Abstract

We provide a general formulation for the design of any dual-surface aplanatic Fresnel optic (including combinations of refractive and reflective surfaces), with categories of devices that had not previously been recognized. Raytrace simulations for representative Fresnel aplanats in collimation (illumination) mode reveal compact designs with radiative efficiencies close to those of their aplanatic continuous non-Fresnel counterparts, and optical performance approaching the thermodynamic limit for radiative transfer.

© 2017 Optical Society of America

Full Article  |  PDF Article
OSA Recommended Articles
New types of refractive-reflective aplanats for maximal flux concentration and collimation

Heylal Mashaal, Daniel Feuermann, and Jeffrey M. Gordon
Opt. Express 23(24) A1541-A1548 (2015)

Aplanatic lenses revisited: the full landscape

Heylal Mashaal, Daniel Feuermann, and Jeffrey M. Gordon
Appl. Opt. 55(10) 2537-2542 (2016)

Aplanatic optics for solar concentration

Jeffrey M. Gordon
Opt. Express 18(S1) A41-A52 (2010)

References

  • View by:
  • |
  • |
  • |

  1. J. Elton, “A light to lighten our darkness: lighthouse optics and the later development of Fresnel’s revolutionary refracting lens 1780–1900,” Int. J. Hist. Eng. Technol. 79(2), 183–244 (2009).
    [Crossref]
  2. W. T. Xie, Y. J. Dai, R. Z. Wang, and K. Sumathy, “Concentrated solar energy applications using Fresnel lenses: A review,” Renew. Sustain. Energy Rev. 15(6), 2588–2606 (2011).
    [Crossref]
  3. R. Leutz and A. Suzuki, Nonimaging Fresnel Lenses (Springer, 2001).
  4. J. Chaves, Introduction to Nonimaging Optics (CRC, 2008).
  5. D. F. Vanderwerf, Applied Prismatic and Reflective Optics (SPIE, 2010).
  6. R. Winston, J. C. Miñano, P. Benítez, N. Shatz, and J. Bortz, Nonimaging Optics (Elsevier, 2005).
  7. J. C. Miñano, P. Benítez, and J. C. González, “RX: a nonimaging concentrator,” Appl. Opt. 34(13), 2226–2235 (1995).
    [Crossref] [PubMed]
  8. P. Benítez and J. C. Miñano, “Ultrahigh-numerical-aperture imaging concentrator,” J. Opt. Soc. Am. A 14(8), 1988–1997 (1997).
    [Crossref]
  9. J. M. Gordon, “Aplanatic optics for solar concentration,” Opt. Express 18, A41–A52 (2010).
    [Crossref]
  10. N. Ostroumov, J. M. Gordon, and D. Feuermann, “Panorama of dual-mirror aplanats for maximum concentration,” Appl. Opt. 48(26), 4926–4931 (2009).
    [Crossref] [PubMed]
  11. H. Mashaal, D. Feuermann, and J. M. Gordon, “New types of refractive-reflective aplanats for maximal flux concentration and collimation,” Opt. Express 23(24), A1541–A1548 (2015).
    [Crossref] [PubMed]
  12. H. Mashaal, D. Feuermann, and J. M. Gordon, “Basic categories of dual-contour reflective-refractive aplanats,” Opt. Lett. 40(21), 4907–4910 (2015).
    [Crossref] [PubMed]
  13. H. Mashaal, D. Feuermann, and J. M. Gordon, “Aplanatic lenses revisited: the full landscape,” Appl. Opt. 55(10), 2537–2542 (2016).
    [Crossref] [PubMed]
  14. W. A. Kleinhans, “Aberrations of curved zone plates and Fresnel lenses,” Appl. Opt. 16(6), 1701–1704 (1977).
    [Crossref] [PubMed]
  15. A. L. Belostotsky and A. S. Leonov, “Design of aplanatic waveguide Frensel lenses and aberration-free planar optical systems,” J. Lightwave Technol. 11(8), 1314–1319 (1993).
    [Crossref]
  16. Y. Sato, K. Mizutani, N. Wakatsuki, and T. Nakamura, “Design for aplanatic Fresnel acoustic lens for underwater imaging,” Jpn. J. Appl. Phys. 48(7), 07GL04 (2009).
    [Crossref]
  17. E. M. Kritchman, A. A. Friesem, and G. Yekutieli, “Efficient Fresnel lens for solar concentration,” Sol. Energy 22(2), 119–123 (1979).
    [Crossref]
  18. E. M. Kritchman, A. A. Friesem, and G. Yekutieli, “Highly concentrating Fresnel lenses,” Appl. Opt. 18(15), 2688–2695 (1979).
    [Crossref] [PubMed]

