**3. Recording materials**

*π d Δn η sin λ χ*  <sup>2</sup> æ ö <sup>=</sup> ç ÷

Bragg condition in the recording plane formed by the two recording beams [13].

in combination with the maximum refractive index modulation Δn available.

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

32 Holographic Materials and Optical Systems

local grating, the requirement Q ≥ 10 has to be satisfied.

conventional optics where Snell's law is used [23].

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

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

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

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

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 neces-

sary for a completely accurate description of diffraction in gratings [18, 24–26].

è ø (5)

(6)

The use of holographic solar concentrators for space or terrestrial photovoltaic applications is a still limited field of research, although the idea has been known for a long time [2]. Among the known materials are the classic substrates based on silver halide emulsions, recently used to obtain a panchromatic holographic material for the fabrication of wavelengthmultiplexed holographic solar concentrators [27] and dichromatic gelatines [28–30], which have shown the best performance in terms of diffraction efficiency and tuning of the refractive index. The most studied holographic materials since the 1970s are those based on polymerization and cross-linking reactions induced by absorption of light, the so-called photopolymers, thanks to the numerous advantages they offer compared with silver halide and dichromatic gelatines. They show high diffraction efficiencies, allow an advantageous real-time monitoring of the recording process, do not require complicated development processes, can be produced from raw materials at low cost and give the possibility to modulate the properties through chemical synthesis. In these materials the grating is registered at a molecular level, and this has a high impact on the resolution. Typically, a photopolymerizable material is composed by a photoinitiator system (photoinitiator or photosensitizer), one or more polyfunctional monomers or oligomers and a polymeric binder. The binder is used to give mechanical stability and must ensure compatibility between all components in order to obtain a homogeneous, transparent material with good optical quality. The formulation can include plasticisers, additives, stabilizers and compounds that increase the photosensitivity of the writing medium. In a system based on radical polymerization, the initiation takes place during the illumination and leads to the production of radicals, which react with the monomers to produce chain initiators. This reaction gives way to the subsequent steps of propagation and growth of the polymer chains. In a writing process, using interference of two laser beams, radical initiation occurs faster in areas of constructive interference, i.e. where the illumination is more intense. Consequently, the polymerization proceeds more rapidly in these regions leading to an increased consumption of the monomers, while the polymerization is limited or absent in the areas of destructive interference (low-light intensity areas). The difference of monomer consumption rate creates a concentration gradient that drives monomer diffusion from dark to illuminated areas [31]. This mass transport proceeds until the monomer is exhausted or no longer able to diffuse through the material, due to the increased viscosity. The polymer concentration distribution will follow the sinusoidal pattern of light intensity. If the refractive index of polymer and binder are different, the result is a permanent modulation of the refractive index, that is, a volume-phase hologram. The refractive index variation is also determined by the density variation of the polymer. At the end of the writing process, a further irradiation of the layer with incoherent light is typically performed, leading to bleaching of the remaining photoinitiator. The first holographic photopolymers were based on liquid mixtures containing acrylamide [32]. Later, polymeric binder such as polyvinyl alcohol or gelatin was used, and diffraction efficiency greater than 80% could be reached [33–35]. This approach was recently used to demonstrate the fabrication of holographic solar concentrators [36]. Also, Sam and Kumar [37] demonstrated the fabrication of holographic solar concentrator in HoloMer 6A photopolymer material with an

