Abstract

It is shown how novel solutions for realistic gradient-index lenses create the possibility of nominally stationary solar photovoltaic concentrators capable of daylong averaged flux concentration levels of order 103.

© 2011 OSA

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References

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    [CrossRef] [PubMed]
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    [CrossRef]
  9. J. C. Maxwell, “On the general laws of optical instruments,” Q. J. Pure Appl. Math. 2, 233–247 (1854).
  10. R. K. Luneburg, The Mathematical Theory of Optics (U. California Press, Berkeley, 1964).
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    [CrossRef]
  12. S. P. Morgan, “General solution of the Luneberg lens problem,” J. Appl. Phys. 29(9), 1358–1368 (1958).
    [CrossRef]
  13. G. Beadie, J. S. Shirk, A. Rosenberg, P. A. Lane, E. Fleet, A. R. Kamdar, Y. Jin, M. Ponting, T. Kazmierczak, Y. Yang, A. Hiltner, and E. Baer, “Optical properties of a bio-inspired gradient refractive index polymer lens,” Opt. Express 16(15), 11540–11547 (2008).
    [PubMed]
  14. C. Ye and R. R. McLeod, “GRIN lens and lens array fabrication with diffusion-driven photopolymer,” Opt. Lett. 33(22), 2575–2577 (2008).
    [CrossRef] [PubMed]
  15. J. Q. Xi and F. Martin, “Schubert, J.K. Kim, E.F. Schubert, M. Chen, S.Y. Lin, W. Liu, and J.A. Smart, “Optical thin-film materials with low refractive index for broadband elimination of Fresnel reflection,” Nat. Photonics 1, 176–179 (2007).
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  19. J. M. Gordon, E. A. Katz, D. Feuermann, and M. Huleihil, “Toward ultra-high-flux photovoltaic concentration,” Appl. Phys. Lett. 84(18), 3642–3644 (2004).
    [CrossRef]
  20. E. A. Katz, J. M. Gordon, W. Tassew, and D. Feuermann, “Photovoltaic characterization of concentrator solar cells by localized irradiation,” J. Appl. Phys. 100(4), 044514 (2006).
    [CrossRef]
  21. O. Korech, B. Hirsch, E. A. Katz, and J. M. Gordon, “High-flux characterization of ultra-small multi-junction concentrator solar cells,” Appl. Phys. Lett. 91(6), 064101 (2007).
    [CrossRef]
  22. A. Goldstein and J. M. Gordon, “Tailored solar optics for maximal optical tolerance and concentration,” Sol. Energy Mater. Sol. Cells . in press.
  23. 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] [PubMed]
  24. J. Sun, T. Israeli, T. A. Reddy, K. Scoles, J. M. Gordon, and D. Feuermann, “Modeling and experimental evaluation of passive heat sinks for miniature high-flux photovoltaic concentrators,” J. Sol. Energy Eng. 127(1), 138–145 (2005).
    [CrossRef]

2010 (3)

K. Araki, T. Yano, and Y. Kuroda, “30 kW concentrator photovoltaic system using dome-shaped Fresnel lenses,” Opt. Express 18(S1), A53–A63 (2010).
[CrossRef] [PubMed]

P. Kotsidas, E. Chatzi, and V. Modi, “Stationary nonimaging lenses for solar concentration,” Appl. Opt. 49(27), 5183–5191 (2010).
[CrossRef] [PubMed]

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] [PubMed]

2008 (2)

G. Beadie, J. S. Shirk, A. Rosenberg, P. A. Lane, E. Fleet, A. R. Kamdar, Y. Jin, M. Ponting, T. Kazmierczak, Y. Yang, A. Hiltner, and E. Baer, “Optical properties of a bio-inspired gradient refractive index polymer lens,” Opt. Express 16(15), 11540–11547 (2008).
[PubMed]

C. Ye and R. R. McLeod, “GRIN lens and lens array fabrication with diffusion-driven photopolymer,” Opt. Lett. 33(22), 2575–2577 (2008).
[CrossRef] [PubMed]

2007 (2)

J. Q. Xi and F. Martin, “Schubert, J.K. Kim, E.F. Schubert, M. Chen, S.Y. Lin, W. Liu, and J.A. Smart, “Optical thin-film materials with low refractive index for broadband elimination of Fresnel reflection,” Nat. Photonics 1, 176–179 (2007).

