Abstract

We identify and evaluate new categories of dual-contour refractive-reflective aplanatic lenses, some of which can satisfy total internal reflection at the secondary surface. Raytrace simulations for a representative design in both solar concentrator and collimator (illumination) mode reveal high efficiency while approaching the thermodynamic limit for radiative transfer.

© 2015 Optical Society of America

Full Article  |  PDF Article
OSA Recommended Articles
Aplanatic Fresnel optics

Heylal Mashaal, Daniel Feuermann, and Jeffrey M. Gordon
Opt. Express 25(8) A274-A282 (2017)

Aplanatic optics for solar concentration

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

Aplanatic lenses revisited: the full landscape

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

References

  • View by:
  • |
  • |
  • |

  1. K. Schwarzschild, “Untersuchungen zur geometrischen Optik I-III,” Abh. Konigl. Ges. Wis. Gottingen Mathphys. Kl. 4, Nos. 1–3 (1905–1906).
  2. A. K. Head, “The two-mirror aplanat,” Proc. Phys. Soc. London Sec. B 70(10), 945–949 (1957).
    [Crossref]
  3. D. Lynden-Bell, “Exact optics: a unification of optical telescope design,” Mon. Not. R. Astron. Soc. 334(4), 787–796 (2002).
    [Crossref]
  4. R. V. Willstrop and D. Lynden-Bell, “Exact optics – II. Exploration of designs on- and off-axis,” Mon. Not. R. Astron. Soc. 342(1), 33–49 (2003).
    [Crossref]
  5. J. M. Gordon and D. Feuermann, “Optical performance at the thermodynamic limit with tailored imaging designs,” Appl. Opt. 44(12), 2327–2331 (2005).
    [Crossref] [PubMed]
  6. R. Winston and J. M. Gordon, “Planar concentrators near the étendue limit,” Opt. Lett. 30(19), 2617–2619 (2005).
    [Crossref] [PubMed]
  7. J. M. Gordon, D. Feuermann, and P. Young, “Unfolded aplanats for high-concentration photovoltaics,” Opt. Lett. 33(10), 1114–1116 (2008).
    [Crossref] [PubMed]
  8. 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]
  9. R. Winston, J. C. Miñano, P. Benítez, N. Shatz, and J. Bortz, Nonimaging Optics (Elsevier, 2005).
  10. J. C. Miñano, P. Benítez, and J. C. González, “RX: a nonimaging concentrator,” Appl. Opt. 34(13), 2226–2235 (1995).
    [Crossref] [PubMed]
  11. P. Benítez and J. C. Miñano, “Ultrahigh-numerical-aperture imaging concentrator,” J. Opt. Soc. Am. A 14(8), 1988–1997 (1997).
    [Crossref]
  12. R. Winston and W. Zhang, “Novel aplanatic designs,” Opt. Lett. 34(19), 3018–3019 (2009).
    [Crossref] [PubMed]
  13. A. Goldstein and J. M. Gordon, “Tailored solar optics for maximal optical tolerance and concentration,” Sol. Energy Mater. Sol. Cells 95(2), 624–629 (2011).
    [Crossref]
  14. J. M. Gordon, E. A. Katz, D. Feuermann, and M. Huleihil, “Toward ultra-high-flux photovoltaic concentration,” Appl. Phys. Lett. 84(18), 3642–3644 (2004).
    [Crossref]
  15. E. A. Katz, J. M. Gordon, W. Tassew, and D. Feueremann, “Photovoltaic characterization of concentrator cells by localized irradiation,” J. Appl. Phys. 100(4), 044514 (2006).
    [Crossref]
  16. O. Korech, B. Hirsch, E. A. Katz, and J. M. Gordon, “High-flux characterization of ultrasmall multijunction concentrator solar cells,” Appl. Phys. Lett. 91(6), 064101 (2007).
    [Crossref]
  17. R. Winston, “Dielectric compound parabolic concentrators,” Appl. Opt. 15(2), 291–292 (1976).
    [Crossref] [PubMed]
  18. X. Ning, R. Winston, and J. O’Gallagher, “Dielectric totally internally reflecting concentrators,” Appl. Opt. 26(2), 300–305 (1987).
    [Crossref] [PubMed]
  19. R. P. Friedman and J. M. Gordon, “Optical designs for ultrahigh-flux infrared and solar energy collection: monolithic dielectric tailored edge-ray concentrators,” Appl. Opt. 35(34), 6684–6691 (1996).
    [Crossref] [PubMed]
  20. J. Bortz and N. Shatz, “Relationships between the generalized functional method and other methods of nonimaging optical design,” Appl. Opt. 50(10), 1488–1500 (2011).
    [Crossref] [PubMed]

