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Abstract
A low-toxicity photopolymer was employed to prepare holographic solar concentrators (HSCs). The main aim of this study is to obtain a versatile holographic element to concentrate the sunlight from different relative positions of the Sun during the day, avoiding the need of expensive tracking systems. Multiplexed holographic elements that combine symmetric and asymmetric holographic lenses of low frequency (545 l/mm) have been recorded in the same plate to concentrate the sunlight from sunrise to sunset. The holographic behavior of HSCs has been studied by measuring the angular diffraction efficiency at 633 nm (close to the maximum response of silicon cells). The efficiency of the complete system “HSC-solar cell” has been evaluated by measuring the short-circuit current (Isc) under solar illumination at different incident angles. This study overcomes the trade-off between good efficiency and high incident acceptance angle, showing an important breakthrough to obtain wide acceptance angle systems.
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1. Introduction
Free-tracking, low-cost, and environmentally friendly solar concentrator systems represent an important challenge in our society to obtain competitive photovoltaic (PV) energy. The study and development of applied optical systems for generating clean and renewable energy is known as green photonics. This includes solar concentrators, solar cells, and environmentally friendly materials.
Sunlight concentration can be obtained with conventional refractive lenses such as Fresnel lenses [1], or reflective elements [2]. Particularly, Fresnel lenses are widely used as traditional concentrators, but they have a small acceptance angle and reflective elements need continuous maintenance of the surface’s reflectivity. Moreover, conventional solar concentrators also require cooling [3] and expensive tracking systems [4] to follow the path of the Sun.
Holographic optical elements (HOEs) can be an alternative to conventional lenses because they are cheaper and more versatile. They provide an extended focus area which contributes to protect solar cells for heating damages [5]. The first HOE as wide-angle solar concentrator was proposed by Ludman in 1982 [6]. Some years later holographic mirrors for solar ultraviolet energy concentration were developed with an acceptance angle around 10° [7]. In recent years HOEs are widely used as solar concentrators, researchers have reported high [8] and low [9,10] spatial frequency holographic concentrators, with operation angle range since 12° to 30°. Different types of holographic lenses, spherical [8,10] and cylindrical [10,11,12], working under high or low photometric conditions [13] have been also developed for solar applications. Kostuk et al. and Zhao et al. describe the characteristics of transmission [14] and reflection [15] holographic lenses for solar concentrators.
Another advantage in using HOEs that produce an extended focus is their capability of dispersing the spectrum and the possibility to avoid non-desired radiation, such as far-infrared radiation (λ > 1100 nm for Si), which heats solar cells, but does not contribute to photo-electric conversion.
To improve the angular acceptance angle of the holographic concentrator (HC) it must have a low spatial frequency [10]. When a low frequency is recorded in a HOE, the working angle of the HC increases [16]. The angular acceptance of HOEs can also be increased by multiplexing several holographic lenses for different reconstruction angles (operation angle range): around 20° [17] or 30° [18,19]. The more multiplexed elements the less diffraction efficiency is obtained [20]. Kao et al. obtained an operation angle range of 30° by using a half-divided double layer sunlight concentrator system [8].
One of the most important aspects when fabricating a holographic solar concentrator (HSC) is the material used to record it. Both dichromated gelatins [12,15,21–23] and photopolymers [10,13,17,24] are excellent holographic materials with the capability of modulating their refractive index modulation, with high spatial resolution, high diffraction efficiency, and low scattering. There is also a commercial photopolymer material, Bayfol HX, which is widely used in holographic applications [8,11,16,18].
Photopolymers are the handiest holographic material that can be modified in terms of both composition and design [25,26]. Other interesting properties are variable thickness, flexible materials, self-processing capability [27], high energetic sensitivity, good dimensional stability and, low cost. The first to store HOEs in photopolymers were Close et al. in 1969 [28]. Since then up to now, the importance of photopolymers is growing enormously, and a great diversity of photopolymer materials has been greatly used in optical applications. However, one of the common components in holographic photopolymers is acrylamide [9,17], which is a toxic compound. For this reason, the latest trend in holographic materials includes environmentally friendly photopolymers with good recycling properties and low toxicity. Our research team has developed a low toxicity photopolymer called “Biophotopol” for recording HOEs, for an extensive range of optical applications [27,29,30]. It has been also demonstrated that a curing stage after recording, improves the stability of multiplexed holograms on this photopolymer [30].
