Abstract

Directly transporting sunlight for use in indoor lighting applications is an efficient way to utilize solar energy. This study proposes a tree-structured light guiding system (TLGS) to collect sunlight and transport it for indoor illumination. The use of asymmetric light couplers in a TLGS increases the amount of accumulated sunlight. An analytic ray tracing model of the asymmetric coupler is proposed to present the angle and height distributions of the propagated rays. The cutoff angles were derived, and this cutoff condition was used to determine which rays are able to travel through the coupling region. In simulations, the couplers with coupling angles (θcoup) of 30° and 50° were conducted, and the large θcoup coupler provided high coupling efficiency (0.450). The orthogonal incidence method was adopted to increase coupling efficiency (0.646), and subsequently the amount of accumulated sunlight. The amount of accumulated sunlight in a TLGS was increased by 44%.

© 2013 Optical Society of America

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2012 (3)

G. Li, R. Zhu, and Y. Yang, “Polymer solar cells,” Nat. Photonics 6, 153–161 (2012).
[CrossRef]

M. A. Green, K. Emery, Y. Hishikawa, W. Warta, and E. D. Dunlop, “Solar cell efficiency tables (version 39),” Prog. Photovoltaics 20, 12–20 (2012).
[CrossRef]

W.-F. Hsu, Y.-T. Shen, and I.-L. Chu, “Asymmetric and symmetric light couplers of daylighting systems for direct indoor lighting,” J. Opt. 14, 125703 (2012).
[CrossRef]

2011 (1)

V. R. M. Lo Verso, A. Pellegrino, and V. Serra, “Light transmission efficiency of daylight guidance systems: an assessment approach based on simulations and measurements in a sun/sky simulator,” Sol. Energy 85, 2789–2801 (2011).
[CrossRef]

2010 (4)

2009 (4)

T. Nakamura, “Optical waveguide system for solar power applications in space,” Proc. SPIE 7423, 74230C (2009).
[CrossRef]

M.-C. Chien, Y. L. Tung, and C.-H. Tien, “Ultracompact backlight-reversed concentration optics,” Appl. Opt. 48, 4142–4148 (2009).
[CrossRef]

A. J.-W. Whang, C.-C. Wang, and Y.-Y. Chen, “Design of cascadable optical unit to compress light for light transmission used for indoor illumination,” Renew. Energy 34, 2280–2295 (2009).
[CrossRef]

A. J.-W. Whang, P.-C. Li, Y.-Y. Chen, and S.-L. Hsieh, “Guiding light from LED array via tapered light pipe for illumination systems design,” J. Display Technol. 5, 104–108 (2009).
[CrossRef]

2007 (1)

M. A. Green, “Thin-film solar cells: review of materials, technologies and commercial status,” J. Mater. Sci. 18, S15–S19 (2007).

2006 (1)

F. Francini, D. Fontani, D. Jafrancesco, L. Mercatelli, and P. Sansoni, “Solar internal lighting using optical collectors and fibres,” Proc. SPIE 6338, 63380O (2006).
[CrossRef]

2005 (2)

A. Tsangrassoulis, L. Doulos, M. Santamouris, M. Fontoynont, F. Maamari, M. Wilson, A. Jacobs, J. Solomon, A. Zimmerman, W. Pohl, and G. Mihalakakou, “On the energy efficiency of a prototype hybrid daylighting system,” Sol. Energy 79, 56–64 (2005).
[CrossRef]

A. Rosemann and H. Kaase, “Lightpipe applications for daylighting systems,” Sol. Energy 78, 772–780 (2005).
[CrossRef]

2004 (1)

J.-L. Scartezzini and G. Courret, “Experimental performance of daylighting systems based on non-imaging optics,” Proc. SPIE 5185, 35–48 (2004).
[CrossRef]

2002 (2)

D. Feuermann, J. M. Gordon, and M. Huleihil, “Solar fiber-optic mini-dish concentrators: first experimental results and field experience,” Sol. Energy 72, 459–472 (2002).
[CrossRef]

M. Kischkoweit-Lopin, “An overview of daylighting systems,” Sol. Energy 73, 77–82 (2002).
[CrossRef]

1999 (2)

A. Shah, P. Torres, R. Tscharner, N. Wyrsch, and H. Keppner, “Photovoltaic technology: the case for thin-film solar cells,” Science 285, 692–698 (1999).
[CrossRef]

O. Zik, J. Karni, and A. Kribus, “The TROF (tower reflector with optical fibers): a new degree of freedom for solar energy systems,” Sol. Energy 67, 13–22 (1999).
[CrossRef]

1995 (1)

G. Yu, J. Gao, J. C. Hummelen, F. Wudl, and A. J. Heeger, “Polymer photovoltaic cells: enhanced efficiencies via a network of internal donor-acceptor heterojunctions,” Science 270, 1789–1791 (1995).
[CrossRef]

1983 (1)

1952 (1)

Aarø, D.