efficiency of 70% and an average efficiency of 56.6% for a wavelength range from 633 to 442 nm. The most common formulations include acrylic acid esters and amides, N-vinyl compounds and allyl esters. Holograms with efficiencies exceeding 95% and refractive index variation until 10−2 have been recorded using visible laser light [38, 39]. One of the best performing materials (DMP 128) was created by Polaroid Corporation and allows recording of reflection and transmission holograms with a spectral range from 442 to 647 nm. This material is a mixture of acrylic monomers such as acrylic acid and N,N'-methylenebisacrylamide in a matrix of poly-N-vinylpyrrolidone and showed 95% diffraction efficiency and a refractive index modulation of 0.03 in films with thickness up to 30 μm [40]. The radical polymerization has many advantages that it proceeds rapidly and the reaction is irreversible, which allows the realization of a single write. However, the main drawback is the high volumetric shrinkage of the material during polymerization. This shrinkage induces distortions of holograms by altering the characteristics of gratings. Several solutions have been adopted to solve this problem, such as the introduction of nanoparticles in the photopolymeric mixture [41]. An interesting solution is that of cationic ring-opening polymerization (CROP) systems, where the volume shrinkage following the polymerization is balanced by an effect of ring opening which produces instead a volume increase [42]. Aprilis HMD has recently commercialized a high-performance material of this type, characterized by two types of monomers that give rise to orthogonal, not interfering chemical reactions. The cationic polymerization is used to produce the cross-linked matrix, while the acrylic monomers polymerize during the hologram writing stage and diffuse according to the concentration gradient mechanism. A further interesting example is that of Reoxan [43], proposed in the late 1970s as a kind of alternative to the photopolymerizable materials because it contains no polymerizable monomers in the binder (usually polymethyl methacrylate (PMMA)) and a sensitizer of anthracene oxidation in place of a photoinitiator. The photosensitizer transfers the energy of the electronic excited state to oxygen which ends up in a singlet state and reacts with anthracene to form a peroxide. Since this transformation is accompanied by a strong change in the ultraviolet (UV) absorption spectrum, the refractive index of the material is reduced, to form a phase hologram. In the subsequent dark step, an increase of the refractive index modulation is observed due to the slow and uniform diffusion of the remaining anthracene molecules throughout the film and further irradiation and oxidation. These systems show excellent optical properties and high stability and can be obtained as films with thickness from a few microns to centimetres.

#### **3.1. Holographic materials for solar concentrators**

In view of possible applications of holographic elements as terrestrial and space solar concentrators, the holographic materials must be able to withstand harsh conditions such as high irradiation and temperatures. In the space they should also withstand much more drastic conditions, due to strong thermal excursions, high vacuum and the presence of high-energy gamma, electronic and protonic radiation originating from the solar wind. In particular high resistance to corrosion by atomic oxygen and a very low outgassing level are required to avoid contamination of the components, although the level of acceptance depends on the destination of use. Currently, no studies are known on the resistance of materials for holographic concentrators in these conditions, and their behaviour is therefore yet to be determined. However, there are durability tests on some of the most widely used materials in conventional Fresneltype solar concentrators, such as elastomers based on silicone and acrylic polymers [44]. The latter represents a significant component of the photopolymer used for holography as a result of the process of photopolymerization of acrylic monomers typically dissolved in a matrix. Polymethyl methacrylate (PMMA) is widely used for the production of lenses for concentrators and protective layers for photovoltaic cells [45], as it guarantees an excellent resistance to UV radiation and a greater than 92% transmittance. The degradation of this type of material in response to UV irradiation mainly takes place with release of an ester radical and subsequent scission of the polymeric chain. Stabilization effects can be induced, for example, by the use of copolymers or through cross-linking of the material [46]. Alternatively, the ultraviolet sensitivity can be reduced by using protective layers or by adding radical scavengers or antioxidants to the formulation of the material. Silicones represent another important class of materials used for the fabrication of solar concentrators. They are characterized by a chemical structure that is less affected by radical photodegradation mechanisms triggered by UV light as in organic polymers. The most widely used polydimethylsiloxane (PDMS) is made of [Si-O]n-type polymeric chains with lateral methyl groups. Since the Si-O binding energy is much higher than that of the C–C bond, PDMS features an excellent stability against UV radiation and resulted very suitable for use in the extraterrestrial environment [47]. Furthermore, a great advantage of this material is the greater optical transmittance compared to PMMA and the tendency to cross-link after irradiation rather than degrade and produce volatile substances, as in the case of acrylic polymers. Starting from these evidences, a promising route towards solar compliant holographic materials is the synthesis of new photopolymers wherein part of the organic material would be replaced with inorganics or hybrid organic/inorganic components, which are less sensitive to thermal and photochemical degradation phenomena. One interesting category from this point of view is that of nanoparticle-polymer composites, that is, photopolymers containing nanoparticles of inorganic species such as SiO2, ZrO2 and TiO2 [48]. The introduction of such nanoparticles was adopted to reduce the shrinkage caused by the polymerization but also helped to obtain higher refractive index modulation [49, 50]. This increase is due not only to the diffusion process of acrylic monomers during the writing process but also to the consequent counterdiffusion of nanoparticles which redistribute in the dark regions of the illumination pattern. Tomita et al. [51] showed that embedding nanoparticles of SiO2 and ZrO2 in photopolymers lead to an effective suppression of thermally induced refractive index and dimensional changes. Similar formulations containing zeolite nanocrystals as inorganic dopant are also reported with the aim to improve compatibility between inorganic particles and polymer and reduce the optical losses due to scattering [52]. Dramatic improvement of photostability can be induced on hybrid organic/inorganic materials by the use of similar inorganic porous components, as demonstrated by the case of Maya Blue pigment. This material is made of the organic blue indigo captured within the layers of a phyllosilicate. It remained unchanged for more than 12 centuries and was proved to resist against organic solvents, acids and alkalis [53]. Materials with a high level of interpenetration between the organic and inorganic networks, and no phase discontinuity can be obtained by exploiting the versatility of the sol-gel chemistry [54]. Although high-optical-quality glasses

