**1. Introduction**

Photovoltaic (PV) electrical energy generation is one of the most sustainable solar energy conversion processes, but its main drawback is the cost. With the current technology, the highest efficiency (37%) is from photovoltaic (PV) cells with triple-junction InGaAs; however, their high cost makes them unattractive. Nevertheless, it is possible to solve this problem by replacing a significant amount of expensive PV material with an optical concentrator. Consequently, in the last 15 years in many fields of application, from the aerospace industry to the domestic applications, people tried to use solar concentration technologies to direct all the exploitable light towards the solar cells. Indeed, solar concentrators, which focus the sun's rays onto the active solar cell area, enable to use solar power also when solar intensity is very weak allowing,

© 2017 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. © 2017 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

at the same time, smaller active areas of solar cells, reducing the size of the expensive portion of the solar power system [1]. However, so far concentrator systems have low spreadin the market due to their high prices mostly induced by (i) complex designs—the small acceptance angle of standard CPVs (e.g. lenses or mirrors) forces to use active solar tracker and (ii) thermal management: the solar cell is excessively heated when illuminated with concentrated solar radiation, and an active or passive cooling system must be taken into account. Holographic optical elements (HOEs) could in part overcome the aforementioned limitations. Holographic PV concentrators were proposed for the first time in the 1980s [2–5]; indeed, holography as an opticaltechnologyismuchmoreversatileandcheaperwithrespecttootherconcentratingoptical systems (lenses or mirrors, for instance). It can also eliminate the need for solar tracking, thus allowing uniform levels of illumination during the course of a day or during different seasons without any moveable parts and so reducing the whole-system complexity [6].

Among holographic concentrators, volume holographic optical elements (V-HOEs) have been proposed for use as solar concentrators [2]. Compared with conventional refractive and reflective optics, V-HOEs can be thinner and more lightweight and have the potential for being very inexpensive in mass production. Moreover, the ability of light manipulation, shown by these diffractive devices, allows replacing standard concentrators with planar optical concentrators for high efficiency and low-cost photovoltaic modules [7]. HOEs have long been suggested for use (i) in a variety of solar collection applications [2–4, 6, 8–10], (ii) in spectral splitting applications to increase the conversion efficiency of PV cells [2, 8, 9] and (iii) in simultaneous concentration and spectral splitting applications [4]. Nevertheless, nowadays, there are only few commercial holographic concentrators, patented by Prism Solar Technologies [11], which work by total internal reflection by means of multiplexed gratings [12]. It has low cost (around 1 \$/W), and it is easy to be integrated into buildings, leading to a cost-effective solar building-integrated concentrating system [13].

The simplest V-HOE is a volume holographic grating (VHG), which consists in a photoinduced modulation of the refractive index in a photosensitive thick film and acts as nonfocusing element; therefore, it simply redirects the light. VHGs are recorded by interference between two collimated light beams and are different from other diffraction gratings based on surface or amplitude modulation [14]. In particular, the most important advantages offered by VHG are:


Additionally, their response can be customized in order to obtain not only grating but also lenses or other optical elements. Indeed, if during the recording process the wavefront of one collimated beam is replaced with a converging one, an interferometric pattern that replaces the response of the focusing optical systems can be generated, obtaining V-HOEs that act as focusing elements. These optical elements produce a converging wavefront, having the same effect as spherical or cylindrical lenses [16]. Furthermore, lenses can be recorded in off-axis configuration, allowing deflection and focusing of the light at the same time. These considerations led to the idea to use holographic gratings and lenses as light deflectors and concentrators. In the absence of holographic deflector devices, the useful conversion area of the sunlight into electrical energy is only the area occupied by the PV cell, as shown in **Figure 1(a)**.

at the same time, smaller active areas of solar cells, reducing the size of the expensive portion of the solar power system [1]. However, so far concentrator systems have low spreadin the market due to their high prices mostly induced by (i) complex designs—the small acceptance angle of standard CPVs (e.g. lenses or mirrors) forces to use active solar tracker and (ii) thermal management: the solar cell is excessively heated when illuminated with concentrated solar radiation, and an active or passive cooling system must be taken into account. Holographic optical elements (HOEs) could in part overcome the aforementioned limitations. Holographic PV concentrators were proposed for the first time in the 1980s [2–5]; indeed, holography as an opticaltechnologyismuchmoreversatileandcheaperwithrespecttootherconcentratingoptical systems (lenses or mirrors, for instance). It can also eliminate the need for solar tracking, thus allowing uniform levels of illumination during the course of a day or during different seasons