Benitez, P.

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

Chang, F.

Chen, C.-A.

Chen, C.-N.

Chen, Y.-Y.

Chien, M.-C.

Chou, K.-H.

Chu, I.-L.

W.-F. Hsu, Y.-T. Shen, and I.-L. Chu, “Asymmetric and symmetric light couplers of daylighting systems for direct indoor lighting,” J. Opt. 14, 125703 (2012).
[CrossRef]

Courret, G.

J.-L. Scartezzini and G. Courret, “Experimental performance of daylighting systems based on non-imaging optics,” Proc. SPIE 5185, 35–48 (2004).
[CrossRef]

Doulos, L.

A. Tsangrassoulis, L. Doulos, M. Santamouris, M. Fontoynont, F. Maamari, M. Wilson, A. Jacobs, J. Solomon, A. Zimmerman, W. Pohl, and G. Mihalakakou, “On the energy efficiency of a prototype hybrid daylighting system,” Sol. Energy 79, 56–64 (2005).
[CrossRef]

Dunlop, E. D.

M. A. Green, K. Emery, Y. Hishikawa, W. Warta, and E. D. Dunlop, “Solar cell efficiency tables (version 39),” Prog. Photovoltaics 20, 12–20 (2012).
[CrossRef]

Emery, K.

M. A. Green, K. Emery, Y. Hishikawa, W. Warta, and E. D. Dunlop, “Solar cell efficiency tables (version 39),” Prog. Photovoltaics 20, 12–20 (2012).
[CrossRef]

Feuermann, D.

D. Feuermann, J. M. Gordon, and M. Huleihil, “Solar fiber-optic mini-dish concentrators: first experimental results and field experience,” Sol. Energy 72, 459–472 (2002).
[CrossRef]

Fontani, D.

F. Francini, D. Fontani, D. Jafrancesco, L. Mercatelli, and P. Sansoni, “Solar internal lighting using optical collectors and fibres,” Proc. SPIE 6338, 63380O (2006).
[CrossRef]

Fontoynont, M.

A. Tsangrassoulis, L. Doulos, M. Santamouris, M. Fontoynont, F. Maamari, M. Wilson, A. Jacobs, J. Solomon, A. Zimmerman, W. Pohl, and G. Mihalakakou, “On the energy efficiency of a prototype hybrid daylighting system,” Sol. Energy 79, 56–64 (2005).
[CrossRef]

Fraas, L. M.

Francini, F.

F. Francini, D. Fontani, D. Jafrancesco, L. Mercatelli, and P. Sansoni, “Solar internal lighting using optical collectors and fibres,” Proc. SPIE 6338, 63380O (2006).
[CrossRef]

Fyenbo, J.

Gao, J.

G. Yu, J. Gao, J. C. Hummelen, F. Wudl, and A. J. Heeger, “Polymer photovoltaic cells: enhanced efficiencies via a network of internal donor-acceptor heterojunctions,” Science 270, 1789–1791 (1995).
[CrossRef]

Gordon, J. M.

D. Feuermann, J. M. Gordon, and M. Huleihil, “Solar fiber-optic mini-dish concentrators: first experimental results and field experience,” Sol. Energy 72, 459–472 (2002).
[CrossRef]

Green, M. A.

M. A. Green, K. Emery, Y. Hishikawa, W. Warta, and E. D. Dunlop, “Solar cell efficiency tables (version 39),” Prog. Photovoltaics 20, 12–20 (2012).
[CrossRef]

M. A. Green, “Thin-film solar cells: review of materials, technologies and commercial status,” J. Mater. Sci. 18, S15–S19 (2007).

Heeger, A. J.

