Abstract

A certain class of microstructured surfaces in 2D geometry is studied on the basis of an approximation of infinitesimal microstructure elements. The macroprofile of the surfaces is then treated as a new type of optical surface with a deflection law that differs from the law of reflection and Snell’s law. We discuss the propagation of wavefronts by general microstructured surfaces and the discontinuity of the eikonal function at the microstructure. Naturally, a classification of the microstructures is obtained (regular and anomalous), and the concept of 2D ideal microstructures is also introduced, since they are used for coupling two macroscopic extended bundles.

© 2006 Optical Society of America

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References

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  1. R. Winston, J. C. Miñano, and P. Benítez, Nonimaging Optics (Elsevier, 2005).
  2. E. M. Kritchman, A. A. Friesem, and G. Yekutieli “Efficient Fresnel lens for solar concentrator,” Sol. Eng. 22, 119–123 (1979).
    [Crossref]
  3. M. J. O’Neill, “Solar concentrator and energy collection system,” U.S. Patent No. 4,069,812 (1978).
  4. H. Ries and R. Leutz, “Tailored Fresnel Optics I - Global Shape,” in Design of Efficient Illumination Systems, J. Koshel ed., Proc. SPIE 5186, 154–158 (2003).
    [Crossref]
  5. V. Medvedev, D. Pelka, and W. A. Parkyn, “Uniform LED illuminator for miniature displays,” in Illumination and Source Engineerin, A. V. Arecchi ed., Proc. SPIE 3428, 142–153 (1998).
    [Crossref]
  6. J. C. Miñano and P. Benítez, “Dispositivo con lente discontinua de reflexión total interna y dioptrico asférico para concentración o colimación de energía radiante,” Spanish patent ES 2,157,846 B1.
  7. J. C. Miñanoet al. “High Efficiency Non-Imaging Optics,” US Patent No. 6,639,733.
  8. J. L. Álvarez, M. Hernández, P. Benítez, and J. C. Miñano, “TIR-R concentrator: a new compact high-gain SMS design,” in Nonimaging Optics: Maximum Efficiency Light Transfer VI, R. Winston ed., Proc. SPIE 4446, 32–42 (2001).
    [Crossref]
  9. J. Chaves and M. Collares-Pereira, “Ideal concentrators with gaps,” Appl. Opt.,  41, 1267–1276 (2002).
    [Crossref] [PubMed]
  10. R. Winston, “Cavity enhancement by controlled directional scattering,” Appl. Opt. 19, 195–197 (1980).
    [Crossref] [PubMed]
  11. J. Bortz, N. Shatz, and R. Winston. “Performance limitations of translationally symmetric nonimaging devices,” in Nonimaging Optics: Maximum Efficiency Light Transfer VI, R. Winston ed., Proc. SPIE, 4446, (2001).
    [Crossref]
  12. R. Leutz and H. Ries. “Micro-structured light guides overcoming the two-dimensional concentration limit,” Appl. Opt. 44, 6885–6889 (2005).
    [Crossref] [PubMed]
  13. T. L. R. Davenport, W. J. Cassarly, and T. A. Hough “Optimization of non-rotationally symmetric angle-to-area converting light pipe systems,” International Optical Design Conference (2006)
  14. W. A. Parkyn and D. Pelka, “Compact non-imaging lens with totally internal reflecting facets,” in Nonimaging Optics: Maximum Efficiency Light Transfer, R. Winston ed., Proc. SPIE 1528, 70–81 (1991).
    [Crossref]
  15. A. Luque and E. Lorenzo, “Conditions of achieving ideal and Lambertian symmetrical solar concentrators,” Appl. Opt. 21, 3736–3738 (1982).
    [Crossref] [PubMed]
  16. R. Leutz and A. Suzuki, Nonimaging Fresnel Lenses: Design and Performance of Solar Concentrators, (Springer Verlag, Heidelberg, 2001).
  17. P. Benitez, et al. “On the analysis of rotational symmetric microstructured surfaces,” Opt. Express (to be published).
    [PubMed]
  18. R. Leutz and H. Ries, “Tailored Fresnel Optics II — The facets,” in Design of Efficient Illumination Systems, J. Koshel ed., Proc. SPIE 5186, 159–165 (2003).
    [Crossref]

2005 (1)

2003 (2)

H. Ries and R. Leutz, “Tailored Fresnel Optics I - Global Shape,” in Design of Efficient Illumination Systems, J. Koshel ed., Proc. SPIE 5186, 154–158 (2003).
[Crossref]

