## 2 Materials and Methods
### Simulation Setup
PMMA was a standard material in LightTools, with a refractive index of 1.49 at 589 nm. The dyes had absorption and emission curves, as shown in Figure 4. The silicon solar cells were modeled as receiver planes with a refraction index of 3.4 at 550 nm. In Figure 4, the red dye had two absorption peaks at 444 and 574 nm and also had a single emission peak at 601 nm. The orange dye had two absorption peaks at 497 and 532 nm and also two emission peaks at 539 and at 581 nm. The Stokes shift of the red and the orange dye was equal to 27 and 7 nm, respectively. Therefore, the red dye showed a larger absorption band and a higher Stokes shift than the orange dye, which means that an LSC PV device with a red luminescent dye might be  
Figure 4: The quantum efficiency curve of a silicon solar cell versus the normalized absorption and emission spectra of the Lumogen red 305 and orange 240 dyes. Figure 5: (**a**) The receiver positions in case 1 and 4; (**b**) the receiver positions in Case 2 and 5; (**c**) the receiver positions in Case 3.  
slightly more efficient. The STC efficiency of the mono c-Si bifacial solar cells, which were attached to the sides and the back of the lightguides, was set at 20%. The ray tracing simulations were carried out under STC with 70% direct and 30% diffuse irradiance, respectively. The direct irradiance source was oriented as perpendicular toward each device in a long distance, while the diffuse irradiance source was positioned surrounding the whole device. The number of rays varied between 1 million and 5 million, which is sufficient for precise analysis. The dye concentration was increased from 5 to 110 ppm where the device reached saturation point, meaning that a further increase in the dye concentration would have led to a decrease in the light passing through the device. The formula that was related to tuning the concentration is presented in Equation (1) [19]  
\[c=\frac{PPM}{Mw} \tag{1}\]  
where \(c\left[mol/m^{3}\right]\) is the concentration, PPM represents the particle per million and \(Mw\left[g/mol\right]\) indicates the molecular weight of the substance. PPM was calculated through Equation (2) [19]. \[1\ PPM=1\ \frac{mg}{L}\ \ 1\ L=0.001\ m^{3} \tag{2}\]  
C was tuned to change the dye concentration for the Lumogen red 305 and orange 240. It has to be taken into account that the orange dye reached the saturation point at a lower concentration compared to the red dye because of two reasons, namely (1) molecular weight and (2) a different absorption coefficient. In addition, the molecular weight of the orange dye was lower than the red dye. This means that the orange dye had a higher concentration than the red dye at an equal ppm. Furthermore, the orange dye had double the absorption coefficient compared to the red dye. As a result, these effects caused an early saturation of the orange dye during the mixing procedure [20]. The efficiency of LSC PV devices was calculated through Equation (3)  
\[\eta_{LSC\ PV}=\ \frac{P_{PV}}{\left(G\times A\right)} \tag{3}\]  
where \(\mathrm{P_{PV}}\ (\mathrm{W})\) is the output power of the solar cells, G is the irradiance (1000 W/m\({}^{2}\)) and A is the aperture area (cm\({}^{2}\)) of the lightguide.