G. Yu, J. Gao, J. C. Hummelen, F. Wudl, and A. J. Heeger, “Polymer photovoltaic cells: enhanced efficiencies via a network of internal donor-acceptor heterojunctions,” Science 270, 1789–1791 (1995).
[CrossRef]

Hishikawa, Y.

M. A. Green, K. Emery, Y. Hishikawa, W. Warta, and E. D. Dunlop, “Solar cell efficiency tables (version 39),” Prog. Photovoltaics 20, 12–20 (2012).
[CrossRef]

Hsieh, S.-L.

Hsu, W.-F.

W.-F. Hsu, Y.-T. Shen, and I.-L. Chu, “Asymmetric and symmetric light couplers of daylighting systems for direct indoor lighting,” J. Opt. 14, 125703 (2012).
[CrossRef]

Huleihil, M.

D. Feuermann, J. M. Gordon, and M. Huleihil, “Solar fiber-optic mini-dish concentrators: first experimental results and field experience,” Sol. Energy 72, 459–472 (2002).
[CrossRef]

Hummelen, J. C.

G. Yu, J. Gao, J. C. Hummelen, F. Wudl, and A. J. Heeger, “Polymer photovoltaic cells: enhanced efficiencies via a network of internal donor-acceptor heterojunctions,” Science 270, 1789–1791 (1995).
[CrossRef]

Jacobs, A.

A. Tsangrassoulis, L. Doulos, M. Santamouris, M. Fontoynont, F. Maamari, M. Wilson, A. Jacobs, J. Solomon, A. Zimmerman, W. Pohl, and G. Mihalakakou, “On the energy efficiency of a prototype hybrid daylighting system,” Sol. Energy 79, 56–64 (2005).
[CrossRef]

Jafrancesco, D.

F. Francini, D. Fontani, D. Jafrancesco, L. Mercatelli, and P. Sansoni, “Solar internal lighting using optical collectors and fibres,” Proc. SPIE 6338, 63380O (2006).
[CrossRef]

Jergensen, M. M.

Kaase, H.

A. Rosemann and H. Kaase, “Lightpipe applications for daylighting systems,” Sol. Energy 78, 772–780 (2005).
[CrossRef]

Karni, J.

O. Zik, J. Karni, and A. Kribus, “The TROF (tower reflector with optical fibers): a new degree of freedom for solar energy systems,” Sol. Energy 67, 13–22 (1999).
[CrossRef]

Keppner, H.

A. Shah, P. Torres, R. Tscharner, N. Wyrsch, and H. Keppner, “Photovoltaic technology: the case for thin-film solar cells,” Science 285, 692–698 (1999).
[CrossRef]

Kischkoweit-Lopin, M.

M. Kischkoweit-Lopin, “An overview of daylighting systems,” Sol. Energy 73, 77–82 (2002).
[CrossRef]

Krebs, F. C.

Kribus, A.

O. Zik, J. Karni, and A. Kribus, “The TROF (tower reflector with optical fibers): a new degree of freedom for solar energy systems,” Sol. Energy 67, 13–22 (1999).
[CrossRef]

Kuo, C.-C.

Lee, Y.-C.

Lee, Z.-Y.

Li, G.

G. Li, R. Zhu, and Y. Yang, “Polymer solar cells,” Nat. Photonics 6, 153–161 (2012).
[CrossRef]

Li, P.-C.

Lilliedal, M. R.

Lo Verso, V. R. M.

V. R. M. Lo Verso, A. Pellegrino, and V. Serra, “Light transmission efficiency of daylight guidance systems: an assessment approach based on simulations and measurements in a sun/sky simulator,” Sol. Energy 85, 2789–2801 (2011).
[CrossRef]

Maamari, F.

A. Tsangrassoulis, L. Doulos, M. Santamouris, M. Fontoynont, F. Maamari, M. Wilson, A. Jacobs, J. Solomon, A. Zimmerman, W. Pohl, and G. Mihalakakou, “On the energy efficiency of a prototype hybrid daylighting system,” Sol. Energy 79, 56–64 (2005).
[CrossRef]

Medford, A. J.

Mercatelli, L.

F. Francini, D. Fontani, D. Jafrancesco, L. Mercatelli, and P. Sansoni, “Solar internal lighting using optical collectors and fibres,” Proc. SPIE 6338, 63380O (2006).
[CrossRef]

Mihalakakou, G.