R. Leutz and H. Ries, “Tailored Fresnel Optics II — The facets,” in Design of Efficient Illumination Systems, J. Koshel ed., Proc. SPIE 5186, 159–165 (2003).
[Crossref]

2002 (1)

2001 (1)

J. L. Álvarez, M. Hernández, P. Benítez, and J. C. Miñano, “TIR-R concentrator: a new compact high-gain SMS design,” in Nonimaging Optics: Maximum Efficiency Light Transfer VI, R. Winston ed., Proc. SPIE 4446, 32–42 (2001).
[Crossref]

1998 (1)

V. Medvedev, D. Pelka, and W. A. Parkyn, “Uniform LED illuminator for miniature displays,” in Illumination and Source Engineerin, A. V. Arecchi ed., Proc. SPIE 3428, 142–153 (1998).
[Crossref]

1991 (1)

W. A. Parkyn and D. Pelka, “Compact non-imaging lens with totally internal reflecting facets,” in Nonimaging Optics: Maximum Efficiency Light Transfer, R. Winston ed., Proc. SPIE 1528, 70–81 (1991).
[Crossref]

1982 (1)

1980 (1)

1979 (1)

E. M. Kritchman, A. A. Friesem, and G. Yekutieli “Efficient Fresnel lens for solar concentrator,” Sol. Eng. 22, 119–123 (1979).
[Crossref]

Álvarez, J. L.

J. L. Álvarez, M. Hernández, P. Benítez, and J. C. Miñano, “TIR-R concentrator: a new compact high-gain SMS design,” in Nonimaging Optics: Maximum Efficiency Light Transfer VI, R. Winston ed., Proc. SPIE 4446, 32–42 (2001).
[Crossref]

Benitez, P.

P. Benitez, et al. “On the analysis of rotational symmetric microstructured surfaces,” Opt. Express (to be published).
[PubMed]

Benítez, P.

J. L. Álvarez, M. Hernández, P. Benítez, and J. C. Miñano, “TIR-R concentrator: a new compact high-gain SMS design,” in Nonimaging Optics: Maximum Efficiency Light Transfer VI, R. Winston ed., Proc. SPIE 4446, 32–42 (2001).
[Crossref]

J. C. Miñano and P. Benítez, “Dispositivo con lente discontinua de reflexión total interna y dioptrico asférico para concentración o colimación de energía radiante,” Spanish patent ES 2,157,846 B1.

R. Winston, J. C. Miñano, and P. Benítez, Nonimaging Optics (Elsevier, 2005).

Bortz, J.

J. Bortz, N. Shatz, and R. Winston. “Performance limitations of translationally symmetric nonimaging devices,” in Nonimaging Optics: Maximum Efficiency Light Transfer VI, R. Winston ed., Proc. SPIE, 4446, (2001).
[Crossref]

Cassarly, W. J.

T. L. R. Davenport, W. J. Cassarly, and T. A. Hough “Optimization of non-rotationally symmetric angle-to-area converting light pipe systems,” International Optical Design Conference (2006)

Chaves, J.

Collares-Pereira, M.

Davenport, T. L. R.

T. L. R. Davenport, W. J. Cassarly, and T. A. Hough “Optimization of non-rotationally symmetric angle-to-area converting light pipe systems,” International Optical Design Conference (2006)

Friesem, A. A.

E. M. Kritchman, A. A. Friesem, and G. Yekutieli “Efficient Fresnel lens for solar concentrator,” Sol. Eng. 22, 119–123 (1979).
[Crossref]

Hernández, M.

J. L. Álvarez, M. Hernández, P. Benítez, and J. C. Miñano, “TIR-R concentrator: a new compact high-gain SMS design,” in Nonimaging Optics: Maximum Efficiency Light Transfer VI, R. Winston ed., Proc. SPIE 4446, 32–42 (2001).
[Crossref]

Hough, T. A.

T. L. R. Davenport, W. J. Cassarly, and T. A. Hough “Optimization of non-rotationally symmetric angle-to-area converting light pipe systems,” International Optical Design Conference (2006)

Kritchman, E. M.

E. M. Kritchman, A. A. Friesem, and G. Yekutieli “Efficient Fresnel lens for solar concentrator,” Sol. Eng. 22, 119–123 (1979).
[Crossref]

Leutz, R.

