We present a waveguide coupling approach for planar waveguide solar concentrator. In this approach, total internal reflection (TIR)-based symmetric air prisms are used as couplers to increase the coupler reflectivity and to maximize the optical efficiency. The proposed concentrator consists of a line focusing cylindrical lens array over a planar waveguide. The TIR-based couplers are located at the focal line of each lens to couple the focused sunlight into the waveguide. The optical system was modeled and simulated with a commercial ray tracing software (Zemax). Results show that the system used with optimized TIR-based couplers can achieve 70% optical efficiency at 50 × geometrical concentration ratio, resulting in a flux concentration ratio of 35 without additional secondary concentrator. An acceptance angle of ± 7.5° is achieved in the x-z plane due to the use of cylindrical lens array as the primary concentrator.
© 2014 Optical Society of America
Concentrated photovoltaic (CPV) systems are of great importance for reducing the cost associated with solar power. CPV systems employ low-cost large optical system to concentrate sunlight onto small area photovoltaic (PV) cells so that the amount of expensive PV cells can be greatly decreased. In conventional CPV systems, imaging lenses or mirrors, such as Fresnel lens  and parabolic concentrators , are used to yield high concentration level. However, these CPV systems suffer from non-uniform flux distribution over the PV cells and require a precise two-axis tracking system to maintain alignment with the sun due to the conservation of etendue . In addition, they require a large vertical distance to achieve high concentration level , which makes them bulky and hard for the tracking system to rotate. A simple approach to shrink the optical system is to divide a single large aperture into a smaller array so that concentrated sunlight can be focused onto each individual PV cells . This approach makes the optical system become thin and compact. However, it is difficult and costly to assemble and interconnect hundreds of small separated PV cells. Therefore, planar waveguide solar concentrator (PWSC) which uses a shared planar waveguide to replace those separated PV cells has been proposed . In this approach, the incident sunlight is firstly concentrated by a lens array and coupled into a shared planar waveguide using coupling structure located at the focal point of each lens. Then the coupled light propagates laterally along the waveguide by total internal reflection (TIR), and finally exits from both edges where PV cells are installed. Thus, a PWSC system mainly consists of three components: a lens array, a planar waveguide, and a coupling structure [6–8]. This design yields a compact, efficient, and light weight CPV system with uniform flux distribution and has potential for low cost roll-to-roll manufacture. Among these components, the coupling structure is important to the PWSC, therefore, it becomes an important aspect in the development of PWSC . Fortunately, a number of different coupling structures, based on scattering , gratings , holograms , and metallic-coated reflectors [6–8], have been reported. A diffuse scattering surface on the waveguide is the simplest coupling structure, but it offers minimal control over the coupling angles which leads to inefficient coupling. Diffractive couplers such as gratings and holograms can offer precise coupling angles. However, they are strong wavelength sensitive which makes them inefficient when used with broadband sunlight. Alternatively, metallic-coated reflective couplers provide clearly defined coupling angles at all wavelengths . However, metallic-coated reflectors exhibit finite reflectivity which leads to a fixed reduction in optical efficiency . Additionally, it is associated with metallic-coated reflective couplers which is wavelength dependencies and hinder efficiency when used with broadband sunlight. Here we present an alternative coupling structure by using an array of TIR-based symmetric air prisms located at the focal point of each lens. The focused sunlight undergoes TIR at the waveguide-air prism interface and redirects into the waveguide. Compared with metallic-coated couplers, TIR-based couplers have following advantages: (1) TIR-based couplers can reflect 100% of the focused sunlight into the waveguide since TIR is a complete reflection. (2) TIR-based couplers can cover a broadband of the solar spectrum since TIR is wavelength insensitive. (3) PWSC using TIR-based couplers has a potential for further cost reduction without requiring reflective metallic coating.
2. Analytic model and performance estimation
PWSC using cylindrical lens array as the primary concentrator has attracted much attention due to its ability to eliminate one axis of tracking [14,15]. Therefore, line focusing cylindrical lens array instead of point focusing spherical lens array is used in our design to increase the acceptance angle and to reduce the requirement on accuracy of the tracking system. Figure 1 illustrates the cross-section view of the proposed PWSC system. A cylindrical lens array acting as the primary concentrator is used to collect incident sunlight into the array of focal lines. A corresponding planar waveguide stays below the lens array separated by a small air-gap. The focused light is coupled into the waveguide by a series of TIR-based symmetric air prism located at each focal line of the lens array. Then the coupled light travels along the waveguide by TIR to reach the PV cells on both edges.