A. Tsangrassoulis, L. Doulos, M. Santamouris, M. Fontoynont, F. Maamari, M. Wilson, A. Jacobs, J. Solomon, A. Zimmerman, W. Pohl, and G. Mihalakakou, “On the energy efficiency of a prototype hybrid daylighting system,” Sol. Energy 79, 56–64 (2005).
[CrossRef]

Minano, J. C.

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

Nakamura, T.

T. Nakamura, “Optical waveguide system for solar power applications in space,” Proc. SPIE 7423, 74230C (2009).
[CrossRef]

Pakalski, H.

Pan, P.-H.

Pellegrino, A.

V. R. M. Lo Verso, A. Pellegrino, and V. Serra, “Light transmission efficiency of daylight guidance systems: an assessment approach based on simulations and measurements in a sun/sky simulator,” Sol. Energy 85, 2789–2801 (2011).
[CrossRef]

Pohl, W.

A. Tsangrassoulis, L. Doulos, M. Santamouris, M. Fontoynont, F. Maamari, M. Wilson, A. Jacobs, J. Solomon, A. Zimmerman, W. Pohl, and G. Mihalakakou, “On the energy efficiency of a prototype hybrid daylighting system,” Sol. Energy 79, 56–64 (2005).
[CrossRef]

Pyle, W. R.

Rosemann, A.

A. Rosemann and H. Kaase, “Lightpipe applications for daylighting systems,” Sol. Energy 78, 772–780 (2005).
[CrossRef]

Ryason, P. R.

Sansoni, P.

F. Francini, D. Fontani, D. Jafrancesco, L. Mercatelli, and P. Sansoni, “Solar internal lighting using optical collectors and fibres,” Proc. SPIE 6338, 63380O (2006).
[CrossRef]

Santamouris, M.

A. Tsangrassoulis, L. Doulos, M. Santamouris, M. Fontoynont, F. Maamari, M. Wilson, A. Jacobs, J. Solomon, A. Zimmerman, W. Pohl, and G. Mihalakakou, “On the energy efficiency of a prototype hybrid daylighting system,” Sol. Energy 79, 56–64 (2005).
[CrossRef]

Scartezzini, J.-L.

J.-L. Scartezzini and G. Courret, “Experimental performance of daylighting systems based on non-imaging optics,” Proc. SPIE 5185, 35–48 (2004).
[CrossRef]

Serra, V.

V. R. M. Lo Verso, A. Pellegrino, and V. Serra, “Light transmission efficiency of daylight guidance systems: an assessment approach based on simulations and measurements in a sun/sky simulator,” Sol. Energy 85, 2789–2801 (2011).
[CrossRef]

Shah, A.

A. Shah, P. Torres, R. Tscharner, N. Wyrsch, and H. Keppner, “Photovoltaic technology: the case for thin-film solar cells,” Science 285, 692–698 (1999).
[CrossRef]

Shen, Y.-T.

W.-F. Hsu, Y.-T. Shen, and I.-L. Chu, “Asymmetric and symmetric light couplers of daylighting systems for direct indoor lighting,” J. Opt. 14, 125703 (2012).
[CrossRef]

Solomon, J.

A. Tsangrassoulis, L. Doulos, M. Santamouris, M. Fontoynont, F. Maamari, M. Wilson, A. Jacobs, J. Solomon, A. Zimmerman, W. Pohl, and G. Mihalakakou, “On the energy efficiency of a prototype hybrid daylighting system,” Sol. Energy 79, 56–64 (2005).
[CrossRef]

Sorel, R. A.

Sun, G.

Sun, W.-S.

Tien, C.-H.

Torres, P.

A. Shah, P. Torres, R. Tscharner, N. Wyrsch, and H. Keppner, “Photovoltaic technology: the case for thin-film solar cells,” Science 285, 692–698 (1999).
[CrossRef]

Tsangrassoulis, A.

A. Tsangrassoulis, L. Doulos, M. Santamouris, M. Fontoynont, F. Maamari, M. Wilson, A. Jacobs, J. Solomon, A. Zimmerman, W. Pohl, and G. Mihalakakou, “On the energy efficiency of a prototype hybrid daylighting system,” Sol. Energy 79, 56–64 (2005).
[CrossRef]

Tscharner, R.