2011 (2)

A. Goldstein and J. M. Gordon, “Tailored solar optics for maximal optical tolerance and concentration,” Sol. Energy Mater. Sol. Cells 95(2), 624–629 (2011).
[Crossref]

J. Bortz and N. Shatz, “Relationships between the generalized functional method and other methods of nonimaging optical design,” Appl. Opt. 50(10), 1488–1500 (2011).
[Crossref] [PubMed]

2009 (2)

2008 (1)

2007 (1)

O. Korech, B. Hirsch, E. A. Katz, and J. M. Gordon, “High-flux characterization of ultrasmall multijunction concentrator solar cells,” Appl. Phys. Lett. 91(6), 064101 (2007).
[Crossref]

2006 (1)

E. A. Katz, J. M. Gordon, W. Tassew, and D. Feueremann, “Photovoltaic characterization of concentrator cells by localized irradiation,” J. Appl. Phys. 100(4), 044514 (2006).
[Crossref]

2005 (2)

2004 (1)

J. M. Gordon, E. A. Katz, D. Feuermann, and M. Huleihil, “Toward ultra-high-flux photovoltaic concentration,” Appl. Phys. Lett. 84(18), 3642–3644 (2004).
[Crossref]

2003 (1)

R. V. Willstrop and D. Lynden-Bell, “Exact optics – II. Exploration of designs on- and off-axis,” Mon. Not. R. Astron. Soc. 342(1), 33–49 (2003).
[Crossref]

2002 (1)

D. Lynden-Bell, “Exact optics: a unification of optical telescope design,” Mon. Not. R. Astron. Soc. 334(4), 787–796 (2002).
[Crossref]

1997 (1)

1996 (1)

1995 (1)

1987 (1)

1976 (1)

1957 (1)

A. K. Head, “The two-mirror aplanat,” Proc. Phys. Soc. London Sec. B 70(10), 945–949 (1957).
[Crossref]

Benítez, P.

Bortz, J.

Feueremann, D.

E. A. Katz, J. M. Gordon, W. Tassew, and D. Feueremann, “Photovoltaic characterization of concentrator cells by localized irradiation,” J. Appl. Phys. 100(4), 044514 (2006).
[Crossref]

Feuermann, D.

Friedman, R. P.

Goldstein, A.

A. Goldstein and J. M. Gordon, “Tailored solar optics for maximal optical tolerance and concentration,” Sol. Energy Mater. Sol. Cells 95(2), 624–629 (2011).
[Crossref]

González, J. C.

Gordon, J. M.

A. Goldstein and J. M. Gordon, “Tailored solar optics for maximal optical tolerance and concentration,” Sol. Energy Mater. Sol. Cells 95(2), 624–629 (2011).
[Crossref]

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. M. Gordon, D. Feuermann, and P. Young, “Unfolded aplanats for high-concentration photovoltaics,” Opt. Lett. 33(10), 1114–1116 (2008).
[Crossref] [PubMed]

O. Korech, B. Hirsch, E. A. Katz, and J. M. Gordon, “High-flux characterization of ultrasmall multijunction concentrator solar cells,” Appl. Phys. Lett. 91(6), 064101 (2007).
[Crossref]

E. A. Katz, J. M. Gordon, W. Tassew, and D. Feueremann, “Photovoltaic characterization of concentrator cells by localized irradiation,” J. Appl. Phys. 100(4), 044514 (2006).
[Crossref]

R. Winston and J. M. Gordon, “Planar concentrators near the étendue limit,” Opt. Lett. 30(19), 2617–2619 (2005).
[Crossref] [PubMed]

J. M. Gordon and D. Feuermann, “Optical performance at the thermodynamic limit with tailored imaging designs,” Appl. Opt. 44(12), 2327–2331 (2005).
[Crossref] [PubMed]

J. M. Gordon, E. A. Katz, D. Feuermann, and M. Huleihil, “Toward ultra-high-flux photovoltaic concentration,” Appl. Phys. Lett. 84(18), 3642–3644 (2004).
[Crossref]

R. P. Friedman and J. M. Gordon, “Optical designs for ultrahigh-flux infrared and solar energy collection: monolithic dielectric tailored edge-ray concentrators,” Appl. Opt. 35(34), 6684–6691 (1996).
[Crossref] [PubMed]

Head, A. K.

