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Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 21, Iss. 17 — Aug. 26, 2013
  • pp: 20073–20089
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Ray-leakage-free sawtooth-shaped planar lightguide solar concentrators

Hong-Yu Wu and Shu-Chun Chu  »View Author Affiliations


Optics Express, Vol. 21, Issue 17, pp. 20073-20089 (2013)
http://dx.doi.org/10.1364/OE.21.020073


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Abstract

This paper details the design of a ray-leakage-free sawtooth-shaped planar lightguide solar concentrator. The concentrator combines Unger’s dimpled planar lightguide solar concentrators [1] with a prism array dimpled planar lightguide solar concentrator. The use of a sawtooth-shaped boundary on the planar lightguide prevents leakages of the guiding ray after multiple reflections in the lightguide. That is, the proposed solar concentrator can achieve a higher geometrical concentration ratio, while maintaining a high optical efficiency at the same time. Numerical results show that the proposed sawtooth-shaped planar lightguide solar concentrator achieves 2300x geometrical concentration ratio without any guiding ray-leakages from the planar lightguide.

© 2013 OSA

1. Introduction

Green energies have become very important for the sake of environmental protection and the energy crisis. Solar energy is one kind of important green energy. Generally, sunlight is collected by a solar collector, and the solar energy is then transferred to heat energy or to electricity by the photovoltaic (PV) cell. Researchers use solar concentrators for achieving high light concentration ratios by collecting sunlight from a large area and directing it to a smaller light-receiving region of PV cells. Parabolic dish type [2

2. D. Feuermann and J. M. Gordon, “High-concentration photovoltaic designs based on miniature parabolic dishes,” Sol. Energy 70(5), 423–430 (2001). [CrossRef]

] and trough type [3

3. Z. Hongfei, T. Tao, D. Jing, and K. Huifang, “Light tracing analysis of a new kind of trough solar concentrator,” Energy Convers. Manage. 52(6), 2373–2377 (2011). [CrossRef]

] sunlight collectors have previously been developed to collect sunlight. Recently, planar lightguide solar concentrators have attracted much attention for their promising thin form-factor, lightweight and inexpensive replacements for the current generation of refractive and reflective solar concentrators [4

4. V. Wittwer, W. Stahl, and A. Goetzberger, “Fluorescent Planar Concentrators,” Sol. Energy Mater. 11(3), 187–197 (1984). [CrossRef]

11

11. S.-C. Chu, H.-Y. Wu, and H.-H. Lin, “Planar lightguide solar concentrator,” Proc. SPIE 8438, 843810, 843810-7 (2012). [CrossRef]

]. The general goal of designing a good planar lightguide solar concentrator is to have a high light concentration ratio and high optical efficiency at the same time.

Generally speaking, the planar lightguide solar concentrator could be classified into two types. One type is the active-type, the fluorescence-based concentrators [4

4. V. Wittwer, W. Stahl, and A. Goetzberger, “Fluorescent Planar Concentrators,” Sol. Energy Mater. 11(3), 187–197 (1984). [CrossRef]

]. Such active concentrators involve repeatedly nonlinear light absorption and light re-emission, where the large light re-emission angular spectrum and the repeatedly nonlinear light absorption lead to its low optical efficiency. The other type of planar lightguide solar concentrator is the passive-type, the non-ray-emitting concentrators [5

5. J. C. Goldschmidt, M. Peters, A. Bosch, H. Helmers, F. Dimroth, S. W. Glunz, and G. Willeke, “Increasing the efficiency of fluorescent concentrator systems,” Sol. Energy Mater. Sol. Cells 93(2), 176–182 (2009). [CrossRef]

11

11. S.-C. Chu, H.-Y. Wu, and H.-H. Lin, “Planar lightguide solar concentrator,” Proc. SPIE 8438, 843810, 843810-7 (2012). [CrossRef]

]. The solar concentrator this paper proposed belongs to this type. A common design for non-ray-emitting-type planar lightguide concentrators usually consists of three parts: the lens array, secondary optical elements and the lightguide itself [6

6. J. H. Karp, E. J. Tremblay, J. M. Hallas, and J. E. Ford, “Orthogonal and secondary concentration in planar micro-optic solar collectors,” Opt. Express 19(S4Suppl 4), A673–A685 (2011). [CrossRef] [PubMed]

8

8. M. Brown, D. Moore, G. Schmidt, and B. Unger, “Measurement and Characterization of Dimpled Planar Light Guide Prototypes,” in Proceedings of International Optical Design Conference, (OSA, 2010), JMB45P. [CrossRef]

]. The lens array of a large sunlight collecting area focuses sunlight from a large area into a lightguide. The secondary optical elements then redirect the focusing light in the direction that the PV cell is situated. Finally, the lightguide of an index higher than the surrounding media guides the redirected sunlight to the PV cell of a small area by total internal reflection (TIR). For example, Karp et al. proposed planar micro-optic solar collectors [6

6. J. H. Karp, E. J. Tremblay, J. M. Hallas, and J. E. Ford, “Orthogonal and secondary concentration in planar micro-optic solar collectors,” Opt. Express 19(S4Suppl 4), A673–A685 (2011). [CrossRef] [PubMed]

, 7

7. J. H. Karp, E. J. Tremblay, and J. E. Ford, “Planar micro-optic solar concentrator,” Opt. Express 18(2), 1122–1133 (2010). [CrossRef] [PubMed]

], which use round and small micro-structures as secondary optical elements. This kind of planar lightguide solar concentrator can stand a great concentration ratio by lowering its interaction probability between micro-structures. In this design, the sequential scattering by other micro-structures leads to guiding ray leakages. Such a decrease in optical efficiency could be reduced by narrowing down the micro-structures, but this might also introduce intrinsic lens coupling loss. Unger et al. proposed dimpled planar lightguide solar concentrators [1

