Abstract

A novel tapered dielectric waveguide solar concentrator is proposed for compound semiconductor solar cells utilizing optical fiber preform. Its light collecting capability is numerically simulated and experimentally demonstrated for feasibility and potential assessments. Utilizing tapered shape of an optical fiber preform with a step-index profile, low loss guidance was enhanced and the limitation in the acceptance angle of solar radiation was alleviated by an order of magnitude. Using a solar simulator the device performances were experimentally investigated and discussed in terms of the photocurrent improvements. Total acceptance angle exceeding ± 6° was experimentally achieved sustaining a high solar flux.

©2010 Optical Society of America

Introduction

Solar energy is arriving on the surface of the earth, which spreads from UV to IR with a maximum irradiance of 1.0 mW/mm2 under clear whether condition with the sun high in the sky at medium latitude, corresponded to 1 sun. In order to increase the irradiance of the solar energy and simultaneously enhance the conversion-efficiency in the photovoltaic cells, solar concentrators are widely used and intensively investigated for many years. In comparison to conventional Fresnel lens systems [1] and conical reflecting mirrors [2], dielectric concentrators have been mainly based on the total internal reflection (TIR) over their parabolic surfaces to provide a flow of solar flux in the axial direction. There have been various efforts to utilize the dielectric concentrator as an integrated optical solution to combine the primary and secondary concentrators. Recently dielectric micro-concentrators for the primary concentrator application have been experimentally demonstrated [3], in contrast to previous applications of dielectric concentrators as the secondary optics along with a separate primary concentrator [4, 5]. In order to further enhance collection efficiency in the compound parabolic concentrators (CPCs), the entrance aperture of truncated concentrators has been modified in an arc shape [6], which still suffered from complicated structures despite improved aspect ratios.

Inhomogeneous index distributions within the CPCs have been also proposed to obtain higher concentration ratios than homogenous single material CPCs [7, 8]. Despite strong potential in the efficient solar flux guiding along the core and excellent capability to modify scale of taper, the tapered dielectric waveguide with a core/clad structure has not been fully investigated for solar concentrator application mainly due to hardness of fabrication. Recent culmination of optical fiber technology has provided advanced capability to manipulate glass or polymers for optical waveguides with arbitrary refractive index profiles and taper shapes. For solar energy applications, most technologies of optical fiber have been mainly limited to the solar flux delivery from a primary concentrator to a solar cell [9, 10]. We believe that optical fiber technology can be directly applied to the concentrator as well the solar flux delivery.

In this paper, a new type of dielectric tapered waveguide solar concentrator (TWSC) is proposed and experimentally demonstrated. It consists of the core and cladding structure along with an adiabatic taper based on silica optical fiber preform. The proposed TWSC device can provide a strong potential to simultaneously improve solar flux guidance with a low loss, and alleviate the solar radiation acceptance angle in the tracking system.

2. Device structure and its parameters

In terms of material choice, we adopted silica glass for the proposed device demonstration. Glass materials for TWSC have definite advantages over polymers such as a higher reliability in optical and mechanical properties at an intense solar flux [11]. Due to highly advanced development in optical fiber fabrication technology, various size of optical fiber performs are available along with flexible core refractive index profile control. Tapering and elongation of silica optical fiber performs are routinely performed in optical fiber fabrication process using a graphite resistance furnace or an oxy-hydrogen torch.

Schematic diagram of the proposed TWSC is shown in Fig. 1(a) . TWSC was made from a segment of optical fiber perform fabricated by modified chemical vapor deposition (MCVD) followed by a tapered process. As depicted in Fig. 1(a), the preform was tapered down using a high temperature oxy-hydrogen in a glass working lathe. Both end-faces of the TWSC were clearly polished to minimize scattering loss. The pristine preform was provided by LS cable co. and it had a step-index profile composed of three layers; the GeO2-SiO2 core, GeO2-P2O5-F co-doped inner cladding and silica outer cladding. The result of laser scanning shows the index profile of the preform in Fig. 1(b). The central dip in Fig. 1(b) is one of common features observed in optical fiber preform fabricated by MCVD process, which is caused by vaporization of GeO2 during the sealing process [12]. The diameter of the whole preform and the core were 33.5 and 9.8 mm, respectively. The inner cladding region ranged from 4.9 to 11.7 mm and its refractive index is nearly matched to that of silica outer cladding. The core composed of GeO2-SiO2 composition provided a step-index waveguide structure with an average relative index difference of 0.313%. One of the preform ends was adiabatically tapered to have a diameter variation from 33.5 down to 11.6mm. The variation of the diameter along the taper is shown in Fig. 1(c).

 

Fig. 1 (a) Structure of the proposed tapered waveguide solar concentrator (TWSC). (b) Index profile of the TWCS in Fig. 1(a). Index difference between core and cladding is given by 0.313% at the wavelength of 635 nm (c) outer diameter variation along the adiabatic taper.

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3. Non-imaging optical simulation for proposed solar concentrator

Parametric analyses were performed for the key waveguide elements such as the core refractive index, core diameter, and TWCS length of the proposed TWSC as shown in Fig. 1. The irradiance and the total power from the tapered end of TWSC were calculated for various tilt angles using a ray tracing method using LightToolsTM. The set-up in the simulation is shown in Fig. 2(a) , where we assumed a 0.5° Lambertian disk source and air mass 1.5G spectrum [13] to reproduce the radiation from sun on the earth in clear sky. Diffused light sources in the atmosphere were not included in the analysis in order to focus on the assessment of the proposed device’s solar concentrating capability and only the direct light from the sun was assumed in the calculation.

