Abstract

Aplanats refer to inherently imaging optics that wholly eliminate both spherical aberration and coma. They typically comprise two refractive and/or reflective surfaces. For radiative transfer (which is typically nonimaging in nature), aplanats can closely approach the thermodynamic bounds for collimation and concentration, especially significant for light-emitting diodes (LEDs), solar energy, and infrared applications. Recently, we identified previously unrecognized basic categories of aplanats and showed how they can offer powerful new possibilities for LED collimation and for concentrating sunlight. Here, we review and elaborate the full scope of aplanat classifications, with illustrative examples of maximum-performance practical optics for all possible combinations of reflective and refractive contours. These examples subsume the latest invention of faceted (Fresnel) aplanats toward achieving greater compactness and lower mass. We also show how hybrid aplanats that combine the basic categories can improve concentrator and collimator performance.

© 2019 Optical Society of America

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References

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  1. A. K. Head, “The two-mirror aplanat,” Proc. Phys. Soc. London B 70, 945–949 (1957).
    [Crossref]
  2. D. Lynden-Bell, “Exact optics: a unification of optical telescope design,” Mon. Not. R. Astron. Soc. 334, 787–796 (2002).
    [Crossref]
  3. N. Ostroumov, J. M. Gordon, and D. Feuermann, “Panorama of dual-mirror aplanats for maximum concentration,” Appl. Opt. 48, 4926–4931 (2009).
    [Crossref]
  4. H. Mashaal, D. Feuermann, and J. M. Gordon, “New types of refractive-reflective aplanats for maximal flux concentration and collimation,” Opt. Express 23, A1541–A1549 (2015).
    [Crossref]
  5. H. Mashaal, D. Feuermann, and J. M. Gordon, “Basic categories of dual-contour reflective refractive aplanats,” Opt. Lett. 40, 4907–4909 (2015).
    [Crossref]
  6. H. Mashaal, D. Feuermann, and J. M. Gordon, “Aplanatic lenses revisited: the full landscape,” Appl. Opt. 55, 2537–2542 (2016).
    [Crossref]
  7. H. Mashaal, D. Feuermann, and J. M. Gordon, “Aplanatic Fresnel optics,” Opt. Express 25, A274–A282 (2017).
    [Crossref]
  8. R. Winston, J. C. Miñano, P. Benítez, N. Shatz, and J. Bortz, Nonimaging Optics (Elsevier, 2005).
  9. D. Feuermann, J. M. Gordon, and T. W. Ng, “Near-field dielectric optics near the thermodynamic limit,” Opt. Eng. 45, 080504 (2006).
    [Crossref]
  10. D. Nakar, D. Feuermann, and J. M. Gordon, “Aplanatic near-field optics for efficient light transfer,” Opt. Eng. 45, 030502 (2006).
    [Crossref]
  11. J. M. Gordon, “Aplanatic optics for solar concentration,” Opt. Express 18, A41–A52 (2010).
    [Crossref]
  12. H. Lu, B. C. Y. Chan, X. Wang, H. T. Chua, C. L. Raston, A. Albu-Yaron, M. Levy, R. Popovitz-Biro, R. Tenne, D. Feuermann, and J. M. Gordon, “High-yield synthesis of silicon carbide nanowires by solar and lamp ablation,” Nanotechnology 24, 335603 (2013).
    [Crossref]
  13. J. C. Miñano, P. Benítez, and J. C. González, “RX: a nonimaging concentrator,” Appl. Opt. 34, 2226–2235 (1995).
    [Crossref]
  14. P. Benítez and J. C. Miñano, “Ultrahigh-numerical-aperture imaging concentrator,” J. Opt. Soc. Am. A 14, 1988–1997 (1997).
    [Crossref]
  15. J. C. Miñano, P. Benítez, L. Jiayao, J. Infante, J. Chaves, and A. Santamaria, “Novel ideal nonimaging designs by multichanneling the phase-space flow,” Proc. SPIE 7652, 765220 (2010).
    [Crossref]

2017 (1)

2016 (1)

2015 (2)

2013 (1)

H. Lu, B. C. Y. Chan, X. Wang, H. T. Chua, C. L. Raston, A. Albu-Yaron, M. Levy, R. Popovitz-Biro, R. Tenne, D. Feuermann, and J. M. Gordon, “High-yield synthesis of silicon carbide nanowires by solar and lamp ablation,” Nanotechnology 24, 335603 (2013).
[Crossref]

2010 (2)

J. M. Gordon, “Aplanatic optics for solar concentration,” Opt. Express 18, A41–A52 (2010).
[Crossref]

J. C. Miñano, P. Benítez, L. Jiayao, J. Infante, J. Chaves, and A. Santamaria, “Novel ideal nonimaging designs by multichanneling the phase-space flow,” Proc. SPIE 7652, 765220 (2010).
[Crossref]