1. B. L. Unger, G. R. Schmidt, and D. T. Moore, “Dimpled planar lightguide solar concentrators,” in Proceedings of International Optical Design Conference, (OSA, 2010), ITuE5P. [CrossRef]

]. This planar solar concentrator uses a smart dimpled structure as the secondary optical elements. The dimpled structure can efficiently redirect the collecting sunlight in the direction of the light exit surface of a lightguide where the PV cell is situated. However, the reflections by the sequential dimpled structures also add an angular spectrum of guided rays which leads to the break in TIR and also leads to the limitation in concentrator optical efficiency and concentrator light concentration ratio. Similarly, reducing the depth of the dimpled structure can successfully decrease the possibility of sequential guiding ray reflections, but it will also narrow down the light-coupling area which introduces the intrinsic lens coupling loss. Increasing the lightguide depth with a fixed dimpled structure depth can also decrease the possibility of sequential guiding ray reflections, but it will also decrease the light concentration ratio of the solar concentrator.

Recently, Moore et al. proposed a kind of planar solar concentrator of “stepped-shape” [9

9. D. Moore, G. R. Schmidt, and B. Unger, “Concentrated photovoltaic stepped planar light guide,” in Proceedings of International Optical Design Conference, (OSA, 2010), JMB46P. [CrossRef]

]; the smart stepped lightguide design successfully avoids guiding-ray interaction with other injection facets, i.e. prevents the ray leakages from the lightguide. The concept of the “stepped-shape” was further explored by Selimoglu et al. [10

10. O. Selimoglu and R. Turan, “Exploration of the horizontally staggered light guides for high concentration CPV applications,” Opt. Express 20(17), 19137–19147 (2012). [CrossRef] [PubMed]

]. With suitable lightguide end-cutting and the secondary compound parabolic concentrators (CPC) design at the lightguide exit port, Selimoglu’s solar concentrator can achieve a high concentration ratio without any ray-leakage from the planar lightguide. In this paper, we detail another design of a ray-leakage-free planar lightguide solar concentrator [11

11. S.-C. Chu, H.-Y. Wu, and H.-H. Lin, “Planar lightguide solar concentrator,” Proc. SPIE 8438, 843810, 843810-7 (2012). [CrossRef]

], i.e. sawtooth-shaped planar lightguide solar concentrators. This design adopts Unger’s smart dimpled structure as the secondary optical element of the lightguide. Besides, in our design, the boundary of the planar lightguide was shaped in a sawtooth-shape on one side. The combination of a sawtooth-shaped lightguide boundary and the dimpled structure horizontally constructs a “stepped-like” structure; thus, the lightguide structure successfully prevents light leakages from the planer lightguide. Moreover, the use of a sawtooth-shaped boundary for the planar lightguide substantially decreases the reflection times of guiding rays in the lightguide; thus, it can achieve higher light concentration ratios while maintaining a high optical efficiency. The numerical results show that while excluding the Fresnel loss at each interface, the proposed sawtooth-shaped planar lightguide solar concentrator design can achieve 2000x-, 735x- and 240x- geometrical concentration ratios with high optical efficiency of 96.80%, 97.93% and 98.99%, respectively, while their dimple structures have different length-width ratios: r = 25, r = 15 and r = 10, respectively. The minor energy loss is introduced by the intrinsic material absorption of the lightguide and microlens array. No guiding ray leakage happened in the lightguide.

This paper is organized as follows. Section 2 describes the design concept of the sawtooth-shaped planar lightguide solar concentrator. Section 3 details the solar concentrator design approach. Section 4 shows the numerical results of the optical properties of the proposed sawtooth-shaped solar concentrator and its comparison to Unger’s dimpled planar lightguide solar concentrator [1

1. B. L. Unger, G. R. Schmidt, and D. T. Moore, “Dimpled planar lightguide solar concentrators,” in Proceedings of International Optical Design Conference, (OSA, 2010), ITuE5P. [CrossRef]

]. Finally, section 5 gives a brief summary of this study, discusses some concerns in regard to making a sawtooth-shaped planar lightguide solar concentrator, and provides a comparison between our concentrator designs and another ray-leakage-free planar solar concentrator.

2. Solar concentrator structure

Figure 1
Fig. 1 Schematic diagram of a sawtooth-shaped planar lightguide solar concentrator.
illustrates the structure of the proposed sawtooth-shaped planar lightguide solar concentrator. The concentrator combines the Unger’s dimpled planar lightguide solar concentrators (on the left) [1

1. B. L. Unger, G. R. Schmidt, and D. T. Moore, “Dimpled planar lightguide solar concentrators,” in Proceedings of International Optical Design Conference, (OSA, 2010), ITuE5P. [CrossRef]

] with a prism array dimpled planar lightguide solar concentrator (on the right). As the common design of a planar lightguide solar concentrator, the concentrator consists of three parts: a lens array, a secondary optical element and the lightguide itself. In this design, sunlight is collected by microlenses in a two-dimensional lens array and is coupled into the planar lightguide using localized secondary optical elements placed at each lens focus. The structure of the secondary optical element used in this design is Unger’s smart dimple structure [1

1. B. L. Unger, G. R. Schmidt, and D. T. Moore, “Dimpled planar lightguide solar concentrators,” in Proceedings of International Optical Design Conference, (OSA, 2010), ITuE5P. [CrossRef]