A. Shah, P. Torres, R. Tscharner, N. Wyrsch, and H. Keppner, “Photovoltaic technology: the case for thin-film solar cells,” Science 285, 692–698 (1999).
[CrossRef]

Tsuei, C.-H.

Tung, Y. L.

Wang, C.-C.

A. J.-W. Whang, C.-C. Wang, and Y.-Y. Chen, “Design of cascadable optical unit to compress light for light transmission used for indoor illumination,” Renew. Energy 34, 2280–2295 (2009).
[CrossRef]

Warta, W.

M. A. Green, K. Emery, Y. Hishikawa, W. Warta, and E. D. Dunlop, “Solar cell efficiency tables (version 39),” Prog. Photovoltaics 20, 12–20 (2012).
[CrossRef]

Whang, A. J.-W.

Williamson, D. E.

Wilson, M.

A. Tsangrassoulis, L. Doulos, M. Santamouris, M. Fontoynont, F. Maamari, M. Wilson, A. Jacobs, J. Solomon, A. Zimmerman, W. Pohl, and G. Mihalakakou, “On the energy efficiency of a prototype hybrid daylighting system,” Sol. Energy 79, 56–64 (2005).
[CrossRef]

Winston, R.

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

Wudl, F.

G. Yu, J. Gao, J. C. Hummelen, F. Wudl, and A. J. Heeger, “Polymer photovoltaic cells: enhanced efficiencies via a network of internal donor-acceptor heterojunctions,” Science 270, 1789–1791 (1995).
[CrossRef]

Wyrsch, N.

A. Shah, P. Torres, R. Tscharner, N. Wyrsch, and H. Keppner, “Photovoltaic technology: the case for thin-film solar cells,” Science 285, 692–698 (1999).
[CrossRef]

Yang, S.-H.

Yang, Y.

G. Li, R. Zhu, and Y. Yang, “Polymer solar cells,” Nat. Photonics 6, 153–161 (2012).
[CrossRef]

Yu, G.

G. Yu, J. Gao, J. C. Hummelen, F. Wudl, and A. J. Heeger, “Polymer photovoltaic cells: enhanced efficiencies via a network of internal donor-acceptor heterojunctions,” Science 270, 1789–1791 (1995).
[CrossRef]

Zhu, R.

G. Li, R. Zhu, and Y. Yang, “Polymer solar cells,” Nat. Photonics 6, 153–161 (2012).
[CrossRef]

Zik, O.

O. Zik, J. Karni, and A. Kribus, “The TROF (tower reflector with optical fibers): a new degree of freedom for solar energy systems,” Sol. Energy 67, 13–22 (1999).
[CrossRef]

Zimmerman, A.

A. Tsangrassoulis, L. Doulos, M. Santamouris, M. Fontoynont, F. Maamari, M. Wilson, A. Jacobs, J. Solomon, A. Zimmerman, W. Pohl, and G. Mihalakakou, “On the energy efficiency of a prototype hybrid daylighting system,” Sol. Energy 79, 56–64 (2005).
[CrossRef]

Appl. Opt. (3)

J. Display Technol. (1)

J. Mater. Sci. (1)

M. A. Green, “Thin-film solar cells: review of materials, technologies and commercial status,” J. Mater. Sci. 18, S15–S19 (2007).

J. Opt. (1)

W.-F. Hsu, Y.-T. Shen, and I.-L. Chu, “Asymmetric and symmetric light couplers of daylighting systems for direct indoor lighting,” J. Opt. 14, 125703 (2012).
[CrossRef]

J. Opt. Soc. Am. (1)

Nat. Photonics (1)

G. Li, R. Zhu, and Y. Yang, “Polymer solar cells,” Nat. Photonics 6, 153–161 (2012).
[CrossRef]

Opt. Express (3)

Proc. SPIE (3)

J.-L. Scartezzini and G. Courret, “Experimental performance of daylighting systems based on non-imaging optics,” Proc. SPIE 5185, 35–48 (2004).
[CrossRef]

T. Nakamura, “Optical waveguide system for solar power applications in space,” Proc. SPIE 7423, 74230C (2009).
[CrossRef]

F. Francini, D. Fontani, D. Jafrancesco, L. Mercatelli, and P. Sansoni, “Solar internal lighting using optical collectors and fibres,” Proc. SPIE 6338, 63380O (2006).
[CrossRef]