The purpose of this work was to develop efficient and environmentally friendly HSCs in a low-toxicity photopolymer with the widest acceptance angle obtained until now. The specific aim was obtaining a multiplexed holographic transmission concentrator (until seven lenses) stored in Biophotopol at a low spatial frequency (545 lines/mm) with 197 µm film thickness. For the first time, a method to obtain multiplexed holographic lenses on the same environmentally friendly plate has been used, it allows collecting solar rays from −40° to +20° incident angle.
2. Materials and methods
The solar concentrators studied in this work were fabricated by holographic methods on an environmentally friendly photopolymer called Biophotopol. They were supported over 6.5×6.5 cm2 glass plates (2.092 mm thickness and 0.059 mm−1 absorption coefficient at 633 nm). The prepolymer solution in water (Table 1) was composed of poly(vinyl alcohol) (PVA) as an inert binder polymer (Mw ∼ 130000), hydrolysis degree = 87.7%), sodium acrylate (C3H3NaO2) as a polymerizable monomer (Mw ∼ 94.04), triethanolamine (TEA) as coinitiator and plasticizer (Mw = 149.19) and sodium salt 5’-riboflavin monophosphate (RF) as sensitizer dye (Mw = 478.33). All compounds were purchased from Merck KGaA (Darmstadt, Germany). The component concentration in the prepolymer solution was adjusted to obtain thin thickness (< 200 µm) multiplexed and non-multiplexed holograms with high performance.
Table 1. Component concentration of the prepolymer solution in water
The prepolymer solution in water was prepared in the laboratory, using a conventional magnetic stirrer, under red light. After that, it was manually deposited over levelled glass plates and stored inside an incubator (Climacell 111, MMM Medcenter Einrichtungen GmbH) overnight (18–25 h) with controlled conditions (60 ± 5% relative humidity and 20 ± 1° temperature).
The holographic setup used in this work is shown in Fig. 1(a). A continuous (CW) diode-pumped laser emitting at λo = 473 nm (Excelsior, Spectra Physics GmbH, Germany) was spatially filtered and then split into two secondary beams (object and reference beam) by using a 2:1 beam splitter cube. A collimated reference beam and a divergent object beam impinged on the photopolymer, producing an interference pattern over the photopolymer. The divergent beam was obtained by using a refractive lens (RL) with a dioptric power of 20 D at a distance 2 f ‘RL (∼10 cm) from the photopolymer surface, obtaining in the symmetric setup an identical spot size (5 mm) as the reference beam. Real photos of the holographic setup are shown in Fig. 1(b), 1(c), and 1(d). Object and reference recording angles (θo and θr) were measured with respect to the normal of the HSC, taking positive angles clockwise and negative angles anticlockwise. Both beams were spatially overlapped at the photopolymer layer and the interbeam angle (θ = θo − θr) was maintained at 14.8° in all registered holograms, obtaining a low central spatial frequency (545 l/mm) and grating period (Λ) of 1.836 µm (Eq. (1))
The sample was rotated around its vertical axis to record symmetric (HC-s) and peristrophic multiplexed holograms composed of two, four and seven holograms (HC-m2, HC-m4, HC-m7, respectively). Therefore, different object θo and reference angle θr were used in each exposition (see Fig. 1(e)). The recording process was completed under safe light conditions, and a photocuring white light process with a LED lamp (13.5 W, 875 lm at 6500 K, 30° Lexman) was performed at the end of the process. The lamp was placed 37.5 cm from the sample for 5 minutes to stop the polymerization process and to bleach the remaining dye of the sample. The physical thickness of the photopolymer layers (h) was measured with a micrometer screw at the end of the experiment.
Fig. 1. a) Recording and reconstructing holographic lens (HL) setup at 473 nm and 633 nm, respectively. Mi: Mirrors; dRL-PL: Distance between the refractive lens and the photopolymer; f’RL: Focal length of the refractive lens; Object and reference recording angles (θo and θr); θm: Measuring angle of reconstructing beam; PC: computer to rotate the platform and to acquire power data; b), c) and d) Real photos of the setup; e) Detail of θo and θr of multiplexed holograms.