2009 (1)

2006 (2)

D. Feuermann, J. M. Gordon, and T. W. Ng, “Near-field dielectric optics near the thermodynamic limit,” Opt. Eng. 45, 080504 (2006).
[Crossref]

D. Nakar, D. Feuermann, and J. M. Gordon, “Aplanatic near-field optics for efficient light transfer,” Opt. Eng. 45, 030502 (2006).
[Crossref]

2002 (1)

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

1997 (1)

1995 (1)

1957 (1)

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

Albu-Yaron, A.

H. Lu, B. C. Y. Chan, X. Wang, H. T. Chua, C. L. Raston, A. Albu-Yaron, M. Levy, R. Popovitz-Biro, R. Tenne, D. Feuermann, and J. M. Gordon, “High-yield synthesis of silicon carbide nanowires by solar and lamp ablation,” Nanotechnology 24, 335603 (2013).
[Crossref]

Benítez, P.

J. C. Miñano, P. Benítez, L. Jiayao, J. Infante, J. Chaves, and A. Santamaria, “Novel ideal nonimaging designs by multichanneling the phase-space flow,” Proc. SPIE 7652, 765220 (2010).
[Crossref]

P. Benítez and J. C. Miñano, “Ultrahigh-numerical-aperture imaging concentrator,” J. Opt. Soc. Am. A 14, 1988–1997 (1997).
[Crossref]

J. C. Miñano, P. Benítez, and J. C. González, “RX: a nonimaging concentrator,” Appl. Opt. 34, 2226–2235 (1995).
[Crossref]

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

Bortz, J.

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

Chan, B. C. Y.

H. Lu, B. C. Y. Chan, X. Wang, H. T. Chua, C. L. Raston, A. Albu-Yaron, M. Levy, R. Popovitz-Biro, R. Tenne, D. Feuermann, and J. M. Gordon, “High-yield synthesis of silicon carbide nanowires by solar and lamp ablation,” Nanotechnology 24, 335603 (2013).
[Crossref]

Chaves, J.

J. C. Miñano, P. Benítez, L. Jiayao, J. Infante, J. Chaves, and A. Santamaria, “Novel ideal nonimaging designs by multichanneling the phase-space flow,” Proc. SPIE 7652, 765220 (2010).
[Crossref]

Chua, H. T.

H. Lu, B. C. Y. Chan, X. Wang, H. T. Chua, C. L. Raston, A. Albu-Yaron, M. Levy, R. Popovitz-Biro, R. Tenne, D. Feuermann, and J. M. Gordon, “High-yield synthesis of silicon carbide nanowires by solar and lamp ablation,” Nanotechnology 24, 335603 (2013).
[Crossref]

Feuermann, D.

González, J. C.

Gordon, J. M.

Head, A. K.

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

Infante, J.

J. C. Miñano, P. Benítez, L. Jiayao, J. Infante, J. Chaves, and A. Santamaria, “Novel ideal nonimaging designs by multichanneling the phase-space flow,” Proc. SPIE 7652, 765220 (2010).
[Crossref]

Jiayao, L.

J. C. Miñano, P. Benítez, L. Jiayao, J. Infante, J. Chaves, and A. Santamaria, “Novel ideal nonimaging designs by multichanneling the phase-space flow,” Proc. SPIE 7652, 765220 (2010).
[Crossref]

Levy, M.

H. Lu, B. C. Y. Chan, X. Wang, H. T. Chua, C. L. Raston, A. Albu-Yaron, M. Levy, R. Popovitz-Biro, R. Tenne, D. Feuermann, and J. M. Gordon, “High-yield synthesis of silicon carbide nanowires by solar and lamp ablation,” Nanotechnology 24, 335603 (2013).
[Crossref]

Lu, H.

H. Lu, B. C. Y. Chan, X. Wang, H. T. Chua, C. L. Raston, A. Albu-Yaron, M. Levy, R. Popovitz-Biro, R. Tenne, D. Feuermann, and J. M. Gordon, “High-yield synthesis of silicon carbide nanowires by solar and lamp ablation,” Nanotechnology 24, 335603 (2013).
[Crossref]

Lynden-Bell, D.

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

Mashaal, H.

Miñano, J. C.