]. Especially, this design modifies the lightguide’s one-side boundary using a sawtooth shape. The simpler modification substantially advances the planar lightguide property. Section 2.1 briefly reviews the smart dimpled structure function, and section 2.2 explains how a sawtooth-shaped lightguide boundary prevents guiding ray leakages. Section 2.3 explains why this design chooses a compound lightguide boundary. Referring to Fig. 1, this paper assumes that sunlight coming from the z-axis is vertically incident on the solar concentrator. The design goal is to collect and guide sunlight along the y-axis to the lightguide exit port where the solar cell is situated without any ray leakages. The wording “ray leakages” means only lightguide energy loss from the guiding rays which breaks the TIR-condition. In accordance with the arrangement of the proposed solar concentrator, as Fig. 1 shows, two important properties of the sawtooth-shaped planar lightguide solar concentrators, geometric concentration ratio Cgeo and optical efficiency η, are given by:
Cgeo=sunlightverticallyincidentareaLightguideexitportarea=LightguidelengthLightguidedepth,
(1)
and
η=Verticallyincidentsunlightenergyenergyatlightguideexitport.
(2)
This paper provides a design for a planar lightguide solar concentrator with a high geometric concentration ratio without optical efficiency decreasing in ray leakages.

2.1 Dimpled air spaces

2.2 Preventing guiding ray leakages by the sawtooth-shaped lightguide boundary

To prevent guiding ray leakages, it is important to make sure that the incident angles of all guiding rays at the lightguide side surface and all dimple side surfaces exceed the critical angle. That is, the TIR condition is maintained until a guiding ray reaches the PV cell. Figure 3(a)
Fig. 3 Diagrams of guiding ray paths in two kinds of planar lightguides. The red arrows plot the guiding ray path in lightguides. (a) Unger’s dimpled planar lightguide. The ray paths show that the decrease in ray incident angle from reflections results in guiding ray leakages. (b) Planar lightguide with sawtooth-shaped boundary. The ray paths show that the sawtooth-shaped boundary successfully prevents the decrease in ray incident angle, i.e. prevents guiding ray leakages.
illustrates the guiding ray paths in Unger’s dimpled planar lightguide [1

1. B. L. Unger, G. R. Schmidt, and D. T. Moore, “Dimpled planar lightguide solar concentrators,” in Proceedings of International Optical Design Conference, (OSA, 2010), ITuE5P. [CrossRef]

]. The guiding ray will gradually leak out from the lightguide owing to the ray-incident-angle decreasing after several reflections. Referring to Fig. 1 and Fig. 3(b), to prevent the decreasing in incident angle of guiding rays, i.e. ray leakages, this design lets the right-side lightguide boundary be a sawtooth shape. The interior angles of each sharp tooth of the sawtooth boundary are the same as the expanding angle of all bypass elements. The side surfaces of the sawtooth boundary correct the change in ray-incident angle resulting from dimpled structure reflection. With the structural arrangement, the focusing conical sunlight from the microlens is directly redirected to the lightguide exit port. The usage of the sawtooth-shaped boundary of the planar lightguide substantially decreases both the number of guiding ray reflection times and the propagating distance of the guiding rays in the lightguide. Figures 4(a)
Fig. 4 Side view of the focusing ray paths from one microlens in two kinds of planar lightguides, (a) Unger’s dimpled planar lightguide, and (b) sawtooth-shaped planar lightguide.
and 4(b) plot the side view of the focusing ray paths from one microlens in Unger’s dimpled planar lightguide and the proposed sawtooth-shaped planar lightguide, respectively. Figure 4 shows that the design of the sawtooth boundary successfully prevents guiding ray leakages from the planar lightguide.

2.3 Maximized solar concentrator’s geometrical concentration ratio

3. Ray-leakage-free solar concentrator model

This section details approaches to find all parameters of the proposed ray-leakage-free sawtooth-shaped planar lightguide solar concentrator.

3.1 Ray-leakage-free propagating length of incident rays in the meridional plane

This section finds the lightguide parallel part length, Lparallel, in which incident rays in the meridional plane can be guided without ray leakage. Here, the meridional plane means the y-z plane that contains the microlens optical axis. Figure 6
Fig. 6 Cross-sectional view of guiding ray paths in a dimpled planar lightguide with parallel boundary. The red lines in Fig. 6(a) show the light interaction between the dimples. Figure 6(b) shows the relation between guiding ray incident angle ϕin and ray leading angle δn..
plots symbols used in this section. Referring to Fig. 6(a), the sunlight in the meridional plane coming from microlenses is redirected toward y-axis by injection elements. After several reflections by the downstream dimple structures, the light rays are redirected in the direction with a leading angle δn. Referring to Fig. 6(b), the leading angle δn is the included angle between the guiding ray with y-z plane, where the suffix n denotes the times that a guiding ray leaves from the dimple columns. The increase of the leading angle δn of a guiding ray by multiple reflections is illustrated in Fig. 6(a), and the value of the leading angle δn is given by:
δn=nα.
(3)
As the leading angle δn of a guiding ray increases, twice the ray-traveling distance between the reflections by dimple structures will decrease, which is given by:
Ln=acot(δn).
(4)
where a is the x-distance between two columns of dimple structures, and Eqs. (3) and (4) hold while only the TIR condition is maintained.

