Abstract

Sizing down the dimensions of solar concentrators for photovoltaic applications offers a number of promising advantages. It provides thinner modules and smaller solar cells, which reduces thermal issues. In this work a plane Fresnel lens design is introduced that is first analyzed with geometrical optics. Because of miniaturization, pure ray tracing may no longer be valid to determine the concentration performance. Therefore, a quantitative wave optical analysis of the miniaturization’s influence on the obtained concentration performance is presented. This better quantitative understanding of the impact of diffraction in microstructured Fresnel lenses might help to optimize the design of several applications in nonimaging optics.

© 2010 Optical Society of America

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References

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  2. R. Leutz and A. Suzuki, Nonimaging Fresnel Lenses: Design and Performance of Solar Concentrators (Springer Verlag, 2001).
  3. C. Algora, E. Ortiz, I. Rey-Stolle, V. Diaz, R. Peña, V. Andreev, V. Khvostikov, and V. Rumyantsev, “A GaAs solar cell with an efficiency of 26.2% at 1000 suns and 25.0% at 2000 suns,” IEEE Trans. Electron Devices  48, 840–844 (2001).
    [CrossRef]
  4. A. Royne, C. Dey, and D. Mills, “Cooling of photovoltaic cells under concentrated illumination: a critical review,” Solar Energy Mater. Sol. Cells  86, 451–483 (2005).
    [CrossRef]
  5. K. Araki, H. Uozumi, and M. Yamaguchi, “A simple passive cooling structure and its heat analysis for 500×concentrator PV module,” in Conference Record IEEE Photovoltaic Specialists Conference (IEEE, 2002), Vol.  29, pp. 1568–1571.
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  16. F. Zernike, “The concept of degree of coherence and its application to optical problems,” Physica  5, 785–795 (1938).
  17. H. Hopkins, “The concept of partial coherence in optics,” Proc. R. Soc. London. Ser. A  1, 263–277 (1951).
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  23. J. R. Biles, “High concentration, spectrum splitting, broad bandwidth, hologram photovoltaic solar collector,” U.S. patent 2009/0114266A1 (7 May 2009).
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    [CrossRef]

2008 (1)

2007 (2)

A. Davis, F. Kühnlenz, and R. Business, “Optical design using Fresnel lenses,” Optik Photonik  4, 52–55 (2007).

S. Kasarova, N. Sultanova, C. Ivanov, and I. Nikolov, “Analysis of the dispersion of optical plastic materials,” Opt. Mater.  29, 1481–1490 (2007).

2005 (1)

A. Royne, C. Dey, and D. Mills, “Cooling of photovoltaic cells under concentrated illumination: a critical review,” Solar Energy Mater. Sol. Cells  86, 451–483 (2005).
[CrossRef]

2004 (2)

A. Imenes and D. Mills, “Spectral beam splitting technology for increased conversion efficiency in solar concentrating systems: a review,” Solar Energy Mater. Sol. Cells  84, 19–69(2004).
[CrossRef]

F. Dubois, M. Novella Requena, C. Minetti, O. Monnom, and E. Istasse, “Partial spatial coherence effects in digital holographic microscopy with a laser source,” Appl. Opt.  43, 1131–1139 (2004).
[CrossRef]

2001 (1)

C. Algora, E. Ortiz, I. Rey-Stolle, V. Diaz, R. Peña, V. Andreev, V. Khvostikov, and V. Rumyantsev, “A GaAs solar cell with an efficiency of 26.2% at 1000 suns and 25.0% at 2000 suns,” IEEE Trans. Electron Devices  48, 840–844 (2001).
[CrossRef]

2000 (1)

R. Swanson, “The promise of concentrators,” Prog. Photovolt. Res. Appl.  8, 93–111 (2000).

1995 (2)

1986 (2)

A. Greynolds, “Vector-formulation of ray-equivalent method for general Gaussian beam propagation,” Proc. SPIE  679, 129–133 (1986).

