# Angular Dependence of Photonic Crystal Coupled to Photovoltaic Solar Cell
## 3 Results and Discussion
### Incident Angle Effect
Thus, effective refractive index for 1 DPC could be extrapolated from this experimental data collection [29]. The most common mistake consists of designing the 1 DPC under normal incidence, so Equation (2) would be simplified into Equation (3):  
\[\lambda_{0}=2 dn_{eff}^{2} \tag{3}\]  
However, as can be observed in Figure 5a, this simplification implies that the 100 nm peak position shift is an overestimation. Because under real operating conditions, the irradiation source tends towards higher incident angles with respect to the photovoltaic system, Equation (3) wrongly assumes that Bragg peak remains at the same position. This natural effect, not considered in Equation (3), has critical consequences for its optical properties. Once the indoor tests determined the relationship between the incident angle and the Bragg peak position of the 1 DPC and limit conditions were identified, the prototypes were characterized under outdoor conditions. This test validated the indoor hypothesis and demonstrated the optical coupling performance under real operating conditions for the photovoltaic device. To investigate the angular incoming irradiation on the optical coupling effect between the 1 DPC and the solar cell, the photocurrent generated by the prototype under outdoor conditions was measured, obtaining more than 2000 experimental data. The location where the experiments were carried out was Seville (Spain), with latitude 37.39\({}^{\circ}\) and longitude -5.97\({}^{\circ}\), during autumn. Two similar prototypes were installed: a solar cell with 1 DPC coupled on top and an identical solar cell without 1 DPC, which served as a reference sample. The photocurrent of both devices was measured. The first remarkable evidence was that when the incoming radiation to the devices was normal, both signals were proportional, as expected. However, this correlation was lost during the sunrise and sunset, due to the high incident angles for the incoming radiation irradiance. Optical coupling losses (\(\eta_{\text{\emph{losses}}}\)), due to the 1 DPC performance, were beyond those expected under the design conditions, as defined in Equation (4) and plotted in Figure 6.  
\[\eta_{\text{\emph{losses}}}=1-\frac{I_{\text{C}}-I_{\text{\emph{PCID}}}}{I_{c}} \tag{4}\]  
where \(I_{\text{\emph{1 DPC}}}\) and \(I_{\text{\emph{C}}}\) represent the photocurrent measured for 1 DPC coupled to the solar cell and the reference solar cell, respectively. Figure 6 shows that these results were fully aligned with the analysis discussed above for the indoor measurements. As the position of the sun varied along the day, the Bragg peak position shifted from the expected value with normal incident light. If this modification was in the range of +/-50\({}^{\circ}\) and the width of the Bragg peak remained almost constant, there was no significant effect on the photovoltaic device. However, when the incident angle was higher than 50\({}^{\circ}\), the Bragg peak was distorted. Furthermore, the Bragg peak position shifted more than 100 nm. As a consequence, maximum reflectivity was significantly reduced and the original gaussian profile of the Bragg peak was the smoothest. Hence, 1 DPC lost their main optical functionalities and the expected optical coupling generated critical losses in the device performance.