## 3 Calculation Results and Analysis  
### Concentrated Light Intensity and Spectral Analysis along the Optical Axis  
The optical efficiency calculations in the optical model are shown in Figure 4a for several distances of the receiver from the Fresnel lens position (Z). The on-focus position is at Z = 110 mm. As can be seen from that, the optical efficiency of the Fresnel lens is related to the distance from the cell to the lens. For Z = 110 and 111 mm, the optical efficiency of the full-wave band is maximum. The optical efficiency of the short-wave band decreases at Z = 112 mm. With the distance from the cell to the lens being further, the optical efficiency of 500 nm decreases to 34.5% at 116 mm. The optical efficiency of long wavelength decreases at Z = 109 mm and the optical efficiency of 1500 nm decreases to 76.4%. When the distance is 108 mm, the optical efficiency of the medium-wave band begins to decrease and the long-wave band continues to decrease which the optical efficiency of 1500 nm has decreased to 59%. The optical efficiency of the lens at different optical axis positions is different, indicating that it is affected by the dispersion effect. When the distance from the lens to the cell is less than the focal distance, long wavelength efficiency decreases because the cell surface cannot cover all illuminations and part of long-band sunlight is lost. For Z > 100 mm, the short band optical efficiency decreases, and part of the short band light cannot be concentrated on the cell surface. When the cell is placed at the focal plane, there is no energy loss, but the short-wave spot is smaller and more concentrated in the center of the cell whose  
Figure 4: (a) Optical efficiency at different optical axis positions (in the range of 300–1700 nm); (b) Radiation power at different positions in the optical axis direction. distribution is seriously non-uniform. It can be seen that due to the dispersion effect, the energy proportion of the three bands irradiated on the cell does not change synchronously, and there is spectral mismatch at different optical axis positions (including on the focal plane). The spectral distribution deviates from the solar spectrum, which is bound to make an adverse impact on the performance of the cell. Figure 4b shows the change in the irradiance power calculated with the position of the optical axis, reflecting the changes in the short, medium and long bands, respectively. It can be seen that the changes in the irradiance power of the medium band and long band are basically the same. The maximum value position is between 110 and 116 mm and the position of the maximum value of the short band radiation power is between 108 and 111 mm which is consistent with the change tendency of the optical efficiency reflected in Figure 4a. Because the radiation power of the short-wave band accounts for about half of the total radiation power, the total change in the radiation power is mainly affected by the short-wave band. In addition to the dispersion effect, the spot focused by the Fresnel lens also has obvious Gaussian distribution. This kind of non-uniformity also has an important impact on the output characteristics of multijunction solar cells [21]. Therefore, this paper explores the change in the spot non-uniformity along the optical axis. Figure 5 shows the spot diagram at typical positions along the optical axis (Z = 108 mm, 109 mm, 110 mm, 111 mm, 112 mm and 114 mm). Concentration ratio is defined as the ratio of the actual irradiance on the cell surface to the standard irradiance (1000 W/m\({}^{2}\)) and the peak to average ratio (PAR) is defined as the ratio of the highest irradiance on the cell surface to the average irradiance on the surface, which is used to quantify the non-uniformity of the spot. When the cell is located at Z = 108 mm, the central focusing ratio is about 283 and the PAR is 4. When the cell is placed near the focal plane (for a range of Z values between 110 and 112 mm), the non-uniformity increases rapidly and the PAR increases to 47.2, 62.7 and 55.0.