Abstract

We propose a generalization of radiative transport theory to account for light propagation in luminescent random media. This theory accounts accurately for the multiple absorption and reemission of light at different wavelengths and for anisotropic luminescence. To test this theory, we apply it to model light propagation in luminescent solar concentrators (LSCs). The source-iteration method is used in two spatial dimensions for LSCs based on semiconductor quantum dots and aligned nanorods. The LSC performance is studied in detail, including its dependence on particle concentration and the anisotropy of the luminescence. The computational results using this theory are compared with Monte Carlo simulations of photon transport and found to agree qualitatively. The proposed approach offers a deterministic methodology, which can be advantageous for analytic and computational modeling. This approach has potential for more efficient and cost-effective LSCs, as well as in other applications involving luminescent radiation.

© 2013 Optical Society of America

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  35. K. Emery, “Reference solar spectral irradiance: air mass 1.5,” Tech. Rep. (ASTM, 2000), http://rredc.nrel.gov/solar/spectra/am1.5 .
  36. E. E. Lewis and W. F. J. Miller, Computational Methods of Neutron Transport (Wiley, 1984).
  37. K. D. Lathrop, “Ray effects in discrete ordinates equations,” Nucl. Sci. Eng. 32, 357–369 (1968).
  38. L. Wang and H. Wu, Biomedical Optics: Principles and Imaging (Wiley, 2007).
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    [CrossRef]
  40. G. Bal and O. Pinaud, “Accuracy of transport models for waves in random media,” Wave Motion 43, 561–578 (2006).
    [CrossRef]

2012 (4)

F. Purcell-Milton and Y. K. Gun’ko, “Quantum dots for luminescent solar concentrators,” J. Mater. Chem. 22, 16687–16697 (2012).
[CrossRef]

H. Hernandez-Noyola, D. H. Potterveld, R. J. Holt, and S. B. Darling, “Optimizing luminescent solar concentrator design,” Energy Environ. Sci. 5, 5798–5802 (2012).
[CrossRef]

P. P. C. Verbunt, S. Tsoi, M. G. Debije, D. J. Broer, C. W. Bastiaansen, C.-W. Lin, and D. K. G. de Boer, “Increased efficiency of luminescent solar concentrators after application of organic wavelength selective mirrors,” Opt. Express 20, A655–A668 (2012).
[CrossRef]

J. Bertolotti, E. G. van Putten, C. Blum, A. Lagendijk, W. L. Vos, and A. P. Mosk, “Non-invasive imaging through opaque scattering layers,” Nature 491, 232–234 (2012).
[CrossRef]

2011 (2)

D. Şahin, B. Ilan, and D. Kelley, “Monte-Carlo simulations of light scattering in luminescent solar concentrators based on semiconductor nanoparticles,” J. Appl. Phys 110, 1–8 (2011).

R. H. Inman, G. V. Scherbatyuk, D. Medvedko, A. Gopinathan, and S. Ghosh, “Cylindrical luminescent solar concentrators with near-infrared quantum dots,” Opt. Express 19, 24308–24313 (2011).
[CrossRef]

2010 (4)

2009 (4)

P. P. C. Verbunt, A. Kaiser, K. Hermans, C. W. M. Bastiaansen, D. J. Broer, and M. G. Debije, “Controlling light emission in luminescent solar concentrators through use of dye molecules aligned in a planar manner by liquid crystals,” Adv. Funct. Mater. 19, 2714–2719 (2009).
[CrossRef]

A. D. Zacharopoulos, P. Svenmarker, J. Axelsson, M. Schweiger, S. R. Arridge, and S. Andersson-Engels, “A matrix-free algorithm for multiple wavelength fluorescence tomography,” Appl. Phys. Lett. 17, 3042–3051 (2009).

C. T. Xu, J. Axelsson, and S. Andersson-Engels, “Fluorescence diffuse optical tomography using upconverting nanoparticles,” Appl. Phys. Lett. 94, 251107 (2009).
[CrossRef]

H. Gao and H. Zhao, “A fast forward solver of radiative transfer equation,” Transp. Theory Stat. Phys. 38, 149–192 (2009).
[CrossRef]

2008 (3)

M. J. Currie, J. K. Mapel, T. D. Heidel, S. Goffri, and M. A. Baldo, “High-efficiency organic solar concentrators for photovoltaics,” Science 321, 226–228 (2008).
[CrossRef]