Among holographic concentrators, volume holographic optical elements (V-HOEs) have been proposed for use as solar concentrators [2]. Compared with conventional refractive and reflective optics, V-HOEs can be thinner and more lightweight and have the potential for being very inexpensive in mass production. Moreover, the ability of light manipulation, shown by these diffractive devices, allows replacing standard concentrators with planar optical concentrators for high efficiency and low-cost photovoltaic modules [7]. HOEs have long been suggested for use (i) in a variety of solar collection applications [2–4, 6, 8–10], (ii) in spectral splitting applications to increase the conversion efficiency of PV cells [2, 8, 9] and (iii) in simultaneous concentration and spectral splitting applications [4]. Nevertheless, nowadays, there are only few commercial holographic concentrators, patented by Prism Solar Technologies [11], which work by total internal reflection by means of multiplexed gratings [12]. It has low cost (around 1 \$/W), and it is easy to be integrated into buildings, leading to a cost-effective

The simplest V-HOE is a volume holographic grating (VHG), which consists in a photoinduced modulation of the refractive index in a photosensitive thick film and acts as nonfocusing element; therefore, it simply redirects the light. VHGs are recorded by interference between two collimated light beams and are different from other diffraction gratings based on surface or amplitude modulation [14]. In particular, the most important advantages offered by

**•** The peak efficiency can be theoretically 100% [15]. In practice, diffraction efficiency of the

**•** The recorded device is easily customizable, and element with multiple optical response can

Additionally, their response can be customized in order to obtain not only grating but also lenses or other optical elements. Indeed, if during the recording process the wavefront of one collimated beam is replaced with a converging one, an interferometric pattern that replaces

without any moveable parts and so reducing the whole-system complexity [6].

solar building-integrated concentrating system [13].

**•** Transmission or reflection gratings can be recorded.

**•** They require a very rapid and low-cost effective manufacturing.

order of 90% can be easily reached.

28 Holographic Materials and Optical Systems

be fabricated (multiplexing).

VHG are:

**Figure 1.** (a) PV module without deflector devices, (b) PV module in the presence of deflector devices and (c) PV module with deflection and concentration of the sunlight.

If a VHG is used as a device to redirect the light, and therefore as a deflector, it is possible to use a configuration like that shown in **Figure 1(b)**. In this arrangement, the incident light on two VHGs is deflected on the same PV cell. Therefore, the collecting surface of the single cell is increased (in this case is tripled), while keeping the constant area occupied by the PV material. To realize a high-efficient holographic solar concentrator, a V-HOE has to be capable not only to deflect the light of the sun but also to concentrate it; in this way the area used by a PV cell can be further reduced, as shown in **Figure 1(c)**.

However, V-HOEs have two characteristics that can affect their performance as solar concentrator: angular selectivity and chromatic selectivity. Due to the angular selectivity, volume holograms have high efficiency only when the incidence direction varies in the plane formed by the two recording beams, and this can be considered as a limitation. Additionally, the efficiency of the volume hologram is related to the wavelength: it is high for a bandwidth centred at a wavelength determined by both the refractive index modulation obtained in the recording material and the angle of incidence. V-HOEs have to be designed in order to present a high efficiency for the spectrum of the sunlight inside the PV conversion range. For multijunction PV cells, the useful solar spectrum ranges from 350 to 1750 nm [17]. This requirement allows minimizing the amount of solar radiation beyond the conversion range (>1700 nm) that reaches the solar cell. Thus, one of the main problems of concentration refractive systems, namely, the heating of the cell, can be managed. Lower cell temperature results in a higher conversion efficiency and thus lower cost/watt [13, 18].

Regarding the aerospace applications, the solar power conversion is vital to the survival of the satellite, and loss of power, even temporarily, can have catastrophic consequences. With the succession of missions that use the technology of solar concentration, since the Galaxy 11 mission launched in 1999 that made use of mirrors, until contemporary missions, researchers tried to reduce the area, weight and footprint occupied by photovoltaic cells. Note that cost is a factor usually addressed by means of the mass (weight) of the system [16]. Additionally, among design parameters, some crucial points related to hostile space environment have to be taken into account. For example, it is important to consider the extreme temperature changes at which the concentrators are subject. However, in this field, only few works are reported in literature; therefore, our results could open the way to a new line of research [19, 20].