Figure 6(b) depicts the relationship between the ray incident angle at the bypass element ϕin and the leading angle δn, i.e. ϕin=π/2δnα/2. The TIR condition, ϕinθC, gives the relation of the maximum guiding ray reflection times N with the critical angle θC:
Nαπ2α2θC.
(5)
Knowing the maximum reflection times of a leakage-free guiding ray shows that the maximum distance of an incident ray in the meridional plane can be guided in a dimpled planar lightguide with a parallel boundary without ray leakages, i.e. leakage-free propagating length, Ll-f:
Llfn=1Nacot(δn).
(6)
However, the actual extended length of the lightguide parallel part, Lparallel, is shorter than the leakage-free propagating length, Ll-f. Referring to the green dotted rectangular area shown in Fig. 7
Fig. 7 Schematic diagram of the combination of lightguide parallel part and lightguide sawtooth part. The green dotted rectangular area shows the conjoint zone. Any reflected ray from bypass elements in the conjoint zone (see dotted red arrow) will not fall on the sawtooth boundary of lightguide sawtooth part.
, any reflected ray from bypass elements in this conjoint zone (see dotted red arrow) will not fall on the sawtooth boundary. That is, the ray incident angle of all guiding rays from the conjoint zone will be changed by the sequential dimple structures and parallel boundary. Thus, the length of the conjoint zone, Loverlapping, should be included in the leakage-free propagating length, Ll-f. Simple geometrical calculations give the lengths of the conjoint zone, the sawtooth part and the parallel part, respectively. That is:
Loverlapping=a2cotδ1,
(8)
Lsawtooth=a×r,
(9)
and

Lparallel=n=1Nacot(δn)a2cotδ1.
(10)

The planar lightguide overall length is Lparallel + Lsawtooth. However, it should be noted that Eqs. (4) to (10) assume that the x-distance between twice the reflections from dimple structures is the same as the x-distance between two columns of dimpled structures a. Actually, the value varies from (a-dx) to (a + dx). Replacing value a of Eqs. (4) to (10) by (a-dx) gives a ray-leakage-free sawtooth-shaped planar lightguide solar concentrator with the shortest lightguide overall length, Lparallel + Lsawtooth, i.e. gives the estimation of the smallest (or the worst) geometrical concentration ratio Cgeo of solar concentrator.

3.2 The increment of the leading angle of skewed incident rays on the sagittal plane

The “skew incident rays” in this paper denotes the focusing rays coming from microlenses with an oblique incident on the planar lightguide which were not contained in the meridional plane, y-z plane. The oblique incident skew rays result in the increase in the guiding ray incident angle at the first bypass element, and also, leading angle δn. This paper uses the symbol δn’ with a comma superscript to denote the leading angle of skew incident rays. Similar to the definition of n in Eq. (3), here n also denotes the times that the guiding ray leaves the dimple columns. Specifically, we use the symbol δini to denote the initial leading angle of skew incident rays, i.e. δ1= δini, i.e., the ray leading angle when it leaves the skew ray-incident dimple column. Accordingly, the leading angle of a guiding skew ray that has left the neighbor column will be δ2’ = δini + α. The sequential skew ray leading angles δ n’ will be:
δn'=δini+(n1)α.
(11)
As Eq. (6) shows, a guiding ray having the largest leading angle leads to the shortest leakage-free propagating length, Ll-f. The oblique incident skew rays result in the increase in the leading angle δn’. Thus, in the lightguide parallel part, the skew incident ray will also be the crucial ray to be guided to the PV cell. In designing a leakage-free solar concentrator, this study uses this most crucial ray to find the lightguide parallel part length, Lparallel. Referring to Fig. 8(a)
Fig. 8 Schematic side view of guiding ray paths in a planar lightguide solar concentrator: (a) the y-z cross-section (the meridional plane), and (b) the x-z cross-section (the sagittal plane).
regarding a focusing ray cone from a micro lens, the most crucial incident ray to be guided in the lightguide is situated at the x-z plane that transverses in the lightguide ray-guiding direction which contains the microlens optical axis. This paper names the plane the sagittal plane. The remainder of this section details how to find the initial leading angle δ ini of the skew incident ray that is situated on the sagittal plane.

Figure 8(b) plots the sagittal plane of the solar concentrator, which illustrates the parameters used in the following discussions. The microlens’ thickness is d1 and its radius is ρ. The air space between the microlens array and lightguide is d2 and half the lightguide thickness is d3. The refractive indexes of the microlens array, air space and lightguide are denoted by symbols n1, n0 and n2, respectively. Symbols θn and θn’ denote the included angles between the surface normal with an incident ray and refracted ray, respectively. The lateral distance of the ray intersect point at each interface to the microlens optical axis is denoted by symbol xn. The suffix of θn, θn’ and xn indicates the interface where each interface is numbered in Fig. 8(b) by an orange rectangle:

3.3 Finding the leakage-free sawtooth-shaped planar lightguide solar concentrator structure

The leakage-free sawtooth-shaped solar concentrator parameters are calculated by the following processes: First, with a given microlens diameter D, thickness d1, index n1, radius ρ (or focal length f) and dimple length-width ratio r, this study uses Eqs. (12) to (16) to find two values, x4 and Δθ, of all incident rays on the sagittal plane. The process finds the most critical ray to be guided by the planar lightguide, where the most crucial ray possesses the largest initial leading angle δini. Second, with a given x-distance between two dimple columns a, this study substitutes the δini of the most crucial ray into Eq. (11) giving the largest leading angles δn’. Substituting δn’ into Eqs. (9) and (10) gives us lightguide sawtooth part length, Lsawtooth and the estimation of the shortest leakage-free lightguide parallel part length, Lparallel. Third, dividing the solar concentrator’s overall length Lparallel + Lsawtooth by the lens diameter D gives the overall longitudinal (i.e. y-direction) square unit number used in constructing the leakage-free solar concentrator, while there is no limits in the lateral (i.e. x-direction) square unit number. Finally, this study constructs the planar lightguide solar concentrator by combining multiple square units of the estimated numbers.

In addition, the parameter-finding processes give the largest lateral ray intersect position at the injection elements of all incident rays, which is denoted by (x4)max. The value provides the estimation of the minimum dimple width dx, and also, provides the limit of the lightguide thickness, dimple length-width ratio r and leakage-free lightguide geometrical concentration ratio Cgeo.

