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Energy Express

  • Editor: Christian Seassal
  • Vol. 22, Iss. S2 — Mar. 10, 2014
  • pp: A198–A204
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Design of a lens-to-channel waveguide system as a solar concentrator structure

Yuxiao Liu, Ran Huang, and Christi K. Madsen  »View Author Affiliations


Optics Express, Vol. 22, Issue S2, pp. A198-A204 (2014)
http://dx.doi.org/10.1364/OE.22.00A198


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Abstract

We present a lens-to-channel waveguide solar concentrator, where the lens array and the channel waveguide act as the primary and the secondary concentrator. Sunlight collected by the lens array is coupled into channel waveguides and exits from one end of the tapered waveguide directly onto photovoltaic cells. A 45° coupler is placed at each lens focal point to couple light into the waveguides. This configuration eliminates any inherent decoupling losses. We provide a detailed math model and simulation results using exemplar system parameters, showing that this structure can achieve 800x concentration at 89.1% optical efficiency under ±0.7° incidence angle.

© 2014 Optical Society of America

1. Introduction

A solar concentrator typically uses a large area optical structure to focus sunlight onto a small area so that high output irradiance can be generated. Ever since the III-V multijunction solar cells were developed, intense investigation has been done regarding to photovoltaic concentrators (CPVs). A CPV projects the concentrated sunlight onto small photovoltaic (PV) cells to reduce the total cost by replacing expensive PV cells with cheap concentrator materials, as well as to get a very high efficiency. III–V multijunction PV cells with efficiencies in excess of 40% under concentrated sunlight have been reported [1

1. A. Luque and S. Hegedus, Handbook of Photovoltaic Science and Engineering, 2nd ed. (John Wiley, 2011), Chap. 8.

]. The final goal of a CPV system is to provide sustainable, highly efficient and cost effective electricity.

A fundamental CPV design is to use a lens array, each concentrating the sunlight directly onto a separated PV cell. Such designs may bring non-uniformity, cooling and connection issues. A new approach of CPV systems was proposed by Karp et al. in 2010 for a planar concentrating structure [2

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

], where those PV cells are replaced by a single slab waveguide. Sunlight is coupled into the waveguide by a series of microstructure at each focal point of the lenses. Then the coupled light travels inside the slab waveguide by total internal reflections (TIRs) and finally exits from both edges directly onto PV cells. 82% theoretical optical efficiency is achieved at 300x concentration under 0.26°incidence angle [2

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

]. Several other designs use similar ideas [3

3. 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(S4), A673–A685 (2011). [CrossRef] [PubMed]

7

7. J. H. Karp and J. E. Ford, “Planar micro-optic solar concentration using multiple imaging lenses into a common slab waveguide,” Proc. SPIE 7407, 74070D (2009). [CrossRef]

]. However, there is an inherent loss mechanism by which light already in the waveguide is decoupled by subsequent couplers, leading to decreased optical efficiency. This decoupling loss is inevitable and a higher concentration ratio or larger tolerance angle will further enhance the loss mechanism. The three-dimensional concentration from the lens array is also lost due to the large thickness of the slab waveguide. Arizono et al. proposed an alternative design where the input end is replaced by multiple branches [8

8. K. Arizono, R. Amano, Y. Okuda, and I. Fujieda, “A concentrator photovoltaic system based on branched planar waveguides,” Proc. SPIE 8468, 84680K (2012).

,9

9. I. Fujieda, K. Arizono, and Y. Okuda, “Design considerations for a concentrator photovoltaic system based on a branched planar waveguide,” J. Photonics Energy 2(1), 021807 (2012). [CrossRef]

]. Ray tracing results show 86.4% efficiency under 108x concentration. Their structure employs much more complex designs comparing to Karp’s due to the use of double TIR surfaces and therefore leads to reduced efficiency in fabrication. In this paper, we propose a novel lens-to-channel waveguide system as a solar concentrator structure. The lens and the tapered waveguide act as the primary and secondary concentrator, respectively. Couplers are placed only at one end of the waveguide to eliminate any decoupling loss in the waveguide. High concentration, efficiency and uniformity at the output end are realized by this simple structure. We study the design parameters and present a detail math model to explore the tradeoffs in this configuration.