 

Fig. 2 (a) Schematic of simulation set-up. Rays are concentrated on the red circle on an entrance aperture. (b) Spectra of incident light and output result. Black squares are solar spectrum of AM 1.5G, and red circles are spectrum of the result.

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In the calculation, a normal incidence of 1 Watt sun light was assumed at the entrance aperture of the TWSC. The corresponding incident irradiance was 1.14 mW/mm2, which is about 1 sun. A 12 mm x 12 mm square detecting surface was placed 0.5 mm apart from the TWSC entrance to measure power of light through an exit aperture.

Refractive index of the core was calculated using Sellmeier equation for GeO2-SiO2 system as Eq. (1) [14].

ncore21=i=13[AiSiO2+χ(AiGeO2AiSiO2)]λ02λ02[liSiO2+χ(liGeO2liSiO2)]2
where A i SiO2, l i SiO2, A i GeO2 and l i GeO2 are the Sellmeier coefficients for the SiO2, GeO2, respectively. λ0 is a vacuum wavelength, and mole fraction of the GeO2 is given as χ. The index difference between GeO2-SiO2 core and SiO2 cladding increases linearly with the mole fraction, χ. The refractive index difference of the optical fiber preform shown in Fig. 1(a) corresponds to approximately 3 mole % of GeO2 doped SiO2 in the core. The refractive index of the inner cladding was nearly matched to that of silica outer cladding with very low dopant concentration and therefore both the inner and outer cladding were assumed to be silica in the simulations.

For a tapered concentrator without the core structure, the concentration ratio is known as A/A', where A is the area of entrance aperture, and A' is that of the exit aperture. In the case of Fig. 1(a), the fundamental concentration ratio without the core is about 8.3. But, if a concentrator has the core-cladding structure with ncore, and ncladding, then the maximum concentration ratio Cmax is given by [15]

Cmax=(nN.A.)2=1ncore2ncladding2
where N.A is numerical aperture on the entrance aperture of TWSC, and n' is the refractive indices of the outside medium. n' becomes 1 if the solar cell is butt-coupled through the air. Considering the index profile in Fig. 1(b), the maximum concentration ratio could reach up to 75. This estimation only accounts for the guided light through the core, yet it is about 9 times higher than the concentration ratio without core.

With the given simulation set-up shown in Fig. 2 and the proposed TWSC in Fig. 1(a), we firstly investigated the impacts of the core refractive index, maintaining the rest of parameters fixed. The irradiance profiles on the detection surface were calculated for three cases; (a) without core or equivalently GeO2 doping ratio χ = 0 mole %, (b) with the core of GeO2 doping ratio χ = 3 mole %, and (c) with the core of GeO2 doping ratio χ = 6 mole %. The results are summarized in Figs. 3(a) , 3(b), and 3(c), respectively. Even without the core as in Fig. 3(a), the TWSC showed significant concentration effects having the maximum irradiance of 60 mW/mm2, and the irradiance was confined in a relatively wide area, a circle within the radius of 2 mm along with a concentric ring shaped distribution. When the core was included with 3 mole % of GeO2 doping as in Fig. 3(b), the irradiance distribution drastically changed near the center of the detector plane especially. The peak irradiance nearly doubled to 106 mW/mm2 and the solar energy was highly confined within a circle with the radius of 0.3 mm. For further increase of GeO2 doping to 6 mole % in the core, the solar energy distribution showed a consistent trend with an increased maximum irradiance of 129 mW/mm2 confined to a smaller area with radius of 0.2mm. Comparison of these three cases is shown in Fig. 3(d) and its inset, where the increase of core refractive index by GeO2 doping resulted in a consistent increment of maximum irradiance along with a better confinement.

 

Fig. 3 Irradiance profiles of normal incidence in a unit of mW/mm2; (a) without core or equivalently GeO2 doping ratio χ = 0 mole %. (b) with the core of GeO2 doping ratio χ = 3 mole %. (c) with the core of GeO2 doping ratio χ = 6 mole %. (d) One dimensional irradiance profiles for different GeO2 doping levels at the line across the center. An inset shows maximum irradiances along with GeO2 doping ratio.

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The simulation results in Fig. 3 showed that the proposed TWSC with a high index core can concentrate the incident solar radiation more efficiently than the bare dielectric concentrator without the core. Note that this high confinement of the solar intensity within a circle of radius less than 1 mm would be optimal for III-V compound semiconductor solar cell applications. The irradiance distributions in Fig. 3 showed a significant variation within the confined spots. These fluctuations are mainly attributed to helical modes along the cladding. The tight confinement of the irradiance might result heating damage on the PV cells. In experiments we used a conventional metal-pin type heat sink, and we could not observe any malfunctions of the proposed device under laboratory environment.