O. Korech, B. Hirsch, E. A. Katz, and J. M. Gordon, “High-flux characterization of ultra-small multi-junction concentrator solar cells,” Appl. Phys. Lett. 91(6), 064101 (2007).
[CrossRef]

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(4), 044514 (2006).
[CrossRef]

2005 (1)

J. Sun, T. Israeli, T. A. Reddy, K. Scoles, J. M. Gordon, and D. Feuermann, “Modeling and experimental evaluation of passive heat sinks for miniature high-flux photovoltaic concentrators,” J. Sol. Energy Eng. 127(1), 138–145 (2005).
[CrossRef]

2004 (1)

J. M. Gordon, E. A. Katz, D. Feuermann, and M. Huleihil, “Toward ultra-high-flux photovoltaic concentration,” Appl. Phys. Lett. 84(18), 3642–3644 (2004).
[CrossRef]

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(6), 459–472 (2002).
[CrossRef]

2000 (1)

J. M. Gordon, “Spherical gradient-index lenses as perfect imaging and maximum power transfer devices,” Appl. Opt. 39(22), 3825–3832 (2000).
[CrossRef]

1958 (1)

S. P. Morgan, “General solution of the Luneberg lens problem,” J. Appl. Phys. 29(9), 1358–1368 (1958).
[CrossRef]

1954 (1)

A. Fletcher, T. Murphy, and A. Young, “Solutions of two optical problems,” Proc. R. Soc. Lond. A 223(1153), 216–225 (1954).
[CrossRef]

1854 (1)

J. C. Maxwell, “On the general laws of optical instruments,” Q. J. Pure Appl. Math. 2, 233–247 (1854).

Araki, K.

K. Araki, T. Yano, and Y. Kuroda, “30 kW concentrator photovoltaic system using dome-shaped Fresnel lenses,” Opt. Express 18(S1), A53–A63 (2010).
[CrossRef] [PubMed]

Baer, E.

G. Beadie, J. S. Shirk, A. Rosenberg, P. A. Lane, E. Fleet, A. R. Kamdar, Y. Jin, M. Ponting, T. Kazmierczak, Y. Yang, A. Hiltner, and E. Baer, “Optical properties of a bio-inspired gradient refractive index polymer lens,” Opt. Express 16(15), 11540–11547 (2008).
[PubMed]

Beadie, G.

G. Beadie, J. S. Shirk, A. Rosenberg, P. A. Lane, E. Fleet, A. R. Kamdar, Y. Jin, M. Ponting, T. Kazmierczak, Y. Yang, A. Hiltner, and E. Baer, “Optical properties of a bio-inspired gradient refractive index polymer lens,” Opt. Express 16(15), 11540–11547 (2008).
[PubMed]

Benítez, P.

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] [PubMed]

Buljan, M.

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] [PubMed]

Chatzi, E.

P. Kotsidas, E. Chatzi, and V. Modi, “Stationary nonimaging lenses for solar concentration,” Appl. Opt. 49(27), 5183–5191 (2010).
[CrossRef] [PubMed]

Chaves, J.

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] [PubMed]

Cvetkovic, A.

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] [PubMed]

Feuermann, D.