Finally, holographic concentrating elements were characterized with unpolarized broadband source and a mono-crystalline silicon (Si) PV cell (PHIWE 2.5×5 cm2). Standard solar simulator source (model 10500, ABET technologies) emitting a continuous solar spectrum (350–1800 nm) has been collimated [29] to reconstruct the real image of the holographic lenses with the converging conjugated beam (Fig. 2).
Fig. 2. Holographic concentrator (HC) reconstructed with the conjugated beam at an incident reconstructing angle (θc). Image angle for blue (θ i-473) and red (θ i-633) of the first order of diffraction.
The diffracted beam of the holographic lenses concentrates the light on the PV cell as an extended focus at incident angle −10° (Fig. 3(a)) and at incident angle −20° (Fig. 3(b)). The chromatic dispersion of the diffracted beam produces an aberrated image at the solar cell surface. This is because each wavelength [31] will diffract at a particular image angle, where θ is the off-axis angle and i, c, o, r are the indices of image, reconstruction, object, and reference beams, respectively, while µ is the ratio between reconstructing and recording wavelength (λc /λo),
Meanwhile, the focus of the recorded holographic lenses [31] to the first order of diffraction studied and reconstructed with a plane wave can be obtained from the following expression (Eq. (3))
Fig. 3. Real image of the holographic concentrator (HC-m2) reconstructed with the conjugated beam of a solar simulator source. a) Incident angle −10°; b) Incident angle −20°.
Meanwhile the angular acceptance of the concentrator-solar cell system has been obtained by measuring the short-circuit current (Isc) value at short-circuit conditions (R = 0Ω) as a function of different incident angles (θc).
3. Results
3.1 Low angular selectivity in a symmetric holographic concentrator
One of the most important parameters of a HSC is its holographic diffraction efficiency (η) at different incident angles and wavelengths. Low angular selectivity and high η under solar light are desired. In other words, high angular and wavelength bandwidth is desired. In this direction, as predicted by Kogelnik’s theory [32], two strategies can be followed to obtain high angular bandwidth in a single volume holographic lens a) to reduce film thickness and b) to reduce spatial frequency. These two strategies contribute to be closer to the intermediate regime (Q ‘/ ν) ≤ 20
Grating and propagation vector magnitude, K and β, respectively, are defined in Eqs. (9) and (10),
The parameter cr (Eq. (7)) is identical to cs in symmetric holograms in which the slope of the fringes (φ) is π/2, but cs also depends on K, β, and φ in asymmetric holograms (φ ≠ π/2) when cos ( φ ) ≠ 0. The theoretical slope of the fringes is determined by the direction of K vector, which is perpendicular with respect to the surface of the fringes (Eq. (11)). The surface of the fringes is determined by the object and reference angle inside of the material, θo’ and θr’, respectively
the Eq. (12) represents the analytical solution obtained by Coupled Wave Theory [32], which predicts the diffraction efficiency (η) at a particular λc around the Bragg angle for a thick transmission phase grating:In this work, we aimed to obtain a good trade-off between high η and high angular bandwidth. To accomplish this aim, we propose to prepare holograms with lower spatial frequency (545 l/mm) and the film thickness which allow to obtain the best trade off. Based on Fig. 4, the best trade-off between high η and high angular bandwidth is achieved with (d = 60 µm).
Fig. 4. a) Theoretical results based on the Kogelnik’s theory for symmetric transmission holographic gratings with n1 = 0.00425, 545 l/mm, and different optical thickness (d). b) Theoretical comparison between volume holograms with frequencies 545 l/mm (blue full line) and 922 l/mm (orange dashed line); n1 = 0.00425; d = 60 µm.
Symmetric holographic concentrator (HC-s) with 545 l/mm; θo = +7.4; θr = −7.4 and exposure H = 33 mJ/cm2 has been experimentally evaluated. The angular bandwidth achieved was increased to 4.2° at 633 nm by using HC-s while the maximum (ηmax) of this HC-s at 633 nm was maintained at around 95%. The maximum is placed at the Bragg angle to 633 nm (±9.93°), in our experiment the hologram was read with the negative Bragg angle (−9.93°) in the symmetric holographic configuration.
