## 3 Calculation Results
According to the analytical technique to identify planar WG and SP modes in OLEDs, the spectral responses of the SP-like TM modes can be approximated by the summation of the respective Lorentzian line shape function [21; 34]  
\[K_{\left[\bot\right),SP}^{TM}(u)\approx\sum_{l=1}^{3}\frac{\sigma_{l}^{TM}}{ \left(u-n_{phase,l}^{TM}/n_{EML}\right)^{2}+\left(\kappa_{l}^{TM}/n_{EML}\right)^ {2}}, \tag{30}\]  
where \(n_{phase,l}^{TM}\) and \(\kappa_{l}^{TM}\) denote the phase index and extinction coefficient of the \(l\)-th confined SP-like TM mode, which corresponds to the real and imaginary parts of the effective mode index. The term \(\sigma_{l}^{TM}\) represents the excitation magnitude and can be determined by the best fitting to the calculation result of the total spectral power density emitted by the horizontally (vertically) oriented dipole emitter, as will be shown in Figure 4. \begin{table}
\begin{tabular}{c c c c} \hline  & **TM0** & **TM1** & **TM2** \\ \hline Effective mode index (\(n_{off}\)) & \(1.849+0.0211i\) & \(2.128+0.0521i\) & \(2.636+0.1447i\) \\ \hline \end{tabular}
\end{table} 
Table 1: Effective mode indices of TM modes obtained by the boundary mode analysis. Figure 4: The calculated TM-polarized power dissipation spectra at three dipole emitter positions for (**a**) horizontal and (**b**) vertical dipole orientations. Three spectral responses of the TM modes (TM0, TM1, and TM2) are fitted to the summation of the respective Lorentzian line shape function represented in Equation (30). The spectral response caused by the near-field (NF) absorption is calculated based on Equation (28) and plotted in the evanescent spectral range of \(u>1\). Figure 4 shows the calculation results of the TM-polarized power dissipation spectra at three dipole emitter positions for horizontal and vertical dipole orientations. The validity of these calculation results is verified through a very good agreement with the calculated power dissipation spectra at the same structure of the top-emitting OLED obtained by a commercial software of SETFOS [35]. As shown in Figure 3, two dipole emitter positions are close to either bottom (\(z_{ex}=10\) nm) or top (\(z_{ex}=240\) nm) Ag metal layers, and the remaining one is located at the middle of the two Ag metal layers (\(z_{ex}=125\) nm). The white-, green-, and magenta-shaded regions refer to the light coupling mechanisms of the air mode (\(0\leq u\leq n_{air}/n_{EML}\)), WG mode (\(n_{air}/n_{EML}<u\leq 1\)), and evanescent modes, (\(1<u<\infty\)), respectively. Three spectral peaks of the SP-like TM modes (TM0, TM1, and TM2) are fitted to the summation of the respective Lorentzian line shape function in Equation (30). To verify the accuracy of the Lorentzian line-shaped spectral responses for the SP-like TM modes, the values of the effective mode index obtained by the best fitting to the total power dissipation spectrum are summarized in Table 2. Irrespective of the dipole positions, the real and imaginary parts of the effective mode index for three TM modes in Table 2 are nearly the same as those calculated by the boundary mode analysis in Table 1. This agreement confirms the validity of the Lorentzian line-shaped spectral responses of three SP-like TM modes obtained by the best fitting to the total power dissipation spectrum. In Figure 4, the aggregate spectral power density of the SP-like TM modes, obtained by summing all the spectral responses of three TM modes, is significantly different from the total spectral power density calculated based on Equation (17) in the evanescent region of \(u>1\). For the dipole positions of \(z_{ex}=10\) and \(240\) nm, the aggregate spectral power density of three SP modes is less than the total spectral power density at the spectral region of \(u>1.523\), which corresponds to the spectral peak position of the SP-like TM2 mode. In contrast, the aggregate spectral power density caused by three SP modes is greater than the total spectral power density when the dipole position is \(z_{ex}=125\) nm.