Abstract

New technologies are emerging that capture and redirect sunlight inside solar cells. This type of light management can significantly increase efficiency, but the device behavior will fundamentally depend on the spatial coherence of the incoming light. This dependence calls for a complete characterization of the spatial coherence of sunlight. Here, we present the first spectral measurements of the spatial degree of coherence of direct, diffuse, and simulated sunlight. An expression is derived for both the cross-spectral density and the spatial degree of coherence in an arbitrarily oriented device plane, including the effects of overcast skies. Implications of the present work are discussed and may lead to a better understanding of light-managing components in solar cells as well as a new class of solar simulator that provides both the same spectrum and spatial coherence as direct sunlight.

© 2015 Optical Society of America

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References

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2014 (6)

M. A. Green, K. Emery, Y. Hishikawa, W. Warta, E. D. Dunlop, “Solar cell efficiency tables (version 43),” Prog. Photovoltaics 22, 1–9 (2014).
[Crossref]

M. L. Brongersma, Y. Cui, S. Fan, “Light management for photovoltaics using high-index nanostructures,” Nat. Mater. 13, 451–460 (2014).
[Crossref]

T. Sun, C. Fei Guo, F. Cao, E. Metin Akinoglu, Y. Wang, M. Giersig, Z. Ren, K. Kempa, “A broadband solar absorber with 12  nm thick ultrathin a-Si layer by using random metallic nanomeshes,” Appl. Phys. Lett. 104, 251119 (2014).
[Crossref]

S. Pattnaik, N. Chakravarty, R. Biswas, V. Dalal, D. Slafer, “Nano-photonic and nano-plasmonic enhancements in thin film silicon solar cells,” Sol. Energ. Mat. Sol. C. 129, 115–123 (2014).

S. Divitt, Z. J. Lapin, L. Novotny, “Measuring coherence functions using non-parallel double slits,” Opt. Express 22, 8277–8290 (2014).
[Crossref]

S. Morawiec, M. J. Mendes, S. A. Filonovich, T. Mateus, S. Mirabella, H. Águas, I. Ferreira, F. Simone, E. Fortunato, R. Martins, F. Priolo, I. Crupi, “Broadband photocurrent enhancement in a-Si:H solar cells with plasmonic back reflectors,” Opt. Express 22, A1059–A1070 (2014).
[Crossref]

2013 (5)

M. van Lare, F. Lenzmann, A. Polman, “Dielectric back scattering patterns for light trapping in thin-film Si solar cells,” Opt. Express 21, 20738–20746 (2013).
[Crossref]

M. Lahiri, E. Wolf, “Propagation of electromagnetic beams of any state of spatial coherence and polarization through multilayered stratified media,” J. Opt. Soc. Am. A 30, 2547–2555 (2013).
[Crossref]

R. A. Pala, J. S. Liu, E. S. Barnard, D. Askarov, E. C. Garnett, S. Fan, M. L. Brongersma, “Optimization of non-periodic plasmonic light-trapping layers for thin-film solar cells,” Nat. Commun. 4, 2095 (2013).
[Crossref]

Y. Kuang, M. D. Vece, J. K. Rath, L. van Dijk, R. E. I. Schropp, “Elongated nanostructures for radial junction solar cells,” Rep. Prog. Phys. 76, 106502 (2013).
[Crossref]

K. Blomstedt, T. Setälä, J. Tervo, J. Turunen, A. T. Friberg, “Partial polarization and electromagnetic spatial coherence of blackbody radiation emanating from an aperture,” Phys. Rev. A 88, 013824 (2013).
[Crossref]

2012 (3)

A. Polman, H. A. Atwater, “Photonic design principles for ultrahigh-efficiency photovoltaics,” Nat. Mater. 11, 174–177 (2012).
[Crossref]

C. Battaglia, C.-M. Hsu, K. Söderström, J. Escarré, F.-J. Haug, M. Charrière, M. Boccard, M. Despeisse, D. T. L. Alexander, M. Cantoni, Y. Cui, C. Ballif, “Light trapping in solar cells: Can periodic beat random?” ACS Nano 6, 2790–2797 (2012).
[Crossref]