A. K. Head, “The two-mirror aplanat,” Proc. Phys. Soc. London Sec. B 70(10), 945–949 (1957).
[Crossref]

Hirsch, B.

O. Korech, B. Hirsch, E. A. Katz, and J. M. Gordon, “High-flux characterization of ultrasmall multijunction concentrator solar cells,” Appl. Phys. Lett. 91(6), 064101 (2007).
[Crossref]

Huleihil, M.

J. M. Gordon, E. A. Katz, D. Feuermann, and M. Huleihil, “Toward ultra-high-flux photovoltaic concentration,” Appl. Phys. Lett. 84(18), 3642–3644 (2004).
[Crossref]

Katz, E. A.

O. Korech, B. Hirsch, E. A. Katz, and J. M. Gordon, “High-flux characterization of ultrasmall multijunction concentrator solar cells,” Appl. Phys. Lett. 91(6), 064101 (2007).
[Crossref]

E. A. Katz, J. M. Gordon, W. Tassew, and D. Feueremann, “Photovoltaic characterization of concentrator cells by localized irradiation,” J. Appl. Phys. 100(4), 044514 (2006).
[Crossref]

J. M. Gordon, E. A. Katz, D. Feuermann, and M. Huleihil, “Toward ultra-high-flux photovoltaic concentration,” Appl. Phys. Lett. 84(18), 3642–3644 (2004).
[Crossref]

Korech, O.

O. Korech, B. Hirsch, E. A. Katz, and J. M. Gordon, “High-flux characterization of ultrasmall multijunction concentrator solar cells,” Appl. Phys. Lett. 91(6), 064101 (2007).
[Crossref]

Lynden-Bell, D.

R. V. Willstrop and D. Lynden-Bell, “Exact optics – II. Exploration of designs on- and off-axis,” Mon. Not. R. Astron. Soc. 342(1), 33–49 (2003).
[Crossref]

D. Lynden-Bell, “Exact optics: a unification of optical telescope design,” Mon. Not. R. Astron. Soc. 334(4), 787–796 (2002).
[Crossref]

Miñano, J. C.

Ning, X.

O’Gallagher, J.

Ostroumov, N.

Schwarzschild, K.

K. Schwarzschild, “Untersuchungen zur geometrischen Optik I-III,” Abh. Konigl. Ges. Wis. Gottingen Mathphys. Kl. 4, Nos. 1–3 (1905–1906).

Shatz, N.

Tassew, W.

E. A. Katz, J. M. Gordon, W. Tassew, and D. Feueremann, “Photovoltaic characterization of concentrator cells by localized irradiation,” J. Appl. Phys. 100(4), 044514 (2006).
[Crossref]

Willstrop, R. V.

R. V. Willstrop and D. Lynden-Bell, “Exact optics – II. Exploration of designs on- and off-axis,” Mon. Not. R. Astron. Soc. 342(1), 33–49 (2003).
[Crossref]

Winston, R.

Young, P.

Zhang, W.

Abh. Konigl. Ges. Wis. Gottingen Mathphys. Kl. (1)

K. Schwarzschild, “Untersuchungen zur geometrischen Optik I-III,” Abh. Konigl. Ges. Wis. Gottingen Mathphys. Kl. 4, Nos. 1–3 (1905–1906).