2016 (1)

2015 (2)

2011 (1)

W. T. Xie, Y. J. Dai, R. Z. Wang, and K. Sumathy, “Concentrated solar energy applications using Fresnel lenses: A review,” Renew. Sustain. Energy Rev. 15(6), 2588–2606 (2011).
[Crossref]

2010 (1)

2009 (3)

N. Ostroumov, J. M. Gordon, and D. Feuermann, “Panorama of dual-mirror aplanats for maximum concentration,” Appl. Opt. 48(26), 4926–4931 (2009).
[Crossref] [PubMed]

J. Elton, “A light to lighten our darkness: lighthouse optics and the later development of Fresnel’s revolutionary refracting lens 1780–1900,” Int. J. Hist. Eng. Technol. 79(2), 183–244 (2009).
[Crossref]

Y. Sato, K. Mizutani, N. Wakatsuki, and T. Nakamura, “Design for aplanatic Fresnel acoustic lens for underwater imaging,” Jpn. J. Appl. Phys. 48(7), 07GL04 (2009).
[Crossref]

1997 (1)

1995 (1)

1993 (1)

A. L. Belostotsky and A. S. Leonov, “Design of aplanatic waveguide Frensel lenses and aberration-free planar optical systems,” J. Lightwave Technol. 11(8), 1314–1319 (1993).
[Crossref]

1979 (2)

E. M. Kritchman, A. A. Friesem, and G. Yekutieli, “Efficient Fresnel lens for solar concentration,” Sol. Energy 22(2), 119–123 (1979).
[Crossref]

E. M. Kritchman, A. A. Friesem, and G. Yekutieli, “Highly concentrating Fresnel lenses,” Appl. Opt. 18(15), 2688–2695 (1979).
[Crossref] [PubMed]

1977 (1)

Belostotsky, A. L.

A. L. Belostotsky and A. S. Leonov, “Design of aplanatic waveguide Frensel lenses and aberration-free planar optical systems,” J. Lightwave Technol. 11(8), 1314–1319 (1993).
[Crossref]

Benítez, P.

Dai, Y. J.

W. T. Xie, Y. J. Dai, R. Z. Wang, and K. Sumathy, “Concentrated solar energy applications using Fresnel lenses: A review,” Renew. Sustain. Energy Rev. 15(6), 2588–2606 (2011).
[Crossref]

Elton, J.

J. Elton, “A light to lighten our darkness: lighthouse optics and the later development of Fresnel’s revolutionary refracting lens 1780–1900,” Int. J. Hist. Eng. Technol. 79(2), 183–244 (2009).
[Crossref]

Feuermann, D.

Friesem, A. A.

E. M. Kritchman, A. A. Friesem, and G. Yekutieli, “Highly concentrating Fresnel lenses,” Appl. Opt. 18(15), 2688–2695 (1979).
[Crossref] [PubMed]

E. M. Kritchman, A. A. Friesem, and G. Yekutieli, “Efficient Fresnel lens for solar concentration,” Sol. Energy 22(2), 119–123 (1979).
[Crossref]

González, J. C.

Gordon, J. M.

Kleinhans, W. A.

Kritchman, E. M.

E. M. Kritchman, A. A. Friesem, and G. Yekutieli, “Highly concentrating Fresnel lenses,” Appl. Opt. 18(15), 2688–2695 (1979).
[Crossref] [PubMed]

E. M. Kritchman, A. A. Friesem, and G. Yekutieli, “Efficient Fresnel lens for solar concentration,” Sol. Energy 22(2), 119–123 (1979).
[Crossref]

Leonov, A. S.

A. L. Belostotsky and A. S. Leonov, “Design of aplanatic waveguide Frensel lenses and aberration-free planar optical systems,” J. Lightwave Technol. 11(8), 1314–1319 (1993).
[Crossref]

Mashaal, H.