R. Leutz and H. Ries. “Micro-structured light guides overcoming the two-dimensional concentration limit,” Appl. Opt. 44, 6885–6889 (2005).
[Crossref] [PubMed]

H. Ries and R. Leutz, “Tailored Fresnel Optics I - Global Shape,” in Design of Efficient Illumination Systems, J. Koshel ed., Proc. SPIE 5186, 154–158 (2003).
[Crossref]

R. Leutz and H. Ries, “Tailored Fresnel Optics II — The facets,” in Design of Efficient Illumination Systems, J. Koshel ed., Proc. SPIE 5186, 159–165 (2003).
[Crossref]

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

Lorenzo, E.

Luque, A.

Medvedev, V.

V. Medvedev, D. Pelka, and W. A. Parkyn, “Uniform LED illuminator for miniature displays,” in Illumination and Source Engineerin, A. V. Arecchi ed., Proc. SPIE 3428, 142–153 (1998).
[Crossref]

Miñano, J. C.

J. L. Álvarez, M. Hernández, P. Benítez, and J. C. Miñano, “TIR-R concentrator: a new compact high-gain SMS design,” in Nonimaging Optics: Maximum Efficiency Light Transfer VI, R. Winston ed., Proc. SPIE 4446, 32–42 (2001).
[Crossref]

J. C. Miñano and P. Benítez, “Dispositivo con lente discontinua de reflexión total interna y dioptrico asférico para concentración o colimación de energía radiante,” Spanish patent ES 2,157,846 B1.

J. C. Miñanoet al. “High Efficiency Non-Imaging Optics,” US Patent No. 6,639,733.

R. Winston, J. C. Miñano, and P. Benítez, Nonimaging Optics (Elsevier, 2005).

O’Neill, M. J.

M. J. O’Neill, “Solar concentrator and energy collection system,” U.S. Patent No. 4,069,812 (1978).

Parkyn, W. A.

V. Medvedev, D. Pelka, and W. A. Parkyn, “Uniform LED illuminator for miniature displays,” in Illumination and Source Engineerin, A. V. Arecchi ed., Proc. SPIE 3428, 142–153 (1998).
[Crossref]

W. A. Parkyn and D. Pelka, “Compact non-imaging lens with totally internal reflecting facets,” in Nonimaging Optics: Maximum Efficiency Light Transfer, R. Winston ed., Proc. SPIE 1528, 70–81 (1991).
[Crossref]

Pelka, D.

V. Medvedev, D. Pelka, and W. A. Parkyn, “Uniform LED illuminator for miniature displays,” in Illumination and Source Engineerin, A. V. Arecchi ed., Proc. SPIE 3428, 142–153 (1998).
[Crossref]

W. A. Parkyn and D. Pelka, “Compact non-imaging lens with totally internal reflecting facets,” in Nonimaging Optics: Maximum Efficiency Light Transfer, R. Winston ed., Proc. SPIE 1528, 70–81 (1991).
[Crossref]

Ries, H.

R. Leutz and H. Ries. “Micro-structured light guides overcoming the two-dimensional concentration limit,” Appl. Opt. 44, 6885–6889 (2005).
[Crossref] [PubMed]

R. Leutz and H. Ries, “Tailored Fresnel Optics II — The facets,” in Design of Efficient Illumination Systems, J. Koshel ed., Proc. SPIE 5186, 159–165 (2003).
[Crossref]

H. Ries and R. Leutz, “Tailored Fresnel Optics I - Global Shape,” in Design of Efficient Illumination Systems, J. Koshel ed., Proc. SPIE 5186, 154–158 (2003).
[Crossref]

Shatz, N.

J. Bortz, N. Shatz, and R. Winston. “Performance limitations of translationally symmetric nonimaging devices,” in Nonimaging Optics: Maximum Efficiency Light Transfer VI, R. Winston ed., Proc. SPIE, 4446, (2001).
[Crossref]

Suzuki, A.

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

Winston, R.

R. Winston, “Cavity enhancement by controlled directional scattering,” Appl. Opt. 19, 195–197 (1980).
[Crossref] [PubMed]

J. Bortz, N. Shatz, and R. Winston. “Performance limitations of translationally symmetric nonimaging devices,” in Nonimaging Optics: Maximum Efficiency Light Transfer VI, R. Winston ed., Proc. SPIE, 4446, (2001).
[Crossref]

R. Winston, J. C. Miñano, and P. Benítez, Nonimaging Optics (Elsevier, 2005).

Yekutieli, G.

