## 2 Design and Analysis of the Proposed Optical System  
### Design of the Proposed Optical System  
Figure 1 illustrates a schematic diagram of the proposed optical system. Initially, solar lightflux is concentrated into multiple linear light beams using a CFL array. The linearly concentrated lightflux is then reflected by multiple prism-shaped geometries formed on  
the exit surface of the lightguide, and reflected lightflux is guided towards the edge of the lightguide by internal reflection in the lightguide. Table 1 presents the design specifications of the CFL array plate. Increasing the pitch of the CFL array results in a greater overall thickness of the optical module to enhance the efficiency at the focal plane of the CFL. To compact the optical module comprising the CFL array plate and the lightguide while maintaining high optical efficiency at the focal plane of the CFL, the pitch and the focal length of the CFL array were set to 10 mm and 11.5 mm, respectively. The CFL array plate consists of 10 CFLs arranged in an array, with a width of 100 mm and a length ensuring a square entrance cross-section of 100 mm. The design wavelength of the CFL was set to 550 nm, the central wavelength of the visible spectrum, which corresponds to the maximum range of solar spectral irradiance. Polymethyl methacrylate (PMMA) with a refractive index of 1.4936 at the design wavelength was considered as the material for the CFL. To analyze the concentration efficiency of the CFL array plate with specifications similar to Table 1, non-sequential ray tracing simulations were conducted using LightTools(tm) (Synopsys, Sunnyvale, CA, USA). During the analysis, solar spectrum data corresponding to the Phoenix (USA) region (latitude 33.5\({}^{\circ}\), longitude \(-\)112.17\({}^{\circ}\)) provided by LightTools(tm) was applied as the spectrum data for the light source [23]. Additionally, the size of the sunlight-simulating light source was set to 10,000 mm\({}^{2}\) to match the size of the CFL array plate. Considering the size of the CFL array plate and the angle of incidence of solar radiation, the distance from the CFL array plate to the light source was set to 16,205 mm. Furthermore, the radiant flux of the sunlight-simulating light source was set to 5 W, proportional to the irradiated area of 10,000 mm\({}^{2}\), and directed to the designed CFL array plate entrance surface. Figure 2 illustrates the results of non-sequential ray tracing analysis of the radiant flux transmitted to the focal plane of the CFL array plate under direct normal incidence (DNI) conditions. This analysis considered transmission and reflection due to the Fresnel loss of the CFL array plate. As shown in Figure 2, a cylindrical focused line array is formed 11.5 mm below the CFL array plate, and it can be observed that some of the incident light flux is reflected and lost at each entrance and exit interface of the CFL array plate. The total radiant flux reaching the focal plane of the designed CFL array plate is 4.6 W, resulting in an optical transmission efficiency of 92% when considering the 5 W of incident radiant flux. The radiant flux reaching the focal area of the CFL array, represented by the blue-line box, is 4.2 W, indicating an optical transmission efficiency of 84% for the CFL array plate. Figure 1: Concept of the proposed optical layout. To transmit the light flux reaching the focal area of the CFL array to the edge of the lighguide, it is necessary to form a lightguide with a prism-shaped exit surface near the focal area of the CFL array, as depicted in Figure 1. In this study, we considered a lightguide with the same cross-sectional area as the CFL array plate, and a thickness of 10 mm. The angle of the prism shape was set to 40\({}^{\circ}\) to maximize the transmission of light flux to the lightguide edge. In this study, we also explored ways to reduce the usage area of high-cost Si PV cells.