P. Einziger, S. Raz, and M. Shapira, “Gabor representation and aperture theory,” J. Opt. Soc. Am. A  3, 508–522 (1986).
[CrossRef]

1985 (2)

A. Greynolds, “Propagation of general astigmatic Gaussian beams along skew ray paths,” Proc. SPIE  560, 33–50 (1985).

J. Arnaud, “Representation of Gaussian beams by complex rays,” Appl. Opt.  24, 538–543 (1985).
[CrossRef]

1979 (2)

E. Kritchman, A. Friesem, and G. Yekutieli, “Highly concentrating Fresnel lenses,” Appl. Opt.  18, 2688–2695 (1979).
[CrossRef]

J. Egger, “Use of Fresnel lenses in optical systems: some advantages and limitations,” Proc. SPIE   193, 63 (1979).

1951 (1)

H. Hopkins, “The concept of partial coherence in optics,” Proc. R. Soc. London. Ser. A  1, 263–277 (1951).

1938 (1)

F. Zernike, “The concept of degree of coherence and its application to optical problems,” Physica  5, 785–795 (1938).

1934 (1)

P. Van Cittert, “Die wahrscheinliche Schwingungsverteilung in einer von einer Lichtquelle direkt oder mittels einer Linse beleuchteten Ebene,” Physica  1, 201–210 (1934).

Algora, C.

C. Algora, E. Ortiz, I. Rey-Stolle, V. Diaz, R. Peña, V. Andreev, V. Khvostikov, and V. Rumyantsev, “A GaAs solar cell with an efficiency of 26.2% at 1000 suns and 25.0% at 2000 suns,” IEEE Trans. Electron Devices  48, 840–844 (2001).
[CrossRef]

Andreev, V.

C. Algora, E. Ortiz, I. Rey-Stolle, V. Diaz, R. Peña, V. Andreev, V. Khvostikov, and V. Rumyantsev, “A GaAs solar cell with an efficiency of 26.2% at 1000 suns and 25.0% at 2000 suns,” IEEE Trans. Electron Devices  48, 840–844 (2001).
[CrossRef]

Araki, K.

K. Araki, H. Uozumi, and M. Yamaguchi, “A simple passive cooling structure and its heat analysis for 500×concentrator PV module,” in Conference Record IEEE Photovoltaic Specialists Conference (IEEE, 2002), Vol.  29, pp. 1568–1571.

Arnaud, J.

Biles, J. R.

J. R. Biles, “High concentration, spectrum splitting, broad bandwidth, hologram photovoltaic solar collector,” U.S. patent 2009/0114266A1 (7 May 2009).

Business, R.

A. Davis, F. Kühnlenz, and R. Business, “Optical design using Fresnel lenses,” Optik Photonik  4, 52–55 (2007).

Caley, A.

Davis, A.

A. Davis, F. Kühnlenz, and R. Business, “Optical design using Fresnel lenses,” Optik Photonik  4, 52–55 (2007).

Dey, C.

A. Royne, C. Dey, and D. Mills, “Cooling of photovoltaic cells under concentrated illumination: a critical review,” Solar Energy Mater. Sol. Cells  86, 451–483 (2005).
[CrossRef]

Diaz, V.

C. Algora, E. Ortiz, I. Rey-Stolle, V. Diaz, R. Peña, V. Andreev, V. Khvostikov, and V. Rumyantsev, “A GaAs solar cell with an efficiency of 26.2% at 1000 suns and 25.0% at 2000 suns,” IEEE Trans. Electron Devices  48, 840–844 (2001).
[CrossRef]

Dubois, F.

Egger, J.

J. Egger, “Use of Fresnel lenses in optical systems: some advantages and limitations,” Proc. SPIE   193, 63 (1979).

Einziger, P.

Friesem, A.

Greynolds, A.

A. Greynolds, “Vector-formulation of ray-equivalent method for general Gaussian beam propagation,” Proc. SPIE  679, 129–133 (1986).