E. M. Kritchman, A. A. Friesem, and G. Yekutieli “Efficient Fresnel lens for solar concentrator,” Sol. Eng. 22, 119–123 (1979).
[Crossref]

Appl. Opt. (4)

Proc. SPIE (5)

W. A. Parkyn and D. Pelka, “Compact non-imaging lens with totally internal reflecting facets,” in Nonimaging Optics: Maximum Efficiency Light Transfer, R. Winston ed., Proc. SPIE 1528, 70–81 (1991).
[Crossref]

R. Leutz and H. Ries, “Tailored Fresnel Optics II — The facets,” in Design of Efficient Illumination Systems, J. Koshel ed., Proc. SPIE 5186, 159–165 (2003).
[Crossref]

H. Ries and R. Leutz, “Tailored Fresnel Optics I - Global Shape,” in Design of Efficient Illumination Systems, J. Koshel ed., Proc. SPIE 5186, 154–158 (2003).
[Crossref]

V. Medvedev, D. Pelka, and W. A. Parkyn, “Uniform LED illuminator for miniature displays,” in Illumination and Source Engineerin, A. V. Arecchi ed., Proc. SPIE 3428, 142–153 (1998).
[Crossref]

J. L. Álvarez, M. Hernández, P. Benítez, and J. C. Miñano, “TIR-R concentrator: a new compact high-gain SMS design,” in Nonimaging Optics: Maximum Efficiency Light Transfer VI, R. Winston ed., Proc. SPIE 4446, 32–42 (2001).
[Crossref]

Sol. Eng. (1)

E. M. Kritchman, A. A. Friesem, and G. Yekutieli “Efficient Fresnel lens for solar concentrator,” Sol. Eng. 22, 119–123 (1979).
[Crossref]

Other (8)

M. J. O’Neill, “Solar concentrator and energy collection system,” U.S. Patent No. 4,069,812 (1978).

R. Winston, J. C. Miñano, and P. Benítez, Nonimaging Optics (Elsevier, 2005).

J. C. Miñano and P. Benítez, “Dispositivo con lente discontinua de reflexión total interna y dioptrico asférico para concentración o colimación de energía radiante,” Spanish patent ES 2,157,846 B1.

J. C. Miñanoet al. “High Efficiency Non-Imaging Optics,” US Patent No. 6,639,733.

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

P. Benitez, et al. “On the analysis of rotational symmetric microstructured surfaces,” Opt. Express (to be published).
[PubMed]

T. L. R. Davenport, W. J. Cassarly, and T. A. Hough “Optimization of non-rotationally symmetric angle-to-area converting light pipe systems,” International Optical Design Conference (2006)

J. Bortz, N. Shatz, and R. Winston. “Performance limitations of translationally symmetric nonimaging devices,” in Nonimaging Optics: Maximum Efficiency Light Transfer VI, R. Winston ed., Proc. SPIE, 4446, (2001).
[Crossref]

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Figures (5)

Fig. 1.
Fig. 1.

Example of microstructured surface: (a) Detail of microstructures, (b) Macroscopic view.

Fig. 2.
Fig. 2.

Microstructured optical surface deflecting bundle B1 into bundle B2 (the ray trajectories have been drawn beyond the optical surface for the definition of the eikonal functions).

Fig. 3.
Fig. 3.

Regular and anomalous deflecting microstructures.

Fig. 4.
Fig. 4.

Ideal microstructured line coupling the rays within directions v-v onto the segment AA

Fig. 5.
Fig. 5.

(a).–(b). Fresnel lens facets that constitute an ideal microstructure. Facet design in a lossless TIR lens for (c) a receiver and an (d) emitter.

Equations (9)

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

D ( s ) = O 1 ( x ( s ) , y ( s ) ) O 2 ( x ( s ) , y ( s ) )
dD ( s ) ds = O 1 ( x ( s ) , y ( s ) ) . ( x ˙ ( s ) , y ˙ ( s ) ) O 2 ( x ( s ) , y ( s ) ) . ( x ˙ ( s ) , y ˙ ( s ) ) =
= n i ( s ) sin θ i ( s ) n d ( s ) sin θ d ( s )
O 1 ( x ( s ) , y ( s ) ) O 2 ( x ( s ) , y ( s ) ) = D ( s ) = 0 s ( n i ( t ) sin θ i ( t ) n d ( t ) sin θ d ( t ) ) dt
dE i = dE d n i ( sin θ i sin θ i ) = n d ( sin θ d sin θ d )
n i sin θ i n d sin θ d = n i sin θ i n d sin θ d D ( s ) = D ( s )
2 y sin α = X A X A
dE i = dE d n i ( sin θ i sin θ i ) = n d ( sin θ d sin θ d )
n i sin θ i + n d sin θ d = n i sin θ i + n d sin θ d S ( s ) = S ( s )

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