Abstract

The exigencies of high-concentration photovoltaics motivate optics that (1) obviate the need for optical bonds, (2) exhibit maximal optical tolerance, (3) are not damaged at off-axis orientation, and (4) allow convenient location of the solar cell and heat sink. We show that dual-mirror unfolded aplanats can satisfy all these criteria. Lens enhancement improves compactness and, with millimeter-scale cells, concentrator depth is only a few centimeters, amenable to precise large-volume fabrication.

© 2008 Optical Society of America

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References

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  1. C. Algora, in Concentrator Photovoltaics, A.Luque and V. M. Andreev, eds. (Springer, 2007), Chap. 5.
  2. J. M. Gordon, in Concentrator Photovoltaics, A.Luque and V.M.Andreev, eds. (Springer, 2007), Chap. 6.
  3. V. D. Rumyantsev, in Concentrator Photovoltaics, A.Luque and V.M.Andreev, eds. (Springer, 2007), Chap. 8.
  4. M. Yamaguchi, K. Araki, and T. Takamoto, in Concentrator Photovoltaics, A.Luque and V.M.Andreev, eds. (Springer, 2007), Chap. 15.
  5. G. Conley and S. Horne, SolFocus Inc. (Technical prospectus and private communication, 2007).
  6. E. A. Katz, J. M. Gordon, W. Tassew, and D. Feuermann, J. Appl. Phys. 100, 044514 (2006).
    [CrossRef]
  7. O. Korech, B. Hirsch, E. A. Katz, and J. M. Gordon, Appl. Phys. Lett. 91, 064101 (2007).
    [CrossRef]
  8. J. Sun, T. Israeli, T. A. Reddy, K. Scoles, J. M. Gordon, and D. Feuermann, J. Sol. Energy Eng. 127, 138 (2005).
    [CrossRef]
  9. J. M. Gordon and D. Feuermann, Appl. Opt. 44, 2327 (2005).
    [CrossRef] [PubMed]
  10. R. Winston and J. M. Gordon, Opt. Lett. 30, 2617 (2005).
    [CrossRef] [PubMed]
  11. G. Glenn, Spectrolab Inc., 12500 Gladstone Avenue, Sylmar, California 91342 (Technical prospectus and private communication, 2004).
  12. G. Herrnring and W. Weidner, U.S. patent 2,819,404 (1958).
  13. D. Korsch, Appl. Opt. 19, 499 (1980).
    [CrossRef] [PubMed]
  14. D. Lynden-Bell, Mon. Not. R. Astron. Soc. 334, 787 (2002).
    [CrossRef]
  15. R. V. Willstrop and D. Lynden-Bell, Mon. Not. R. Astron. Soc. 342, 33 (2003).
    [CrossRef]
  16. A. K. Head, Proc. Phys. Soc. London Sect. B 70, 945 (1957).
    [CrossRef]
  17. A. Rabl, Active Solar Collectors and Their Applications (Oxford U. Press, 1985), Chap. 5.
  18. J. M. Gordon, D. Feuermann, and P. Young, ''Unfolded aplanatic optics for maximum-performance solar concentration,'' patent pending, 16 Dec. 2007.

2007 (6)

C. Algora, in Concentrator Photovoltaics, A.Luque and V. M. Andreev, eds. (Springer, 2007), Chap. 5.

J. M. Gordon, in Concentrator Photovoltaics, A.Luque and V.M.Andreev, eds. (Springer, 2007), Chap. 6.

V. D. Rumyantsev, in Concentrator Photovoltaics, A.Luque and V.M.Andreev, eds. (Springer, 2007), Chap. 8.

M. Yamaguchi, K. Araki, and T. Takamoto, in Concentrator Photovoltaics, A.Luque and V.M.Andreev, eds. (Springer, 2007), Chap. 15.