E. A. Katz, J. M. Gordon, W. Tassew, and D. Feuermann, “Photovoltaic characterization of concentrator solar cells by localized irradiation,” J. Appl. Phys. 100(4), 044514 (2006).
[CrossRef]

J. Sun, T. Israeli, T. A. Reddy, K. Scoles, J. M. Gordon, and D. Feuermann, “Modeling and experimental evaluation of passive heat sinks for miniature high-flux photovoltaic concentrators,” J. Sol. Energy Eng. 127(1), 138–145 (2005).
[CrossRef]

J. M. Gordon, E. A. Katz, D. Feuermann, and M. Huleihil, “Toward ultra-high-flux photovoltaic concentration,” Appl. Phys. Lett. 84(18), 3642–3644 (2004).
[CrossRef]

D. Feuermann, J. M. Gordon, and M. Huleihil, “Solar fiber-optic mini-dish concentrators: first experimental results and field experience,” Sol. Energy 72(6), 459–472 (2002).
[CrossRef]

Fleet, E.

G. Beadie, J. S. Shirk, A. Rosenberg, P. A. Lane, E. Fleet, A. R. Kamdar, Y. Jin, M. Ponting, T. Kazmierczak, Y. Yang, A. Hiltner, and E. Baer, “Optical properties of a bio-inspired gradient refractive index polymer lens,” Opt. Express 16(15), 11540–11547 (2008).
[PubMed]

Fletcher, A.

A. Fletcher, T. Murphy, and A. Young, “Solutions of two optical problems,” Proc. R. Soc. Lond. A 223(1153), 216–225 (1954).
[CrossRef]

Goldstein, A.

A. Goldstein and J. M. Gordon, “Tailored solar optics for maximal optical tolerance and concentration,” Sol. Energy Mater. Sol. Cells . in press.

Gordon, J. M.

O. Korech, B. Hirsch, E. A. Katz, and J. M. Gordon, “High-flux characterization of ultra-small multi-junction concentrator solar cells,” Appl. Phys. Lett. 91(6), 064101 (2007).
[CrossRef]

E. A. Katz, J. M. Gordon, W. Tassew, and D. Feuermann, “Photovoltaic characterization of concentrator solar cells by localized irradiation,” J. Appl. Phys. 100(4), 044514 (2006).
[CrossRef]

J. Sun, T. Israeli, T. A. Reddy, K. Scoles, J. M. Gordon, and D. Feuermann, “Modeling and experimental evaluation of passive heat sinks for miniature high-flux photovoltaic concentrators,” J. Sol. Energy Eng. 127(1), 138–145 (2005).
[CrossRef]

J. M. Gordon, E. A. Katz, D. Feuermann, and M. Huleihil, “Toward ultra-high-flux photovoltaic concentration,” Appl. Phys. Lett. 84(18), 3642–3644 (2004).
[CrossRef]

D. Feuermann, J. M. Gordon, and M. Huleihil, “Solar fiber-optic mini-dish concentrators: first experimental results and field experience,” Sol. Energy 72(6), 459–472 (2002).
[CrossRef]

J. M. Gordon, “Spherical gradient-index lenses as perfect imaging and maximum power transfer devices,” Appl. Opt. 39(22), 3825–3832 (2000).
[CrossRef]

A. Goldstein and J. M. Gordon, “Tailored solar optics for maximal optical tolerance and concentration,” Sol. Energy Mater. Sol. Cells . in press.

Hernández, M.

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] [PubMed]

Hiltner, A.

G. Beadie, J. S. Shirk, A. Rosenberg, P. A. Lane, E. Fleet, A. R. Kamdar, Y. Jin, M. Ponting, T. Kazmierczak, Y. Yang, A. Hiltner, and E. Baer, “Optical properties of a bio-inspired gradient refractive index polymer lens,” Opt. Express 16(15), 11540–11547 (2008).
[PubMed]

Hirsch, B.

O. Korech, B. Hirsch, E. A. Katz, and J. M. Gordon, “High-flux characterization of ultra-small multi-junction concentrator solar cells,” Appl. Phys. Lett. 91(6), 064101 (2007).
[CrossRef]

Huleihil, M.