Geometrical concentration ratio Cgeo, optical efficiency η, and flux concentration ratio Cflux are three main figures of merit for evaluating the performance of solar concentrators. Cgeo is defined as the ratio of the input to output area of the concentrator. For the proposed structure, this ratio is given by,6] as depicted in inset B of Fig. 1. The stepped-thickness waveguide can avoid guiding-ray interaction with subsequent couplers features and eliminate waveguide decoupling loss , but planar waveguide can provide a larger attainable Cgeo since it maintains a uniform thickness when the length is increased . Cflux = η × Cgeo denotes the concentration level present at the output of the concentrator.
The major difference between the metallic-coated couplers and the TIR-based couplers is the coupler reflectivity. The metallic-coated couplers exhibit a relatively low reflectivity while the TIR-based couplers exhibit 100% reflectivity. Therefore, to estimate the influence of coupler reflectivity and waveguide geometry on optical efficiency, an analytic model has been developed. The following equations are used to calculate the optical efficiency of the PWSC using cylindrical lens array as the primary concentrator [14,15]:Fig. 2.
In calculation, the optical efficiency from an input position P is firstly calculated according to Eq. (2) as the transmission probability raised to the number of interactions (P tan Ф/2H) with the top surface of the waveguide for each coupling angle Ф. Then, coupler reflectivity and material absorption are taken into account in Eq. (3). Finally, the total optical efficiency of the concentrator, given by Eq. (4), is computed by integrating over all coupling angles and over all positions. It should be noted that the influence of the geometry of the air-prism coupler on the waveguide decoupling loss is not included in Eq. (2). Using a PWSC with an F/# = F/1.81 cylindrical lens, a waveguide with a common used optical glass material F2 (nd = 1.62, α = 1.8 × 10−4 cm−1), and a coupling angle of 10° as an example, the calculated optical efficiency as functions of waveguide length and thickness for three different coupler reflectivities of R = 100%, 95%, and 90% are shown in Figs. 3(a)–3(c), respectively. To accurately calculate the optical efficiency, all coupled ray angles must be taken into account. However, the variation of the optical efficiency with different waveguide geometries and different coupler reflectivities has the same trend with or without considering all coupled ray angles. Therefore, the coupling angle Ф = 10° is considered as a fixed value for simplicity. It can be seen from Figs. 3(a)–3(c) that for different coupler reflectivities, the optical efficiency is increased with the increase of the waveguide thickness and the decrease of the waveguide length. However, Cgeo is increased with the increase of the waveguide length and the decrease of the waveguide thickness, as indicated by Eq. (1). Therefore, geometries with the highest η and Cgeo present at opposite corners of the figures. This is because the number of interactions with the top surface of the waveguide increases as waveguide length increases or waveguide thickness decreases, which leads to additional absorption and waveguide decoupling loss. Conversely, short and thick waveguides minimize the number of interactions with the top surface of the waveguide, which yields higher optical efficiency, but provides lower Cgeo. Therefore, there is a need to find a tradeoff between η and Cgeo when defining the dimension of the concentrator. Figure 3(d) shows the relationship between η and Cgeo with three different coupler reflectivities by extracting from the results in Figs. 3(a)–3(c). It can be seen that, the optical efficiency exhibits the same decreasing tendencies with increasing the Cgeo for different coupler reflectivity, implying that a decrease in coupler reflectivity leads to a fixed reduction in η at all Cgeo. Compared to metallic-coated couplers , TIR-based couplers with R = 100% can maximize the optical efficiency of the PWSC system by a fixed percentage due to the increase of coupler reflectivity.
3. Simulations and discussions
To explore the practical performance of the PWSC using the TIR-based symmetric air prisms as couplers, as an example, a system with Cgeo up to 100 × has been modeled and simulated by Zemax ray tracing software. The wavelength range of the light source is selected from 0.4 to 1.6 μm. In the design, common optical glass materials BK7 (nd = 1.5168, α = 3 × 10−6 cm−1) and F2 are selected for cylindrical lens array and planar waveguide, respectively. The detailed parameters of the system are presented in Table 1.
