# Angular Dependence of Photonic Crystal Coupled to Photovoltaic Solar Cell
## 1 Introduction  
One-dimensional photonic crystal (1 DPC) is a well-known concept with broad fields of application since their discovery in 1987 [1, 2]. Their initial development was motivated to improve laser and optical fiber technologies [3, 4, 5], but today they have been extended to other commercial devices, like optical filters [6, 7], high Q-photonic cavities [8, 9], photocatalysis [10, 11], high-temperature sensitive sensors [12], magnetoplasmonics [13], metamaterials [14], light tailoring [15], or even energy functionalization. [16]. Photonic crystals are also present in nature: these structured materials are present, for example, in ants to reflect light, and therefore, to reduce their temperature; butterflies use these periodic structures on their wings to scatter the light and generate their distinctive iridescent color [16]. Furthermore, they are used by chameleons for rapid modifications of their color during social interactions [17]. In the last years, the strong progress in photonic technologies has led to a growing interest in this field, opening the possibility of new applications, including renewable energies. Some examples of these new applications are energy-harvesting windows [18], luminescent solar concentrators [19], photonic color back reflector [20], solar energy trapping [21], filters to avoid thermal heating of the device [22, 23], or beam splitters to combine different solar technologies [24]. The easiest way to design 1 DPC is to create a structure using materials with a well-defined periodic patterning in the dielectric function. Because of this design, these artificial materials allow a broader energy range initially forbidden, so light is capable of being shaped and bent. The length scale of this spatial variation determines the spectral range of the photonic crystal. Efficiency of any solar cell technology depends, among other parameters, first, on the solar spectral distribution, and second, on the absorbance spectrum of the material used as active semiconductor. Thus, on one hand, the solar spectrum is very broad, from 300 to over 2500 nm. On the other hand, not all photons are absorbed by the semiconductors, due to a mismatch between their band gap and the incoming photon energy. Consequently, [PERSON] and [PERSON] calculated that the maximum theoretical efficiency for a single-junction solar cell technology is approximately 30% [25]. In addition, those nonabsorbed photons produce an increase of the solar cell temperature due to thermal energy transfer, with negative effects. Therefore, it would be desirable to create metamaterials whose optical properties were adapted to the solar spectrum at the particular location where photovoltaic plants are to be installed. A mechanism that has been proposed to prevent the increase in temperature is to use photonic crystals as selective filters of the solar spectrum on the solar cell [22; 23]. The advantage of this beam splitter concept is that 1 DPC acts as a selective mirror component only for a well-defined solar irradiance spectral range, while transparency is maintained for the rest of the spectrum. The key parameter to optimize the 1 DPC design consists of adjusting the reflection peak (Bragg peak) to the photon energy, in order to reflect it. For instance, Figure 1a shows the spectral response of a 1 DPC, designed to reflect the near infrared irradiation that generates thermal losses in the solar cell. However, it remains transparent to the visible solar spectrum to allow the photovoltaic effect in the semiconductor. Good matching between 1 DPC transmission spectrum (red line) and spectral response of the solar cell (blue dots) might be achieved. However, if the purpose of the 1 DPC is to act as back selective reflector, the most convenient conditions vary, as illustrated in Figure 1b: the device reflects photons within the visible range, while the near infrared spectrum is transmitted.