The effects of the core radius have been also investigated for three cases a = 4.9 mm, 2a, and 1/2a as depicted in Fig. 4(a) , and the results are summarized in Figs. 4(b), 4(c), and 4(d), respectively. In the simulation the relative ratio of the core-cladding was maintained along the whole taper similar to Fig. 1(c). The main concern for the core variation was the device’s response to the tilt angle, which correspond to the angle between the angle of the normal irradiance from the light source and the TWSC axis. The total power from the tapered end was calculated as a function of the incident angles in the range from 0 to 10°, for various core refractive indices with 0, 3, and 6 mole percent GeO2 doping. Due to the scattering loss and rays exiting the critical angle in the taper the output power reaches to about 0.91 Watts, which corresponds to about 9% loss. The loss includes Fresnel reflection loss at the air-glass interface on both ends of TWSC, which amounts to ~8%. The acceptance angle of a solar concentrator has been defined to the maximum tilt angel of which the total output energy is dropped to 95% of the normal incidence value [1] or equivalently to 0.86 Watt.

 

Fig. 4 (a) Schematics of the TWSCs with various core sizes a = 11mm, 20, and 1/2 a. Total power at the tapered output of TWSC as a function of the incident angle for the TWSC; (b) with core radius = a, (c) core radius = 2a, (d) core radius = a/2.

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In Fig. 4(b) the response to the tilt angle was plotted for the core diameter of a = 9.8 mm and three refractive indices, 0, 3, and 6 mole % GeO2 doping in the core were investigated. It is noted that for the case of 0 mole % doping, the figure showed a significantly different slope near the tilt angle of 6°. When the core was included with 3 and 6 mole % GeO2 doping, the output power maintains its value until the acceptance angle of ~6.8°. The simulation results in Fig. 4(b), indicate that the upper limit of the acceptance angle increased from 6° to 6.8° by including the GeO2 doped core. Note that this acceptance angle range predicted in the proposed TWSC is an order of magnitude improvement compared with the acceptance angle of 0.37° provided by the current state of art Fresnel zone plate type solar concentrators [1].

In Figs. 4(c) and 4(d), we further investigated the effects of waveguides over the acceptance angle by varying the core radius by factor of 2 and 1/2, respectively. When the core radius was enlarged by factor of 2, further improvement of the acceptance angle was achieved especially for the 3 mole % GeO2 doping case, whose acceptance angle exceeded 7.2° as in Fig. 4(c). However when the core radius reduced to half, the impact of the core refractive indices became almost negligible as in Fig. 4(d). It is therefore predicted that the waveguide effects combined with the core radius and refractive index could significantly enhance the acceptance angle of a solar concentrator by orders of magnitude. It is also noted that there would exist optimal doping rate to maximize the acceptance angle as indicated by Fig. 4(c), where the 3 mole % doping case showed a larger acceptance angle than both the lower (χ = 0%) and higher (χ = 6%) doping cases. Further optimization of core parameters is being investigated by the authors to maximize the acceptance angle to alleviate systematic burden in solar tracking units.

In the proposed TWSC, the overall length exceeds 200 mm, which is comparable to focal length of prior diffractive or reflective solar concentrators. It would be an important factor to further reduce the aspect ratio of concentrators in the system and module level. The TWSC can be divided into two segments along the axial direction; the cylinder segment and the taper segment as indicated by Fig. 5(a) . We have investigated the impact of the lengths of the two segments and assess the capability to minimize the aspect ratio of TWSC. Due to high viscosity of silica preforms even in high temperature exceeding 2,000°C, changing taper section length is a much more difficult task than simply cutting the cylindrical length. We therefore fixed the taper section length to 71.6 mm as used in the experiments, and we investigated the impact of cylinder length, x, over the total power.

 

Fig. 5 (a) Structural parameters of TWSC in the axial direction; taper segment and cylinder segment. (b) Total power at the tapered output as a function of the incident angle for a TWSC without cylinder segment. The inlet shows numerical simulation results for all-silica TWSC without core. (c) Total power versus tilt angle for the TWSC. The core was doped with 3 mole % GeO2 and plots are overlaid for various cylinder segment lengths.

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In Fig. 5(b), we simulated a case where the cylinder segment was absent and TWSC is composed of only the taper segment. In contrast to the results in Fig. 4, inclusion of the high refractive index core did not alter the acceptance angle significantly and in fact it did decrease by ~0.5°. When there is no core such that TWSC is composed of all-silica, the cylinder segment did not play any role to change the acceptance angle as indicated by the inset of 
Fig. 5(b). Therefore the aspect ratio could be further reduced using only the taper segment in the case of all-silica TWSC without core. The silica can be replaced by other high refractive index material and small aspect ratio of TWSC with homogeneous composition is being investigated by the authors.

In the following simulations, effects of the cylinder segment length were further analyzed assuming the core structure as in Fig. 1(b) with 3 mole % GeO2 doping, and the results are summarized in Fig. 5(c). Here four different cylinder lengths were considered 0, 80, 100, and 134mm (as in Fig. 1(a)). It is noted that within the tilt angle of 3°, there was no distinction among different cylinder lengths and the impact of cylinder segment became dominant as the tilt increases further. For TWSCs with the core, the cylinder segment did increase the acceptance angle beyond 7° as shown in Fig. 5(c) and it is speculated that there would exist an optimal cylindrical segment length for a given waveguide structure with certain core radius and refractive index.