A. Greynolds, “Propagation of general astigmatic Gaussian beams along skew ray paths,” Proc. SPIE  560, 33–50 (1985).

Herzig, H.

Hopkins, H.

H. Hopkins, “The concept of partial coherence in optics,” Proc. R. Soc. London. Ser. A  1, 263–277 (1951).

Imenes, A.

A. Imenes and D. Mills, “Spectral beam splitting technology for increased conversion efficiency in solar concentrating systems: a review,” Solar Energy Mater. Sol. Cells  84, 19–69(2004).
[CrossRef]

Istasse, E.

Ivanov, C.

S. Kasarova, N. Sultanova, C. Ivanov, and I. Nikolov, “Analysis of the dispersion of optical plastic materials,” Opt. Mater.  29, 1481–1490 (2007).

Kasarova, S.

S. Kasarova, N. Sultanova, C. Ivanov, and I. Nikolov, “Analysis of the dispersion of optical plastic materials,” Opt. Mater.  29, 1481–1490 (2007).

Khvostikov, V.

C. Algora, E. Ortiz, I. Rey-Stolle, V. Diaz, R. Peña, V. Andreev, V. Khvostikov, and V. Rumyantsev, “A GaAs solar cell with an efficiency of 26.2% at 1000 suns and 25.0% at 2000 suns,” IEEE Trans. Electron Devices  48, 840–844 (2001).
[CrossRef]

Kritchman, E.

Kühnlenz, F.

A. Davis, F. Kühnlenz, and R. Business, “Optical design using Fresnel lenses,” Optik Photonik  4, 52–55 (2007).

Kunz, R.

Kurtz, S.

S. Kurtz, “Opportunities and challenges for development of a mature concentrating photovoltaic power industry,” Tech. Rep. NREL/TP-520–43208 (National Renewable Energy Laboratory, 2009).

Leutz, R.

R. Leutz and A. Suzuki, Nonimaging Fresnel Lenses: Design and Performance of Solar Concentrators (Springer Verlag, 2001).

Liu, J.

Mandel, L.

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University Press, 1995).

Mills, D.

A. Royne, C. Dey, and D. Mills, “Cooling of photovoltaic cells under concentrated illumination: a critical review,” Solar Energy Mater. Sol. Cells  86, 451–483 (2005).
[CrossRef]

A. Imenes and D. Mills, “Spectral beam splitting technology for increased conversion efficiency in solar concentrating systems: a review,” Solar Energy Mater. Sol. Cells  84, 19–69(2004).
[CrossRef]

Minetti, C.

Monnom, O.

Nikolov, I.

S. Kasarova, N. Sultanova, C. Ivanov, and I. Nikolov, “Analysis of the dispersion of optical plastic materials,” Opt. Mater.  29, 1481–1490 (2007).

Ortiz, E.

C. Algora, E. Ortiz, I. Rey-Stolle, V. Diaz, R. Peña, V. Andreev, V. Khvostikov, and V. Rumyantsev, “A GaAs solar cell with an efficiency of 26.2% at 1000 suns and 25.0% at 2000 suns,” IEEE Trans. Electron Devices  48, 840–844 (2001).
[CrossRef]

Peña, R.

C. Algora, E. Ortiz, I. Rey-Stolle, V. Diaz, R. Peña, V. Andreev, V. Khvostikov, and V. Rumyantsev, “A GaAs solar cell with an efficiency of 26.2% at 1000 suns and 25.0% at 2000 suns,” IEEE Trans. Electron Devices  48, 840–844 (2001).
[CrossRef]

Raz, S.

Requena, M. Novella

Rey-Stolle, I.

C. Algora, E. Ortiz, I. Rey-Stolle, V. Diaz, R. Peña, V. Andreev, V. Khvostikov, and V. Rumyantsev, “A GaAs solar cell with an efficiency of 26.2% at 1000 suns and 25.0% at 2000 suns,” IEEE Trans. Electron Devices  48, 840–844 (2001).
[CrossRef]

Rossi, M.