G. Conley and S. Horne, SolFocus Inc. (Technical prospectus and private communication, 2007).

O. Korech, B. Hirsch, E. A. Katz, and J. M. Gordon, Appl. Phys. Lett. 91, 064101 (2007).
[CrossRef]

2006 (1)

E. A. Katz, J. M. Gordon, W. Tassew, and D. Feuermann, J. Appl. Phys. 100, 044514 (2006).
[CrossRef]

2005 (3)

J. Sun, T. Israeli, T. A. Reddy, K. Scoles, J. M. Gordon, and D. Feuermann, J. Sol. Energy Eng. 127, 138 (2005).
[CrossRef]

J. M. Gordon and D. Feuermann, Appl. Opt. 44, 2327 (2005).
[CrossRef] [PubMed]

R. Winston and J. M. Gordon, Opt. Lett. 30, 2617 (2005).
[CrossRef] [PubMed]

2004 (1)

G. Glenn, Spectrolab Inc., 12500 Gladstone Avenue, Sylmar, California 91342 (Technical prospectus and private communication, 2004).

2003 (1)

R. V. Willstrop and D. Lynden-Bell, Mon. Not. R. Astron. Soc. 342, 33 (2003).
[CrossRef]

2002 (1)

D. Lynden-Bell, Mon. Not. R. Astron. Soc. 334, 787 (2002).
[CrossRef]

1985 (1)

A. Rabl, Active Solar Collectors and Their Applications (Oxford U. Press, 1985), Chap. 5.

1980 (1)

1958 (1)

G. Herrnring and W. Weidner, U.S. patent 2,819,404 (1958).

1957 (1)

A. K. Head, Proc. Phys. Soc. London Sect. B 70, 945 (1957).
[CrossRef]

Algora, C.

C. Algora, in Concentrator Photovoltaics, A.Luque and V. M. Andreev, eds. (Springer, 2007), Chap. 5.

Andreev, V. M.

C. Algora, in Concentrator Photovoltaics, A.Luque and V. M. Andreev, eds. (Springer, 2007), Chap. 5.

Araki, K.

M. Yamaguchi, K. Araki, and T. Takamoto, in Concentrator Photovoltaics, A.Luque and V.M.Andreev, eds. (Springer, 2007), Chap. 15.

Conley, G.

G. Conley and S. Horne, SolFocus Inc. (Technical prospectus and private communication, 2007).

Feuermann, D.

E. A. Katz, J. M. Gordon, W. Tassew, and D. Feuermann, J. Appl. Phys. 100, 044514 (2006).
[CrossRef]

J. M. Gordon and D. Feuermann, Appl. Opt. 44, 2327 (2005).
[CrossRef] [PubMed]

J. Sun, T. Israeli, T. A. Reddy, K. Scoles, J. M. Gordon, and D. Feuermann, J. Sol. Energy Eng. 127, 138 (2005).
[CrossRef]

J. M. Gordon, D. Feuermann, and P. Young, ''Unfolded aplanatic optics for maximum-performance solar concentration,'' patent pending, 16 Dec. 2007.

Glenn, G.

G. Glenn, Spectrolab Inc., 12500 Gladstone Avenue, Sylmar, California 91342 (Technical prospectus and private communication, 2004).

Gordon, J. M.

O. Korech, B. Hirsch, E. A. Katz, and J. M. Gordon, Appl. Phys. Lett. 91, 064101 (2007).
[CrossRef]

J. M. Gordon, in Concentrator Photovoltaics, A.Luque and V.M.Andreev, eds. (Springer, 2007), Chap. 6.

E. A. Katz, J. M. Gordon, W. Tassew, and D. Feuermann, J. Appl. Phys. 100, 044514 (2006).
[CrossRef]

J. M. Gordon and D. Feuermann, Appl. Opt. 44, 2327 (2005).
[CrossRef] [PubMed]

R. Winston and J. M. Gordon, Opt. Lett. 30, 2617 (2005).
[CrossRef] [PubMed]

J. Sun, T. Israeli, T. A. Reddy, K. Scoles, J. M. Gordon, and D. Feuermann, J. Sol. Energy Eng. 127, 138 (2005).
[CrossRef]

J. M. Gordon, D. Feuermann, and P. Young, ''Unfolded aplanatic optics for maximum-performance solar concentration,'' patent pending, 16 Dec. 2007.

Head, A. K.

A. K. Head, Proc. Phys. Soc. London Sect. B 70, 945 (1957).
[CrossRef]

Herrnring, G.