Firstly, the experimental angular and conjugated scan reconstruction at 633 nm of HC-s has been fitted with the Kogelnik’s Theory (Fig. 5(a)). The theoretical parameters of the fit obtained are n1 = 0.00425, d = 60 µm, and Q ‘/ν = 37.282. Due to Q ‘/ ν being higher than 20, the hologram can be considered in the volume or Bragg regime. Secondly, the angular response of the HC-s has been evaluated by using a PV solar setup connected to an electronic circuit for measuring Isc (at V = 0 V) vs different incident angles (−40.0° < θc < 20.0°) under a solar simulator source. The He-Ne laser (633 nm) was replaced by a solar simulator source with wide spectrum, while the calibrated laser power detector used in the monochromatic characterization was replaced by a digital multimeter to measure Isc. As we can see in Fig. 5(a) (blue-left axis) a wide acceptance angle (more than 20°) was achieved by using a solar simulator source to illuminate the PV solar cell.
Fig. 5. a) Experimental angular scan (red dots) and Kogelnik fit (black line) of HC-s at 633 nm (right axis) and relative short-circuit current (Isc) as a function of incident angle (blue dots) under solar simulator source (left axis). Blue full line is a guide to the eye. b) Electrical characteristic curve of HC-s at two incident angles: −10.0° and −7.5°.
Thirdly, the solar simulator beam was impinged to the reverse of the HC-s at two conjugated reconstructing angles (θc): −10.0° and −7.5°, corresponding to those in which a ηmax at red and blue wavelength is obtained. In each incident angle, the diffracted beam illuminates the solar cell to measure the electrical characteristic curves (I-V) for different load resistances. A classical I-V and power-potential (P-V) curves of a conventional silicon PV cell have been obtained in both incident angles with the setup described in section 2. In Fig. 5(b), a high electrical current at low potentials (from 0.00 to 0.25 V) and a drastic decrement of electrical current at high potentials (from 0.35 to 0.38 V) are demonstrated. Therefore, maximum electrical power produced by the Si solar cell used was obtained between 0.25 to 0.35 V. The electric current and power values measured were relative to the solar simulator power that impinge to the solar cell (around 35 mW/cm2).
Therefore, low film thickness and low spatial frequency are key parameters for achieving a wide acceptance angle with a single hologram. Here we have demonstrated theoretically and experimentally that a reduction of the spatial frequency from 922 l/mm to 545 l/mm in a symmetric hologram increases the acceptance angle at 633 nm around two times, and it is possible to obtain around 20° angular bandwidth under solar illumination with a low-toxicity single and symmetric holographic concentrator with a low spatial frequency and thin thickness.
3.2 Thin multiplexed holographic concentrators
To design solar concentrators, without the need of expensive solar tracking systems, it is desired to increase the acceptance angle on the solar cells to 120° (Fig. 6). The strategy of decreasing film thickness of the volume hologram based on Biophotopol material is limited to the η achieved and the thinner film thickness than can be obtained by decanting by gravity. For this reason, in the present work, we propose to perform a peristrophic multiplexed HOE in the same plate that concentrates sunlight in the photocell from different incident angles. The optical thickness characterizes the angular selectivity of the holograms and determines the separation between two consecutive holograms in angular peristrophic multiplexing.
Fig. 6. Proposed arrangement of two holographic solar concentrators and two solar cells for daily performance (without solar tracking system).
Thin films of Biophotopol as used in section 3.1 were used to record two and four holographic lenses in the same spot. Variable exposures have been employed to record peristrophic multiplexed holographic concentrators with equalized η. Table 2 specifies the register order of the different holographic lenses (HL No.), θo and θr with respect to the normal of the photopolymer layer, the slant angle when the hologram was recorded (φ) and when it was reconstructed (φc), the exposure (H) in each holographic lens, and η. The difference between φ and φc in asymmetric holograms is explained by the position change of the plate at reconstruction stage respect to the recording stage, light impinges on the photopolymer at the recording stage (Fig. 1), meanwhile light impinges on the glass side at the reconstructing stage (Fig. 2). Therefore, the slant of the fringes at the reconstruction stage must be obtained as shown in Eq. (15):
The first multiplexed and thin holographic concentrator (HC-m2) was recorded by two consecutive exposures. Firstly, an asymmetric hologram (θo = 0.0°; θr = −14.8°) was exposed (H = 6.0 mJ/cm2), and then the sample was rotated 7.4° around its vertical axis to record a symmetric holographic lens (θo = +7.4°; θr = −7.4°) with the same spatial frequency but with three times more exposure (H = 18.0 mJ/cm2) than the previous one. The angular rotation between consecutive recordings was chosen to obtain good results when multiplexed holograms were reconstructing under solar light. The exposure times (t) were chosen considering equalized ηmax at 633 nm.