2. The lens-to-channel waveguide system

3. Parameter designs and performance estimation

Assuming the lens array consists of only thin lenses (paraxial approximation), a spot sized=2ftanδM will be formed at each lens focal point if the incoming light field has a half angle δM (Fig. 2).
Fig. 2 The aberration-free lens focuses incoming light onto its paraxial image plane.
The geometric concentration ratio Cl of the lens is
Cl=(Dd)2=1[2(f/D)tanδM]2;
(3)
and the marginal ray angle θM after the lens,
θM=arctan[tanδM+12(f/D)].
(4)
We define the f-number (F/#) as the ratio between the lens paraxial focal length f and the lens diameter D. The output of the lens array is therefore totally determined by δM and F/#. As previously stated, C1=0.5Cl is the fundamental concentration factor of the structure.

The main loss mechanisms in our structure include coupling loss, propagation loss and Fresnel reflection loss. We begin our discussion by evaluating the coupler design. An angled waveguide/air TIR coupler interface is placed at each focal point of the lens array, which acts as a turning mirror redirecting light after the lens into the waveguide. Since TIR is not wavelength sensitive, the coupler can cover a broad range of the solar spectrum. The coupling efficiency ηC depends on the marginal ray angle θM and the waveguide core material refractive index nw. Consider a beam of light θ after the lens (θMθθM). It will be first refracted at the air/cladding/waveguide interface before hitting the coupler. According to Snell’s law, sinθ=nwsinγ. We express the light ki=k(sinγcosΩ,cosγ,sinγsinΩ) using angle definitions in Fig. 3(a).
Fig. 3 (a) Each coupler is a tilted waveguide/air interface. (b) An illustrative plot of the reflection angles in XZ plane ϕx0=arctan(kx0/kz0) and YZ plane ϕy0=arctan(ky0/kz0). Each ellipse represents a reflection angle range for one particular coupler angle β. It is clear that the 45°coupler yields the minimum angles in both planes.
Only light with incidence angle larger than the critical angle can be coupled into the waveguide. Meanwhile, the reflected light kr=(kx0,ky0,kz0) is
kr=k(sinγcosΩ,cosθy1sin2γcos2Ω,sinθy1sin2γcos2Ω),
(5)
where θy=2βarctan(tanγsinΩ). Since both ky0 and kz0 are a function of 2β, β=45° is a unique angle leading to a symmetrical profile as shown in Fig. 3(b). Both of the reflection angles in XZ and YZ planes reach the minimum value. We stress that any other angles will require a larger waveguide numerical aperture (NA) to confine the reflected light. Consequently a coupler angle β=45° is always desired. Assuming the change of the spot size in the waveguide material (comparing to air) is negligible, the minimum waveguide thickness is t=dC.

We evaluate the waveguide propagation loss in the fundamental part by inspecting one waveguide unit (Fig. 4).
Fig. 4 One waveguide unit cell of the concentrator.
Consider a light ray with an angle δ entering at lens P(δMδδM, 1PN). Assuming the reflected light is kr=(kx0,ky0,kz0), the total distance for a specific light ray travels in the fundamental waveguide can be expressed as
LP(P,Ω,δ)=[(P1)+1/2]D×cosΘkz0/|kr|.
(6)
The propagation loss is estimated as the exponential decay of the distance multiplied by the waveguide material absorption coefficient α, ηP=<pδMδM02πexp(αLP)dΩdδ>. After entering the tapered waveguide structure, however, the light kr=(kx0,ky0,kz0) gains 2σ in XZ plane propagation angle every time it hits the sidewalls. In other words, the light angular space becomes larger as additional concentration is achieved. The total distance LT in the tapered waveguide the light travels can be expressed as
LT(Ω,δ)=W0×cos(ϕ0σ)cos2(ϕ0σ)4lNtanσ+4lN2tan2σ2sinσ×(kx02+kz02)/|k|2,
(7)
where ϕ0 is the reflected light initial angle in the XZ plane. Similarly, the propagation loss in the tapered waveguide is estimated as ηT=δMδM02πexp(αLT)dΩdδ. Combining all the losses discussed above, we express the total optical efficiency as η=ηR×ηC×ηP×ηT,where ηR represents the total Fresnel reflection losses.