3.1 Minimum and optimum basic angle of symmetric air prism coupler
In the coupling approach reported by Karp et al. , to avoid shadowing effects, the basic angle of symmetric metallic-coated prism couplers is fixed at 30°. For this proposed coupling approach, the basic angle of the symmetric air prism coupler has a minimum value to redirect the whole focused sunlight into the waveguide and an optimum value to achieve the highest optical efficiency. The marginal ray which enters from the edge of the lens needs the largest tilt to TIR at the waveguide-air prism interface. To couple the whole focused sunlight into the waveguide, the incident angle of the marginal ray θI must exceed the critical angle θC for TIR. Therefore, θI has a minimum value θImin which can be expressed as,Fig. 4). Therefore, θB has a minimum value θBmin which can be calculated by,17],
According to Eqs. (5) and (7), the calculated θImin = 38.1° and θM = 9.9°. Therefore, the minimum basic angle of the symmetric air prism coupler for material F2 waveguide is 48°. When θB reaches the minimum value, all focused sunlight can undergo TIR at the waveguide-air prism interface and be coupled into the waveguide. However, in this case, the marginal rays redirect with a small coupling angle Ф. As a consequence, they strike the adjacent coupler immediately and decouple upon second TIR as loss, as shown in Fig. 4. By increasing θB to allow the marginal rays to couple with a larger Ф can mitigate this effect. However, the number of interactions (P tan Ф/2H) with the top surface of the waveguide, and thus the absorption and waveguide decoupling loss, is increased with the increasing Ф. Consequently, there exists an optimum θB for the symmetric air prism coupler. Figure 5 shows η as a function of θB for three different Cgeo. It can be seen that η exhibits a similar variation tendency with the increase of θB for different Cgeo. The maximum η is obtained at θB = 50° for different Cgeo, which implies that the optimum basic angle of the symmetric air prism coupler for F2 waveguide is 50°. In the following Zemax calculations, optimized symmetric air prism couplers with basic angle of 50° are used.
3.2 Optical efficiency
With optimized TIR-based couplers, optical efficiency is simulated for Cgeo up to 100 × . Figure 6 shows the simulated optical efficiency at different losses and the corresponding flux concentration ratio as functions of Cgeo. It can be seen that with the waveguide decoupling loss only, η is almost linearly decreased with the increase of Cgeo. When all the losses including Fresnel reflection, material absorption, and waveguide decoupling losses are taken into account, the curve exhibits a similar decreasing tendency to that considering only waveguide decoupling loss. This implies that Fresnel reflection and material absorption losses lead to a fixed percentage reduction in the optical efficiency for all Cgeo. At Cgeo = 50, the concentrator system achieves 81% optical efficiency with the waveguide decoupling loss only and achieves 70% optical efficiency when including all losses. Compared to the PWSC using spherical lens array as the primary concentrator, which achieves over 90% optical efficiency at Cgeo = 50 , the optical efficiency for the concentrator proposed here is relatively low. This is because the total area of the waveguide surface covered by the couplers, and thus the waveguide decoupling loss, is much larger in the proposed concentrator. By using cylindrical lens array as the primary concentrator, the proposed PWSC system sacrifices a portion of optical efficiency in exchange for larger acceptance angle, which will be discussed in Section 3.3. Because an increase in Cgeo leads to the decrease in η, their product Cflux is an overall figure of merit for evaluating the performance of the concentrator. It can be seen from Fig. 6 that though η is decreased almost linearly with the increasing Cgeo, while Cflux exhibits an ascending trend with the increase of Cgeo. At Cgeo = 50, the optical efficiency drops to 70% while Cflux increases to 35 × .
In addition, an equivalent system can be achieved by changing the location of the air prism couplers. By altering the thickness of the lens array, the focal plane of the lens array is shifted from the top surface to the lower surface of the waveguide with an identical F/#. In this case, the air prism couplers are located on the lower surface to couple the focused sunlight into the waveguide. This yields an equivalent system with similar optical performance, which indicates that the proposed coupling approach using TIR-based air prisms as couplers for PWSC is practical whether the couplers are located on the top or lower surface of the waveguide. Therefore, from the viewpoint of fabrication, the air prism couplers can be chosen to locate on the lower surface so that the waveguide prototype would be fabricated by molding process. This will be looked at in the future work.