Miñano, J. C.

Mizutani, K.

Y. Sato, K. Mizutani, N. Wakatsuki, and T. Nakamura, “Design for aplanatic Fresnel acoustic lens for underwater imaging,” Jpn. J. Appl. Phys. 48(7), 07GL04 (2009).
[Crossref]

Nakamura, T.

Y. Sato, K. Mizutani, N. Wakatsuki, and T. Nakamura, “Design for aplanatic Fresnel acoustic lens for underwater imaging,” Jpn. J. Appl. Phys. 48(7), 07GL04 (2009).
[Crossref]

Ostroumov, N.

Sato, Y.

Y. Sato, K. Mizutani, N. Wakatsuki, and T. Nakamura, “Design for aplanatic Fresnel acoustic lens for underwater imaging,” Jpn. J. Appl. Phys. 48(7), 07GL04 (2009).
[Crossref]

Sumathy, K.

W. T. Xie, Y. J. Dai, R. Z. Wang, and K. Sumathy, “Concentrated solar energy applications using Fresnel lenses: A review,” Renew. Sustain. Energy Rev. 15(6), 2588–2606 (2011).
[Crossref]

Wakatsuki, N.

Y. Sato, K. Mizutani, N. Wakatsuki, and T. Nakamura, “Design for aplanatic Fresnel acoustic lens for underwater imaging,” Jpn. J. Appl. Phys. 48(7), 07GL04 (2009).
[Crossref]

Wang, R. Z.

W. T. Xie, Y. J. Dai, R. Z. Wang, and K. Sumathy, “Concentrated solar energy applications using Fresnel lenses: A review,” Renew. Sustain. Energy Rev. 15(6), 2588–2606 (2011).
[Crossref]

Xie, W. T.

W. T. Xie, Y. J. Dai, R. Z. Wang, and K. Sumathy, “Concentrated solar energy applications using Fresnel lenses: A review,” Renew. Sustain. Energy Rev. 15(6), 2588–2606 (2011).
[Crossref]

Yekutieli, G.

E. M. Kritchman, A. A. Friesem, and G. Yekutieli, “Efficient Fresnel lens for solar concentration,” Sol. Energy 22(2), 119–123 (1979).
[Crossref]

E. M. Kritchman, A. A. Friesem, and G. Yekutieli, “Highly concentrating Fresnel lenses,” Appl. Opt. 18(15), 2688–2695 (1979).
[Crossref] [PubMed]

Appl. Opt. (5)

Int. J. Hist. Eng. Technol. (1)

J. Elton, “A light to lighten our darkness: lighthouse optics and the later development of Fresnel’s revolutionary refracting lens 1780–1900,” Int. J. Hist. Eng. Technol. 79(2), 183–244 (2009).
[Crossref]

J. Lightwave Technol. (1)

A. L. Belostotsky and A. S. Leonov, “Design of aplanatic waveguide Frensel lenses and aberration-free planar optical systems,” J. Lightwave Technol. 11(8), 1314–1319 (1993).
[Crossref]

J. Opt. Soc. Am. A (1)

Jpn. J. Appl. Phys. (1)

Y. Sato, K. Mizutani, N. Wakatsuki, and T. Nakamura, “Design for aplanatic Fresnel acoustic lens for underwater imaging,” Jpn. J. Appl. Phys. 48(7), 07GL04 (2009).
[Crossref]

Opt. Express (2)

Opt. Lett. (1)

Renew. Sustain. Energy Rev. (1)

W. T. Xie, Y. J. Dai, R. Z. Wang, and K. Sumathy, “Concentrated solar energy applications using Fresnel lenses: A review,” Renew. Sustain. Energy Rev. 15(6), 2588–2606 (2011).
[Crossref]

Sol. Energy (1)

E. M. Kritchman, A. A. Friesem, and G. Yekutieli, “Efficient Fresnel lens for solar concentration,” Sol. Energy 22(2), 119–123 (1979).
[Crossref]

Other (4)

R. Leutz and A. Suzuki, Nonimaging Fresnel Lenses (Springer, 2001).

J. Chaves, Introduction to Nonimaging Optics (CRC, 2008).

D. F. Vanderwerf, Applied Prismatic and Reflective Optics (SPIE, 2010).

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

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

Cross-section for a continuous-surface (non-Fresnel) RR aplanat, from the collimation perspective. The focus f at the center of the source is located at the origin of the coordinate system. The exit wavefront is denoted by w.f.