With this aim, in this chapter, we explore the opportunity to record a holographic solar concentrator by using a photopolymeric material as recording medium. In particular, two different configurations of holographic lenses, namely, a spherical lens and a cylindrical lens, are investigated in terms of both recording process and optical response characterization. As a final point, we suggest the possibility to use this photopolymer to realize holographic solar concentrator for space applications.

### **2. Theoretical background**

A generic V-HOE-based solar concentrator system generates electrical power by using a V-HOE to concentrate a large area of sunlight onto a small PV cell. The efficiency of the whole system can be evaluated as

$$\eta\_{\boldsymbol{\gamma}} = \frac{\iint \mathcal{S}\left(\boldsymbol{\lambda}, \boldsymbol{\zeta}^\*\right) \eta\left(\boldsymbol{\lambda}, \boldsymbol{\zeta}^\*\right) \eta\_{\boldsymbol{\gamma}\boldsymbol{\gamma}}\left(\boldsymbol{\lambda}, \boldsymbol{\zeta}^\*\right) d\boldsymbol{\lambda} d\boldsymbol{d}}{\iint \mathcal{S}\left(\boldsymbol{\lambda}, \boldsymbol{\zeta}^\*\right) d\boldsymbol{\lambda} d\boldsymbol{d}} \tag{1}$$

where *S* is the solar spectrum (air mass (AM) coefficient, followed by a number, is commonly used to characterize the performance of solar cells. Generally, AM1.5 for earth, AM0 for space), η is the V-HOE diffraction efficiency and ηPV is the efficiency of the photovoltaic cells. All the terms are function of the wavelength (λ) and the sun illumination (ζ). The latter is function of the daily and seasonal sun trajectory and of the tilted angle between the V-HOE and PV cell. Thus, in order to evaluate, the performance of the whole system is instrumental to maximize the diffraction efficiency of the V-HOE. Since each point of a V-HOE can be locally seen as a plane holographic grating, the theoretical approach to evaluate the diffraction efficiency of a VHG has been examined.

**Figure 2** illustrates the model of a transmission VHG, where a refractive index spatial sinusoidal modulation (Δn) with period Λ is recorded inside a material with a thickness *d*. The grating is slanted with an angle of ϕ. θi is the incident angle, and θd is the diffracted angle considered inside the holographic material. The use of Kogelnik's theory [15] is widely accepted for analytically modelling the behaviour of volume photopolymer holograms. This theory allows relating some volume gratings' physical characteristics, such as thickness, spatial frequency/fringe spacing and depth of refractive index modulation, to their diffraction efficiency and angular/chromatic selectivity.

Volume Holographic Optical Elements as Solar Concentrators http://dx.doi.org/10.5772/66200 31

**Figure 2.** Model of a transmission VHG.

a factor usually addressed by means of the mass (weight) of the system [16]. Additionally, among design parameters, some crucial points related to hostile space environment have to be taken into account. For example, it is important to consider the extreme temperature changes at which the concentrators are subject. However, in this field, only few works are reported in

With this aim, in this chapter, we explore the opportunity to record a holographic solar concentrator by using a photopolymeric material as recording medium. In particular, two different configurations of holographic lenses, namely, a spherical lens and a cylindrical lens, are investigated in terms of both recording process and optical response characterization. As a final point, we suggest the possibility to use this photopolymer to realize holographic solar

A generic V-HOE-based solar concentrator system generates electrical power by using a V-HOE to concentrate a large area of sunlight onto a small PV cell. The efficiency of the whole

where *S* is the solar spectrum (air mass (AM) coefficient, followed by a number, is commonly used to characterize the performance of solar cells. Generally, AM1.5 for earth, AM0 for space), η is the V-HOE diffraction efficiency and ηPV is the efficiency of the photovoltaic cells. All the terms are function of the wavelength (λ) and the sun illumination (ζ). The latter is function of the daily and seasonal sun trajectory and of the tilted angle between the V-HOE and PV cell. Thus, in order to evaluate, the performance of the whole system is instrumental to maximize the diffraction efficiency of the V-HOE. Since each point of a V-HOE can be locally seen as a plane holographic grating, the theoretical approach to evaluate the diffraction efficiency of a

**Figure 2** illustrates the model of a transmission VHG, where a refractive index spatial sinusoidal modulation (Δn) with period Λ is recorded inside a material with a thickness *d*. The

considered inside the holographic material. The use of Kogelnik's theory [15] is widely accepted for analytically modelling the behaviour of volume photopolymer holograms. This theory allows relating some volume gratings' physical characteristics, such as thickness, spatial frequency/fringe spacing and depth of refractive index modulation, to their diffraction

is the incident angle, and θd is the diffracted angle

(1)

literature; therefore, our results could open the way to a new line of research [19, 20].

concentrator for space applications.

