Abstract

The concept of the vector flux field was first introduced as a photometrical theory and later developed in the field of nonimaging optics; it has provided new perspectives in the design of concentrators, overcoming standard ray tracing techniques. The flux field method has shown that reflective concentrators with the geometry of the field lines achieve the theoretical limit of concentration. In this paper we study the role of surfaces orthogonal to the field vector J. For rotationally symmetric systems J is orthogonal to its curl, and then a family of surfaces orthogonal to the lines of J exists, which can be called the family of surfaces of constant pseudopotential. Using the concept of the flux tube, it is possible to demonstrate that refractive concentrators with the shape of these pseudopotential surfaces achieve the theoretical limit of concentration.

© 2011 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. A. Gershun, “The light field,” J. Math. Phys. 18, 51–151 (1939).
  2. P. Moon and D. E. Spencer, Photic Field (Massachusetts Institute of Technology Press, 1981).
  3. J. T. Withrop, “Propagation of structural information in optical wave fields,” J. Opt. Soc. Am. 61, 15–30 (1971).
    [CrossRef]
  4. R. Winston and W. T. Welford “Geometrical vector flux and some new nonimaging concentrators,” J. Opt. Soc. Am. 69, 532–536 (1979).
    [CrossRef]
  5. 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]
  6. R. Winston, J. C. Miñano, and P. Benitez, with contributions by N. Shatz and J. C. Bortz, Nonimaging Optics (Elsevier Academic, 2005).
  7. A. García-Botella, A. A. Fernández-Balbuena, D. Vázquez, E. Bernabeu, and A. González-Cano, “Hyperparabolic concentrators,” Appl. Opt. 48, 712–715 (2009).
    [CrossRef] [PubMed]
  8. V. Fock, “Zur Berechnung der Beleuchtungsstärke,” Zeitschrift für Physik 28, 102–118 (1924).
    [CrossRef]
  9. TracePro software, http://www.lambdares.com/.
  10. J. O’Gallagher, Nonimaging Optics in Solar Energy (Morgan & Claypool, 2008).

2009 (1)

1979 (2)

1971 (1)

1939 (1)

A. Gershun, “The light field,” J. Math. Phys. 18, 51–151 (1939).

1924 (1)

V. Fock, “Zur Berechnung der Beleuchtungsstärke,” Zeitschrift für Physik 28, 102–118 (1924).
[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, E.

Bortz, J. C.

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

Fernández-Balbuena, A. A.

Fock, V.

V. Fock, “Zur Berechnung der Beleuchtungsstärke,” Zeitschrift für Physik 28, 102–118 (1924).
[CrossRef]

García-Botella, A.

Gershun, A.

A. Gershun, “The light field,” J. Math. Phys. 18, 51–151 (1939).

González-Cano, A.

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.

J. O’Gallagher, Nonimaging Optics in Solar Energy (Morgan & Claypool, 2008).

Shatz, N.

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

Spencer, D. E.

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

Vázquez, D.

Welford, W. T.

Winston, R.

Withrop, J. T.

Appl. Opt. (1)

J. Math. Phys. (1)

A. Gershun, “The light field,” J. Math. Phys. 18, 51–151 (1939).

J. Opt. Soc. Am. (3)

Zeitschrift für Physik (1)

V. Fock, “Zur Berechnung der Beleuchtungsstärke,” Zeitschrift für Physik 28, 102–118 (1924).
[CrossRef]

Other (4)

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

J. O’Gallagher, Nonimaging Optics in Solar Energy (Morgan & Claypool, 2008).

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

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

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (6)

Fig. 1
Fig. 1

Field lines and pseudopotential lines produced by a Lambertian strip.

Fig. 2
Fig. 2

Flux tube produced by a Lambertian disk; the wall of the tube is tangent to the J vector.

Fig. 3
Fig. 3

(a) Field line produced by a Lambertian disk and a spherical diopter, n 1 = 1.51 and n 2 = 1 —nonpseudopotential interface, (b) field line produced by a Lambertian disk and a refractive ellipse with A and A as foci, n 1 = 1.51 and n 2 = 1 —pseudopotential interface.

Fig. 4
Fig. 4

Finite source concentrator built by the rotational symmetry of the profile in Fig. 3b; the dielectric interface is an oblate spheroid.

Fig. 5
Fig. 5

Field lines and pseudopotential lines produced by a truncated wedge.

Fig. 6
Fig. 6

Transmission angle curves for 2D dielectric CPC with different interface geometries. Dash-dotted curve, curved interface with r = 200 mm ; dashed curve, curved interface with r = 400 mm ; solid curve, flat pseudopotential interface.

Equations (4)

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

curl J 0 .
( J ( 1 ) J ( 2 ) ) · N = 0 ,
( J ( 1 ) J ( 2 ) ) × N = Q ,
T max = ( n R out R in ) 2 = 0.2052 ,

Metrics