Abstract

We present a family of three-dimensional concentrators constructed from the photic field generated by a Lambertian emitter. The profile of these concentrators is obtained from the field lines for a two-dimensional truncated wedge and is based on the union between a hyperbola and a tilted parabola. By revolution of this profile, we obtain hyperparabolic concentrators (HPCs). In the limiting case when the focal length of the hyperbola becomes the radius of the exit aperture, the HPC becomes the well-known compound parabolic concentrator. On the other hand, when the focal length of the hyperbola becomes infinite, the HPC achieves the thermodynamic limit of concentration.

© 2009 Optical Society of America

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References

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  1. R. Winston, J. C. Miñano, and P. Benitez, with contributions by N. Shatz and J. C. Bortz, Nonimaging Optics (Elsevier Academic, 2005).
  2. D. Jenkins, R. Winston, J. Bliss, J. O'Gallagher, A. Lewandowski, and C. Bingham, “Solar concentration of 50000 achieved with output power approaching 1 kW,” J. Sol. Energy Eng. 118, 141-145 (1996).
    [CrossRef]
  3. R. Winston and W. T. Welford, “Geometrical vector flux and some new nonimaging concentrators,” J. Opt. Soc. Am. 69, 532-536 (1979).
    [CrossRef]
  4. P. Moon and D. E. Spencer, Photic Field (Massachusetts Institute of Technology Press, 1981).
  5. J. O'Gallagher and R. Winston, “Test of a trumpet secondary concentrator with a paraboloidal dish primary,” Sol. Energy 36, 37-44 (1986).
    [CrossRef]
  6. A. Garcia-Botella, A. A. Fernandez-Balbuean, D. Vázquez, and E. Bernabeu, “Ideal 3D asymmetric concentrator,” Sol. Energy 83, 113-117 (2009).
    [CrossRef]
  7. R. Winston and W. T. Welford, “Ideal flux concentrators as shapes that do not disturb the geometrical vector flux field: a new derivation of the compound parabolic concentrator,” J. Opt. Soc. Am. 69, 536-539 (1979).
    [CrossRef]
  8. P. Greenman, “Geometrical vector flux sinks and ideal flux concentrators,” J. Opt. Soc. Am. 71, 777-779 (1981).
    [CrossRef]
  9. A. Garcia-Botella, A. A. Fernanndez-Balbuena, and E. Bernabeu, “Elliptical concentrators,” Appl. Opt. 45, 7622-7627 (2006).
    [CrossRef] [PubMed]
  10. Tracepro software, http://www.lambdares.com/.
  11. R. L. Garwin, “The design of liquid scintillation cells,” Rev. Sci. Instrum. 23, 755-757 (1952).
    [CrossRef]

2009 (1)

A. Garcia-Botella, A. A. Fernandez-Balbuean, D. Vázquez, and E. Bernabeu, “Ideal 3D asymmetric concentrator,” Sol. Energy 83, 113-117 (2009).
[CrossRef]

2006 (1)

1996 (1)

D. Jenkins, R. Winston, J. Bliss, J. O'Gallagher, A. Lewandowski, and C. Bingham, “Solar concentration of 50000 achieved with output power approaching 1 kW,” J. Sol. Energy Eng. 118, 141-145 (1996).
[CrossRef]

1986 (1)

J. O'Gallagher and R. Winston, “Test of a trumpet secondary concentrator with a paraboloidal dish primary,” Sol. Energy 36, 37-44 (1986).
[CrossRef]

1981 (1)

1979 (2)

1952 (1)

R. L. Garwin, “The design of liquid scintillation cells,” Rev. Sci. Instrum. 23, 755-757 (1952).
[CrossRef]

Benitez, P.

R. Winston, J. C. Miñano, and P. Benitez, with contributions by N. Shatz and J. C. Bortz, Nonimaging Optics (Elsevier Academic, 2005).

Bernabeu,

Bernabeu, E.

A. Garcia-Botella, A. A. Fernandez-Balbuean, D. Vázquez, and E. Bernabeu, “Ideal 3D asymmetric concentrator,” Sol. Energy 83, 113-117 (2009).
[CrossRef]

Bingham, C.

D. Jenkins, R. Winston, J. Bliss, J. O'Gallagher, A. Lewandowski, and C. Bingham, “Solar concentration of 50000 achieved with output power approaching 1 kW,” 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 50000 achieved with output power approaching 1 kW,” J. Sol. Energy Eng. 118, 141-145 (1996).
[CrossRef]

Fernandez-Balbuean, A. A.

A. Garcia-Botella, A. A. Fernandez-Balbuean, D. Vázquez, and E. Bernabeu, “Ideal 3D asymmetric concentrator,” Sol. Energy 83, 113-117 (2009).
[CrossRef]

Fernanndez-Balbuena,

Garcia-Botella, A.

A. Garcia-Botella, A. A. Fernandez-Balbuean, D. Vázquez, and E. Bernabeu, “Ideal 3D asymmetric concentrator,” Sol. Energy 83, 113-117 (2009).
[CrossRef]

A. Garcia-Botella, A. A. Fernanndez-Balbuena, and E. Bernabeu, “Elliptical concentrators,” Appl. Opt. 45, 7622-7627 (2006).
[CrossRef] [PubMed]

Garwin, R. L.

R. L. Garwin, “The design of liquid scintillation cells,” Rev. Sci. Instrum. 23, 755-757 (1952).
[CrossRef]

Greenman, P.

Jenkins, D.

D. Jenkins, R. Winston, J. Bliss, J. O'Gallagher, A. Lewandowski, and C. Bingham, “Solar concentration of 50000 achieved with output power approaching 1 kW,” J. Sol. Energy Eng. 118, 141-145 (1996).
[CrossRef]

Lewandowski, A.