Prog. Photovoltaics (1)

M. A. Green, K. Emery, Y. Hishikawa, W. Warta, and E. D. Dunlop, “Solar cell efficiency tables (version 39),” Prog. Photovoltaics 20, 12–20 (2012).
[CrossRef]

Renew. Energy (1)

A. J.-W. Whang, C.-C. Wang, and Y.-Y. Chen, “Design of cascadable optical unit to compress light for light transmission used for indoor illumination,” Renew. Energy 34, 2280–2295 (2009).
[CrossRef]

Science (2)

G. Yu, J. Gao, J. C. Hummelen, F. Wudl, and A. J. Heeger, “Polymer photovoltaic cells: enhanced efficiencies via a network of internal donor-acceptor heterojunctions,” Science 270, 1789–1791 (1995).
[CrossRef]

A. Shah, P. Torres, R. Tscharner, N. Wyrsch, and H. Keppner, “Photovoltaic technology: the case for thin-film solar cells,” Science 285, 692–698 (1999).
[CrossRef]

Sol. Energy (6)

M. Kischkoweit-Lopin, “An overview of daylighting systems,” Sol. Energy 73, 77–82 (2002).
[CrossRef]

D. Feuermann, J. M. Gordon, and M. Huleihil, “Solar fiber-optic mini-dish concentrators: first experimental results and field experience,” Sol. Energy 72, 459–472 (2002).
[CrossRef]

A. Rosemann and H. Kaase, “Lightpipe applications for daylighting systems,” Sol. Energy 78, 772–780 (2005).
[CrossRef]

V. R. M. Lo Verso, A. Pellegrino, and V. Serra, “Light transmission efficiency of daylight guidance systems: an assessment approach based on simulations and measurements in a sun/sky simulator,” Sol. Energy 85, 2789–2801 (2011).
[CrossRef]

A. Tsangrassoulis, L. Doulos, M. Santamouris, M. Fontoynont, F. Maamari, M. Wilson, A. Jacobs, J. Solomon, A. Zimmerman, W. Pohl, and G. Mihalakakou, “On the energy efficiency of a prototype hybrid daylighting system,” Sol. Energy 79, 56–64 (2005).
[CrossRef]

O. Zik, J. Karni, and A. Kribus, “The TROF (tower reflector with optical fibers): a new degree of freedom for solar energy systems,” Sol. Energy 67, 13–22 (1999).
[CrossRef]

Other (1)

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

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Figures (19)

Fig. 1.
Fig. 1.

Application of a direct lighting system to tunnel illumination.

Fig. 2.
Fig. 2.

Schematic diagram of the input section of a tree-structured light guiding system (TLGS).

Fig. 3.
Fig. 3.

Accumulated sunlight versus the number of sunlight collectors. Assuming that the average coupling efficiencies of the symmetric and asymmetric couplers are equal, i.e., η sym = ( η b + η t ) / 2 = 0.6 .

Fig. 4.
Fig. 4.

Geometry of asymmetric coupler connecting rectangular light guides.

Fig. 5.
Fig. 5.

Ray tracing in a parallel plane of an asymmetric coupler. The blue ray arrives at the exit of coupler with m ref = 2 and M R = 2 . The red ray, without intercepting the coupling circle, reflects backward after three reflections.

Fig. 6.
Fig. 6.

Geometry of asymmetric coupler and ray tracing in a perpendicular plane. Lines A t and A b are parallel to the coupling plane, and N is the normal of the bottom boundary.

Fig. 7.
Fig. 7.

Cutoff angles of the light rays at height y in , θ max > θ α in > θ min .

Fig. 8.
Fig. 8.

Distribution of (a) propagation angle (in air) and (b) normalized height of incident rays.

Fig. 9.
Fig. 9.

Distribution of (a) propagation angle and (b) number of reflections of the transmitted rays for an asymmetric coupler with θ coup = 30 ° .

Fig. 10.
Fig. 10.

Distribution of (a) propagation angle and (b) number of reflections of the transmitted rays for an asymmetric coupler with θ coup = 50 ° .

Fig. 11.
Fig. 11.

Distribution of (a) propagation angle (in air) and (b) normalized height of the output rays for an asymmetric coupler with θ coup = 30 ° .