L. H. Slooff, E. E. Bende, A. R. Burgers, T. Budel, M. Pravettoni, R. P. Kenny, E. D. Dunlop, and A. Büchtemann, “A luminescent solar concentrator with 7.1% power conversion efficiency,” Phys. Status Solidi RRL 2, 257–259 (2008).
[CrossRef]

G. Y. Panasyuk, Z.-M. Wang, J. C. Schotland, and V. A. Markel, “Fluorescent optical tomography with large data sets,” Opt. Lett. 33, 1744–1746 (2008).
[CrossRef]

2007 (1)

V. Sholin, J. D. Olson, and S. A. Carter, “Semiconducting polymers and quantum dots in luminescent solar concentrators for solar energy harvesting,” J. Appl. Phys. 101, 123114 (2007).
[CrossRef]

2006 (1)

G. Bal and O. Pinaud, “Accuracy of transport models for waves in random media,” Wave Motion 43, 561–578 (2006).
[CrossRef]

2004 (1)

A. Chatten, K. Barnham, B. Buxton, N. Ekins-Daukes, and M. Malik, “Quantum dot solar concentrators,” Semiconductors 38, 909–917 (2004).
[CrossRef]

2003 (2)

A. D. Kim and M. Moscoso, “Radiative transfer computations for optical beams,” J. Comput. Phys. 185, 50–60 (2003).
[CrossRef]

W. W. Yu, L. Qu, W. Guo, and X. Peng, “Experimental determination of extinction coefficient of CdTe, CdSe, and CdS nanocrystals,” Chem. Matter 15, 2854–2860 (2003).
[CrossRef]

1995 (1)

L. Wang, S. L. Jacques, and L. Zheng, “Monte Carlo modeling of photon transport in multi-layered tissues,” Comput. Methods Programs Biomed. 47, 131–146 (1995).
[CrossRef]

1986 (1)

J. T. Kajiya, “The rendering equation,” Comput. Graph. 20, 143–150 (1986).
[CrossRef]

1985 (1)

1981 (1)

1979 (1)

1969 (1)

1968 (1)

K. D. Lathrop, “Ray effects in discrete ordinates equations,” Nucl. Sci. Eng. 32, 357–369 (1968).

1941 (1)

J. G. Henyey and J. L. Greenstein, “Diffuse radiation in the galaxy,” J. Astrophys. 93, 70–83 (1941).
[CrossRef]

Andersson-Engels, S.

A. D. Zacharopoulos, P. Svenmarker, J. Axelsson, M. Schweiger, S. R. Arridge, and S. Andersson-Engels, “A matrix-free algorithm for multiple wavelength fluorescence tomography,” Appl. Phys. Lett. 17, 3042–3051 (2009).

C. T. Xu, J. Axelsson, and S. Andersson-Engels, “Fluorescence diffuse optical tomography using upconverting nanoparticles,” Appl. Phys. Lett. 94, 251107 (2009).
[CrossRef]

Arridge, S. R.

A. D. Zacharopoulos, P. Svenmarker, J. Axelsson, M. Schweiger, S. R. Arridge, and S. Andersson-Engels, “A matrix-free algorithm for multiple wavelength fluorescence tomography,” Appl. Phys. Lett. 17, 3042–3051 (2009).

Axelsson, J.

C. T. Xu, J. Axelsson, and S. Andersson-Engels, “Fluorescence diffuse optical tomography using upconverting nanoparticles,” Appl. Phys. Lett. 94, 251107 (2009).
[CrossRef]

A. D. Zacharopoulos, P. Svenmarker, J. Axelsson, M. Schweiger, S. R. Arridge, and S. Andersson-Engels, “A matrix-free algorithm for multiple wavelength fluorescence tomography,” Appl. Phys. Lett. 17, 3042–3051 (2009).

Bal, G.

G. Bal and O. Pinaud, “Accuracy of transport models for waves in random media,” Wave Motion 43, 561–578 (2006).
[CrossRef]

Baldo, M. A.

C. L. Mulder, P. D. Reusswig, A. M. Velázquez, H. Kim, C. Rotschild, and M. A. Baldo, “Dye alignment in luminescent solar concentrators: I. Vertical alignment for improved waveguide coupling,” Opt. Express 18, A79–A90 (2010).
[CrossRef]

M. J. Currie, J. K. Mapel, T. D. Heidel, S. Goffri, and M. A. Baldo, “High-efficiency organic solar concentrators for photovoltaics,” Science 321, 226–228 (2008).
[CrossRef]

Barnham, K.

A. Chatten, K. Barnham, B. Buxton, N. Ekins-Daukes, and M. Malik, “Quantum dot solar concentrators,” Semiconductors 38, 909–917 (2004).
[CrossRef]

Bastiaansen, C. W.

