## 3 Results and Discussion
For further revealing the mechanism of concave-convex circular composite structure sidewall on light extraction, the propagation of transverse electric (TE) and transverse magnetic (TM) polarized blue photons with a radio of 1.8:1 were simulated by using finite-difference time-domain (FDTD) method [37; 38; 39]. The FDTD simulation model of the different sidewall structures and the corresponding simulated electric-magnetic field intensity distribution nearby the sidewalls are shown in the Figure 2:1 To avoid unnecessary reflected light, the top and bottom boundaries used perfectly matched layers (PML). The lateral boundaries used periodic due to the sidewalls pattern was periodic [40]. The polarized point sources with a wavelength of 457 nm were placed in the MQW [39]. The left and right boundary were 17 \(\upmu\)m far from the polarized point sources, respectively. As well, the relative distance between the polarized point sources and the sidewall of the devices A-F is 2 \(\upmu\)m, as shown in Figure 2:2 To measure \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Device** & **Saturation Current** & **Saturation Light** & **Enhancement of Light** \\  & **Density (A/cm\({}^{2}\))** & **Output Power (mW)** & **Output Power** \\ \hline Device A (Flat) & 2420.3 & 37.08 & 0\% \\ Device B (Concave) & 2433.1 & 37.46 & 1\% \\ Device C (2 \(\upmu\)m) & 2458.5 & 39.75 & 7.2\% \\ Device D (2.5 \(\upmu\)m) & 2458.5 & 39.09 & 5.4\% \\ Device E (3 \(\upmu\)m) & 2458.5 & 38.67 & 4.3\% \\ Device F (3.5 \(\upmu\)m) & 2458.5 & 38.11 & 2.8\% \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The saturation light output power (LOP) and LOP enhancement of all studied devices. Figure 6: LOP and WPE as a function of current density of all devices. the total output power and the escaped power, two detection monitors were placed around the polarized point sources and in air near the sidewalls, respectively. The grid size in computational domain was 10 nm. The simulation parameters such as the refractive index could be found in [41; 42; 43]. From the Figure 8, the polarized photons emitting from flat sidewall is mainly confined in the center region. Compared with the flat sidewall, the polarized photons also emitting from the both sides of center region in the concave circular sidewall and concave-convex circular composite structure sidewall in addition to the center region. As well, the total polarized photons emitting from concave circular sidewall and concave-convex circular composite structure sidewall are improved to varying degrees, especially in the concave-convex circular composite structure sidewall. This indicates that the enhancement mainly due to the reduction of the total internal reflection at the sidewall. Figure 9 shows simulated sidewall LEE enhancement factors of all sidewall structures. When the radius of the concave- and convex-circle is 2 \(\upmu\)m, the concave-convex circular composite structure sidewall obtains the largest LEE, which is in accord with the experimental results of Device C. It is further proved that the concave-convex circular composite structure sidewall is an effective approach to improve the LEE. Figure 8: **(a–c)** Electric field-magnetic intensity distribution (left) and FDTD simulation model (right) of the flat sidewall (Device A), concave circular sidewall (Device B) and concave-convex circular composite structure sidewall (Device C). Figure 7: EL intensity versus wavelength of studied devices.