Appl. Opt. (7)

Appl. Phys. Lett. (2)

J. M. Gordon, E. A. Katz, D. Feuermann, and M. Huleihil, “Toward ultra-high-flux photovoltaic concentration,” Appl. Phys. Lett. 84(18), 3642–3644 (2004).
[Crossref]

O. Korech, B. Hirsch, E. A. Katz, and J. M. Gordon, “High-flux characterization of ultrasmall multijunction concentrator solar cells,” Appl. Phys. Lett. 91(6), 064101 (2007).
[Crossref]

J. Appl. Phys. (1)

E. A. Katz, J. M. Gordon, W. Tassew, and D. Feueremann, “Photovoltaic characterization of concentrator cells by localized irradiation,” J. Appl. Phys. 100(4), 044514 (2006).
[Crossref]

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

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

D. Lynden-Bell, “Exact optics: a unification of optical telescope design,” Mon. Not. R. Astron. Soc. 334(4), 787–796 (2002).
[Crossref]

R. V. Willstrop and D. Lynden-Bell, “Exact optics – II. Exploration of designs on- and off-axis,” Mon. Not. R. Astron. Soc. 342(1), 33–49 (2003).
[Crossref]

Opt. Lett. (3)

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

A. K. Head, “The two-mirror aplanat,” Proc. Phys. Soc. London Sec. B 70(10), 945–949 (1957).
[Crossref]

Sol. Energy Mater. Sol. Cells (1)

A. Goldstein and J. M. Gordon, “Tailored solar optics for maximal optical tolerance and concentration,” Sol. Energy Mater. Sol. Cells 95(2), 624–629 (2011).
[Crossref]

Other (1)

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 (5)

Fig. 1
Fig. 1 RX aplanat geometry. The focus f is located at the origin of the coordinate system. This particular illustration corresponds to design parameters {c = 1, p = −1, s = 1} (vide infra).
Fig. 2
Fig. 2 The 3 RX aplanat categories that require a mirrored secondary. RX-2A is the point-source limit of the nonimaging SMS RX concentrator depicted in [10,11]. RX-2B is distinguished from RX-2A by a convex vs concave secondary. In all cases, representative ray trajectories are shown. ‘f’ denotes the focus, and w.f. the normal incident wave-front. All drawings have the same scale.
Fig. 3
Fig. 3 The 3 RX aplanat categories that can satisfy TIR at the secondary surface. Note that RX-5B achieves TIR by a void in the dielectric. Categories RX-4 and RX-5A can be combined to form a hybrid solution. In all cases, representative ray trajectories are shown, with ‘f’ being the focus and w.f. denoting the normal incident wave-front. All drawings have the same scale.
Fig. 4
Fig. 4 (a) Flux maps (semi-log plot) for the axisymmetric hybrid concentrator (filled with BK7 glass, n = 1.52 at a wavelength of 522 nm) for a range of realistic θs values. Local concentration is plotted against radial position r on the absorber (normalized by its respective thermodynamic limit rth) for both monochromatic radiation and the full solar spectrum, toward distinguishing the contributions of geometric and chromatic aberration. Ideal concentrators would exhibit a step function with a cutoff at an abscissa value of unity. (b) Efficiency as a function of absorber area A normalized to its thermodynamic limit value Ath. Ideal concentrators would exhibit a strict proportionality, up to unit efficiency.
Fig. 5
Fig. 5 Collimation efficiency for the axisymmetric hybrid aplanat in Fig. 3, from a monochromatic lambertian emitter. n = 1.52. The abscissa is the ratio of the projected solid angle (at far field) Ω relative to its value at the thermodynamic limit Ωth.

Tables (1)

Tables Icon

Table 1 Summary of the parameters used for the illustrations in Figs. 2-3. n = 1.52. The design Rp is 1.0. Aplanat construction covers 0 ≤ Xp ≤ 1 unless truncation was necessary (as indicated in the table and expounded in the text). The hybrid in Fig. 3 is based on the parameters listed for the RX-4 and RX-5A designs from which it is formed.

Equations (7)

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

C max = ( N A exit / N A entry ) 2 = ( n sin ( θ exit ) / sin ( θ s ) ) 2 ,
L 1 + n L 2 + n L 3 = c o n s t .
F = r / sin ( φ ) = c o n s t .
H p Y p + n ( X p X s ) 2 + ( Y p Y s ) 2 + n X s 2 + Y s 2 n ( H p H s ) 2 + ( R p + c R s ) 2 n H s 2 + R s 2 = 0 ,
d Y p d X p = m 2 n 2 + p n 2 ( 1 + m 2 2 ) ( 1 + m 2 2 n 2 m 2 2 ) ,
Y s = s R p X s X p ( 1 + H s 2 R s 2 ) 1 ,
d Y s d X s = 1 1 m 2 m 1 m 2 + m 1 ± ( 1 m 2 m 1 m 2 + m 1 ) 2 + 1 ,

Metrics