J. M. Gordon, E. A. Katz, D. Feuermann, and M. Huleihil, “Toward ultra-high-flux photovoltaic concentration,” Appl. Phys. Lett. 84(18), 3642–3644 (2004).
[CrossRef]

D. Feuermann, J. M. Gordon, and M. Huleihil, “Solar fiber-optic mini-dish concentrators: first experimental results and field experience,” Sol. Energy 72(6), 459–472 (2002).
[CrossRef]

Israeli, T.

J. Sun, T. Israeli, T. A. Reddy, K. Scoles, J. M. Gordon, and D. Feuermann, “Modeling and experimental evaluation of passive heat sinks for miniature high-flux photovoltaic concentrators,” J. Sol. Energy Eng. 127(1), 138–145 (2005).
[CrossRef]

Jin, Y.

G. Beadie, J. S. Shirk, A. Rosenberg, P. A. Lane, E. Fleet, A. R. Kamdar, Y. Jin, M. Ponting, T. Kazmierczak, Y. Yang, A. Hiltner, and E. Baer, “Optical properties of a bio-inspired gradient refractive index polymer lens,” Opt. Express 16(15), 11540–11547 (2008).
[PubMed]

Kamdar, A. R.

G. Beadie, J. S. Shirk, A. Rosenberg, P. A. Lane, E. Fleet, A. R. Kamdar, Y. Jin, M. Ponting, T. Kazmierczak, Y. Yang, A. Hiltner, and E. Baer, “Optical properties of a bio-inspired gradient refractive index polymer lens,” Opt. Express 16(15), 11540–11547 (2008).
[PubMed]

Katz, E. A.

O. Korech, B. Hirsch, E. A. Katz, and J. M. Gordon, “High-flux characterization of ultra-small multi-junction concentrator solar cells,” Appl. Phys. Lett. 91(6), 064101 (2007).
[CrossRef]

E. A. Katz, J. M. Gordon, W. Tassew, and D. Feuermann, “Photovoltaic characterization of concentrator solar cells by localized irradiation,” J. Appl. Phys. 100(4), 044514 (2006).
[CrossRef]

J. M. Gordon, E. A. Katz, D. Feuermann, and M. Huleihil, “Toward ultra-high-flux photovoltaic concentration,” Appl. Phys. Lett. 84(18), 3642–3644 (2004).
[CrossRef]

Kazmierczak, T.

G. Beadie, J. S. Shirk, A. Rosenberg, P. A. Lane, E. Fleet, A. R. Kamdar, Y. Jin, M. Ponting, T. Kazmierczak, Y. Yang, A. Hiltner, and E. Baer, “Optical properties of a bio-inspired gradient refractive index polymer lens,” Opt. Express 16(15), 11540–11547 (2008).
[PubMed]

Korech, O.

O. Korech, B. Hirsch, E. A. Katz, and J. M. Gordon, “High-flux characterization of ultra-small multi-junction concentrator solar cells,” Appl. Phys. Lett. 91(6), 064101 (2007).
[CrossRef]

Kotsidas, P.

P. Kotsidas, E. Chatzi, and V. Modi, “Stationary nonimaging lenses for solar concentration,” Appl. Opt. 49(27), 5183–5191 (2010).
[CrossRef] [PubMed]

Kuroda, Y.

K. Araki, T. Yano, and Y. Kuroda, “30 kW concentrator photovoltaic system using dome-shaped Fresnel lenses,” Opt. Express 18(S1), A53–A63 (2010).
[CrossRef] [PubMed]

Lane, P. A.

G. Beadie, J. S. Shirk, A. Rosenberg, P. A. Lane, E. Fleet, A. R. Kamdar, Y. Jin, M. Ponting, T. Kazmierczak, Y. Yang, A. Hiltner, and E. Baer, “Optical properties of a bio-inspired gradient refractive index polymer lens,” Opt. Express 16(15), 11540–11547 (2008).
[PubMed]

Martin, F.

J. Q. Xi and F. Martin, “Schubert, J.K. Kim, E.F. Schubert, M. Chen, S.Y. Lin, W. Liu, and J.A. Smart, “Optical thin-film materials with low refractive index for broadband elimination of Fresnel reflection,” Nat. Photonics 1, 176–179 (2007).