Fig. 2
Fig. 2

Geometry of a sample RR Fresnel aplanat (lens). Points Pi represent the boundary points of aperture zone i, and points Si represent the boundary points of source zone i.

Fig. 3
Fig. 3

(a) RX Fresnel aplanat (with c = −1, p = −1, s = 1, sub-category RX-2A in [11]), with the aperture facets constrained to have the same height, for the case {n1 = 1, n2 = n3 = 1.52}. (b) A curved RR Fresnel aplanat (with c = −1, p = −1, s = −1, sub-category RR-1A in [13]), for the case {n1 = n3 = 1, n2 = 1.52}. The boundary points of the primary and secondary zones reside on circles of different radii, both centered at the focus. (c) RR design (with c = −1, p = −1, s = −1, sub-category RR-1A in [13]), constrained such that the primary Fresnel zones have equal widths, for the case {n1 = n3 = 1.52, n2 = 1}. (d) The continuous non-Fresnel aplanat of Fig. 3(e) re-designed as a Fresnel aplanat constrained to have equal heights for the facets of the aperture contour. A continuous non-Fresnel RR aplanat of the type shown in Fig. 3(c) is introduced in the center of the optic in order to reduce nominal gap losses. (e) Continuous non-Fresnel XR aplanat (with c = −1, p = 1, s = −1, sub-category XR-3 in [12]), for the case {n1 = n2 = 1, n3 = 1.52}. Dashed outlines in (a)-(c) refer to the corresponding continuous non-Fresnel aplanats.

Fig. 4
Fig. 4

Raytrace illustration for the limit of a point source, for an (a) XR Fresnel aplanat with a central non-Fresnel RR aplanatic lens introduced to basically eliminate optical losses stemming from the inherent central gap in the aplanat design, and (b) RR Fresnel aplanat.

Fig. 5
Fig. 5

Radiative efficiency generated with a monochromatic extended Lambertian emitter, for Fresnel (F, dashed curves with marker identifiers) and continuous non-Fresnel (NF, solid curves) aplanats. (a) RR design of Fig. 3(c). (b) XR designs of Fig. 3(e) and Fig. 3(d) but without a central aplanatic lens that basically eliminates gap losses. The abscissa is the ratio of the projected solid angle at far-field Ω to its value at the thermodynamic limit Ωth. Results are presented for collimation half-angles of 5 (blue), 10 (red), 20 (green) and 40 (purple) mrad.

Fig. 6
Fig. 6

Radiative efficiency generated with a monochromatic extended Lambertian emitter for the XR Fresnel aplanat of Fig. 3(d), with (FL, dashed curves with marker identifiers) and without (F, solid curves) a central aplanatic lens. The abscissa is the ratio of the projected solid angle at far-field Ω relative to its value at the thermodynamic limit Ωth. Results are presented for collimation half-angles of 5 (blue), 10 (red), 20 (green) and 40 (purple) mrad.

Equations (7)

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

A exit / A s = (N A s /N A exit ) 2 = { n s sin θ s /[ n exit sin θ exit ] } 2 ,
n 1 L 1 + n 2 L 2 + n 3 L 3 =cons t 1 .
F=r/sinϕ=cons t 2
n 1 ( H a Y a )+ n 2 ( X a X s ) 2 + ( Y a Y s ) 2 + n 3 X s 2 + Y s 2 n 2 ( H a H s ) 2 + ( R a +c R s ) 2 n 3 H s 2 + R s 2 =0,
{ Refraction: d Y a d X a = m ( n 2 / n 1 ) 2 +p ( n 2 / n 1 ) 2 ( m 2 +1 ) ( m 2 +1 ( n 2 / n 1 ) 2 m 2 ) Reflection: d Y a d X a = 1 m+p m 2 +1 ,
Y s =s X s ( R a X a ) 2 ( 1+ H s 2 R s 2 )1 .
F i = R p,i /sin θ s =cons t 3 .

Metrics