Royne, A.

A. Royne, C. Dey, and D. Mills, “Cooling of photovoltaic cells under concentrated illumination: a critical review,” Solar Energy Mater. Sol. Cells  86, 451–483 (2005).
[CrossRef]

Rumyantsev, V.

C. Algora, E. Ortiz, I. Rey-Stolle, V. Diaz, R. Peña, V. Andreev, V. Khvostikov, and V. Rumyantsev, “A GaAs solar cell with an efficiency of 26.2% at 1000 suns and 25.0% at 2000 suns,” IEEE Trans. Electron Devices  48, 840–844 (2001).
[CrossRef]

Shapira, M.

Sinzinger, S.

Sultanova, N.

S. Kasarova, N. Sultanova, C. Ivanov, and I. Nikolov, “Analysis of the dispersion of optical plastic materials,” Opt. Mater.  29, 1481–1490 (2007).

Suzuki, A.

R. Leutz and A. Suzuki, Nonimaging Fresnel Lenses: Design and Performance of Solar Concentrators (Springer Verlag, 2001).

Swanson, R.

R. Swanson, “The promise of concentrators,” Prog. Photovolt. Res. Appl.  8, 93–111 (2000).

Taghizadeh, M.

Testorf, M.

Uozumi, H.

K. Araki, H. Uozumi, and M. Yamaguchi, “A simple passive cooling structure and its heat analysis for 500×concentrator PV module,” in Conference Record IEEE Photovoltaic Specialists Conference (IEEE, 2002), Vol.  29, pp. 1568–1571.

Van Cittert, P.

P. Van Cittert, “Die wahrscheinliche Schwingungsverteilung in einer von einer Lichtquelle direkt oder mittels einer Linse beleuchteten Ebene,” Physica  1, 201–210 (1934).

Waddie, A.

Wolf, E.

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University Press, 1995).

Yamaguchi, M.

K. Araki, H. Uozumi, and M. Yamaguchi, “A simple passive cooling structure and its heat analysis for 500×concentrator PV module,” in Conference Record IEEE Photovoltaic Specialists Conference (IEEE, 2002), Vol.  29, pp. 1568–1571.

Yekutieli, G.

Zernike, F.

F. Zernike, “The concept of degree of coherence and its application to optical problems,” Physica  5, 785–795 (1938).

Appl. Opt. (6)

IEEE Trans. Electron Devices (1)

C. Algora, E. Ortiz, I. Rey-Stolle, V. Diaz, R. Peña, V. Andreev, V. Khvostikov, and V. Rumyantsev, “A GaAs solar cell with an efficiency of 26.2% at 1000 suns and 25.0% at 2000 suns,” IEEE Trans. Electron Devices  48, 840–844 (2001).
[CrossRef]

J. Opt. Soc. Am. A (1)

Opt. Mater. (1)

S. Kasarova, N. Sultanova, C. Ivanov, and I. Nikolov, “Analysis of the dispersion of optical plastic materials,” Opt. Mater.  29, 1481–1490 (2007).

Optik Photonik (1)

A. Davis, F. Kühnlenz, and R. Business, “Optical design using Fresnel lenses,” Optik Photonik  4, 52–55 (2007).

Physica (2)

P. Van Cittert, “Die wahrscheinliche Schwingungsverteilung in einer von einer Lichtquelle direkt oder mittels einer Linse beleuchteten Ebene,” Physica  1, 201–210 (1934).

F. Zernike, “The concept of degree of coherence and its application to optical problems,” Physica  5, 785–795 (1938).

Proc. R. Soc. London. Ser. A (1)

H. Hopkins, “The concept of partial coherence in optics,” Proc. R. Soc. London. Ser. A  1, 263–277 (1951).

Proc. SPIE (3)

A. Greynolds, “Propagation of general astigmatic Gaussian beams along skew ray paths,” Proc. SPIE  560, 33–50 (1985).

A. Greynolds, “Vector-formulation of ray-equivalent method for general Gaussian beam propagation,” Proc. SPIE  679, 129–133 (1986).

