## 3 Calculation Results  
Figure 2 shows the multilayer structure of a top-emitting OLED, which is taken from [25]. The device is composed of 100-nm Ag as a reflective bottom anode, 250-nm Alq\({}_{3}\) (tris-(8-hydroxyquinoline) aluminum) as an EML, 37-nm Ag as a semi-transparent top cathode, and 87-nm N, N-bis(naphthalen-1-yl)-N, N-bis(phenyl)-benzidine (NPB) as the capping layer. All results are calculated at the wavelength of \(\lambda=520\) nm, which corresponds to the photoluminescence peak of Alq\({}_{3}\) in the literature [6]. The complex refractive indices of the materials shown in Figure 2 are obtained from the literature [26; 27]. As organic materials in an OLED have relatively similar refractive indices [28; 29; 30], it is sometimes considered that all organic layers such as the electron transport layer and EML have the same refractive index value [31] or assumed that all the organic layers are integrated into the one organic layer. In Figure 2, it is assumed that both exciton generation and carrier transport occur at the EML. This simple structure of the top-emitting OLED is better to show the calculation results and optical analysis, which makes it easier and more intuitive for readers to understand the theoretical model and analysis of the NF absorption. The dipole emitter assumes to have a delta function distribution, which is positioned \(z_{\text{ex}}\) away from the interface between the Ag reflective bottom anode and EML. Figure 3 shows the calculated spatial profiles of the normalized electric field intensity of TM modes confined in the top-emitting OLED. The arrows indicate three dipole emitter positions, which will be used in the calculation results of Figure 4. These spatial profiles of the TM modes are calculated based on the boundary mode analysis performed by a commercial software of COMSOL Multiphysics [32]. The validity of the calculated eigenvalues and eigenfunctions obtained by the boundary mode analysis is confirmed through the agreement of the calculation results obtained by our homemade simulation code based on the transfer matrix method-based waveguide analysis of the OLED [21; 33]. As shown in Figure 3, all TM modes are closely confined near the Ag metal/organic interfaces, which shows a typical characteristic of SP modes. Effective mode indices of three TM modes are shown in Table 1. The terms TM0, TM1, and TM2 are named in the ascending order of the real part of their effective mode index shown in Table 1. The imaginary part of the effective mode index corresponds to the extinction coefficient of each TM mode. The real parts of all the effective mode indices in Table 1 are greater than \(n_{EML}=1.73\), which also confirms that all the TM modes in this top-emitting OLED structure are SP mode-like confined mode [21]. Figure 3: Spatial distributions of the normalized electric field intensities of TM modes confined in the top-emitting OLED. Three TM modes, having a typical characteristic of surface plasmon (SP) modes, are denoted as TM0, TM1, and TM2, which are named in the ascending order of the real part of their effective mode index shown in Table 1. The arrows indicate three dipole emitter positions, which will be used in the calculation results of Figure 4.  
Figure 2: Device structure of a top-emitting OLED along with the corresponding layer thickness and complex refractive index. To simplify the calculation, both exciton generation and carrier transport are assumed to occur at the Alq\({}_{3}\) EML layer. The dipole emitter with the wavelength of 520 nm is assumed to be isotropic and to have the \(\delta\)-distributed emission zone, which is positioned \(z_{ex}\) away from the interface between the reflective bottom anode and EML.