Bastiaansen, C. W. M.

P. P. C. Verbunt, A. Kaiser, K. Hermans, C. W. M. Bastiaansen, D. J. Broer, and M. G. Debije, “Controlling light emission in luminescent solar concentrators through use of dye molecules aligned in a planar manner by liquid crystals,” Adv. Funct. Mater. 19, 2714–2719 (2009).
[CrossRef]

Batchelder, J. S.

Bende, E. E.

L. H. Slooff, E. E. Bende, A. R. Burgers, T. Budel, M. Pravettoni, R. P. Kenny, E. D. Dunlop, and A. Büchtemann, “A luminescent solar concentrator with 7.1% power conversion efficiency,” Phys. Status Solidi RRL 2, 257–259 (2008).
[CrossRef]

Bertolotti, J.

J. Bertolotti, E. G. van Putten, C. Blum, A. Lagendijk, W. L. Vos, and A. P. Mosk, “Non-invasive imaging through opaque scattering layers,” Nature 491, 232–234 (2012).
[CrossRef]

Blum, C.

J. Bertolotti, E. G. van Putten, C. Blum, A. Lagendijk, W. L. Vos, and A. P. Mosk, “Non-invasive imaging through opaque scattering layers,” Nature 491, 232–234 (2012).
[CrossRef]

Broer, D. J.

Büchtemann, A.

L. H. Slooff, E. E. Bende, A. R. Burgers, T. Budel, M. Pravettoni, R. P. Kenny, E. D. Dunlop, and A. Büchtemann, “A luminescent solar concentrator with 7.1% power conversion efficiency,” Phys. Status Solidi RRL 2, 257–259 (2008).
[CrossRef]

Budel, T.

L. H. Slooff, E. E. Bende, A. R. Burgers, T. Budel, M. Pravettoni, R. P. Kenny, E. D. Dunlop, and A. Büchtemann, “A luminescent solar concentrator with 7.1% power conversion efficiency,” Phys. Status Solidi RRL 2, 257–259 (2008).
[CrossRef]

Burgers, A. R.

L. H. Slooff, E. E. Bende, A. R. Burgers, T. Budel, M. Pravettoni, R. P. Kenny, E. D. Dunlop, and A. Büchtemann, “A luminescent solar concentrator with 7.1% power conversion efficiency,” Phys. Status Solidi RRL 2, 257–259 (2008).
[CrossRef]

Buxton, B.

A. Chatten, K. Barnham, B. Buxton, N. Ekins-Daukes, and M. Malik, “Quantum dot solar concentrators,” Semiconductors 38, 909–917 (2004).
[CrossRef]

Carrascosa, M.

Carter, S. A.

V. Sholin, J. D. Olson, and S. A. Carter, “Semiconducting polymers and quantum dots in luminescent solar concentrators for solar energy harvesting,” J. Appl. Phys. 101, 123114 (2007).
[CrossRef]

Case, K. M.

K. M. Case and P. F. Zweifel, Linear Transport Theory(Addison-Wesley, 1967).

Chandrasekhar, S.

S. Chandrasekhar, Radiative Transfer (Dover, 1960).

Chatten, A.

A. Chatten, K. Barnham, B. Buxton, N. Ekins-Daukes, and M. Malik, “Quantum dot solar concentrators,” Semiconductors 38, 909–917 (2004).
[CrossRef]

Cole, T.

Cooke, D. D.

Currie, M. J.

M. J. Currie, J. K. Mapel, T. D. Heidel, S. Goffri, and M. A. Baldo, “High-efficiency organic solar concentrators for photovoltaics,” Science 321, 226–228 (2008).
[CrossRef]

Cusso, F.

Darling, S. B.

H. Hernandez-Noyola, D. H. Potterveld, R. J. Holt, and S. B. Darling, “Optimizing luminescent solar concentrator design,” Energy Environ. Sci. 5, 5798–5802 (2012).
[CrossRef]

de Boer, D. K. G.

de Cardona, M. S.

Debije, M. G.

Dunlop, E. D.

L. H. Slooff, E. E. Bende, A. R. Burgers, T. Budel, M. Pravettoni, R. P. Kenny, E. D. Dunlop, and A. Büchtemann, “A luminescent solar concentrator with 7.1% power conversion efficiency,” Phys. Status Solidi RRL 2, 257–259 (2008).
[CrossRef]

Ekins-Daukes, N.