Through the detailed numerical analyses whose results are summarized in Figs. 3-5, we found significant advantages of the proposed TWCS with the core/clad structure over the homogeneous dielectric taper. In the homogenous dielectric taper, the core is absent and GeO2 concentration is 0%. By adding the core in the TWSC, we found significantly higher irradiance as in Fig. 3(d), along with a wider and more uniform power distribution as in 
Figs. 4(c), Fig. 5(c).

Another important parameter in the TWCS is the taper profile as shown in Fig. 1(c). A hyperbolic taper, or trumpet structured taper, has been regarded as one of ideal profiles [16] to conserve étendue. Figure 6 shows proposed TWSC can be approximated to a hyperbola in the exit ends to make it satisfy the étendue conservation conditions. In order to conserve the conditions, it is required in the hyperbolic concentrator to satisfy [17]:

2a2c=sinθ
where 2a is diameter of an actual exit aperture of a concentrator, and 2c is diameter of a virtual aperture. Note that 2c is the distance between two foci (F1, F2) of hyperbolas as depicted in Fig. 6(a). The θ is tangent angle of asymptotic line so that Eq. (3) can be rewritten as
ac=sin(tan1(ab))  (b=c2a2)
In Fig. 6(b), the actual taper profile of the proposed TWCS is overlaid with a hyperbolic curve by solid and dashed lines, respectively. The proposed TWCS taper profile was well fitted with a hyperbolic curve and the estimated parameters a, c were 5.8 and 20.8 mm, respectively, which gives a/c factor of 0.2788. Therefore we found that the proposed TWCS’s taper is well approximated to a hyperbolic profile, which is one of ideal concentrator profiles.

 

Fig. 6 (a) Schematic of a hyperbolic concentrator. Asymptotes are shown in dashed lines. F1 and F2 are foci of hyperbolic curves. (b) Solid line is the actual shape of the proposed TWSC and dashed line is a hyperbolic curve with a focal point placed at 20.8 mm from origin.

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4. Experimental results

In order to assess the potential and capability of the proposed TWSC, the optical fiber preform fabricated by MCVD process was tapered using an oxyhydrogen torch and the final dimension of the device is described in Figs. 1(a), 1(b). The end faces of the TWSC have been polished to reduce the scattering loss. The experimental setup is shown in Fig. 7 .

 

Fig. 7 (a) A solar simulator used in the experiment. (b) An experimental set-up. An III-V solar cell on heat sink is placed under the TWSC. (c) Schematic of the experiment. A numerical aperture of the TWSC is shown by a red cone.

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A solar simulator is designed to reproduce the sun with power of 1 sun (1 mW/mm2), and a screen is placed to block whole light except rays through the TWSC. Concentrated light through the TWSC is combined at a solar cell to generate photocurrent. Concentration power of the TWSC as a function of the incident angle was deduced by measuring the photocurrent from the solar cell. As depicted in Fig. 7, we used an III-V solar cell from Spectrolab, Inc. and a solar simulator (WXS-220S-L2) from Wacom Electric Co. Ltd. to measure concentration characteristics of the TWSC along with incident angles. An exit aperture of TWSC was butt-coupled to the solar cell with efficiency of 28.9% at ambient room temperature. The solar cell with a size of 10 mm x 10 mm was in contact with a base metal heat sink to maintain temperature condition. After alignment, the TWSC and solar cell were illuminated by the simulator with power of 1 sun and spectrum of AM 1.5G to measure the photocurrent and current density from solar cell. An exit aperture of the simulator can be tilt in various angles to test the angular tolerance.

The measured photocurrents versus voltages (I-V) characteristics at various angles are summarized in Fig. 8(a) . It is noted that the TWSC indeed provided 4 times higher current output at normal incidence angle (Angle 0°) than without the concentrator. This concentration ratio was less than theoretical estimation and the reduction was mainly attributed scattering loss at the input surface of TWCS. Optical quality polishing should improve the concentration ratio and further improvements are being pursued by the authors. Current density variation over the incident angle was also measured and the results are summarized in Fig. 8(b). Simulation results for TWCS with a 3 mole % GeO2 doped core were also overlaid in the figure, where the size of a detection surface was set to match the solar cell used in the experiments. Simulation in square dots showed an excellent agreement with experiments in circular dots. The inset of Fig. 8(b) is an enlarged graph for the incident angle from −10° to 10°. The current density over 95% of the peak value was maintained in the incident angle range from −6° to 6°. Note that in this interval, stable solar flux collection can be made without any mechanically tracking assistants.

 

Fig. 8 Results from an III-V group solar cell; (a) I-V curves along incident angles. (b) Current densities along incident angles. An inlet shows enlarged plots in the range of incident angles from −10° to 10°.

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In order to fully facilitate the acceptance angle in the proposed TWCS, a static system would not be appropriate and the device should be mounted on a tracking system. Within the 6 degree of acceptance angle, the solar flux maintained 95% of its peak value in the proposed TWCS, which can definitely reduce the mechanical loads in the linear translation and rotational motion control. It is highly possible that the tracking system can allow a buffer zone to maintain a certain level of output power during the recovery time for the system to back-up in the case of system failure.