Fig. 12.
Fig. 12.

Distribution of (a) propagation angle (in air) and (b) normalized height of the output rays for an asymmetric coupler with θ coup = 30 ° .

Fig. 13.
Fig. 13.

Angular distribution of the light rays (a), (b) from the trunk guide and (c), (d) from the branch guide, for θ coup = 30 ° and 50°.

Fig. 14.
Fig. 14.

Angular coupling efficiency ( Δ η θ ) of asymmetric couplers with θ coup = 30 ° and 50°. The results were obtained from MATLAB (solid) and LightTools (dashed) simulations.

Fig. 15.
Fig. 15.

Accumulated coupling efficiency of asymmetric couplers with θ coup = 30 ° and 50°. The central angle θ was 0°. The results were obtained from MATLAB (solid) and LightTools (dashed) simulations.

Fig. 16.
Fig. 16.

Change in the distribution of incident angle θ β in due to a perpendicular shift in the incident rays when θ α = 0 ° . According to (b), the estimated η θ + Δ θ were 1.0 and 0.685 for θ coup 30 ° and θ coup 50 ° couplers, respectively.

Fig. 17.
Fig. 17.

Ray tracing simulation using LightTools.

Fig. 18.
Fig. 18.

Sunlight accumulated by N sunlight collectors connected by the θ coup 30 ° (green circle) and θ coup 50 ° couplers (blue square) in TLGS.

Fig. 19.
Fig. 19.

Two sunlight collector setups for directing incident sunlight toward the perpendicular plane of the coupler in order to increase the coupling efficiency and maximize the amount of accumulated sunlight.

Tables (2)

Tables Icon

Table 1. Accumulated Coupling Efficiency ( η θ ± Δ θ ) of Asymmetric Couplers

Tables Icon

Table 2. Accumulated Coupling Efficiency ( η θ ± Δ θ ) of the Asymmetric Couplers with Incident Rays in the Parallel Plane ( θ β = 0 ° ) and the Perpendicular Plane ( θ α = 0 ° )a

Equations (21)

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E N t = E con × η c η g ( η b + η b η t + + η b η t N 2 + η t N 1 ) for N 2 ,
E N t = E con η c η g ( η b 1 η t N 1 1 η t + η t N 1 ) for N 2 .
E N t = E con η c η g η sym ( 1 η sym N 1 1 η sym + η sym N 2 ) for N 2 .
θ c p = 90 ° θ c ,
θ C in = sin 1 [ y in W cos ( θ α in ) sin ( θ coup ) + sin ( θ α in ) · ( 1 + cos ( θ coup ) ) ] θ α in ,
m ref = 2 θ C in / ( 2 θ coup ) ,
θ X in = tan 1 [ cos ( m ref θ coup ) sin ( θ α in + θ C in ) tan ( θ α in ) cos ( θ coup ) cos ( θ coup ) sin ( m ref θ coup ) sin ( θ α in + θ C in ) ] ,
M R = θ X in / θ coup ,
θ α out = ( 1 ) M R ( θ α in + m ref θ coup ) .
y out W = [ sin ( θ α in + θ C in ) sin ( θ α in + m ref θ coup ) cos ( θ coup ) ] · | tan ( θ α out ) | sin ( θ coup ) .
θ β in = cos 1 ( sin θ coup cos θ β ) .
θ β p = sin 1 ( sin θ coup cos θ β ) .
θ C in _ max = π / 2 + θ 1 θ 2 ,
θ 1 = tan 1 ( y in W · sin θ coup 1 + cos θ coup ) ,
θ 2 = csc 1 [ ( y in W sin θ coup ) 2 + ( 1 + cos θ coup ) 2 ] .
θ α in ( m o ) = tan 1 ( sin m o y in w sin θ coup 1 + cos θ coup cos m o θ coup ) .
θ max = max ( θ α in ( m ref ) , θ α in ( m ref + ) ) .
θ C in _ min = θ 1 + θ 2 π / 2 ,
θ min = min ( θ α in ( m ref ) , θ α in ( m ref + ) ) .
Δ η θ = L out ( θ ) L in ( θ ) ,
η θ ± Δ θ E out E in = θ Δ θ θ + Δ θ L out ( θ ) d θ θ Δ θ θ + Δ θ L in ( θ ) d θ .

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