Table 2. Exposure and reconstructing parameters of holographic lenses (HC-m2 and HC-m4).
The experimental angular scan for the HC-m2 at 633 nm produces ηmax at θc = −18.3° in the asymmetric HL-m2(1) and at θc = −9.9° in the symmetric HL-m2(2). The exposures were chosen to obtain equalized ηmax at 633 nm, ηmax1 = 52%, and ηmax2 = 49% respectively. The theoretical Bragg angle at 633 nm for the symmetric HL of 545 l/mm matches with the experimental results, but there is a small shift in the asymmetric lens of 1.5° (Fig. 7(a)). The shrinkage produced after recording asymmetric or slanted holograms justifies the shift on ηmax position [22] between the theoretical Bragg angle and the reconstructed angle with maximum efficiency. On the other hand, the distance between maxima allows to obtain excellent results when HC-m2 is reconstructed under solar light, as shown in Fig. 7(b). Maxima of HC-m2 are partially overlapped obtaining more than 50% of relative electric current efficiency between θc = −22.0° and θc = −12.0°.
Fig. 7. Angular scan of HC-m2. a) Diffraction efficiency at 633; b) Short-circuit current measured in the photocell under solar simulator illumination.
Aiming to increase the acceptance angle of the HC-m2, we decided to increase the number of holographic lenses in the same HC up to 4, following a similar schedule to that explained in HC-m2. The specific exposure of each HL at 633 nm it is shown in Fig. 8(a) and it is described in Table 2, in which we can observe HL-m4(1) and HL-m4(2) with more than 50% of ηmax but the two last HLs with around 30%. With this holographic configuration, an angular acceptance quite higher than 30.0° was achieved, while maintaining a high electronic response in the photocell under solar illumination with an angular bandwidth around 45° (Fig. 8(b)). This is explained by the fact that wavelengths other than 633 nm can contribute to the current intensity produced by the photocell at incidence angles +2.4° and −11.1°. Moreover, the PV cell surface is larger than the photodiode power sensor surface and therefore higher diffraction orders can impinge on the photocell.
Fig. 8. Angular scan of HC-m4. a) Diffraction efficiency at 633; b) Short-circuit current measured in the photocell under solar simulator illumination.
3.3 Wide acceptance angle multiplexed hologram in thick film
The more multiplexed lenses the more angular bandwidth is achieved, whereas low film thickness limits the strategy of multiplexing a high number of holograms in the same plate [20]. In this work, we have explored the possibilities to overcome the trade-off between high efficiency and wide acceptance angle by increasing the holographic lenses stored in the HC up to 7 holographic elements in a thicker film (197 µm).
Variable exposures have been employed to record seven multiplexed holographic lenses with equalized ηmax. HC-m7 were recorded starting at θo = −14.8° and θr = −29.6°, rotating the sample 7.4° after each exposure until the position θo = +29.6° and θr = +14.8°, respectively. The reconstruction results are shown in Table 3 and Fig. 9(a), while a real device photo (HC-m7) daylight illuminated is shown in Fig. 9(b).
Fig. 9. a) Angular selectivity of peristrophic multiplexed holographic concentrator composed by seven holographic lenses (HC-m7). Diffraction efficiency at 633 nm. (Red line is a guide to the eye). b) Real device photo (HC-m7) daylight illuminated.