Maxwell, J. C.

J. C. Maxwell, “On the general laws of optical instruments,” Q. J. Pure Appl. Math. 2, 233–247 (1854).

McLeod, R. R.

C. Ye and R. R. McLeod, “GRIN lens and lens array fabrication with diffusion-driven photopolymer,” Opt. Lett. 33(22), 2575–2577 (2008).
[CrossRef] [PubMed]

Miñano, J. C.

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] [PubMed]

Modi, V.

P. Kotsidas, E. Chatzi, and V. Modi, “Stationary nonimaging lenses for solar concentration,” Appl. Opt. 49(27), 5183–5191 (2010).
[CrossRef] [PubMed]

Mohedano, R.

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] [PubMed]

Morgan, S. P.

S. P. Morgan, “General solution of the Luneberg lens problem,” J. Appl. Phys. 29(9), 1358–1368 (1958).
[CrossRef]

Murphy, T.

A. Fletcher, T. Murphy, and A. Young, “Solutions of two optical problems,” Proc. R. Soc. Lond. A 223(1153), 216–225 (1954).
[CrossRef]

Ponting, M.

G. Beadie, J. S. Shirk, A. Rosenberg, P. A. Lane, E. Fleet, A. R. Kamdar, Y. Jin, M. Ponting, T. Kazmierczak, Y. Yang, A. Hiltner, and E. Baer, “Optical properties of a bio-inspired gradient refractive index polymer lens,” Opt. Express 16(15), 11540–11547 (2008).
[PubMed]

Reddy, T. A.

J. Sun, T. Israeli, T. A. Reddy, K. Scoles, J. M. Gordon, and D. Feuermann, “Modeling and experimental evaluation of passive heat sinks for miniature high-flux photovoltaic concentrators,” J. Sol. Energy Eng. 127(1), 138–145 (2005).
[CrossRef]

Rosenberg, A.

G. Beadie, J. S. Shirk, A. Rosenberg, P. A. Lane, E. Fleet, A. R. Kamdar, Y. Jin, M. Ponting, T. Kazmierczak, Y. Yang, A. Hiltner, and E. Baer, “Optical properties of a bio-inspired gradient refractive index polymer lens,” Opt. Express 16(15), 11540–11547 (2008).
[PubMed]

Scoles, K.

J. Sun, T. Israeli, T. A. Reddy, K. Scoles, J. M. Gordon, and D. Feuermann, “Modeling and experimental evaluation of passive heat sinks for miniature high-flux photovoltaic concentrators,” J. Sol. Energy Eng. 127(1), 138–145 (2005).
[CrossRef]

Shirk, J. S.

G. Beadie, J. S. Shirk, A. Rosenberg, P. A. Lane, E. Fleet, A. R. Kamdar, Y. Jin, M. Ponting, T. Kazmierczak, Y. Yang, A. Hiltner, and E. Baer, “Optical properties of a bio-inspired gradient refractive index polymer lens,” Opt. Express 16(15), 11540–11547 (2008).
[PubMed]

Sun, J.

J. Sun, T. Israeli, T. A. Reddy, K. Scoles, J. M. Gordon, and D. Feuermann, “Modeling and experimental evaluation of passive heat sinks for miniature high-flux photovoltaic concentrators,” J. Sol. Energy Eng. 127(1), 138–145 (2005).
[CrossRef]

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(4), 044514 (2006).
[CrossRef]

Xi, J. Q.

J. Q. Xi and F. Martin, “Schubert, J.K. Kim, E.F. Schubert, M. Chen, S.Y. Lin, W. Liu, and J.A. Smart, “Optical thin-film materials with low refractive index for broadband elimination of Fresnel reflection,” Nat. Photonics 1, 176–179 (2007).

Yang, Y.