H. Mashaal, A. Goldstein, D. Feuermann, J. M. Gordon, “First direct measurement of the spatial coherence of sunlight,” Opt. Lett. 37, 3516–3518 (2012).
[Crossref]

2011 (2)

H. Mashaal, J. M. Gordon, “Fundamental bounds for antenna harvesting of sunlight,” Opt. Lett. 36, 900–902 (2011).
[Crossref]

V. E. Ferry, M. A. Verschuuren, M. C. v. Lare, R. E. I. Schropp, H. A. Atwater, A. Polman, “Optimized spatial correlations for broadband light trapping nanopatterns in high efficiency ultrathin film a-Si:H solar cells,” Nano Lett. 11, 4239–4245 (2011).

2010 (1)

E. Garnett, P. Yang, “Light trapping in silicon nanowire solar cells,” Nano Lett. 10, 1082–1087 (2010).

2004 (3)

2003 (1)

1998 (1)

R. Popescu, G. Deodatis, J. Prevost, “Simulation of homogeneous nonGaussian stochastic vector fields,” Probabilist. Eng. Mech. 13, 1–13 (1998).

1995 (1)

1994 (1)

H. Neckel, D. Labs, “Solar limb darkening 1986–1990 (λλ303 to 1099  nm),” Sol. Phys. 153, 91–114 (1994).
[Crossref]

1983 (1)

1967 (1)

C. L. Mehta, E. Wolf, “Coherence properties of blackbody radiation. III. Cross-spectral tensors,” Phys. Rev. 161, 1328–1334 (1967).
[Crossref]

1957 (1)

Agarwal, G. S.

Águas, H.

Alexander, D. T. L.

C. Battaglia, C.-M. Hsu, K. Söderström, J. Escarré, F.-J. Haug, M. Charrière, M. Boccard, M. Despeisse, D. T. L. Alexander, M. Cantoni, Y. Cui, C. Ballif, “Light trapping in solar cells: Can periodic beat random?” ACS Nano 6, 2790–2797 (2012).
[Crossref]

Askarov, D.

R. A. Pala, J. S. Liu, E. S. Barnard, D. Askarov, E. C. Garnett, S. Fan, M. L. Brongersma, “Optimization of non-periodic plasmonic light-trapping layers for thin-film solar cells,” Nat. Commun. 4, 2095 (2013).
[Crossref]

Atwater, H. A.

A. Polman, H. A. Atwater, “Photonic design principles for ultrahigh-efficiency photovoltaics,” Nat. Mater. 11, 174–177 (2012).
[Crossref]

V. E. Ferry, M. A. Verschuuren, M. C. v. Lare, R. E. I. Schropp, H. A. Atwater, A. Polman, “Optimized spatial correlations for broadband light trapping nanopatterns in high efficiency ultrathin film a-Si:H solar cells,” Nano Lett. 11, 4239–4245 (2011).

Ballif, C.

C. Battaglia, C.-M. Hsu, K. Söderström, J. Escarré, F.-J. Haug, M. Charrière, M. Boccard, M. Despeisse, D. T. L. Alexander, M. Cantoni, Y. Cui, C. Ballif, “Light trapping in solar cells: Can periodic beat random?” ACS Nano 6, 2790–2797 (2012).
[Crossref]

Barnard, E. S.

R. A. Pala, J. S. Liu, E. S. Barnard, D. Askarov, E. C. Garnett, S. Fan, M. L. Brongersma, “Optimization of non-periodic plasmonic light-trapping layers for thin-film solar cells,” Nat. Commun. 4, 2095 (2013).
[Crossref]

Battaglia, C.

C. Battaglia, C.-M. Hsu, K. Söderström, J. Escarré, F.-J. Haug, M. Charrière, M. Boccard, M. Despeisse, D. T. L. Alexander, M. Cantoni, Y. Cui, C. Ballif, “Light trapping in solar cells: Can periodic beat random?” ACS Nano 6, 2790–2797 (2012).
[Crossref]

Beran, M.

M. Beran, G. Parrent, Theory of Partial Coherence (The Society of Photo-optical Instrumentation Engineers, 1974).

Biswas, R.