A. Chatten, K. Barnham, B. Buxton, N. Ekins-Daukes, and M. Malik, “Quantum dot solar concentrators,” Semiconductors 38, 909–917 (2004).
[CrossRef]

Emery, K.

K. Emery, “Reference solar spectral irradiance: air mass 1.5,” Tech. Rep. (ASTM, 2000), http://rredc.nrel.gov/solar/spectra/am1.5 .

Fayer, M. D.

Gao, H.

H. Gao and H. Zhao, “A fast forward solver of radiative transfer equation,” Transp. Theory Stat. Phys. 38, 149–192 (2009).
[CrossRef]

Ghosh, S.

Glassner, A. S.

A. S. Glassner, Principles of Digital Images Synthesis (Morgan Kaufmann, 1995).

Goffri, S.

M. J. Currie, J. K. Mapel, T. D. Heidel, S. Goffri, and M. A. Baldo, “High-efficiency organic solar concentrators for photovoltaics,” Science 321, 226–228 (2008).
[CrossRef]

Gopinathan, A.

Greenstein, J. L.

J. G. Henyey and J. L. Greenstein, “Diffuse radiation in the galaxy,” J. Astrophys. 93, 70–83 (1941).
[CrossRef]

Gun’ko, Y. K.

F. Purcell-Milton and Y. K. Gun’ko, “Quantum dots for luminescent solar concentrators,” J. Mater. Chem. 22, 16687–16697 (2012).
[CrossRef]

Guo, W.

W. W. Yu, L. Qu, W. Guo, and X. Peng, “Experimental determination of extinction coefficient of CdTe, CdSe, and CdS nanocrystals,” Chem. Matter 15, 2854–2860 (2003).
[CrossRef]

Hecht, E.

E. Hecht, Optics (Addison-Wesley, 1987).

Heidel, T. D.

M. J. Currie, J. K. Mapel, T. D. Heidel, S. Goffri, and M. A. Baldo, “High-efficiency organic solar concentrators for photovoltaics,” Science 321, 226–228 (2008).
[CrossRef]

Henyey, J. G.

J. G. Henyey and J. L. Greenstein, “Diffuse radiation in the galaxy,” J. Astrophys. 93, 70–83 (1941).
[CrossRef]

Hermans, K.

P. P. C. Verbunt, A. Kaiser, K. Hermans, C. W. M. Bastiaansen, D. J. Broer, and M. G. Debije, “Controlling light emission in luminescent solar concentrators through use of dye molecules aligned in a planar manner by liquid crystals,” Adv. Funct. Mater. 19, 2714–2719 (2009).
[CrossRef]

Hernandez-Noyola, H.

H. Hernandez-Noyola, D. H. Potterveld, R. J. Holt, and S. B. Darling, “Optimizing luminescent solar concentrator design,” Energy Environ. Sci. 5, 5798–5802 (2012).
[CrossRef]

Holt, R. J.

H. Hernandez-Noyola, D. H. Potterveld, R. J. Holt, and S. B. Darling, “Optimizing luminescent solar concentrator design,” Energy Environ. Sci. 5, 5798–5802 (2012).
[CrossRef]

Ilan, B.

D. Şahin, B. Ilan, and D. Kelley, “Monte-Carlo simulations of light scattering in luminescent solar concentrators based on semiconductor nanoparticles,” J. Appl. Phys 110, 1–8 (2011).

Inman, R. H.

Ishimaru, A.

A. Ishimaru, Wave Propagation and Scattering in Random Media (Wiley-IEEE, 1999).

Jacques, S. L.

L. Wang, S. L. Jacques, and L. Zheng, “Monte Carlo modeling of photon transport in multi-layered tissues,” Comput. Methods Programs Biomed. 47, 131–146 (1995).
[CrossRef]

S. A. Prahl, M. Keizer, S. L. Jacques, and A. J. Welch, “A Monte Carlo model of light propagation in tissue,” in SPIE Proceedings of Dosimetry of Laser Radiation in Medicine and Biology, Vol. IS(5), SPIE Institute Series (SPIE, 1989), pp. 102–111.

Jaque, F.

Jensen, H. W.

H. W. Jensen, Realistic Image Synthesis Using Photon Mapping (AK Peters, 2001).

Johnson, B. L.

S. McDowall, B. L. Johnson, and D. L. Patrick, “Simulations of luminescent solar concentrators: effects of polarization and fluorophore alignment,” J. Appl. Phys. 108, 053508 (2010).
[CrossRef]

Kaiser, A.