J. Egger, “Use of Fresnel lenses in optical systems: some advantages and limitations,” Proc. SPIE   193, 63 (1979).

Prog. Photovolt. Res. Appl. (1)

R. Swanson, “The promise of concentrators,” Prog. Photovolt. Res. Appl.  8, 93–111 (2000).

Solar Energy Mater. Sol. Cells (2)

A. Royne, C. Dey, and D. Mills, “Cooling of photovoltaic cells under concentrated illumination: a critical review,” Solar Energy Mater. Sol. Cells  86, 451–483 (2005).
[CrossRef]

A. Imenes and D. Mills, “Spectral beam splitting technology for increased conversion efficiency in solar concentrating systems: a review,” Solar Energy Mater. Sol. Cells  84, 19–69(2004).
[CrossRef]

Other (5)

J. R. Biles, “High concentration, spectrum splitting, broad bandwidth, hologram photovoltaic solar collector,” U.S. patent 2009/0114266A1 (7 May 2009).

K. Araki, H. Uozumi, and M. Yamaguchi, “A simple passive cooling structure and its heat analysis for 500×concentrator PV module,” in Conference Record IEEE Photovoltaic Specialists Conference (IEEE, 2002), Vol.  29, pp. 1568–1571.

S. Kurtz, “Opportunities and challenges for development of a mature concentrating photovoltaic power industry,” Tech. Rep. NREL/TP-520–43208 (National Renewable Energy Laboratory, 2009).

R. Leutz and A. Suzuki, Nonimaging Fresnel Lenses: Design and Performance of Solar Concentrators (Springer Verlag, 2001).

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University Press, 1995).

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Figures (7)

Fig. 1
Fig. 1

Schematic representation of the used Fresnel lens design. Marked parameters are the working distance W, lens diameter D, prism width d, wedge angle α, and collecting angle γ.

Fig. 2
Fig. 2

Exemplary prisms for impact of finite sized prism (a) and divergence angle of the source (b) on characteristic spot sizes D p and D σ , respectively.

Fig. 3
Fig. 3

Characteristic spot ratios D σ / D for the Sun’s half divergence angle 4.7 mrad and D p / D for three different numbers of prisms against collecting angle γ.

Fig. 4
Fig. 4

Concentration ratio against number of prisms for three different f-numbers.

Fig. 5
Fig. 5

Intensity cross sections for p = 10 (a) and p = 50 (b): comparison of geometrical optics (GO) and wave optical (WO) simulations.

Fig. 6
Fig. 6

Comparison of the concentration ratio against the number of prisms for geometrical optics (GO) and wave optical (WO) simulations. The f-number varies from F / # = 0.7 (a), F / # = 1 (b), to F / # = 1.3 (c).

Fig. 7
Fig. 7

(a) Concentration ratio against wavelength for three different Fresnel lenses with p = 10 , 30, and 50 prisms, respectively, and F / # = 1 . (b) Comparison of the concentration ratio against wavelength for geometrical optics (GO) and wave optical (WO) simulations for p = 35 and F / # = 1 .

Equations (8)

Equations on this page are rendered with MathJax. Learn more.

γ ( i ) = 90 ° arctan ( 2 p F / # i 1 / 2 ) .
α ( i ) = arccos ( n cos γ ( i ) ( 1 + n 2 2 n cos γ ( i ) ) 1 / 2 ) .
C = 0.9 A σ A rec .
D p ( i ) = D 2 p cos α ( i ) cos β ( i ) cos ( β ( i ) α ( i ) ) .
D σ ( i ) = D ( F / # 1 4 p tan α ( i ) ) ( tan γ + ( i ) tan γ ( i ) ) .
γ ± ( i ) = α ( i ) + arcsin ( n sin ( α ( i ) ± θ ) ) .
r c = 0.16 λ sin ( θ ) ,
E ( r ) = 0 r r I ( r ) d r ,

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