J. C. Miñano, P. Benítez, L. Jiayao, J. Infante, J. Chaves, and A. Santamaria, “Novel ideal nonimaging designs by multichanneling the phase-space flow,” Proc. SPIE 7652, 765220 (2010).
[Crossref]

P. Benítez and J. C. Miñano, “Ultrahigh-numerical-aperture imaging concentrator,” J. Opt. Soc. Am. A 14, 1988–1997 (1997).
[Crossref]

J. C. Miñano, P. Benítez, and J. C. González, “RX: a nonimaging concentrator,” Appl. Opt. 34, 2226–2235 (1995).
[Crossref]

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

Nakar, D.

D. Nakar, D. Feuermann, and J. M. Gordon, “Aplanatic near-field optics for efficient light transfer,” Opt. Eng. 45, 030502 (2006).
[Crossref]

Ng, T. W.

D. Feuermann, J. M. Gordon, and T. W. Ng, “Near-field dielectric optics near the thermodynamic limit,” Opt. Eng. 45, 080504 (2006).
[Crossref]

Ostroumov, N.

Popovitz-Biro, R.

H. Lu, B. C. Y. Chan, X. Wang, H. T. Chua, C. L. Raston, A. Albu-Yaron, M. Levy, R. Popovitz-Biro, R. Tenne, D. Feuermann, and J. M. Gordon, “High-yield synthesis of silicon carbide nanowires by solar and lamp ablation,” Nanotechnology 24, 335603 (2013).
[Crossref]

Raston, C. L.

H. Lu, B. C. Y. Chan, X. Wang, H. T. Chua, C. L. Raston, A. Albu-Yaron, M. Levy, R. Popovitz-Biro, R. Tenne, D. Feuermann, and J. M. Gordon, “High-yield synthesis of silicon carbide nanowires by solar and lamp ablation,” Nanotechnology 24, 335603 (2013).
[Crossref]

Santamaria, A.

J. C. Miñano, P. Benítez, L. Jiayao, J. Infante, J. Chaves, and A. Santamaria, “Novel ideal nonimaging designs by multichanneling the phase-space flow,” Proc. SPIE 7652, 765220 (2010).
[Crossref]

Shatz, N.

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

Tenne, R.

H. Lu, B. C. Y. Chan, X. Wang, H. T. Chua, C. L. Raston, A. Albu-Yaron, M. Levy, R. Popovitz-Biro, R. Tenne, D. Feuermann, and J. M. Gordon, “High-yield synthesis of silicon carbide nanowires by solar and lamp ablation,” Nanotechnology 24, 335603 (2013).
[Crossref]

Wang, X.

H. Lu, B. C. Y. Chan, X. Wang, H. T. Chua, C. L. Raston, A. Albu-Yaron, M. Levy, R. Popovitz-Biro, R. Tenne, D. Feuermann, and J. M. Gordon, “High-yield synthesis of silicon carbide nanowires by solar and lamp ablation,” Nanotechnology 24, 335603 (2013).
[Crossref]

Winston, R.

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

Appl. Opt. (3)

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

Mon. Not. R. Astron. Soc. (1)

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

Nanotechnology (1)

H. Lu, B. C. Y. Chan, X. Wang, H. T. Chua, C. L. Raston, A. Albu-Yaron, M. Levy, R. Popovitz-Biro, R. Tenne, D. Feuermann, and J. M. Gordon, “High-yield synthesis of silicon carbide nanowires by solar and lamp ablation,” Nanotechnology 24, 335603 (2013).
[Crossref]

Opt. Eng. (2)

D. Feuermann, J. M. Gordon, and T. W. Ng, “Near-field dielectric optics near the thermodynamic limit,” Opt. Eng. 45, 080504 (2006).
[Crossref]

D. Nakar, D. Feuermann, and J. M. Gordon, “Aplanatic near-field optics for efficient light transfer,” Opt. Eng. 45, 030502 (2006).
[Crossref]

Opt. Express (3)

Opt. Lett. (1)

Proc. Phys. Soc. London B (1)

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

Proc. SPIE (1)

J. C. Miñano, P. Benítez, L. Jiayao, J. Infante, J. Chaves, and A. Santamaria, “Novel ideal nonimaging designs by multichanneling the phase-space flow,” Proc. SPIE 7652, 765220 (2010).
[Crossref]

Other (1)

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

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Figures (17)