4. Simulation results and discussion

As an example, we simulate an 800x concentration system performance under different tolerance angles and f-numbers. The waveguide material is assumed to be F2 glass (nw=1.64,α=1.8×104cm1), with an air cladding and a silica substrate (ns=1.46, nc=1). Each of the lenses has a diameter of 1mm. An index-matching detector space is assumed and Fresnel reflection is intentionally neglected. Figure 5(a) illustrates the optical efficiency dependence on f-numbers under different maximum incident angles. The left portion of the increasing efficiency is coupler TIR limited in that the marginal ray angle is large under small f-numbers and there is light with angles exceeding the critical angle at the coupler surface. The coupler surface is the limiting factor in these scenarios. If these surfaces are replaced by reflective metal layers, the limiting factor would become the waveguide/substrate interface, i.e. the waveguide NA, instead. The right portion of the decreasing efficiency, in contrast, is determined by the tapered waveguide concentration ability. Since larger f-numbers bring smaller marginal ray angles as well as small concentration, it requires more concentration from the tapered waveguide part. When it reaches the maximum waveguide concentration, the efficiency begins to drop. There exists an optimum f-number for a particular system. As can be read from Fig. 5(a), for all tolerance angles smaller than 0.55° (note the solar angular width is ±0.26°), there is no inherent loss in the structure, which is much better than the 60% (or 84% for the orthogonal structure) in Karp’s designs [2

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

,3

3. 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(S4), A673–A685 (2011). [CrossRef] [PubMed]

].
Fig. 5 (a) An exemplar plot of optical efficiency under different f-numbers and tolerance angles, whereα=1.8×104cm1, nw=nd=1.64, ns=1.46 andnc=1. (b) The performance of the waveguide concentrator. The efficiency remains the same until C2~7.9.

It is worth noting that the incident angle in the YZ plane δMYZ is always the limiting factor comparing to that in the XZ plane δMXZ since the maximum incident angle at the coupler interface is determined by δMYZ (the normal of the coupler surface is in the YZ plane) and the critical angle at the waveguide/substrate interface is much smaller than those at other interfaces. It indicates the proposed structure is promising for one-axis tracking. Active tracking may be implemented for the YZ plane while passive tracking can be used for the XZ plane. The same tracking configuration using a micro-tracking lateral translation stage can be adopted from [10

10. K. Baker, J. Karp, J. Hallas, and J. Ford, “Practical implementation of a planar micro-optic solar concentrator,” Proc. SPIE 8485, 848504 (2012).

]. The detailed discussion is beyond the scope of this paper and will be presented in the future.

In order to explore the maximum concentration can be generated by the tapered waveguide, Fig. 5(b) shows the efficiency plot based on a given f-number (F/#=3) and incident angle (δM=±0.7°). It turns out that the efficiency begins to drop at around 7.9x concentration, which is approaching to the 2D etendue limit 9.3x. The maximum waveguide concentration would be achieved when the output light angle is the critical angle θc, which can be expressed as
C2max=112lNtanσ=cosθcsin(ϕ0M+σ)cosθcsinϕ0M,
(8)
where ϕ0M is the maximum reflected half angle. Recall the ideal 2D concentrationC2Dideal=1/sinϕ0M [11

11. W. T. Welford and R. Winston, The Optics of Nonimaging Concentrators (Academic, 1978), Chap. 2.

]. Equation (8) indicates that the tapered waveguide can be viewed as a near-ideal concentrator. If the critical angle is small, its concentration ability would approach to the 2D etendue limit.