Table 3. Exposure and reconstructing parameters of thick multiplexed holographic concentrators (HC-m7).a
The best result achieved by multiplexing seven holographic lenses meets our expectations of achieving a wide angle. A real photo of extended focal spots when illuminated with the solar simulator at four incident angles, −33°, −25°, 0°, and 16°, are shown in Fig. 10(a), 10(b), 10(c), 10(d), respectively. As we can observe in Fig. 10(e) the solar cell produces a good response of Isc when the solar simulator beam impinges over the HC-m7 with an incident angle between −40° and +20°. Despite diffraction efficiency peaks measured at 633 nm tend to decrease at positive angles (Fig. 9(a)) the Isc measured on the photocell at the same angles tend to increase (Fig. 10(e)). This is explained since wavelengths other than 633 nm can contribute to the current intensity produced by the photocell at positive angles and, also extended focus is more concentrated as we can see in Fig. 10(d).
Fig. 10. Angular scan of seven multiplexed lenses (HC-m7). Pictures of the focal spot produced by HC-m7 when illuminated with the solar simulator and its dependence with the incident angle: a) −33°; b) −25°; c) 0°; d) 16°. E) Short-circuit current measured in the photocell under solar simulator illumination at different incident reconstruction angles (blue line is a guide to the eye).
The more Isc measured, the more efficiency is obtained a specific angle. The system efficiency (HC-m7) is good because the Isc does not drop to zero in an interval of 60° (Fig.10e). These results open huge possibilities for producing environmentally friendly HCs, that follow the daily variation of the path of the Sun [15], without the need of expensive tracking systems. Moreover, the behavior of the HC remains stable during more than six months. The diffraction efficiency and Isc vs angle reach the same values and do not show any remarkable modification over time.
4. Discussion
The trade-off achieved between wide acceptance angle and good diffraction efficiency of HCs illuminated under solar simulator source represents an important milestone in the area. Until now, the high acceptance angle obtained in a multiplexed holographic concentrator design was published by Lee et al. in 2016. The design was composed of three angular multiplexed lenses in Bayfol material with very low thickness, 17 µm. The ηmax at 532 nm was 27%, 35%, and 23%, respectively, while the maximum acceptance angle achieved was 35° [18]. Aswathy et al. developed a similar holographic concentrator design in a thicker (130 µm) and non-commercialized material two years later [17]. The material used was nickel ion photopolymer while ηmax was similar and the acceptance angle (20°) lower than the previous one, see Table 4.
Kao et al. proposed a HSC design based on Bayfol HX200 photopolymer two years ago [8]. They used two layers of photopolymer material to obtain a wide acceptance angle (30°) and good diffraction efficiency at 532 nm; and three layers of photopolymer to obtain a trichromatic volume multilayer concentrator [16] with high diffraction efficiency but low acceptance angle. Acrylamide based photopolymer has been also used to obtain HCs, whereas the toxicity of this compounds is presented as a disadvantage in comparison with environmentally friendly photopolymers [9,10].
The latest advances related to the acceptance angle and holographic diffraction efficiency of HCs at monochromatic and coherent wavelength based in different photopolymers are summarized in Table 4. This table offers a good comparison between the scientific literature and the present work. However, to evaluate the efficiency of the system under real conditions it is needed to consider a solar spectrum and the solar cell response [10,11,12] as we presented and discussed in the present work.
Table 4. Acceptance angle and diffraction efficiency (η) of different holographic concentrators HCs.a
5. Conclusions
Holographic technology is presented as outstanding method to obtain efficient, thin, low-cost, and versatile lenses, able to work under a wide acceptance angle. The greatest contribution of this work is the possibility of concentrates sunlight coming from the entire spot into the solar cell with a wide acceptance angle and without the need of any mechanical movement (solar tracking system). The proposed system of this work was composed by two solar cells and two HC composed by seven multiplexed lenses (HC-m7). With this efficient system it will be possible to focus sunlight on the photocell with an acceptance angle of 120°, maintaining Isc with few variations and without dropping to zero inside this interval. The results represent a great scientific advance with respect to what has been previously published in a low toxicity and environmentally compatible photopolymer. The proposed multiplexed solar concentrator design opens the way to develop advanced HC in a low-cost and low-toxicity photopolymer.
Funding
Universidad de Alicante (UAFPU20-23); Generalitat Valenciana (CDEIGENT/2018/024, IDIFEDER/2021/014, PROMETEO/2021/006); Ministerio de Ciencia e Innovación (PID2019-106601RB-I00).
Acknowledgments
F. M. Ferreras and V. Navarro-Fuster for technical assistance.
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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