G. Herrnring and W. Weidner, U.S. patent 2,819,404 (1958).

Hirsch, B.

O. Korech, B. Hirsch, E. A. Katz, and J. M. Gordon, Appl. Phys. Lett. 91, 064101 (2007).
[CrossRef]

Horne, S.

G. Conley and S. Horne, SolFocus Inc. (Technical prospectus and private communication, 2007).

Israeli, T.

J. Sun, T. Israeli, T. A. Reddy, K. Scoles, J. M. Gordon, and D. Feuermann, J. Sol. Energy Eng. 127, 138 (2005).
[CrossRef]

Katz, E. A.

O. Korech, B. Hirsch, E. A. Katz, and J. M. Gordon, Appl. Phys. Lett. 91, 064101 (2007).
[CrossRef]

E. A. Katz, J. M. Gordon, W. Tassew, and D. Feuermann, J. Appl. Phys. 100, 044514 (2006).
[CrossRef]

Korech, O.

O. Korech, B. Hirsch, E. A. Katz, and J. M. Gordon, Appl. Phys. Lett. 91, 064101 (2007).
[CrossRef]

Korsch, D.

Lynden-Bell, D.

R. V. Willstrop and D. Lynden-Bell, Mon. Not. R. Astron. Soc. 342, 33 (2003).
[CrossRef]

D. Lynden-Bell, Mon. Not. R. Astron. Soc. 334, 787 (2002).
[CrossRef]

Rabl, A.

A. Rabl, Active Solar Collectors and Their Applications (Oxford U. Press, 1985), Chap. 5.

Reddy, T. A.

J. Sun, T. Israeli, T. A. Reddy, K. Scoles, J. M. Gordon, and D. Feuermann, J. Sol. Energy Eng. 127, 138 (2005).
[CrossRef]

Rumyantsev, V. D.

V. D. Rumyantsev, in Concentrator Photovoltaics, A.Luque and V.M.Andreev, eds. (Springer, 2007), Chap. 8.

Scoles, K.

J. Sun, T. Israeli, T. A. Reddy, K. Scoles, J. M. Gordon, and D. Feuermann, J. Sol. Energy Eng. 127, 138 (2005).
[CrossRef]

Sun, J.

J. Sun, T. Israeli, T. A. Reddy, K. Scoles, J. M. Gordon, and D. Feuermann, J. Sol. Energy Eng. 127, 138 (2005).
[CrossRef]

Takamoto, T.

M. Yamaguchi, K. Araki, and T. Takamoto, in Concentrator Photovoltaics, A.Luque and V.M.Andreev, eds. (Springer, 2007), Chap. 15.

Tassew, W.

E. A. Katz, J. M. Gordon, W. Tassew, and D. Feuermann, J. Appl. Phys. 100, 044514 (2006).
[CrossRef]

Weidner, W.

G. Herrnring and W. Weidner, U.S. patent 2,819,404 (1958).

Willstrop, R. V.

R. V. Willstrop and D. Lynden-Bell, Mon. Not. R. Astron. Soc. 342, 33 (2003).
[CrossRef]

Winston, R.

Yamaguchi, M.

M. Yamaguchi, K. Araki, and T. Takamoto, in Concentrator Photovoltaics, A.Luque and V.M.Andreev, eds. (Springer, 2007), Chap. 15.

Young, P.

J. M. Gordon, D. Feuermann, and P. Young, ''Unfolded aplanatic optics for maximum-performance solar concentration,'' patent pending, 16 Dec. 2007.

Appl. Opt. (2)

Appl. Phys. Lett. (1)

O. Korech, B. Hirsch, E. A. Katz, and J. M. Gordon, Appl. Phys. Lett. 91, 064101 (2007).
[CrossRef]

J. Appl. Phys. (1)

E. A. Katz, J. M. Gordon, W. Tassew, and D. Feuermann, J. Appl. Phys. 100, 044514 (2006).
[CrossRef]

J. Sol. Energy Eng. (1)

J. Sun, T. Israeli, T. A. Reddy, K. Scoles, J. M. Gordon, and D. Feuermann, J. Sol. Energy Eng. 127, 138 (2005).
[CrossRef]

Mon. Not. R. Astron. Soc. (2)