Using Eqs. (3), (4) and (8), we can estimate the upper limit of the concentration ratio without considering any coupling losses. The two concentration stages, C1max and C2max can be respectively expressed as
C1max=12[2(f/D)tanδM]2,
(9)
C2maxcosθcsinϕ0Mnwcosθcsin{arctan[tanδM+12(f/D)]}.
(10)
Fig. 6 An exemplar plot of the estimated maximum concentration as a function of f-numbers and tolerance angles, wherenw=1.64.
The total concentration Cmax=C1max×C2maxis therefore a function of δM and F/#=f/D. Given the waveguide material nw, the maximum achievable concentration is calculated using Eqs. (9) and (10). An exemplar plot using parameters in Fig. 5(a) is shown in Fig. 6, which corresponds to the right part (waveguide limited) in Fig. 5(a). Note the small F/# region is hard to realize since its large angle will finally be limited by the TIR conditions at the coupler interface (left portion in Fig. 5(a)).

We also perform a ray tracing simulation using ZEMAX to explore the practical performance of the system at 800x. An ideal blackbody source from 400nm to 1900nm at 5777K with ±0.7° incidence angle is set as the light source to simulate the incoming useful sunlight. The3×12,D=1mmlens array is made of BK7 glass and each lens is optimized to yield the minimum spot size. An anti-reflection layer MgF2 is deposited on the top surface of the lens array. The input surface area is 3mm*12mm, while the output area is 0.083mm*0.54mm (C1=145x,C2=5.6x). All the losses including scattering, Fresnel reflections and material absorptions are accounted for. Since the Fresnel reflection loss at the air/waveguide surface is a severe problem resulting from the big refractive index difference between F2 and air, a layer of PDMS is inserted between the waveguide and the lens array to eliminate the air gap. It acts as both an index matching medium and a supporting structure for the lens array. We simulate this optimized structure in ZEMAX. The Fresnel reflection loss is reduced while the propagation loss increases by ~2% due to the absorption peaks of PDMS [12

12. S. Kopetz, D. Cai, E. Rabe, and A. Neyer, “PDMS-based optical waveguide layer for integration in electrical–optical circuit boards,” AEU Int. J. Electron. Commun. 61(3), 163–167 (2007). [CrossRef]

]. A total optical efficiency of 89.1% is achieved for this 800x system with uniform output. Table 1 shows the loss chart of the optimized practical system.

Table 1. Efficiency Chart for the Optimized Practical Setup

table-icon
View This Table

5. Conclusion

We propose a lens-to-channel waveguide concentrator system which avoids any inherent decoupling loss in the waveguide. Detailed math models both for concentration calculation and optical efficiency estimation are provided using geometric optics analysis. Simulation results indicate that a coupler angle β=45° is the best to achieve high efficiency as well as maximum waveguide concentration. ZEMAX simulations provide an optimized structure with an index matching layer, showing 89.1% optical efficiency at 800x for a practical setup.

References and links

1.

A. Luque and S. Hegedus, Handbook of Photovoltaic Science and Engineering, 2nd ed. (John Wiley, 2011), Chap. 8.

2.

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

3.

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(S4), A673–A685 (2011). [CrossRef] [PubMed]

4.

W. C. Shieh and G. D. Su, “Compact solar concentrator designed by minilens and slab waveguide,” Proc. SPIE 8108, 81080H (2011). [CrossRef]

5.

S. Bouchard and S. Thibault, “Planar waveguide concentrator used with a seasonal tracker,” Appl. Opt. 51(28), 6848–6854 (2012). [CrossRef] [PubMed]

6.

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

7.

J. H. Karp and J. E. Ford, “Planar micro-optic solar concentration using multiple imaging lenses into a common slab waveguide,” Proc. SPIE 7407, 74070D (2009). [CrossRef]

8.