P. P. C. Verbunt, A. Kaiser, K. Hermans, C. W. M. Bastiaansen, D. J. Broer, and M. G. Debije, “Controlling light emission in luminescent solar concentrators through use of dye molecules aligned in a planar manner by liquid crystals,” Adv. Funct. Mater. 19, 2714–2719 (2009).
[CrossRef]

Kajiya, J. T.

J. T. Kajiya, “The rendering equation,” Comput. Graph. 20, 143–150 (1986).
[CrossRef]

Keizer, M.

S. A. Prahl, M. Keizer, S. L. Jacques, and A. J. Welch, “A Monte Carlo model of light propagation in tissue,” in SPIE Proceedings of Dosimetry of Laser Radiation in Medicine and Biology, Vol. IS(5), SPIE Institute Series (SPIE, 1989), pp. 102–111.

Kelley, D.

D. Şahin, B. Ilan, and D. Kelley, “Monte-Carlo simulations of light scattering in luminescent solar concentrators based on semiconductor nanoparticles,” J. Appl. Phys 110, 1–8 (2011).

Kenny, R. P.

L. H. Slooff, E. E. Bende, A. R. Burgers, T. Budel, M. Pravettoni, R. P. Kenny, E. D. Dunlop, and A. Büchtemann, “A luminescent solar concentrator with 7.1% power conversion efficiency,” Phys. Status Solidi RRL 2, 257–259 (2008).
[CrossRef]

Kerker, M.

Kim, A. D.

A. D. Kim and M. Moscoso, “Radiative transfer computations for optical beams,” J. Comput. Phys. 185, 50–60 (2003).
[CrossRef]

Kim, H.

Lagendijk, A.

J. Bertolotti, E. G. van Putten, C. Blum, A. Lagendijk, W. L. Vos, and A. P. Mosk, “Non-invasive imaging through opaque scattering layers,” Nature 491, 232–234 (2012).
[CrossRef]

Lathrop, K. D.

K. D. Lathrop, “Ray effects in discrete ordinates equations,” Nucl. Sci. Eng. 32, 357–369 (1968).

Lewis, E. E.

E. E. Lewis and W. F. J. Miller, Computational Methods of Neutron Transport (Wiley, 1984).

Lin, C.-W.

Malik, M.

A. Chatten, K. Barnham, B. Buxton, N. Ekins-Daukes, and M. Malik, “Quantum dot solar concentrators,” Semiconductors 38, 909–917 (2004).
[CrossRef]

Mapel, J. K.

M. J. Currie, J. K. Mapel, T. D. Heidel, S. Goffri, and M. A. Baldo, “High-efficiency organic solar concentrators for photovoltaics,” Science 321, 226–228 (2008).
[CrossRef]

Markel, V. A.

McDowall, S.

S. McDowall, B. L. Johnson, and D. L. Patrick, “Simulations of luminescent solar concentrators: effects of polarization and fluorophore alignment,” J. Appl. Phys. 108, 053508 (2010).
[CrossRef]

Medvedko, D.

Meseguer, F.

Miller, W. F. J.

E. E. Lewis and W. F. J. Miller, Computational Methods of Neutron Transport (Wiley, 1984).

Moscoso, M.

A. D. Kim and M. Moscoso, “Radiative transfer computations for optical beams,” J. Comput. Phys. 185, 50–60 (2003).
[CrossRef]

Mosk, A. P.

J. Bertolotti, E. G. van Putten, C. Blum, A. Lagendijk, W. L. Vos, and A. P. Mosk, “Non-invasive imaging through opaque scattering layers,” Nature 491, 232–234 (2012).
[CrossRef]

Mulder, C. L.

Olson, J. D.

V. Sholin, J. D. Olson, and S. A. Carter, “Semiconducting polymers and quantum dots in luminescent solar concentrators for solar energy harvesting,” J. Appl. Phys. 101, 123114 (2007).
[CrossRef]

Olson, R. W.

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[CrossRef]

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W. W. Yu, L. Qu, W. Guo, and X. Peng, “Experimental determination of extinction coefficient of CdTe, CdSe, and CdS nanocrystals,” Chem. Matter 15, 2854–2860 (2003).
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Pilon, L.

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G. Bal and O. Pinaud, “Accuracy of transport models for waves in random media,” Wave Motion 43, 561–578 (2006).
[CrossRef]

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H. Hernandez-Noyola, D. H. Potterveld, R. J. Holt, and S. B. Darling, “Optimizing luminescent solar concentrator design,” Energy Environ. Sci. 5, 5798–5802 (2012).
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Pravettoni, M.

