## 2 Theory  
A schematic diagram of the OLED multilayer micro-cavity (MMC) structure is shown in Figure 1a. The thickness of each layer \(j\) (\(j=1,2,\cdots,n\)) is \(d_{j}\), and the complex refractive index is designated as \(\widetilde{n}_{j}=n_{j}+i\kappa_{j}\), which indicates the refractive index and extinction coefficient, respectively. It is assumed that all layers are isotropic and homogeneous with planar and parallel interfaces. In accordance with other optical models of OLEDs [4; 6; 12; 14], the EML is assumed to be lossless for the sake of simplicity. The dipole emitter, which is \(z_{xx}\) away from the left boundary of the EML, emits monochrome light with the wavelength of \(\lambda\). Light polarizations of transverse electric (TE) and transverse magnetic (TM) modes are denoted as the TE and TM superscripts. In Figure 1a, \(t_{e,+(-)}^{\rm TE(TM)}\) and \(t_{e,+(-)}^{\rm TE(TM)}\) represent the reflection and transmission coefficients from the EML to the upper (lower) ambient layer, where the +(\(-\)) sign in \(r_{e,+(-)}^{\text{TE(TM)}}\) and \(t_{e,+(-)}^{\text{TE(TM)}}\) denotes the upper (lower) direction. Figure 1b shows the polarization-dependent sign convention of electric and magnetic field amplitudes on transmission and reflection based on the Verdet convention, where polarization-dependent Fresnel reflection and transmission coefficients from layer \(j\) to \(j+1\) are expressed as [18]  
\[r_{j,j+1}^{\text{TM}}=\frac{\tilde{\eta}_{j+1}^{2}k_{z,j}-\tilde{\eta}_{j}^{2}k _{z,j+1}}{\tilde{\eta}_{j+1}^{2}k_{z,j}+\tilde{\eta}_{j}^{2}k_{z,j+1}},\ \ \ r_{j,j+1}^{\text{TE}}=\frac{k_{z,j}-k_{z,j+1}}{k_{z,j}+k_{z,j+1}}, \tag{1}\]  
\[\text{t}_{j,j+1}^{\text{TM}}=\ 1+r_{j,j+1}^{\text{TM}},\ \ \ \text{t}_{j,j+1}^{\text{TE}}=\ 1+r_{j,j+1}^{\text{TE}}. \tag{2}\]  
when the wave number in free space is \(k_{0}=2\pi/\lambda\), and the \(z\) components of the wave number in \(j\)-th and \((j+1)\)-th layers are \(k_{z,j}=k_{0}\tilde{\eta_{j}}\sqrt{1-\left(n_{e}/\tilde{\eta_{j}}\right)^{2}u^ {2}}\) and \(k_{z,j+1}=k_{0}\tilde{\eta_{j+1}}\sqrt{1-\left(n_{e}/\tilde{\eta_{j+1}}\right) ^{2}u^{2}}\), respectively. Here, \(n_{e}\) is the refractive index at the EML. The schematic diagram of wave vector components is shown in Figure 1c when the dipole emitter located at the EML emits the electromagnetic wave with the emission angle of \(\theta_{e}\). Here, \(\mathbf{k}_{xy}\) is the in-plane component of \(\mathbf{k}_{e}\), and \(u\) denotes the normalized in-plane wave vector, which is later used instead of \(\mathbf{k}_{xy}\) for the purpose of simple mathematical manipulation. In Figure 1a, \(r_{e,+(-)}^{\text{TE(TM)}}\) and \(t_{e,+(-)}^{\text{TE(TM)}}\) can be determined from the system reflection and transmission coefficients between layer \(j\) and layer \(m+1(0)\), which can be iteratively calculated as [22]  
\[r_{e,+}^{\text{TE(TM)}}=r_{j,m+1}^{\text{TE(TM)}}=\frac{r_{j,j+1}^{\text{TE(TM )}}+r_{j+1,m+1}^{\text{TE(TM)}}\exp\bigl{(}2 ik_{z,j+1}d_{j+1}\bigr{)}}{1+r_{j, j+1}^{\text{TE(TM)}}r_{j+1,m+1}^{\text{TE(TM)}}\exp\bigl{(}2 ik_{z,j+1}d_{j+1} \bigr{)}}, \tag{3}\]  
Figure 1: (**a**) Schematic diagram of the organic light-emitting diode (OLED) multilayer micro-cavity (MMC) structure. (**b**) Sign configuration of the transverse electric (TE)- and transverse magnetic (TM)-polarized electric and magnetic field amplitudes on reflection and transmission based on the Verdet convention. (**c**) Schematic diagram of the wave vector components in the emission layer (EML).