3.3 Acceptance angle
The acceptance angle of the concentrator is defined as the incident angle within which the optical efficiency drops to 90% of its maximum value. The acceptance angle determines the required accuracy of the tracking system mounted upon the concentrator. For a smaller acceptance angle, the precision requirement on the tracking system is higher. The proposed PWSC with cylindrical lens array as the primary concentrator has different acceptance angles in the y-z plane and the x-z plane.
The acceptance angle in the y-z plane depends on the width W of the air prism coupler. Larger coupler widths allow the focused sunlight remain incident on the coupler over large incident angle so that the acceptance angle increases. Figure 7(a) shows the normalized optical efficiency as a function of incident angle in the y-z plane for three different W at Cgeo = 50. It can be seen that the achieved acceptance angle increases from ± 0.30° to ± 0.45° and ± 0.63° when W is increased from 90 to 130 and 170 μm, respectively. However, larger coupler widths also increase waveguide decoupling loss as there is an increased chance on secondary interaction with the coupler. Figure 7(b) shows η for three different coupler widths as a function of Cgeo. It can be seen that η is decreased with the increasing W for all Cgeo. At Cgeo = 50, η is decreased from 70% to 60% and 50% as W is increased from 90 to 130 and 170μm, respectively. This indicates that increasing W sacrifices a portion of optical efficiency in exchange for lager acceptance angle in the y-z plane. In addition, micro-tracking accomplished through small lateral translations of the lens array with respect to the waveguide can be applied in the y-z plane to further increase the acceptance angle and eliminate the bulky rotating tracking system .
As specified in Fig. 1, the axis of the cylindrical lens extends along the x-direction. The acceptance angle in the x-z plane depends on the defocusing effect caused by obliquely incident rays, which enlarges the energy distribution on the focus plane . Therefore, with the same coupler width, a portion of the focused sunlight is missed from the coupling prism and decoupled as loss. The simulated normalized efficiency as a function of the incident angle in the x-z plane at Cgeo = 50 is plotted in Fig. 8.The insets (a)−(d) of Fig. 8 illustrate the energy distribution on the focal plane of the lens with incident angle of 0°, 5°, 10°, and 15°, respectively. Inset (a) shows that normal incidence sunlight is focused into a line without defocusing. Inset (b) shows that when the incident angle is increased to 5°, the effect of defocusing is not serious so that the optical efficiency decreases slightly. Inset (c) shows that when the incident angle is increased to 10°, the focused sunlight is spread on a larger area which leads to a significant decrease in the optical efficiency. Inset (d) shows that when the incident angle is increased to 15°, the effect of defocus becomes more serious and causes a serious decrease in the optical efficiency. From Fig. 8, it can be seen that the acceptance angle in the x-z plane is ± 7.5° which is much larger than that for the spherical lens array ( ± 0.26°) . This indicates that by using line focusing cylindrical lens array as the primary concentrator, the acceptance angle can be greatly increased without sacrificing too much optical efficiency. Therefore, PWSC using cylindrical lens array instead of spherical lens array as the primary concentrator can lower the accuracy requirement and reduce the cost of the tracking system.
A planar waveguide solar concentrator using TIR-based symmetric air prisms as couplers to maximize the optical efficiency by increasing the reflectivity of the coupler had been designed and discussed. An analytic model was developed to estimate the influence of coupler reflectivity R on optical efficiency. The results show that an increase in R leads to an increase in overall optical efficiency of the concentrator at all Cgeo. Therefore, TIR-based couplers with R = 100% can maximize the optical efficiency of the PWSC system. To explore the practical performance of the PWSC system using TIR-based couplers, an example optical system was modeled and simulated with Zemax. Simulation results indicate that the coupler with a basic angle θB = 50° is the best for a F2 material waveguide to achieve high optical efficiency. With optimized TIR-based couplers, 70% optical efficiency and 35 × flux concentration ratio were achieved at Cgeo = 50 for the proposed concentrator system. In addition, the acceptance angles in the y-z plane and the x-z plane were also analyzed. By using the line focusing cylindrical lens array as the primary concentrator, an acceptance of ± 7.5° was achieved in the x-z plane.
The authors acknowledge Mr. Hongbao Xin for assistance in preparation of this manuscript. This work was supported by the National Basic Research Program of China (973 Program) (No. 2012CB933704) and the Program for Changjiang Scholars and Innovative Research Team in University (IRT13042).
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