4. Conclusion

A dielectric concentrator is proposed with a step-index core-cladding structure tapered in a hyperbolic profile for III-V semiconductor photovoltaic applications. The proposed device, tapered waveguide solar concentrator (TWCS), is based on unique combination of the germanosilicate core and the hyperbolic taper profile to enable a high confinement of solar flux over 100mW/mm2 within a circle of radius 0.3mm in theory. A wide acceptance angle over ±6∘ was also predicted, which is an order of magnitude larger than prior arts. Impacts of structural parameters such as core refractive index, core diameter, un-tapered cylinder length and taper profiles over the solar concentration performance were thoroughly analyzed to find that there would be existed optimal ranges for those parameters to further improve the solar concentration efficiency. In experiments a tapered optical fiber preform made of a germanosilicate core of and silica cladding was combined with a III-V semiconductor solar cell to generate a photo current 4 times enhancement and wide acceptance angle from -6° to 6°. Further improvements such as antireflection coating and high refractive index plastic material with low optical loss are being pursued by the authors to enhance photocurrents and reduce aspect ratio.

Acknowledgments

This work was supported in part by the NRF under Grant ROA-2008-000-20054-0, Grant R15-2004-024-00000-0, and Grant 2008-8-1893 (the European Community's Seventh Framework Programme [FP7/2007-2013] under Grant agreement n° 219299, Gospel), Grant 2009-8-1339, Grant 2009-0093823, in part by the ITEP under Grant 2009-8-0809, and in part by the Brain Korea 21 Project of the KRF. And authors thanks to Optomagic Co. who measures an index profile of the TWSC.

References and links

1. H. Lerchenmuller, A. Hakenjos, I. Heile, B. Burger, and O. Stalter, “From FLATCON pilot systems to the first power plant,” presented at the International conference on solar concentrators for the generation of electricity or hydrogen, El Escorial, Spain, 12–16, Mar. 2007.

2. S. Horne, G. Conley, J. Gordon, D. Fork, P. Meada, E. Schrader, and T. Zimmermann, “A solid 500 sun compound concentrator PV design,” in Proceedings of IEEE 4th World Conference on Photovoltaic Energy Conversion (Institute of Electrical and Electronics Engineers, New York, 2006), pp. 694–697.

3. O. Korech, J. M. Gordon, E. A. Katz, D. Feuermann, and N. Eisenberg, “Dielectric microconcentrators for efficiency enhancement in concentrator solar cells,” Opt. Lett. 32, 2789–2791 (2007). [CrossRef]   [PubMed]  

4. R. Winston and J. M. Gordon, “Planar concentrators near the étendue limit,” Opt. Lett. 30, 2617–2619 (2005). [CrossRef]   [PubMed]  

5. D. Jenkins, R. Winston, J. Bliss, J. O'Gallagher, A. Lewandowski, and C. Bingham, “Solar concentration of 50,000 achieved with output power approaching 1kW,” J. Sol. Energy Eng. 118, 141–145 (1996). [CrossRef]  

6. X. Ning, R. Winston, and J. O’Gallagher, “Dielectric totally internally reflecting concentrators,” Appl. Opt. 26, 300–305 (1987). [CrossRef]   [PubMed]  

7. A. Cutolo, L. Carlomusto, F. Reale, and I. Rendina, “Tapered and inhomogeneous dielectric light concentrators,” Appl. Opt. 29, 1353–1364 (1990). [CrossRef]   [PubMed]  

8. M. Blanc, J. Pollard, G. Marchand, and R. Henri, “Multi-directional non-imaging radiations concentrator and/or deconcentrator device,” US Patent 4697867 (1987).

9. D. Feuermann, J. M. Gordon, and M. Huleihil, “Solar fiber-optic mini-dish concentrators: first experimental results and field experience,” Sol. Energy 72, 459–472 (2002). [CrossRef]  

10. E. A. Katz, J. M. Gordon, W. Tassew, and D. Feuermann, “Photovoltaic characterization of concentrator solar cells by localized irradiation,” J. Appl. Phys. 100, 044514 (2006). [CrossRef]  

11. T. J. Suleski and R. D. Te Kolste, “Fabrication trends for free-space microoptics,” J. Lightwave Technol. 23, 633–646 (2005). [CrossRef]  

12. S. R. Nagel, J. B. Macchesney, and K. L. Walker, “An overview of the modified chemical vapor deposition (MCVD) process and performance,” IEEE J. Quantum Electron. 18, 459–476 (1982). [CrossRef]  

13. International Organization for Standardization, “Solar energy-Reference solar spectral irradiance at the ground at different receiving conditions-Part 1: Direct normal and hemispherical solar irradiance for air mass 1.5,” ISO9845, 1 (1992).