30 Holographic Materials and Optical Systems

**2. Theoretical background**

system can be evaluated as

VHG has been examined.

grating is slanted with an angle of ϕ. θi

efficiency and angular/chromatic selectivity.

According to Kogelnik's theory, the diffraction efficiency (η) for a lossless material can be theoretically evaluated as

$$\eta = \left(\frac{\pi d \lambda n}{\lambda \chi}\right)^2 \stackrel{\text{sinc}}{\text{sinc}}^2 \sqrt{\left(\frac{\pi d \lambda n}{\lambda \chi}\right)^2 + \left(\frac{\pi d \cos \theta\_s}{2 \chi^2}\right)^2} \tag{2}$$

where the parameters ϑ and χ are defined as

$$\mathcal{B} = K \cos \left(\phi - \mathcal{O}\_{\cdot}\right) - \frac{K^2}{4\pi m} \lambda \tag{3}$$

$$\chi = \sqrt{\cos \Theta\_i \left(\cos \Theta\_i - \frac{K}{\beta} \cos \Phi\right)}\tag{4}$$

where K = 2π/Λ is the length of the grating vector normal to the fringes (see **Figure 2**), while *n* is the average refractive index of the holographic medium (after the recording process) and β = 2π*n*/λ is the average propagation constant. Eq. (2) allows designing gratings with high diffraction efficiency that operate over large angular and wavelength bandwidth ranges. In particular, when the Bragg condition is satisfied, i.e. 2βcos(Φ−θB) = K (where θi = θB is the Bragg angle), the parameter ϑ = 0 and χ = − cos − 2 . Thus, the diffraction efficiency *<sup>η</sup>* can be theoretically evaluated as

$$\eta = \sin^2\left(\frac{\pi \text{ d } \Delta \text{m}}{\lambda \text{ } \chi}\right) \tag{5}$$

As expected, the angle at which the diffraction intensity is maximum is strictly related to the incident wavelength [14]. While regarding the angular selectivity, hologram diffraction efficiency drops very quickly when the direction of the incident radiation does not fulfil the Bragg condition in the recording plane formed by the two recording beams [13].

For solar applications, a high efficiency is required for the whole useful solar spectrum (350– 1750 nm) and for each position of the sun. Eq. (2) can be used to easily quantify how much the Bragg condition is violated either in terms of wavelength or in terms of incident angle (detuning analysis). This analysis is fundamental to design the VHG in terms of *d* and Δn. In particular, the detuning range can be extended minimizing the recording material thickness in combination with the maximum refractive index modulation Δn available.

It is useful to evaluate the so-called Q factor, defined as

$$Q = \frac{2\,\pi kd}{nA} \tag{6}$$

This parameter allows to estimate if the recorded hologram is a volume and not a surface hologram. Indeed, a holographic grating is considered to be thin (surface hologram) when Q ≤ 1, thick (volume hologram) when Q ≥ 10 [21]. However, angular and chromatic selectivity increases when parameter Q increases; thereby, for solar application it is better to adopt a Q value close to the limit of 10. For a VHG, the behaviour is the same in all the points of the hologram. If the solar concentrator is realized by means of a V-HOE, the efficiency and its angular and chromatic selectivity vary at each point of the hologram. However, a V-HOE can be locally seen as a plane holographic grating, so the aforementioned approach can be employed to sample point by point the behaviour of the V-HOE [12, 22]. Obviously, for each local grating, the requirement Q ≥ 10 has to be satisfied.

It is important to point out that if a V-HOE is used as solar concentrator, in order to determine the image ray direction, the grating equation has to be considered differently from the conventional optics where Snell's law is used [23].

The approach of Kogelnik can be also used to evaluate the dependence of the diffraction efficiency on the polarization. In fact, since solar illumination is randomly polarized, it is necessary to divide the incident optical power into both states of polarization and averaging the respective diffraction in order to evaluate the global efficiency of the concentrator [15, 16]. Thus, Kogelnik's coupled wave theory is enough to analytically predict the effect of the first useful parameters, such as wavelength, incident angle, grating thickness, index modulation and polarization state. However, a rigorous solution of the coupled wave equations is necessary for a completely accurate description of diffraction in gratings [18, 24–26].