4. Simulation results

This section provides a numerical simulation of the optical properties of the leakage-free sawtooth-shaped planar lightguide solar concentrator. All simulations in this paper were modeled by the commercial ray-tracing simulation package, LightTools [12

12. Software LightTools, See website: http://www.opticalres.com/lt/ltprodds_f.html.

]. First, we use the approaches addressed in section 3.3 to construct leakage-free solar concentrators. The solar concentrator parameters used in simulations are addressed as follows. This study constructs the planar lightguide solar concentrator by combining several square units with lateral dimensions of the microlenses, i.e. 5 mm × 5 mm. The material of the microlens and lightguide are both BK7, and the thickness of the microlens is 3 mm. Dimple structure of three different length-width ratios, of r = 25, r = 15, and r = 10, are constructed. Dividing the microlens diameter by the length-width ratio r gives the dimple structure thicknesses of three cases, i.e. 0.20 mm, 0.33 mm, and 0.50 mm, respectively. Since each injection element is situated at the focus of a microlens, the x-distance between two columns of dimpled structures a will be the same as the microlens diameter, naturally.

4.1 Confirm ray-leakage-free property of the sawtooth-shaped planar lightguide solar concentrator

The major concern of this study is preventing the most crucial loss of the lightguide, i.e., the ray leakage from the planar lightguide. Thus, all simulation results shown in this section ignore the energy loss from the Fresnel loss at all surfaces and the material absorptions. This study includes discussions on the Fresnel loss and material absorptions in section 4.3. In all simulations of this section, sunlight of wavelength 0.55 μm is vertically incident on the solar concentrator. Moreover, to show the improvement of the proposed sawtooth-shaped concentrator on Unger’s dimpled lightguide concentrator [1

1. B. L. Unger, G. R. Schmidt, and D. T. Moore, “Dimpled planar lightguide solar concentrators,” in Proceedings of International Optical Design Conference, (OSA, 2010), ITuE5P. [CrossRef]

], all simulation results shown in this sections include the results of Unger’s dimpled lightguide solar concentrator.

Two main optical parameters of the planar lightguide solar concentrators, geometric concentration ratio Cgeo and optical efficiency η are calculated from simulations, where the definitions of two parameters are given by Eqs. (1) and (2). Figures 10(a)
Fig. 10 Geometrical concentration ratio of the ray-leakage-free planar lightguide solar concentrators versus the focal length of the microlenses while their dimple structures have different length-width ratios: (a) r = 25, (b) r = 15, and (c) r = 10. The solid blue and black lines show the results of the proposed sawtooth-shaped planar lightguide solar concentrators and Unger’s dimpled planar lightguide solar concentrators, respectively. While the dotted red lines show the smallest estimated Cgeo of the ray-leakage-free sawtooth-shaped planar lightguide solar calculated by Eqs. (4) to (10).
and 10(b) show the relation between the Cgeo of solar concentrators with microlens focal lengths ranging from 24 mm to 50 mm, while the dimple structures possess three different length-width ratios, r = 25, r = 15, and r = 10, respectively. The red-dotted line in Fig. 10 plots the smallest estimated Cgeo for the ray-leakage-free sawtooth-shaped planar lightguide solar concentrators, i.e. calculating the leakage-free solar concentrator’s overall length by replacing value a of Eqs. (4) to (10) by (a-dx). Since the real x-distance between twice reflections from the two dimple column ranges between (a-dx) and (a + dx), the proposed ray-leakage-free sawtooth-shaped solar concentrators surely have a greater Cgeo than estimated. This study finds the real ray-leakage-free overall length of solar concentrators by adding more square units into the solar concentrators until the lightguide leaks any guiding rays. The real ray-leakage-free overall length of solar concentrators is the length of total square units along y-axis before the ray leakage happens. The real Cgeo of a ray-leakage-free sawtooth-shaped solar concentrator is calculated by dividing the real ray-leakage-free overall length by the lightguide depth. The blue and black solid lines in Fig. 10 plot the real Cgeo of the proposed sawtooth-shaped solar concentrators and Unger’s dimpled planar lightguide solar concentrators, respectively.

As a comparison with Unger’s dimple lightguide solar concentrator, this study also discusses the non-ray-leakage-free situations of two kinds of solar concentrators. That is, this study simulates how the optical efficiency of these two kinds of solar concentrators decreases when the lightguide length exceeds their ray-leakage-free length. Figures 11(a)
Fig. 11 Optical efficiencies of the two kinds of planar lightguide solar concentrators versus the geometrical concentration ratios when their dimple structures have different length-width ratios: (a) r = 25, (b) r = 15, and (c) r = 10. This figure shows how the optical efficiency of these two kinds of solar concentrators decreases when the lightguide length exceeds their ray-leakage-free length. The blue and red lines show results of the proposed sawtooth-shaped planar lightguide solar concentrators and Unger’s dimpled planar lightguide solar concentrators, respectively.
, 11(b), and 11(c) show the relation between the optical efficiency with a Cgeo of two kinds of solar concentrators when the dimple structures possess three different length-width ratios, r = 25, r = 15, and r = 10, respectively. In this discussion, we choose the microlens focal lengths as 24 mm at random. The blue and red lines plot the situations of the proposed sawtooth-shaped solar concentrator and Unger’s dimpled solar concentrator, respectively. Numerical results show that while two kinds of solar concentrators were constructed with the same geometrical concentration ratio Cgeo and with the same dimple structure, the proposed sawtooth-shaped solar concentrator can always achieve a better optical efficiency than Unger’s solar concentrator.