L. H. Slooff, E. E. Bende, A. R. Burgers, T. Budel, M. Pravettoni, R. P. Kenny, E. D. Dunlop, and A. Büchtemann, “A luminescent solar concentrator with 7.1% power conversion efficiency,” Phys. Status Solidi RRL 2, 257–259 (2008).
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F. Purcell-Milton and Y. K. Gun’ko, “Quantum dots for luminescent solar concentrators,” J. Mater. Chem. 22, 16687–16697 (2012).
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W. W. Yu, L. Qu, W. Guo, and X. Peng, “Experimental determination of extinction coefficient of CdTe, CdSe, and CdS nanocrystals,” Chem. Matter 15, 2854–2860 (2003).
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V. Sholin, J. D. Olson, and S. A. Carter, “Semiconducting polymers and quantum dots in luminescent solar concentrators for solar energy harvesting,” J. Appl. Phys. 101, 123114 (2007).
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J. Bertolotti, E. G. van Putten, C. Blum, A. Lagendijk, W. L. Vos, and A. P. Mosk, “Non-invasive imaging through opaque scattering layers,” Nature 491, 232–234 (2012).
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S. A. Prahl, M. Keizer, S. L. Jacques, and A. J. Welch, “A Monte Carlo model of light propagation in tissue,” in SPIE Proceedings of Dosimetry of Laser Radiation in Medicine and Biology, Vol. IS(5), SPIE Institute Series (SPIE, 1989), pp. 102–111.

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L. Wang and H. Wu, Biomedical Optics: Principles and Imaging (Wiley, 2007).

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C. T. Xu, J. Axelsson, and S. Andersson-Engels, “Fluorescence diffuse optical tomography using upconverting nanoparticles,” Appl. Phys. Lett. 94, 251107 (2009).
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W. W. Yu, L. Qu, W. Guo, and X. Peng, “Experimental determination of extinction coefficient of CdTe, CdSe, and CdS nanocrystals,” Chem. Matter 15, 2854–2860 (2003).
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Zacharopoulos, A. D.

A. D. Zacharopoulos, P. Svenmarker, J. Axelsson, M. Schweiger, S. R. Arridge, and S. Andersson-Engels, “A matrix-free algorithm for multiple wavelength fluorescence tomography,” Appl. Phys. Lett. 17, 3042–3051 (2009).

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H. Gao and H. Zhao, “A fast forward solver of radiative transfer equation,” Transp. Theory Stat. Phys. 38, 149–192 (2009).
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L. Wang, S. L. Jacques, and L. Zheng, “Monte Carlo modeling of photon transport in multi-layered tissues,” Comput. Methods Programs Biomed. 47, 131–146 (1995).
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[CrossRef]

Appl. Opt. (4)

Appl. Phys. Lett. (2)

A. D. Zacharopoulos, P. Svenmarker, J. Axelsson, M. Schweiger, S. R. Arridge, and S. Andersson-Engels, “A matrix-free algorithm for multiple wavelength fluorescence tomography,” Appl. Phys. Lett. 17, 3042–3051 (2009).

C. T. Xu, J. Axelsson, and S. Andersson-Engels, “Fluorescence diffuse optical tomography using upconverting nanoparticles,” Appl. Phys. Lett. 94, 251107 (2009).
[CrossRef]

Chem. Matter (1)

W. W. Yu, L. Qu, W. Guo, and X. Peng, “Experimental determination of extinction coefficient of CdTe, CdSe, and CdS nanocrystals,” Chem. Matter 15, 2854–2860 (2003).
[CrossRef]

Comput. Graph. (1)

J. T. Kajiya, “The rendering equation,” Comput. Graph. 20, 143–150 (1986).
[CrossRef]

Comput. Methods Programs Biomed. (1)

L. Wang, S. L. Jacques, and L. Zheng, “Monte Carlo modeling of photon transport in multi-layered tissues,” Comput. Methods Programs Biomed. 47, 131–146 (1995).
[CrossRef]

Energy Environ. Sci. (1)

H. Hernandez-Noyola, D. H. Potterveld, R. J. Holt, and S. B. Darling, “Optimizing luminescent solar concentrator design,” Energy Environ. Sci. 5, 5798–5802 (2012).
[CrossRef]

J. Appl. Phys (1)

D. Şahin, B. Ilan, and D. Kelley, “Monte-Carlo simulations of light scattering in luminescent solar concentrators based on semiconductor nanoparticles,” J. Appl. Phys 110, 1–8 (2011).