14. J. W. Fleming, “Dispersion in GeO2-SiO2 glasses,” Appl. Opt. 23, 4486–4493 (1984). [CrossRef]   [PubMed]  

15. R. Winston, J. C. Minano, and P. Benitez, Nonimaging optics (Elservier, New York, 2005), Chapt. 2.

16. R. Winston and W. T. Welford, “Geometrical vector flux and some new nonimaging concentrator,” J. Opt. Soc. Am. 69, 532–536 (1979). [CrossRef]  

17. J. M. Gordon, “Complementary construction of ideal nonimaging concentrators and its applications,” Appl. Opt. 35, 5677–5682 (1996). [CrossRef]   [PubMed]  

References

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  1. H. Lerchenmuller, A. Hakenjos, I. Heile, B. Burger, and O. Stalter, “From FLATCON pilot systems to the first power plant,” presented at the International conference on solar concentrators for the generation of electricity or hydrogen, El Escorial, Spain, 12–16, Mar. 2007.
  2. S. Horne, G. Conley, J. Gordon, D. Fork, P. Meada, E. Schrader, and T. Zimmermann, “A solid 500 sun compound concentrator PV design,” in Proceedings of IEEE 4th World Conference on Photovoltaic Energy Conversion (Institute of Electrical and Electronics Engineers, New York, 2006), pp. 694–697.
  3. O. Korech, J. M. Gordon, E. A. Katz, D. Feuermann, and N. Eisenberg, “Dielectric microconcentrators for efficiency enhancement in concentrator solar cells,” Opt. Lett. 32, 2789–2791 (2007).
    [Crossref] [PubMed]
  4. R. Winston and J. M. Gordon, “Planar concentrators near the étendue limit,” Opt. Lett. 30, 2617–2619 (2005).
    [Crossref] [PubMed]
  5. D. Jenkins, R. Winston, J. Bliss, J. O'Gallagher, A. Lewandowski, and C. Bingham, “Solar concentration of 50,000 achieved with output power approaching 1kW,” J. Sol. Energy Eng. 118, 141–145 (1996).
    [Crossref]
  6. X. Ning, R. Winston, and J. O’Gallagher, “Dielectric totally internally reflecting concentrators,” Appl. Opt. 26, 300–305 (1987).
    [Crossref] [PubMed]
  7. A. Cutolo, L. Carlomusto, F. Reale, and I. Rendina, “Tapered and inhomogeneous dielectric light concentrators,” Appl. Opt. 29, 1353–1364 (1990).
    [Crossref] [PubMed]
  8. M. Blanc, J. Pollard, G. Marchand, and R. Henri, “Multi-directional non-imaging radiations concentrator and/or deconcentrator device,” US Patent 4697867 (1987).
  9. D. Feuermann, J. M. Gordon, and M. Huleihil, “Solar fiber-optic mini-dish concentrators: first experimental results and field experience,” Sol. Energy 72, 459–472 (2002).
    [Crossref]
  10. E. A. Katz, J. M. Gordon, W. Tassew, and D. Feuermann, “Photovoltaic characterization of concentrator solar cells by localized irradiation,” J. Appl. Phys. 100, 044514 (2006).
    [Crossref]
  11. T. J. Suleski and R. D. Te Kolste, “Fabrication trends for free-space microoptics,” J. Lightwave Technol. 23, 633–646 (2005).
    [Crossref]
  12. S. R. Nagel, J. B. Macchesney, and K. L. Walker, “An overview of the modified chemical vapor deposition (MCVD) process and performance,” IEEE J. Quantum Electron. 18, 459–476 (1982).
    [Crossref]
  13. International Organization for Standardization, “Solar energy-Reference solar spectral irradiance at the ground at different receiving conditions-Part 1: Direct normal and hemispherical solar irradiance for air mass 1.5,” ISO9845, 1 (1992).
  14. J. W. Fleming, “Dispersion in GeO2-SiO2 glasses,” Appl. Opt. 23, 4486–4493 (1984).
    [Crossref] [PubMed]
  15. R. Winston, J. C. Minano, and P. Benitez, Nonimaging optics (Elservier, New York, 2005), Chapt. 2.
  16. R. Winston and W. T. Welford, “Geometrical vector flux and some new nonimaging concentrator,” J. Opt. Soc. Am. 69, 532–536 (1979).
    [Crossref]
  17. J. M. Gordon, “Complementary construction of ideal nonimaging concentrators and its applications,” Appl. Opt. 35, 5677–5682 (1996).
    [Crossref] [PubMed]

2007 (1)

2006 (1)

E. A. Katz, J. M. Gordon, W. Tassew, and D. Feuermann, “Photovoltaic characterization of concentrator solar cells by localized irradiation,” J. Appl. Phys. 100, 044514 (2006).
[Crossref]

2005 (2)

2002 (1)

D. Feuermann, J. M. Gordon, and M. Huleihil, “Solar fiber-optic mini-dish concentrators: first experimental results and field experience,” Sol. Energy 72, 459–472 (2002).
[Crossref]

1996 (2)

D. Jenkins, R. Winston, J. Bliss, J. O'Gallagher, A. Lewandowski, and C. Bingham, “Solar concentration of 50,000 achieved with output power approaching 1kW,” J. Sol. Energy Eng. 118, 141–145 (1996).
[Crossref]

J. M. Gordon, “Complementary construction of ideal nonimaging concentrators and its applications,” Appl. Opt. 35, 5677–5682 (1996).
[Crossref] [PubMed]

1990 (1)

1987 (1)

1984 (1)

1982 (1)

S. R. Nagel, J. B. Macchesney, and K. L. Walker, “An overview of the modified chemical vapor deposition (MCVD) process and performance,” IEEE J. Quantum Electron. 18, 459–476 (1982).
[Crossref]

1979 (1)

Bingham, C.

D. Jenkins, R. Winston, J. Bliss, J. O'Gallagher, A. Lewandowski, and C. Bingham, “Solar concentration of 50,000 achieved with output power approaching 1kW,” J. Sol. Energy Eng. 118, 141–145 (1996).
[Crossref]

Bliss, J.