4.2 Concentration-acceptance product (CAP)

Geometric concentration ratio Cgeo and acceptance angle α are two important characteristics of solar concentrators, where the acceptance angle α is defined as the ray-incident angle at which the optical efficiency of concentrator drops by 10%. It is known that these two parameters are not independent; thus, another parameter CAP (Concentration-acceptance product) is used to show the performance of concentrators [13

13. P. Benítez, J. C. Miñano, P. Zamora, R. Mohedano, A. Cvetkovic, M. Buljan, J. Chaves, and M. Hernández, “High performance Fresnel-based photovoltaic concentrator,” Opt. Express 18(S1), A25–A40 (2010). [CrossRef]

]. The CAP value is defined as:
CAP=Cgeosinα.
(18)
Equation (18) shows that a good concentrator will possess high CAP value. Figure 12
Fig. 12 Concentration-acceptance product (CAP) of the ray-leakage-free planar lightguide solar concentrators; while their dimple structures have different length-width ratios: (a) r = 25, (b) r = 15 and (b) r = 10. The black lines indicate the models of the ray-leakage-free sawtooth-shaped concentrators constructed in section 4.1. And the blue lines show the corresponding CAP value of each concentrator.
shows the corresponding CAP values of all ray-leakage-free sawtooth-shaped solar concentrators constructed in section 4.1. In Fig. 12, the black lines indicate the models of the ray-leakage-free sawtooth-shaped concentrators constructed in section 4.1, and the blue lines show the corresponding CAP value of each concentrator. The CAP values of all sawtooth-shaped concentrators are ranged between 0.093 and 0.189.

Figure 12 shows that using a lens array of a shorter focal length in the proposed sawtooth-shaped concentrator can make the proposed sawtooth-shaped concentrator a higher CAP value because, while using the microlens of a small focal length, the tilted incident ray will cause a less focal shift at the injection element. Also, a large focal shift at the injection element that departs from the injection element will lead to the decoupled loss (ray leakages). In the proposed sawtooth-shaped planar lightguide solar concentrator, the focal length of lens array is limited by the TIR-condition at the tilted surface of the injection element. The CAP value of the sawtooth-shaped concentrator can be further increased by using mirror coating at the tilted surface of the injection element, while also using a lens array of shorter focal length.

Figure 13
Fig. 13 Efficiency versus the incident-ray tilted angle. The blue, red and black lines plot the result of three ray-leakage-free sawtooth-shaped concentrators while their dimple length-width ratio r and concentration ratio are: (r = 10, Cgeo = 240), (r = 15, Cgeo = 735), and (r = 25, Cgeo = 2000), respectively. The solid and dotted lines show the efficiencies of concentrators while the incident rays are tilted about the y-axis and x-axis, respectively.
plots the curve “efficiency versus incident-ray tilted angle” of three ray-leakage-free planar lightguide solar concentrators that possess the largest acceptance angle α, while their dimple structures have different length-width ratios (r = 25, r = 15, and r = 10). The solid and dotted lines show the efficiencies of concentrators, while the incident rays are tilted about the y-axis and x-axis, respectively. Figure 13 shows that as the dimple length-width ratio r increases, the acceptance angle of the ray-leakage-free sawtooth-shaped solar concentrator decreases. The acceptance angle of three concentrators: (r = 10, Cgeo = 240), (r = 15, Cgeo = 735) and (r = 25, Cgeo = 2000), are greater than ± 0.47°, ± 0.33° and ± 0.18°, respectively. Similarly, the acceptance angle of the sawtooth-shaped concentrator can be further increased by using mirror coating at the tilted surface of the injection element as well as using a lens array of shorter focal length.

4.3 Optical efficiency and solar spectrum response

The major concern of this study is preventing the most crucial loss of the planar lightguide solar concentrator, i.e. the ray leakage from the planar lightguide. Thus, numerical simulations of section 4.1 and 4.2 considered only the energy loss from the ray leakage from the lightguide, without including the other two major kinds of energy losses, i.e. Fresnel loss at each interface and the material absorption. Figure 14
Fig. 14 Real optical efficiencies of sawtooth-shaped planar lightguide solar concentrators when their dimple structures have different length-width ratios: (a) r = 25, (b) r = 15 and (c) r = 10. The simulation results shown in this figure include the Fresnel loss and the material absorption. The black lines indicate the models of the ray-leakage-free sawtooth-shaped concentrators that were constructed in section 4.1. Blue lines show the corresponding optical efficiency of each concentrator when the incident light is normally incident monochromatic light of wavelength 0.55 μm. Red lines show the corresponding optical efficiency of each concentrator when the incident light possesses ± 0.26° divergence angle and the Air Mass 1.5 Solar Spectrum [14].
shows the real optical efficiency of the ray-leakage-free sawtooth-shaped planar lightguide solar concentrator, while including Fresnel loss and material absorption in simulations. In the simulations of Fig. 14, the lens array has MgF2 AR coating on both side, and both lens array and lightguide include the absorption coefficient of the BK7, 3 × 10−6 cm−1. In Fig. 14, the black lines indicate the models of the ray-leakage-free sawtooth-shaped concentrators that were constructed in section 4.1. The blue and red lines show real optical efficiency of the sawtooth-shaped concentrators while the incident light are “vertically incident monochromatic light of wavelength 0.55 μm” and “light possessing ±0.26° divergence angle and the Air Mass 1.5 Solar Spectrum” [14], respectively.

The blue lines of Fig. 14 show the sum of the Fresnel loss and the material absorption of the sawtooth-shaped solar concentrator for a vertically incident monochromatic light. For vertically incident monochromatic light of wavelength 0.55 μm, the sawtooth-shaped solar concentrator can achieve concentration ratios: 2000x, 735x and 240x, without any ray leakage, while their dimple structures have different length-width ratios: r = 25, r = 15 and r = 10, respectively. The optical efficiencies of the three sawtooth-shaped concentrators are: 90.25%, 91.30% and 92.29%, respectively. The material absorption losses of the three sawtooth-shaped concentrators are only: 3.20%, 2.07% and 1.01%, respectively. The other energy losses are all coming from the Fresnel loss. The major Fresnel reflection loss occurs at the air/lightguide interface. Replacing the airspace between the lens array and the lightguide by a low-index guiding layer can reduce the Fresnel reflection loss at two air/material interfaces. The sum of the Fresnel reflection loss and material absorption of all sawtooth-shaped solar concentrators for a vertically incident light are all smaller than 10%, where the material absorption loss is around 1~3% and the Fresnel reflection loss is around 7%.