J. Appl. Phys. (2)

S. McDowall, B. L. Johnson, and D. L. Patrick, “Simulations of luminescent solar concentrators: effects of polarization and fluorophore alignment,” J. Appl. Phys. 108, 053508 (2010).
[CrossRef]

V. Sholin, J. D. Olson, and S. A. Carter, “Semiconducting polymers and quantum dots in luminescent solar concentrators for solar energy harvesting,” J. Appl. Phys. 101, 123114 (2007).
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J. Comput. Phys. (1)

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J. Mater. Chem. (1)

F. Purcell-Milton and Y. K. Gun’ko, “Quantum dots for luminescent solar concentrators,” J. Mater. Chem. 22, 16687–16697 (2012).
[CrossRef]

J. Opt. Soc. Am. (1)

Nature (1)

J. Bertolotti, E. G. van Putten, C. Blum, A. Lagendijk, W. L. Vos, and A. P. Mosk, “Non-invasive imaging through opaque scattering layers,” Nature 491, 232–234 (2012).
[CrossRef]

Nucl. Sci. Eng. (1)

K. D. Lathrop, “Ray effects in discrete ordinates equations,” Nucl. Sci. Eng. 32, 357–369 (1968).

Opt. Express (4)

Opt. Lett. (1)

Phys. Status Solidi RRL (1)

L. H. Slooff, E. E. Bende, A. R. Burgers, T. Budel, M. Pravettoni, R. P. Kenny, E. D. Dunlop, and A. Büchtemann, “A luminescent solar concentrator with 7.1% power conversion efficiency,” Phys. Status Solidi RRL 2, 257–259 (2008).
[CrossRef]

Science (1)

M. J. Currie, J. K. Mapel, T. D. Heidel, S. Goffri, and M. A. Baldo, “High-efficiency organic solar concentrators for photovoltaics,” Science 321, 226–228 (2008).
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Semiconductors (1)

A. Chatten, K. Barnham, B. Buxton, N. Ekins-Daukes, and M. Malik, “Quantum dot solar concentrators,” Semiconductors 38, 909–917 (2004).
[CrossRef]

Transp. Theory Stat. Phys. (1)

H. Gao and H. Zhao, “A fast forward solver of radiative transfer equation,” Transp. Theory Stat. Phys. 38, 149–192 (2009).
[CrossRef]

Wave Motion (1)

G. Bal and O. Pinaud, “Accuracy of transport models for waves in random media,” Wave Motion 43, 561–578 (2006).
[CrossRef]

Other (10)

L. Wang and H. Wu, Biomedical Optics: Principles and Imaging (Wiley, 2007).

S. A. Prahl, M. Keizer, S. L. Jacques, and A. J. Welch, “A Monte Carlo model of light propagation in tissue,” in SPIE Proceedings of Dosimetry of Laser Radiation in Medicine and Biology, Vol. IS(5), SPIE Institute Series (SPIE, 1989), pp. 102–111.

S. Chandrasekhar, Radiative Transfer (Dover, 1960).

A. Ishimaru, Wave Propagation and Scattering in Random Media (Wiley-IEEE, 1999).

K. M. Case and P. F. Zweifel, Linear Transport Theory(Addison-Wesley, 1967).

E. Hecht, Optics (Addison-Wesley, 1987).

K. Emery, “Reference solar spectral irradiance: air mass 1.5,” Tech. Rep. (ASTM, 2000), http://rredc.nrel.gov/solar/spectra/am1.5 .

E. E. Lewis and W. F. J. Miller, Computational Methods of Neutron Transport (Wiley, 1984).

A. S. Glassner, Principles of Digital Images Synthesis (Morgan Kaufmann, 1995).

H. W. Jensen, Realistic Image Synthesis Using Photon Mapping (AK Peters, 2001).

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Figures (10)

Fig. 1.
Fig. 1.

Illustration of light propagation in an LSC. Sunlight (solid arrow) is incident on the top surface, absorbed and reemitted by fluorescent nanoparticles (small spheres), and guided toward the PV cell on the right edge.

Fig. 2.
Fig. 2.

Normalized absorption and re-emission spectra [i.e., fa(λ) and fr(λ), respectively] corresponding to semiconductor CdSe–CdTe nanoparticles (from [13]).

Fig. 3.
Fig. 3.

Illustration of light propagation in a 3D LSC based on anisotropic nanorods. A PV cell is located at the right edge. Perfect mirrors are assumed to cover the bottom surface and all the other edges.

Fig. 4.
Fig. 4.