K. Arizono, R. Amano, Y. Okuda, and I. Fujieda, “A concentrator photovoltaic system based on branched planar waveguides,” Proc. SPIE 8468, 84680K (2012).

9.

I. Fujieda, K. Arizono, and Y. Okuda, “Design considerations for a concentrator photovoltaic system based on a branched planar waveguide,” J. Photonics Energy 2(1), 021807 (2012). [CrossRef]

10.

K. Baker, J. Karp, J. Hallas, and J. Ford, “Practical implementation of a planar micro-optic solar concentrator,” Proc. SPIE 8485, 848504 (2012).

11.

W. T. Welford and R. Winston, The Optics of Nonimaging Concentrators (Academic, 1978), Chap. 2.

12.

S. Kopetz, D. Cai, E. Rabe, and A. Neyer, “PDMS-based optical waveguide layer for integration in electrical–optical circuit boards,” AEU Int. J. Electron. Commun. 61(3), 163–167 (2007). [CrossRef]

OCIS Codes
(220.1770) Optical design and fabrication : Concentrators
(230.7380) Optical devices : Waveguides, channeled
(350.6050) Other areas of optics : Solar energy
(080.2175) Geometric optics : Etendue

ToC Category:
Waveguide Concentrators

History
Original Manuscript: December 2, 2013
Revised Manuscript: January 5, 2014
Manuscript Accepted: January 6, 2014
Published: January 15, 2014

Virtual Issues
Renewable Energy and the Environment (2014) Optics Express

Citation
Yuxiao Liu, Ran Huang, and Christi K. Madsen, "Design of a lens-to-channel waveguide system as a solar concentrator structure," Opt. Express 22, A198-A204 (2014)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-22-S2-A198


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References

  1. A. Luque and S. Hegedus, Handbook of Photovoltaic Science and Engineering, 2nd ed. (John Wiley, 2011), Chap. 8.
  2. J. H. Karp, E. J. Tremblay, and J. E. Ford, “Planar micro-optic solar concentrator,” Opt. Express18(2), 1122–1133 (2010). [CrossRef] [PubMed]
  3. 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(S4), A673–A685 (2011). [CrossRef] [PubMed]
  4. W. C. Shieh and G. D. Su, “Compact solar concentrator designed by minilens and slab waveguide,” Proc. SPIE8108, 81080H (2011). [CrossRef]
  5. S. Bouchard and S. Thibault, “Planar waveguide concentrator used with a seasonal tracker,” Appl. Opt.51(28), 6848–6854 (2012). [CrossRef] [PubMed]
  6. S. C. Chu, H. Y. Wu, and H. H. Lin, “Planar lightguide solar concentrator,” Proc. SPIE8438, 843810 (2012). [CrossRef]
  7. J. H. Karp and J. E. Ford, “Planar micro-optic solar concentration using multiple imaging lenses into a common slab waveguide,” Proc. SPIE7407, 74070D (2009). [CrossRef]
  8. K. Arizono, R. Amano, Y. Okuda, and I. Fujieda, “A concentrator photovoltaic system based on branched planar waveguides,” Proc. SPIE8468, 84680K (2012).
  9. I. Fujieda, K. Arizono, and Y. Okuda, “Design considerations for a concentrator photovoltaic system based on a branched planar waveguide,” J. Photonics Energy2(1), 021807 (2012). [CrossRef]
  10. K. Baker, J. Karp, J. Hallas, and J. Ford, “Practical implementation of a planar micro-optic solar concentrator,” Proc. SPIE8485, 848504 (2012).
  11. W. T. Welford and R. Winston, The Optics of Nonimaging Concentrators (Academic, 1978), Chap. 2.
  12. S. Kopetz, D. Cai, E. Rabe, and A. Neyer, “PDMS-based optical waveguide layer for integration in electrical–optical circuit boards,” AEU Int. J. Electron. Commun.61(3), 163–167 (2007). [CrossRef]

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