D. Jenkins, R. Winston, J. Bliss, J. O'Gallagher, A. Lewandowski, and C. Bingham, “Solar concentration of 50,000 achieved with output power approaching 1kW,” J. Sol. Energy Eng. 118, 141–145 (1996).
[Crossref]

Carlomusto, L.

Cutolo, A.

Eisenberg, N.

Feuermann, D.

O. Korech, J. M. Gordon, E. A. Katz, D. Feuermann, and N. Eisenberg, “Dielectric microconcentrators for efficiency enhancement in concentrator solar cells,” Opt. Lett. 32, 2789–2791 (2007).
[Crossref] [PubMed]

E. A. Katz, J. M. Gordon, W. Tassew, and D. Feuermann, “Photovoltaic characterization of concentrator solar cells by localized irradiation,” J. Appl. Phys. 100, 044514 (2006).
[Crossref]

D. Feuermann, J. M. Gordon, and M. Huleihil, “Solar fiber-optic mini-dish concentrators: first experimental results and field experience,” Sol. Energy 72, 459–472 (2002).
[Crossref]

Fleming, J. W.

Gordon, J. M.

O. Korech, J. M. Gordon, E. A. Katz, D. Feuermann, and N. Eisenberg, “Dielectric microconcentrators for efficiency enhancement in concentrator solar cells,” Opt. Lett. 32, 2789–2791 (2007).
[Crossref] [PubMed]

E. A. Katz, J. M. Gordon, W. Tassew, and D. Feuermann, “Photovoltaic characterization of concentrator solar cells by localized irradiation,” J. Appl. Phys. 100, 044514 (2006).
[Crossref]

R. Winston and J. M. Gordon, “Planar concentrators near the étendue limit,” Opt. Lett. 30, 2617–2619 (2005).
[Crossref] [PubMed]

D. Feuermann, J. M. Gordon, and M. Huleihil, “Solar fiber-optic mini-dish concentrators: first experimental results and field experience,” Sol. Energy 72, 459–472 (2002).
[Crossref]

J. M. Gordon, “Complementary construction of ideal nonimaging concentrators and its applications,” Appl. Opt. 35, 5677–5682 (1996).
[Crossref] [PubMed]

Huleihil, M.

D. Feuermann, J. M. Gordon, and M. Huleihil, “Solar fiber-optic mini-dish concentrators: first experimental results and field experience,” Sol. Energy 72, 459–472 (2002).
[Crossref]

Jenkins, D.

D. Jenkins, R. Winston, J. Bliss, J. O'Gallagher, A. Lewandowski, and C. Bingham, “Solar concentration of 50,000 achieved with output power approaching 1kW,” J. Sol. Energy Eng. 118, 141–145 (1996).
[Crossref]

Katz, E. A.

O. Korech, J. M. Gordon, E. A. Katz, D. Feuermann, and N. Eisenberg, “Dielectric microconcentrators for efficiency enhancement in concentrator solar cells,” Opt. Lett. 32, 2789–2791 (2007).
[Crossref] [PubMed]

E. A. Katz, J. M. Gordon, W. Tassew, and D. Feuermann, “Photovoltaic characterization of concentrator solar cells by localized irradiation,” J. Appl. Phys. 100, 044514 (2006).
[Crossref]

Korech, O.

Lewandowski, A.

D. Jenkins, R. Winston, J. Bliss, J. O'Gallagher, A. Lewandowski, and C. Bingham, “Solar concentration of 50,000 achieved with output power approaching 1kW,” J. Sol. Energy Eng. 118, 141–145 (1996).
[Crossref]

Macchesney, J. B.

S. R. Nagel, J. B. Macchesney, and K. L. Walker, “An overview of the modified chemical vapor deposition (MCVD) process and performance,” IEEE J. Quantum Electron. 18, 459–476 (1982).
[Crossref]

Nagel, S. R.

S. R. Nagel, J. B. Macchesney, and K. L. Walker, “An overview of the modified chemical vapor deposition (MCVD) process and performance,” IEEE J. Quantum Electron. 18, 459–476 (1982).
[Crossref]

Ning, X.

O’Gallagher, J.

O'Gallagher, J.

D. Jenkins, R. Winston, J. Bliss, J. O'Gallagher, A. Lewandowski, and C. Bingham, “Solar concentration of 50,000 achieved with output power approaching 1kW,” J. Sol. Energy Eng. 118, 141–145 (1996).
[Crossref]

Reale, F.

Rendina, I.

Suleski, T. J.

Tassew, W.

E. A. Katz, J. M. Gordon, W. Tassew, and D. Feuermann, “Photovoltaic characterization of concentrator solar cells by localized irradiation,” J. Appl. Phys. 100, 044514 (2006).
[Crossref]

Te Kolste, R. D.

Walker, K. L.

S. R. Nagel, J. B. Macchesney, and K. L. Walker, “An overview of the modified chemical vapor deposition (MCVD) process and performance,” IEEE J. Quantum Electron. 18, 459–476 (1982).
[Crossref]

Welford, W. T.

Winston, R.