Dependence of the reemission phase function in Eq. (12) on the polar angle φ for isotropic quantum dots (g=0, dotted–dashed line) and aligned nanorods (g=0.75, solid curve). The nanorods luminesce preferentially along the x axis, i.e., φ=0 and φ=π.

Fig. 5.
Fig. 5.

Convergence of the LRTE solution as a function of iteration number (loglog plot).

Fig. 6.
Fig. 6.

Wavelength-averaged optical efficiency [Eq. (19) (solid)], the averaged escape losses from the top surface [Eq. (20), dots], and the combined absorption losses [Eq. (22), dashes], as functions of the absorption constant, μa (in [1/cm]) using aligned nanorods (g=0.75).

Fig. 7.
Fig. 7.

Wavelength-averaged optical efficiency (left axis) and LSC optical gain (right axis) as functions of the anisotropy factor.

Fig. 8.
Fig. 8.

Wavelength-averaged optical efficiency with μa=600 and g=0.75 as a function of the geometric gain factor G=(lx/lz) with lz=0.4[cm].

Fig. 9.
Fig. 9.

LSC optical gain for the same parameters as in Fig. 8.

Fig. 10.
Fig. 10.

Wavelength-averaged optical efficiency as a function of the absorption constant obtained using the LRTE (solid) and MC (dashes).

Equations (37)

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I(x,Ω,λ,t):D×S2×Λ×[0,tmax]R0
1cIt+Ω·I+μaLaIμrLrI=0,
Pabs(Δs;λ)=110ϵ(λ)MΔs,
μa=ln(10)MΛϵ(λ)dλ.
fa(λ)=ϵ(λ)Λϵ(λ)dλ.
LaI=fa(λ)I.
LrI=ΛS2Kr(λ,λ,Ω,Ω)I(x,Ω,λ)dΩdλ,
Kr(λ,λ,Ω,Ω)=δ(λλ)pr(Ω,Ω),
1cIt+Ω·I=μaI+μtS2pr(Ω,Ω)I(x,Ω)dΩ,
Ω·I+μaf(λ)IμrLrI=0.
LrI=pr(Ω;g)fr(λ)S2Λfa(λ)IdΩdλ,
μr=QYμa.
I=Sb+RIonΓin,Γin={(x,Ω,λ)D×S2×Λ,Ω·ν<0},
cosφIx+sinφIz+μafa(λ)Iμrfr(λ)pr(φ;g)02πΛfa(λ)Idφdλ=0.
pr(φ;g)=12π1g212gcos2φ+g2.
I(lx2,z,φ,λ)=0,φ(π2,3π2).
I(lx2,z,φ,λ)=I(lx2,z,π+φ,λ),φ(π2,π2),
I(x,lz2,φ,λ)=I(x,lz2,2πφ,λ),φ(π,2π).
I(x,lz2,φ,λ)=[1R(φ)]I(x,lz2,φ,λ)+R(φ)I(x,lz2,φ,λ),
Sb(φ,λ)=fsol(λ)e8(φ3π2)2,φ(π,2π),
I(x,z,φ,λ)Ii,j,m,ks=0maxiterIi,j,m,k(s),
I(s)(x,z,φ,λ)=maxi,j,m,k|Ii,j,m,k(s)|Δ
ηpv(λ)=Φpv(λ)Φsol(λ),
Φpv(λ)=lz2lz2π2π2I(lx2,z,φ,λ)dφdz,
Φsol(λ)=lxπ2πSb(φ,λ)dφ.
Φsol(λ)=Clxfsol(λ),C0.62.
η¯pv=Ληpv(λ)dλΛΦsol(λ)dλ,
η¯top=ΛΦtop(λ)dλΛΦsol(λ)dλ,
Φtop(λ)=lx2lx20π[1R(φ)]I(x,lz2,φ,λ)dφdx,
η¯abs=1η¯pvη¯top.
Γ¯=η¯pv×G,GAtopApvlxlz,
ξPabs(2lz,λi),
P(φ;g)=12π{Θ(φ;g),φ[0,π/2),π+Θ(φ;g),φ[π/2,3π/2),2π+Θ(φ;g),φ[3π/2,2π),
Θ(φ;g)=tan1(g˜tanφ),g˜=1g1+g.
φ={tan1[g˜tan(2πξ)],ξ[0,1/4);tan1[g˜tan(π(2ξ1))],ξ[1/4,3/4);tan1[g˜tan(2π(ξ1))],ξ[3/4,1),
x=x+Δscosφ,z=z+Δssinφ,
Δs=1ϵ(λ)Mlog10ξ,

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