D. Jenkins, R. Winston, J. Bliss, J. O'Gallagher, A. Lewandowski, and C. Bingham, “Solar concentration of 50000 achieved with output power approaching 1 kW,” J. Sol. Energy Eng. 118, 141-145 (1996).
[CrossRef]

Miñano, J. C.

R. Winston, J. C. Miñano, and P. Benitez, with contributions by N. Shatz and J. C. Bortz, Nonimaging Optics (Elsevier Academic, 2005).

Moon, P.

P. Moon and D. E. Spencer, Photic Field (Massachusetts Institute of Technology Press, 1981).

O'Gallagher, J.

D. Jenkins, R. Winston, J. Bliss, J. O'Gallagher, A. Lewandowski, and C. Bingham, “Solar concentration of 50000 achieved with output power approaching 1 kW,” J. Sol. Energy Eng. 118, 141-145 (1996).
[CrossRef]

J. O'Gallagher and R. Winston, “Test of a trumpet secondary concentrator with a paraboloidal dish primary,” Sol. Energy 36, 37-44 (1986).
[CrossRef]

Spencer, D. E.

P. Moon and D. E. Spencer, Photic Field (Massachusetts Institute of Technology Press, 1981).

Vázquez, D.

A. Garcia-Botella, A. A. Fernandez-Balbuean, D. Vázquez, and E. Bernabeu, “Ideal 3D asymmetric concentrator,” Sol. Energy 83, 113-117 (2009).
[CrossRef]

Welford, W. T.

Winston, R.

D. Jenkins, R. Winston, J. Bliss, J. O'Gallagher, A. Lewandowski, and C. Bingham, “Solar concentration of 50000 achieved with output power approaching 1 kW,” J. Sol. Energy Eng. 118, 141-145 (1996).
[CrossRef]

J. O'Gallagher and R. Winston, “Test of a trumpet secondary concentrator with a paraboloidal dish primary,” Sol. Energy 36, 37-44 (1986).
[CrossRef]

R. Winston and W. T. Welford, “Ideal flux concentrators as shapes that do not disturb the geometrical vector flux field: a new derivation of the compound parabolic concentrator,” J. Opt. Soc. Am. 69, 536-539 (1979).
[CrossRef]

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

R. Winston, J. C. Miñano, and P. Benitez, with contributions by N. Shatz and J. C. Bortz, Nonimaging Optics (Elsevier Academic, 2005).

Appl. Opt. (1)

J. Opt. Soc. Am. (3)

J. Sol. Energy Eng. (1)

D. Jenkins, R. Winston, J. Bliss, J. O'Gallagher, A. Lewandowski, and C. Bingham, “Solar concentration of 50000 achieved with output power approaching 1 kW,” J. Sol. Energy Eng. 118, 141-145 (1996).
[CrossRef]

Rev. Sci. Instrum. (1)

R. L. Garwin, “The design of liquid scintillation cells,” Rev. Sci. Instrum. 23, 755-757 (1952).
[CrossRef]

Sol. Energy (2)

J. O'Gallagher and R. Winston, “Test of a trumpet secondary concentrator with a paraboloidal dish primary,” Sol. Energy 36, 37-44 (1986).
[CrossRef]

A. Garcia-Botella, A. A. Fernandez-Balbuean, D. Vázquez, and E. Bernabeu, “Ideal 3D asymmetric concentrator,” Sol. Energy 83, 113-117 (2009).
[CrossRef]

Other (3)

R. Winston, J. C. Miñano, and P. Benitez, with contributions by N. Shatz and J. C. Bortz, Nonimaging Optics (Elsevier Academic, 2005).

Tracepro software, http://www.lambdares.com/.

P. Moon and D. E. Spencer, Photic Field (Massachusetts Institute of Technology Press, 1981).

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Figures (6)

Fig. 1
Fig. 1

Flow lines for the 2D truncated wedge, it shows HPC and CPC profiles.

Fig. 2
Fig. 2

Geometric profile of the HPC.

Fig. 3
Fig. 3

Three 3D HPCs with different hyperbola focal lengths of f a = 18 mm , f b = 30 mm , and f c = 60 mm , and the same acceptance angle θ = 30 ° and radius of exit aperture a = 12 mm .

Fig. 4
Fig. 4

Transmission-angle curves for six 3D HPCs with θ = 10 ° , a = 12 mm : CPC (a, dashed curve), f = 18 mm (curve b), f = 30 mm (curve c), f = 60 mm (curve d), f = 120 mm (curve e), and f = 240 mm (curve f).

Fig. 5
Fig. 5

Transmission-angle curves for six 3D HPCs with θ = 30 ° , a = 12 mm : CPC (a, dashed curve), f = 18 mm (curve b), f = 30 mm (curve c), f = 60 mm (curve d), f = 120 mm (curve e) and f = 240 mm (curve f).

Fig. 6
Fig. 6

Transmission-angle curves for six 3D HPCs with θ = 50 ° , a = 12 mm : CPC (a, dashed curve), f = 18 mm (curve b), f = 30 mm (curve c), f = 60 mm (curve d), f = 120 mm (curve e) and f = 240 mm (curve f).

Equations (4)

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L = ( f + a sin θ ) cot θ .
x u = ( f 2 a 2 ) ( f tan θ a sec θ ) ( f 2 tan 2 θ a 2 sec 2 θ ) .
f p = ( f + a sin θ ) sin θ = f sin θ + a .
y 2 a 2 x 2 f 2 a 2 = 1 , 0 x x u , [ ( y + f ) cos θ + x sin θ ] 2 = 4 ( f sin θ + a ) [ x cos θ ( y + f ) sin θ + f sin θ + a ] , x u x L .

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