G. Beadie, J. S. Shirk, A. Rosenberg, P. A. Lane, E. Fleet, A. R. Kamdar, Y. Jin, M. Ponting, T. Kazmierczak, Y. Yang, A. Hiltner, and E. Baer, “Optical properties of a bio-inspired gradient refractive index polymer lens,” Opt. Express 16(15), 11540–11547 (2008).
[PubMed]

Yano, T.

K. Araki, T. Yano, and Y. Kuroda, “30 kW concentrator photovoltaic system using dome-shaped Fresnel lenses,” Opt. Express 18(S1), A53–A63 (2010).
[CrossRef] [PubMed]

Ye, C.

C. Ye and R. R. McLeod, “GRIN lens and lens array fabrication with diffusion-driven photopolymer,” Opt. Lett. 33(22), 2575–2577 (2008).
[CrossRef] [PubMed]

Young, A.

A. Fletcher, T. Murphy, and A. Young, “Solutions of two optical problems,” Proc. R. Soc. Lond. A 223(1153), 216–225 (1954).
[CrossRef]

Zamora, P.

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] [PubMed]

Appl. Opt. (2)

P. Kotsidas, E. Chatzi, and V. Modi, “Stationary nonimaging lenses for solar concentration,” Appl. Opt. 49(27), 5183–5191 (2010).
[CrossRef] [PubMed]

J. M. Gordon, “Spherical gradient-index lenses as perfect imaging and maximum power transfer devices,” Appl. Opt. 39(22), 3825–3832 (2000).
[CrossRef]

Appl. Phys. Lett. (2)

J. M. Gordon, E. A. Katz, D. Feuermann, and M. Huleihil, “Toward ultra-high-flux photovoltaic concentration,” Appl. Phys. Lett. 84(18), 3642–3644 (2004).
[CrossRef]

O. Korech, B. Hirsch, E. A. Katz, and J. M. Gordon, “High-flux characterization of ultra-small multi-junction concentrator solar cells,” Appl. Phys. Lett. 91(6), 064101 (2007).
[CrossRef]

J. Appl. Phys. (2)

E. A. Katz, J. M. Gordon, W. Tassew, and D. Feuermann, “Photovoltaic characterization of concentrator solar cells by localized irradiation,” J. Appl. Phys. 100(4), 044514 (2006).
[CrossRef]

S. P. Morgan, “General solution of the Luneberg lens problem,” J. Appl. Phys. 29(9), 1358–1368 (1958).
[CrossRef]

J. Sol. Energy Eng. (1)

J. Sun, T. Israeli, T. A. Reddy, K. Scoles, J. M. Gordon, and D. Feuermann, “Modeling and experimental evaluation of passive heat sinks for miniature high-flux photovoltaic concentrators,” J. Sol. Energy Eng. 127(1), 138–145 (2005).
[CrossRef]

Nat. Photonics (1)

J. Q. Xi and F. Martin, “Schubert, J.K. Kim, E.F. Schubert, M. Chen, S.Y. Lin, W. Liu, and J.A. Smart, “Optical thin-film materials with low refractive index for broadband elimination of Fresnel reflection,” Nat. Photonics 1, 176–179 (2007).

Opt. Express (3)

G. Beadie, J. S. Shirk, A. Rosenberg, P. A. Lane, E. Fleet, A. R. Kamdar, Y. Jin, M. Ponting, T. Kazmierczak, Y. Yang, A. Hiltner, and E. Baer, “Optical properties of a bio-inspired gradient refractive index polymer lens,” Opt. Express 16(15), 11540–11547 (2008).
[PubMed]

K. Araki, T. Yano, and Y. Kuroda, “30 kW concentrator photovoltaic system using dome-shaped Fresnel lenses,” Opt. Express 18(S1), A53–A63 (2010).
[CrossRef] [PubMed]

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Figures (9)