D. Lynden-Bell, Mon. Not. R. Astron. Soc. 334, 787 (2002).
[CrossRef]

R. V. Willstrop and D. Lynden-Bell, Mon. Not. R. Astron. Soc. 342, 33 (2003).
[CrossRef]

Opt. Lett. (1)

Proc. Phys. Soc. London Sect. B (1)

A. K. Head, Proc. Phys. Soc. London Sect. B 70, 945 (1957).
[CrossRef]

Other (9)

A. Rabl, Active Solar Collectors and Their Applications (Oxford U. Press, 1985), Chap. 5.

J. M. Gordon, D. Feuermann, and P. Young, ''Unfolded aplanatic optics for maximum-performance solar concentration,'' patent pending, 16 Dec. 2007.

G. Glenn, Spectrolab Inc., 12500 Gladstone Avenue, Sylmar, California 91342 (Technical prospectus and private communication, 2004).

G. Herrnring and W. Weidner, U.S. patent 2,819,404 (1958).

C. Algora, in Concentrator Photovoltaics, A.Luque and V. M. Andreev, eds. (Springer, 2007), Chap. 5.

J. M. Gordon, in Concentrator Photovoltaics, A.Luque and V.M.Andreev, eds. (Springer, 2007), Chap. 6.

V. D. Rumyantsev, in Concentrator Photovoltaics, A.Luque and V.M.Andreev, eds. (Springer, 2007), Chap. 8.

M. Yamaguchi, K. Araki, and T. Takamoto, in Concentrator Photovoltaics, A.Luque and V.M.Andreev, eds. (Springer, 2007), Chap. 15.

G. Conley and S. Horne, SolFocus Inc. (Technical prospectus and private communication, 2007).

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Figures (5)

Fig. 1
Fig. 1

Dual-mirror folded aplanat PV concentrators [2, 5] designed for C f = 500 suns with an optical bond at a glass–PV cell interface: (a) air-filled, with a glass terminal concentrator; (b) all-glass, externally mirrored.

Fig. 2
Fig. 2

Cross section of a glazed axisymmetric dual-mirror unfolded aplanat. Solid contours are mirrored surfaces. Dotted curves are unbuilt continuations calculated with Eq. (2). The cell (not shown) is centered at focus F. Here u = 0.162 , K = 1.072 , W = 0.03 , A R = 2.02 , and sin ( θ e ) = 0.9 is the largest value up to which reflective losses remain about the same as those at normal incidence for concentrator cells [11].

Fig. 3
Fig. 3

Cross section of a dual-mirror unfolded aplanat with an f/4 planoconvex lens of diameter equal to that of the waist: u = 0.305 , K = 1.122 , sin ( θ e ) = 0.9 , W = 0.1 , and A R = 1.28 . A raytrace at incidence angle 5 ° illustrates robustness off-axis.

Fig. 4
Fig. 4

Cross section of paraboloids with the absorber at the focus. Entry radius = sin ( θ e ) = 0.9 . (a) W = 0.03 , A R = 2.28 ; (b) W = 0.1 , A R = 1.21 , f/4 lens.

Fig. 5
Fig. 5

Angular tolerance of nominal 500-sun concentrators: (a) for the lensless aplanat (Fig. 2) and paraboloid [Fig. 4a] and (b) with a lens, for the aplanat (Fig. 3) and paraboloid [Fig. 4b]. Dotted vertical lines denote the bound of Eq. (1).

Equations (8)

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

θ t n sin ( θ e ) C g θ s ,
r p = sin ( ϕ ) ,
x p = u cos 2 ( ϕ 2 ) + ( g ( ϕ ) u ) ( 1 K f ( ϕ ) ) cos 4 ( ϕ 2 ) ,
r s = 2 K u f ( ϕ ) tan ( ϕ 2 ) K f ( ϕ ) tan 2 ( ϕ 2 ) + g ( ϕ ) ,
x s = r s cot ( ϕ ) ,
g ( ϕ ) = u ( 1 u ) tan 2 ( ϕ 2 ) ,
f ( ϕ ) = g ( ϕ ) u u ( u 1 ) ,
0 ϕ θ e .

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