efficiency of 70% and an average efficiency of 56.6% for a wavelength range from 633 to 442 nm. The most common formulations include acrylic acid esters and amides, N-vinyl compounds and allyl esters. Holograms with efficiencies exceeding 95% and refractive index variation until 10−2 have been recorded using visible laser light [38, 39]. One of the best performing materials (DMP 128) was created by Polaroid Corporation and allows recording of reflection and transmission holograms with a spectral range from 442 to 647 nm. This material is a mixture of acrylic monomers such as acrylic acid and N,N'-methylenebisacrylamide in a matrix of poly-N-vinylpyrrolidone and showed 95% diffraction efficiency and a refractive index modulation of 0.03 in films with thickness up to 30 μm [40]. The radical polymerization has many advantages that it proceeds rapidly and the reaction is irreversible, which allows the realization of a single write. However, the main drawback is the high volumetric shrinkage of the material during polymerization. This shrinkage induces distortions of holograms by altering the characteristics of gratings. Several solutions have been adopted to solve this problem, such as the introduction of nanoparticles in the photopolymeric mixture [41]. An interesting solution is that of cationic ring-opening polymerization (CROP) systems, where the volume shrinkage following the polymerization is balanced by an effect of ring opening which produces instead a volume increase [42]. Aprilis HMD has recently commercialized a high-performance material of this type, characterized by two types of monomers that give rise to orthogonal, not interfering chemical reactions. The cationic polymerization is used to produce the cross-linked matrix, while the acrylic monomers polymerize during the hologram writing stage and diffuse according to the concentration gradient mechanism. A further interesting example is that of Reoxan [43], proposed in the late 1970s as a kind of alternative to the photopolymerizable materials because it contains no polymerizable monomers in the binder (usually polymethyl methacrylate (PMMA)) and a sensitizer of anthracene oxidation in place of a photoinitiator. The photosensitizer transfers the energy of the electronic excited state to oxygen which ends up in a singlet state and reacts with anthracene to form a peroxide. Since this transformation is accompanied by a strong change in the ultraviolet (UV) absorption spectrum, the refractive index of the material is reduced, to form a phase hologram. In the subsequent dark step, an increase of the refractive index modulation is observed due to the slow and uniform diffusion of the remaining anthracene molecules throughout the film and further irradiation and oxidation. These systems show excellent optical properties and high stability and can be obtained as

films with thickness from a few microns to centimetres.

In view of possible applications of holographic elements as terrestrial and space solar concentrators, the holographic materials must be able to withstand harsh conditions such as high irradiation and temperatures. In the space they should also withstand much more drastic conditions, due to strong thermal excursions, high vacuum and the presence of high-energy gamma, electronic and protonic radiation originating from the solar wind. In particular high resistance to corrosion by atomic oxygen and a very low outgassing level are required to avoid contamination of the components, although the level of acceptance depends on the destination of use. Currently, no studies are known on the resistance of materials for holographic concen-

**3.1. Holographic materials for solar concentrators**

34 Holographic Materials and Optical Systems

can be produced under mild conditions, the preparation (hydrolysis and condensation) requires relatively long times to produce a consolidated material [54]. The generic approach is to dissolve the photopolymerizable species in the liquid precursors (typically modified organoalkoxysilanes) of the glassy material in a single reaction mixture, followed by hydrolysis and gelification which lead to the formation of a glassy matrix. By this approach samples of high thickness with good mechanical properties, low shrinking and high thermal and chemical stability can be obtained [55]. Some variants have been proposed to increase the refractive index change after exposure, such as the addition of titanium or zirconium alcoholates to the initial mixture [56] or using low refractive index monomers [57]. A further alternative is to increase the refractive index of the photosensitive material by introducing reactive species with high refractive index species (HRIS) [58]. This solution led to refractive index modulations up to 0,015. A further advantage of this approach seems to be that high refractive index species are dispersed in molecular form with respect to systems containing nanoparticles [59].