Appl. Opt. (4)

IEEE J. Quantum Electron. (1)

S. R. Nagel, J. B. Macchesney, and K. L. Walker, “An overview of the modified chemical vapor deposition (MCVD) process and performance,” IEEE J. Quantum Electron. 18, 459–476 (1982).
[Crossref]

J. Appl. Phys. (1)

E. A. Katz, J. M. Gordon, W. Tassew, and D. Feuermann, “Photovoltaic characterization of concentrator solar cells by localized irradiation,” J. Appl. Phys. 100, 044514 (2006).
[Crossref]

J. Lightwave Technol. (1)

J. Opt. Soc. Am. (1)

J. Sol. Energy Eng. (1)

D. Jenkins, R. Winston, J. Bliss, J. O'Gallagher, A. Lewandowski, and C. Bingham, “Solar concentration of 50,000 achieved with output power approaching 1kW,” J. Sol. Energy Eng. 118, 141–145 (1996).
[Crossref]

Opt. Lett. (2)

Sol. Energy (1)

D. Feuermann, J. M. Gordon, and M. Huleihil, “Solar fiber-optic mini-dish concentrators: first experimental results and field experience,” Sol. Energy 72, 459–472 (2002).
[Crossref]

Other (5)

M. Blanc, J. Pollard, G. Marchand, and R. Henri, “Multi-directional non-imaging radiations concentrator and/or deconcentrator device,” US Patent 4697867 (1987).

H. Lerchenmuller, A. Hakenjos, I. Heile, B. Burger, and O. Stalter, “From FLATCON pilot systems to the first power plant,” presented at the International conference on solar concentrators for the generation of electricity or hydrogen, El Escorial, Spain, 12–16, Mar. 2007.

S. Horne, G. Conley, J. Gordon, D. Fork, P. Meada, E. Schrader, and T. Zimmermann, “A solid 500 sun compound concentrator PV design,” in Proceedings of IEEE 4th World Conference on Photovoltaic Energy Conversion (Institute of Electrical and Electronics Engineers, New York, 2006), pp. 694–697.

R. Winston, J. C. Minano, and P. Benitez, Nonimaging optics (Elservier, New York, 2005), Chapt. 2.

International Organization for Standardization, “Solar energy-Reference solar spectral irradiance at the ground at different receiving conditions-Part 1: Direct normal and hemispherical solar irradiance for air mass 1.5,” ISO9845, 1 (1992).

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Figures (8)

Fig. 1
Fig. 1 (a) Structure of the proposed tapered waveguide solar concentrator (TWSC). (b) Index profile of the TWCS in Fig. 1(a). Index difference between core and cladding is given by 0.313% at the wavelength of 635 nm (c) outer diameter variation along the adiabatic taper.
Fig. 2
Fig. 2 (a) Schematic of simulation set-up. Rays are concentrated on the red circle on an entrance aperture. (b) Spectra of incident light and output result. Black squares are solar spectrum of AM 1.5G, and red circles are spectrum of the result.
Fig. 3
Fig. 3 Irradiance profiles of normal incidence in a unit of mW/mm2; (a) without core or equivalently GeO2 doping ratio χ = 0 mole %. (b) with the core of GeO2 doping ratio χ = 3 mole %. (c) with the core of GeO2 doping ratio χ = 6 mole %. (d) One dimensional irradiance profiles for different GeO2 doping levels at the line across the center. An inset shows maximum irradiances along with GeO2 doping ratio.
Fig. 4
Fig. 4 (a) Schematics of the TWSCs with various core sizes a = 11mm, 20, and 1/2 a. Total power at the tapered output of TWSC as a function of the incident angle for the TWSC; (b) with core radius = a, (c) core radius = 2a, (d) core radius = a/2.
Fig. 5
Fig. 5 (a) Structural parameters of TWSC in the axial direction; taper segment and cylinder segment. (b) Total power at the tapered output as a function of the incident angle for a TWSC without cylinder segment. The inlet shows numerical simulation results for all-silica TWSC without core. (c) Total power versus tilt angle for the TWSC. The core was doped with 3 mole % GeO2 and plots are overlaid for various cylinder segment lengths.
Fig. 6
Fig. 6 (a) Schematic of a hyperbolic concentrator. Asymptotes are shown in dashed lines. F1 and F2 are foci of hyperbolic curves. (b) Solid line is the actual shape of the proposed TWSC and dashed line is a hyperbolic curve with a focal point placed at 20.8 mm from origin.
Fig. 7
Fig. 7 (a) A solar simulator used in the experiment. (b) An experimental set-up. An III-V solar cell on heat sink is placed under the TWSC. (c) Schematic of the experiment. A numerical aperture of the TWSC is shown by a red cone.
Fig. 8
Fig. 8 Results from an III-V group solar cell; (a) I-V curves along incident angles. (b) Current densities along incident angles. An inlet shows enlarged plots in the range of incident angles from −10° to 10°.

Equations (4)

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n c o r e 2 1 = i = 1 3 [ A i S i O 2 + χ ( A i G e O 2 A i S i O 2 ) ] λ 0 2 λ 0 2 [ l i S i O 2 + χ ( l i G e O 2 l i S i O 2 ) ] 2
C max = ( n N . A . ) 2 = 1 n c o r e 2 n c l a d d i n g 2
2 a 2 c = sin θ
a c = sin ( tan 1 ( a b ) )    ( b= c 2 a 2 )

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