i\phi_{01}}+|r_{12}|e^{i\phi_{0}}e^{2i2p-2 q}=|r_{12}|e^{-2q}(e^{i\phi_{01}}+e^{i(\phi_{12}+2p)})=|r_{12}|e^{-2q}e^{i( \phi_{12}+2p)}(e^{i(2m+1)\pi}+1)\)\(=0\). This means perfect absorption because the energy reflectance \(R=\left|r\right|^{2}=0\) and the energy transmittance \(T=0\). Since we are interested in the case where the thin film is almost transparent (\(n_{1}=n+i\kappa,\ \kappa\ll 1,\ \kappa\ll n,\ q\ll 1\)) but has a small absorption, it can be approximately assumed that \(r_{01}\) is real and \(\left|r_{12}\right|\approx 1\) by TIR. Then, the approximate condition for CPA to be realized is  
\[\left|r_{01}\right|\approx e^{-2q} \tag{4}\]  
Figure 1: Schematic of SCCPA with substrate 0, thin film 1, and surrounding medium 2. Collimated white light incident from the side of the substrate enters the thin film and is totally reflected at the interface between the thin film and the surrounding medium. From \(q\ll 1\), we know that \(|r_{01}|\) must be close enough to 1. Therefore, note that Equations (10) and (11) in Ref [17] are approximate conditions for CPA and are not strictly correct. To realize SCCPA in a transparent thin film using TIR, the following conditions must be satisfied, assuming that the thin film has very weak absorption (\(n_{1}=n+i\kappa\), \(0<\kappa\ll n,n_{1}\approx n(\mathrm{real})\)) as a prerequisite:  
1. The reflectance at the interface between the film and the substrate must be high [Equation (4)]. 2. The film material must have a higher refractive index \(n_{1}\) than the surrounding medium \(n_{2}\) for TIR (\(n_{1}>n_{2}\)). 3.