## 2 Materials and Methods
### Simulation Setup  
In this research, the LSC PV devices were simulated in the ray tracing software LightTools. The mathematical technique that is implemented to trace light paths in an optical system is called \"ray tracing\". This method traces the light paths based on a number of factors related to the physical interaction of the photons with their surroundings, such as absorption, refraction, reflection, total internal reflection (TIR), emission and transmission. In an LSC PV device, the photons go through events that are both stochastic and probabilistic by nature. As such, Monte Carlo ray tracing has proven to be a very useful method to predict the performance of LSC PV devices and to calculate their optical efficiency (OE) [17]. In this study, the incident photons were traced from their entry into the LSC PV device, until they were absorbed, re-emitted and escaped from the devices, or were collected by the solar cells attached [18]. There are different types of software that can be used to conduct the ray tracing simulation of an LSC PV device. However, the software LightTools was chosen in this study due to its ability to handle complex geometries and to simulate the LSC PV devices under standard test conditions (STC: 1000 W/m\({}^{2}\), AM 1.5 spectrum and 25 \({}^{\circ}\)C). Furthermore, LightTools provides many robust design features and visualization tools to create a 3D model of the LSC PV device and to accurately evaluate its performance. As mentioned before, the rectangular lightguides consisted of PMMA (as the host material) which was mixed with two luminescent dyes, namely Lumogen red 305 and Lumogen orange 240. These organic dyes have a high photoluminescence quantum yield (PLQY). Moreover, these organic dyes are \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Case**} & \multirow{2}{*}{**Configuration**} & \multirow{2}{*}{\
\begin{tabular}{c} **Number** \\ **of Cubes** \\ \end{tabular} } & \multirow{2}{*}{
\begin{tabular}{c} **Cubes** \\ **Dimensions** \\ \end{tabular} } & \multicolumn{2}{c}{**PV Cell**} & \multicolumn{2}{c}{**PV Cell**} & \multicolumn{2}{c}{**Number**} & \multicolumn{1}{c}{**Number**} \\  & & & **Dimensions-Cells** & **Dimensions-Cells** & **of Cells** & **of Cells** \\  & & & **on Sides** & **on Back** & **on Sides** & **on Back** \\ \hline
1 & 5 unit cubes & 5 & \(1\times 1\times 1\) cm\({}^{3}\) & \(1\times 1\times 0.02\) cm\({}^{3}\) & \(1\times 1\times 0.02\) cm\({}^{3}\) & 4 & 5 \\
2 & 3 by 3 unit cubes & 9 & \(1\times 1\times 1\) cm\({}^{3}\) & \(1\times 1\times 0.02\) cm\({}^{3}\) & \(1\times 1\times 0.02\) cm\({}^{3}\) & 12 & 9 \\
3 & 5 by 5 unit cubes & 25 & \(1\times 1\times 1\) cm\({}^{3}\) & \(1\times 1\times 0.02\) cm\({}^{3}\) & \(1\times 1\times 0.02\) cm\({}^{3}\) & 40 & 25 \\
4 & 5 rectangular cuboids & 5 & \(5\times 5\times 1\) cm\({}^{3}\) & \(5\times 1\times 0.02\) cm\({}^{3}\) & \(5\times 5\times 0.02\) cm\({}^{3}\) & 4 & 5 \\
5 & 3 by rectangular cuboids & 9 & \(5\times 5\times 1\) cm\({}^{3}\) & \(5\times 1\times 0.02\) cm\({}^{3}\) & \(5\times 5\times 0.02\) cm\({}^{3}\) & 12 & 9 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The configurations of the simulated LSC PV devices. Figure 3: The geometry of the LSC PV device shown in Case 3 of Table 1: (**a**) top view of device; (**b**) the orange sphere shows the diffuse irradiance and the red line indicates the direction of the direct beam irradiance. inexpensive and have a simple mixing procedure with PMMA, in comparison with other luminescent materials. Lumogen red 305 and orange 240 are highly matched to the band gap of the silicon solar cells when compared to other dyes. Figure 4 depicts the absorption and emission spectra of Lumogen red 305, orange 240 dyes, versus the quantum efficiency curve of a silicon solar cell. For each device, a 3D model was created of all of the physical components, which was imported into LightTools for the 3D ray tracing simulations--see Figure 5. In this 3D model, the material properties were defined as follows.