The red lines of Fig. 14 show the solar spectrum response of the sawtooth-shaped solar concentrator. The results show that for an on-axis incident sunlight (light possessing ± 0.26° divergence angle and the Air Mass 1.5 Solar Spectrum), the sawtooth-shaped solar concentrator can achieve concentration ratios: 2000x, 735x and 240x, and optical efficiencies: 69.6%, 85.9% and 90.7%, while their dimple structures have different length-width ratios: r = 25, r = 15, r = 10, respectively. The low optical efficiency of the (r = 25, Cgeo = 2000) sawtooth-shaped concentrator results from its concentrator acceptance angle ( ± 0.18°) being smaller than the divergence angle of sunlight ( ± 0.26°). The sawtooth-shaped concentrators possessing length-width ratio between r = 25 and r = 15 can still achieve both high concentration ratio and high optical efficiency.

5. Discussions and summary

In summary, this study details the design of a ray-leakage-free sawtooth-shaped planar lightguide solar concentrator. In this design, the combination of a sawtooth-shaped lightguide boundary and the dimpled structure horizontally constructs a “step-like” structure; thus, the lightguide structure successfully prevents light leakages from the planer lightguide. Besides, the use of the sawtooth-shaped boundary of the planar lightguide substantially decreases both the guiding ray reflection times and the propagating distance of guiding rays in the lightguide. Thus, the proposed planar lightguide solar concentrator can achieve a higher light concentration ratio while maintaining high optical efficiency. Using the design approach shown in this paper, one can construct ray-leakage-free planar lightguide solar concentrators with a high geometrical concentration ratio, and without any ray-leakage energy from the lightguide. Numerical results of this study show that for vertically incident monochromatic light of wavelength 0.55 μm, the sawtooth-shaped solar concentrator can achieve concentration ratios of 2300x, 750x and 310x, without any ray leakage, while their dimple structures have different length-width ratios: r = 25, r = 15 and r = 10, respectively. The totals of the Fresnel reflection loss and material absorption of the sawtooth-shaped solar concentrator for a vertically incident light of all sawtooth-shaped concentrators are smaller than 10%. For an on-axis incident sunlight (light possessing ± 0.26° divergence angle and the Air Mass 1.5 Solar Spectrum), the sawtooth-shaped solar concentrator can achieve concentration ratios of 2000x, 735x and 240x, and optical efficiencies of 69.6%, 85.9% and 90.7%, while their dimple structures have different length-width ratios: r = 25, r = 15 and r = 10, respectively.

In comparison with Selimoglu’s ray-leakage-free planar lightguide solar concentrator (Cgeo = 1000x, α = ± 1.0°, η = 96.5%) [10

10. O. Selimoglu and R. Turan, “Exploration of the horizontally staggered light guides for high concentration CPV applications,” Opt. Express 20(17), 19137–19147 (2012). [CrossRef] [PubMed]

], the (r = 15, f = 24mm) sawtooth-shaped solar concentrator seems to possess worse characteristics (Cgeo = 735x, α = ± 0.33°, η = 91.2%). However, the performance of the proposed sawtooth-shaped planar lightguide solar concentrator can easily be substantially improved. First, using secondary concentrator design (e.g. CPC) at the lightguide exit port can multiply the concentrator Cgeo right away. Second, from the discussion in section 4.2, it is known that using mirror coating at the tilted surface of the injection element accompanying with using a lens array of shorter focal length can substantially increase the concentrator acceptance angle α. The achievement of the high acceptance angle of Selimoglu’s concentrator actually resulted from setting the reflective injection surfaces with “ideal reflectors”. Third, replacing the airspace between the lens array and lightguide by a low-index guiding layer can reduce the Fresnel reflection loss at two air/material interfaces.

Acknowledgment:

This work was supported by the Industrial Technology Research Institute and Advanced Optoelectronic Technology Center, National Cheng Kung University, under projects from the Ministry of Education and the National Science Council (NSC 99-2112-M-006-007-MY3) and (NSC 102-2112-M-006 −006 -MY3) of Taiwan.

References and links

1.

B. L. Unger, G. R. Schmidt, and D. T. Moore, “Dimpled planar lightguide solar concentrators,” in Proceedings of International Optical Design Conference, (OSA, 2010), ITuE5P. [CrossRef]

2.

D. Feuermann and J. M. Gordon, “High-concentration photovoltaic designs based on miniature parabolic dishes,” Sol. Energy 70(5), 423–430 (2001). [CrossRef]

3.

Z. Hongfei, T. Tao, D. Jing, and K. Huifang, “Light tracing analysis of a new kind of trough solar concentrator,” Energy Convers. Manage. 52(6), 2373–2377 (2011). [CrossRef]

4.

V. Wittwer, W. Stahl, and A. Goetzberger, “Fluorescent Planar Concentrators,” Sol. Energy Mater. 11(3), 187–197 (1984). [CrossRef]

5.

J. C. Goldschmidt, M. Peters, A. Bosch, H. Helmers, F. Dimroth, S. W. Glunz, and G. Willeke, “Increasing the efficiency of fluorescent concentrator systems,” Sol. Energy Mater. Sol. Cells 93(2), 176–182 (2009). [CrossRef]

6.

J. H. Karp, E. J. Tremblay, J. M. Hallas, and J. E. Ford, “Orthogonal and secondary concentration in planar micro-optic solar collectors,” Opt. Express 19(S4Suppl 4), A673–A685 (2011). [CrossRef] [PubMed]

7.