Fig. 1.
Fig. 1. Construction for the dual-mirror aplanats [3] (XX) in concentrator mode.
Fig. 2.
Fig. 2. Construction for XR aplanats [5] in concentrator mode.
Fig. 3.
Fig. 3. Construction for RX aplanats [4] in concentrator mode.
Fig. 4.
Fig. 4. Construction for RR aplanats (in collimator mode) [6]. The focus (light source) is at f. θe is the maximum-emission half-angle from the light source, and w.f. denotes the normal collimated wavefront.
Fig. 5.
Fig. 5. Drawing and photograph of a dual-mirror (XX) aplanatic solar concentrator that achieves a net flux concentration of 30,000. It has been used for driving chemical reactors at temperatures that can exceed 3000K for the generation of singular nanostructures [12]. Its design parameters are K=0.04, s=0.70, and NA=0.98 [see Eq. (1)].
Fig. 6.
Fig. 6. Examples of XX aplanats beyond the type illustrated in Fig. 5, illustrated in concentrator mode [3]. Starting from the upper left and moving counterclockwise, the respective {s,K} values are {5.0, 0.00477}; {−0.162, −1.072}; {0.0445, −0.152}; {0.19, −5.22}; {−3.84, 0.03}; {−0.61, −0.23}. In all cases, NA=0.9.
Fig. 7.
Fig. 7. Five physically admissible classes of XR aplanats illustrated in concentrator mode [5]. Dielectric elements are indicated as colored regions. The normal incident wavefront is denoted by w.f. and the focus (absorber) by f.
Fig. 8.
Fig. 8. Three classes of RX aplanats that require a mirrored secondary [4]. RX-2A is the point source limit of the nonimaging simultaneous multiple surface (SMS) method concentrator developed in [13,14]. RX-2B is distinguished from RX-2A by a convex versus a concave secondary. The focus is denoted by f, and w.f. indicates the normal incident wavefront.
Fig. 9.
Fig. 9. Three classes of RX aplanats (in concentrator mode) where the reflection (“X”) is based on total internal reflection [4]. The device is produced from a single piece of dielectric. RX-5B has a small hollow internal space. In all instances, the absorber resides inside (and is optically coupled to) the dielectric.
Fig. 10.
Fig. 10. Examples of the three physically admissible solutions for RR aplanats where the focus is in air, in collimator mode [6].
Fig. 11.
Fig. 11. Examples of the five physically admissible categories of complementary XR aplanats in concentrator mode.
Fig. 12.
Fig. 12. Examples of the six categories of physically admissible complementary RX aplanats in concentrator mode.
Fig. 13.
Fig. 13. Examples of the three physically meaningful solutions for complementary RR aplanats, in collimator mode.
Fig. 14.
Fig. 14. (a) Example of a hybrid RX aplanat [4], which combines the RX-4 and RX-5A designs of Fig. 9, illustrated in concentrator mode. (b) Photograph of the device manufactured from acrylic as an LED collimator.
Fig. 15.
Fig. 15. (a) Front view of the mounted collimator of Fig. 14(b). (b) Photograph of the far-field flux map on a white screen. About 10% of the emitted light is distributed outside the central spot, stemming from rays emitted by the LEDs that miss the (total internal) reflective contour and hence are not collimated.
Fig. 16.
Fig. 16. Construction of a Fresnel RR aplanat, shown in collimator mode. Pi and Si denote the primary and secondary boundaries for each individual aplanatic facet (subscript i runs from 1 at the rim of the optic to n at the final facet closest to the optic axis).
Fig. 17.
Fig. 17. Examples of Fresnel (a) RX and (b) RR aplanats (in concentrator mode). The former has its focus f in air, while for the latter the focus is inside the dielectric with the contours of the original RR aplanat indicated by solid black curves toward appraising the marked reduction in the amount of dielectric required.

Equations (5)

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rp=sin(ϕ);xp=scos2(ϕ/2)+(g(ϕ)/s)(1Kf(ϕ))cos4(ϕ/2),rs=2sKf(ϕ)tan(ϕ/2)Kf(ϕ)tan2(ϕ/2)+g(ϕ);xs=rscot(ϕ),whereg(ϕ)=s(1s)tan2(ϕ/2)andf(ϕ)=|g(ϕ)/s|s/(s1).
HpYp+(XpXs)2+(YpYs)2+nXs2+Ys2(HpHs)2+(Rp+cRs)2nHs2+Rs2=0,dYpdXp=1m+pm21;Ys=s·RpXsXp·(1+Hs2Rs2)1,
HpYp+n(XpXs)2+(YpYs)2+nXs2+Ys2n(HpHs)2+(Rp+c·Rs)2nHs2+Rs2=0,dYpdXp=mn2+pn2(1+m2)(1+m2n2m2);Ys=s·RpXsXp·(1+Hs2Rs2)1,
HpYp+(XpXs)2+(YpYs)2+nXs2+Ys2(HpHs)2+(Rp+cRs)2nHs2+Rs2=0,dYpdXp=mn2+pn2(1+m2)(1+m2n2m2),Ys=s·Xs·(RpXp)2(1+Hs2Rs2)1,
Cmax=NA2/sin2(Θs),

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