## 3 Optimum Design of SOE
### Broadband Solar Spectrum Simulation with KOD II--SOE  
In the preceding sections, the KOD II SOE was selected as the best SOE, and its optical performance was simulated with a single wavelength at 550 nm. Since the solar spectrum is broadband, ranging from 280 nm to 2500 nm, it is necessary to predict the actual characteristics of the CPV unit with the KOD II SOE under broadband spectrum. Based on the response of the III-V solar cell made from INGaP/GaAs/Ge, the broadband simulation was performed in the spectrum ranging from 400 nm-1300 nm in this study. In addition, the dependency of index of refraction of the urethane and BK7 on the wavelength was also considered in the simulation. In the simulation, the wavelength range (400 nm-1300 nm) was divided into smaller segments of 100 nm, as listed in Table 5.  
Figure 22 shows the simulated optical efficiency of the CPV unit with the KOD II SOE in single wavelength (550 nm) and broadband (400 nm-1300 nm). The simulation results reveal that the optical efficiency from broadband spectrum is higher than those from single wavelength. More specifically, the optical efficiency under normal incidence from broadband spectrum is 87% and the optical efficiency from single wavelength is 85%. In addition, the acceptance angles from the two simulation scenarios are the same, both is 1.7\({}^{\circ}\). Table 6 summarizes the optical performance of CPV unit with KOD II SOE with broadband and single-wavelength simulation.  
\begin{table}
\begin{tabular}{c c c} \hline
**Wavelength (nm)** & **Radiant Flux on POE (W)** & **Percentage (\%)** \\ \hline
400–500 & 0.19 & 15.46 \\
501–600 & 0.21 & 17.79 \\
601–700 & 0.2 & 16.74 \\
701–800 & 0.17 & 13.95 \\
801–900 & 0.14 & 11.65 \\
901–1000 & 0.08 & 7.04 \\
1001–1100 & 0.1 & 8.1 \\
1101–1200 & 0.05 & 4 \\
1201–1300 & 0.07 & 5.47 \\ Sum & 1.2 & 100 \\ \hline \end{tabular}
\end{table}
Table 5: Radiant flux for broadband spectral simulation.  
Figure 23(a,b) show the irradiance distribution on the receiver from broadband simulation with KOD II-type SOE when the incidence angle is 0\({}^{\circ}\) and 1.7\({}^{\circ}\), respectively. By comparing Figure 23a and Figure 14a, it is found that the irradiance is more localized in the central region of the solar cell based on broadband simulation. This phenomena results from the fact that the index of refraction of the Fresnel lens is decreasing with an increase of wavelength. Therefore, the irradiance distribution on the solar cell under broadband simulation was not as uniform as that under a single wavelength of 550 nm. The presented optimization process in this study was based on the simulation of single-wave length. In the future, a further optimization can be conducted considering the broadband solar spectrum and the response of specific solar cell.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Optical Performance** & \
\begin{tabular}{c} **Broadband** \\ **(400 nm–1300 nm)** \\ \end{tabular} &
\begin{tabular}{c} **Single Wavelength** \\ **(550 nm)** \\ \end{tabular} \\ \hline Acceptance angle (degree) & 1.7 & 1.7 \\ Optical efficiency under normal incidence (\%) & 87 & 85 \\ Optical efficiency at the acceptance angle (\%) & 79.2 & 76.9 \\ Peak value of irradiance on the receiver under normal incidence (W/mm\({}^{2}\)) & 0.9236 & 1.1374 \\ \hline \hline \end{tabular}
\end{table}
Table 6: Comparison of optical performance of CPV unit with KOD II SOE with broadband and single-wavelength simulation.  
Figure 22: Optical efficiency of broadband (400 nm–1300 nm) and single wavelength (550 nm) simulation.