J. H. Karp, E. J. Tremblay, and J. E. Ford, “Planar micro-optic solar concentrator,” Opt. Express 18(2), 1122–1133 (2010). [CrossRef] [PubMed]

8.

M. Brown, D. Moore, G. Schmidt, and B. Unger, “Measurement and Characterization of Dimpled Planar Light Guide Prototypes,” in Proceedings of International Optical Design Conference, (OSA, 2010), JMB45P. [CrossRef]

9.

D. Moore, G. R. Schmidt, and B. Unger, “Concentrated photovoltaic stepped planar light guide,” in Proceedings of International Optical Design Conference, (OSA, 2010), JMB46P. [CrossRef]

10.

O. Selimoglu and R. Turan, “Exploration of the horizontally staggered light guides for high concentration CPV applications,” Opt. Express 20(17), 19137–19147 (2012). [CrossRef] [PubMed]

11.

S.-C. Chu, H.-Y. Wu, and H.-H. Lin, “Planar lightguide solar concentrator,” Proc. SPIE 8438, 843810, 843810-7 (2012). [CrossRef]

12.

Software LightTools, See website: http://www.opticalres.com/lt/ltprodds_f.html.

13.

P. Benítez, J. C. Miñano, P. Zamora, R. Mohedano, A. Cvetkovic, M. Buljan, J. Chaves, and M. Hernández, “High performance Fresnel-based photovoltaic concentrator,” Opt. Express 18(S1), A25–A40 (2010). [CrossRef]

14.

See website: http://rredc.nrel.gov/solar/spectra/am1.5/

15.

G. E. Engineering Thermoplastics Design Guide, See website: http://www.pdnotebook.com/wp-content/themes/thesis_18/custom/images/GE_plastic_design.pdf

16.

Design Guidelines – DSM, See website: http://www.dsm.com/en_US/downloads/dep/designbroch05USweb.pdf

OCIS Codes
(220.1770) Optical design and fabrication : Concentrators
(230.7400) Optical devices : Waveguides, slab
(350.6050) Other areas of optics : Solar energy

ToC Category:
Solar Energy

History
Original Manuscript: June 14, 2013
Revised Manuscript: August 4, 2013
Manuscript Accepted: August 6, 2013
Published: August 19, 2013

Citation
Hong-Yu Wu and Shu-Chun Chu, "Ray-leakage-free sawtooth-shaped planar lightguide solar concentrators," Opt. Express 21, 20073-20089 (2013)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-17-20073


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References

  1. B. L. Unger, G. R. Schmidt, and D. T. Moore, “Dimpled planar lightguide solar concentrators,” in Proceedings of International Optical Design Conference, (OSA, 2010), ITuE5P. [CrossRef]
  2. D. Feuermann and J. M. Gordon, “High-concentration photovoltaic designs based on miniature parabolic dishes,” Sol. Energy70(5), 423–430 (2001). [CrossRef]
  3. Z. Hongfei, T. Tao, D. Jing, and K. Huifang, “Light tracing analysis of a new kind of trough solar concentrator,” Energy Convers. Manage.52(6), 2373–2377 (2011). [CrossRef]
  4. V. Wittwer, W. Stahl, and A. Goetzberger, “Fluorescent Planar Concentrators,” Sol. Energy Mater.11(3), 187–197 (1984). [CrossRef]
  5. J. C. Goldschmidt, M. Peters, A. Bosch, H. Helmers, F. Dimroth, S. W. Glunz, and G. Willeke, “Increasing the efficiency of fluorescent concentrator systems,” Sol. Energy Mater. Sol. Cells93(2), 176–182 (2009). [CrossRef]
  6. J. H. Karp, E. J. Tremblay, J. M. Hallas, and J. E. Ford, “Orthogonal and secondary concentration in planar micro-optic solar collectors,” Opt. Express19(S4Suppl 4), A673–A685 (2011). [CrossRef] [PubMed]
  7. J. H. Karp, E. J. Tremblay, and J. E. Ford, “Planar micro-optic solar concentrator,” Opt. Express18(2), 1122–1133 (2010). [CrossRef] [PubMed]
  8. M. Brown, D. Moore, G. Schmidt, and B. Unger, “Measurement and Characterization of Dimpled Planar Light Guide Prototypes,” in Proceedings of International Optical Design Conference, (OSA, 2010), JMB45P. [CrossRef]
  9. D. Moore, G. R. Schmidt, and B. Unger, “Concentrated photovoltaic stepped planar light guide,” in Proceedings of International Optical Design Conference, (OSA, 2010), JMB46P. [CrossRef]
  10. O. Selimoglu and R. Turan, “Exploration of the horizontally staggered light guides for high concentration CPV applications,” Opt. Express20(17), 19137–19147 (2012). [CrossRef] [PubMed]
  11. S.-C. Chu, H.-Y. Wu, and H.-H. Lin, “Planar lightguide solar concentrator,” Proc. SPIE8438, 843810, 843810-7 (2012). [CrossRef]
  12. Software LightTools, See website: http://www.opticalres.com/lt/ltprodds_f.html .
  13. P. Benítez, J. C. Miñano, P. Zamora, R. Mohedano, A. Cvetkovic, M. Buljan, J. Chaves, and M. Hernández, “High performance Fresnel-based photovoltaic concentrator,” Opt. Express18(S1), A25–A40 (2010). [CrossRef]
  14. See website: http://rredc.nrel.gov/solar/spectra/am1.5/
  15. G. E. Engineering Thermoplastics Design Guide, See website: http://www.pdnotebook.com/wp-content/themes/thesis_18/custom/images/GE_plastic_design.pdf
  16. Design Guidelines – DSM, See website: http://www.dsm.com/en_US/downloads/dep/designbroch05USweb.pdf

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