Fig. 1
Fig. 1

(a) Schematic of spherical GRIN lens motion inside a stationary, sealed module the back of which is a static plate (serving double duty as a passive heat sink) to which mm-scale solar cells are thermally bonded. The internal micro-tracker moves the lens array along the surface of a virtual sphere such that the lens focus always lies along the line connecting the lens center to that of the sun. (The extent to which absorber power density must be diluted due to the solar image projected onto the static absorber being elliptical and depending on incidence angle is illustrated below in Section 3, Fig. 5.) Complete stationarity dictates an ostensible loss in collectible energy of ~30% (annual average, clear climate, mid-latitude) because either (b) spacing the lenses results in uncollected radiation, or (c) the lenses are closely packed and incur mutual shading. (d) Angled view of a sample module, purposely undersized in order to illustrate sufficient detail of lens placement.

Fig. 2
Fig. 2

Sample raytraces for perfect-imaging spherical GRIN lenses. The refractive index profile n(r) (r denotes radial position) is noted when expressible analytically. (a) Source and focus are diametrically opposite on the sphere’s surface (Maxwell [9]). (b) Far-field source to a focus on the sphere’s surface (F = 1) (Luneburg [10]). (c) Far-field source and arbitrary F [11]. In (a)-(c), the profiles were restricted to continuous functions, and required n(1) = 1 as well as sizable Δn. (d)-(e) Morgan [12] demonstrated solutions when a homogeneous exterior shell is permitted (the interior profile is continuous), for arbitrary F, illustrated here for two distinct values of the exterior shell’s index and thickness that yield the same F = 1.74 as in part (c).

Fig. 3
Fig. 3

n(r) for the lenses in Fig. 2: (a) Maxwell’s lens, (b) Luneburg’s lens (F = 1), (c) a completely continuum-profile lens of F = 1.74 based on [11]; (d,e) two examples of a F = 1.74 lens comprising an outer uniform shell and an inner continuum distribution (calculations based on [12]) where the minimum n is well above unity and Δn is relatively small.

Fig. 4
Fig. 4

Thickness of the constant-index outer shell as a function of F, for a broad range of nconstant .

Fig. 5
Fig. 5

(a) Focal spot on the static planar absorber at incidence angles θ from 0 to 60° (~8 hr/day of solar beam collection) illustrated for F = 1.74. (b) Enlargement restricted to θ = 0-50°. Substantial power density dilution is required only at the very largest incidence angles. θacc = 5 mrad.

Fig. 6
Fig. 6

Loss of collectible radiation due to concentrated light striking the underside of the static absorber plane. The sphere’s radius is defined as the unit of length. There is no loss at F ≥ √3.

Fig. 8
Fig. 8

Quantifying dispersion losses. Efficiency-concentration curves were generated based on the nominally monochromatic wavelength used for designing the lens, and then based on the AM1.5D solar spectrum. The vertical indicator at C/Cmax = 0.1 highlights that dispersion losses would basically be negligible for current practical CPV designs.

Fig. 7
Fig. 7

The dependence of the efficiency-concentration characteristic on F.

Fig. 9
Fig. 9

Sensitivity to misalignment: efficiency-concentration curves as the absorber is displaced from its intended position, in units of the minimum (θ = 0) focal spot radius R (refer to Fig. 5). For the illustrative CPV scenario with C = 1300 and C/Cmax = 0.1 (the vertical dotted line), R = 0.15 mm, and considerable misalignment incurs only a near-negligible loss.

Equations (4)

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C m a x =   ( N A e x i t / sin ( θ acc ) ) 2
2 r * ( κ ) 1 κ   d r r ρ 2 κ 2 = arcsin κ F + arcsin κ ,     0 κ 1            ρ ( r ) = r n ( r )  
ω ( ρ , F ) = 1 π ρ 1 arcsin ( κ F ) κ 2 ρ 2 d κ ,       Ω ( ρ ) = 2 π ρ 1 G ( κ ) κ 2 ρ 2 d κ ,       G ( κ ) = a 1   κ r ρ 2 κ 2 d r  
arcsin ( 1 F ) 2 a 1   d r r ρ 2 1   . 

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