S. Pattnaik, N. Chakravarty, R. Biswas, V. Dalal, D. Slafer, “Nano-photonic and nano-plasmonic enhancements in thin film silicon solar cells,” Sol. Energ. Mat. Sol. C. 129, 115–123 (2014).

Blomstedt, K.

K. Blomstedt, T. Setälä, J. Tervo, J. Turunen, A. T. Friberg, “Partial polarization and electromagnetic spatial coherence of blackbody radiation emanating from an aperture,” Phys. Rev. A 88, 013824 (2013).
[Crossref]

Boccard, M.

C. Battaglia, C.-M. Hsu, K. Söderström, J. Escarré, F.-J. Haug, M. Charrière, M. Boccard, M. Despeisse, D. T. L. Alexander, M. Cantoni, Y. Cui, C. Ballif, “Light trapping in solar cells: Can periodic beat random?” ACS Nano 6, 2790–2797 (2012).
[Crossref]

Bohren, C. F.

C. F. Bohren, “Atmospheric optics,” in The Optics Encyclopedia (Wiley-VCH Verlag GmbH and Co. KGaA, 2007).

Born, M.

M. Born, E. Wolf, Principles of Optics, 7th ed. (Cambridge University, 1999).

Brongersma, M. L.

M. L. Brongersma, Y. Cui, S. Fan, “Light management for photovoltaics using high-index nanostructures,” Nat. Mater. 13, 451–460 (2014).
[Crossref]

R. A. Pala, J. S. Liu, E. S. Barnard, D. Askarov, E. C. Garnett, S. Fan, M. L. Brongersma, “Optimization of non-periodic plasmonic light-trapping layers for thin-film solar cells,” Nat. Commun. 4, 2095 (2013).
[Crossref]

Cantoni, M.

C. Battaglia, C.-M. Hsu, K. Söderström, J. Escarré, F.-J. Haug, M. Charrière, M. Boccard, M. Despeisse, D. T. L. Alexander, M. Cantoni, Y. Cui, C. Ballif, “Light trapping in solar cells: Can periodic beat random?” ACS Nano 6, 2790–2797 (2012).
[Crossref]

Cao, F.

T. Sun, C. Fei Guo, F. Cao, E. Metin Akinoglu, Y. Wang, M. Giersig, Z. Ren, K. Kempa, “A broadband solar absorber with 12  nm thick ultrathin a-Si layer by using random metallic nanomeshes,” Appl. Phys. Lett. 104, 251119 (2014).
[Crossref]

Chakravarty, N.

S. Pattnaik, N. Chakravarty, R. Biswas, V. Dalal, D. Slafer, “Nano-photonic and nano-plasmonic enhancements in thin film silicon solar cells,” Sol. Energ. Mat. Sol. C. 129, 115–123 (2014).

Charrière, M.

C. Battaglia, C.-M. Hsu, K. Söderström, J. Escarré, F.-J. Haug, M. Charrière, M. Boccard, M. Despeisse, D. T. L. Alexander, M. Cantoni, Y. Cui, C. Ballif, “Light trapping in solar cells: Can periodic beat random?” ACS Nano 6, 2790–2797 (2012).
[Crossref]

Collin, R. E.

R. E. Collin, F. J. Zucker, Antenna Theory Part 1 (McGraw-Hill, 1969).

Crupi, I.

Cui, Y.

M. L. Brongersma, Y. Cui, S. Fan, “Light management for photovoltaics using high-index nanostructures,” Nat. Mater. 13, 451–460 (2014).
[Crossref]

C. Battaglia, C.-M. Hsu, K. Söderström, J. Escarré, F.-J. Haug, M. Charrière, M. Boccard, M. Despeisse, D. T. L. Alexander, M. Cantoni, Y. Cui, C. Ballif, “Light trapping in solar cells: Can periodic beat random?” ACS Nano 6, 2790–2797 (2012).
[Crossref]

Dalal, V.

S. Pattnaik, N. Chakravarty, R. Biswas, V. Dalal, D. Slafer, “Nano-photonic and nano-plasmonic enhancements in thin film silicon solar cells,” Sol. Energ. Mat. Sol. C. 129, 115–123 (2014).

Deodatis, G.

R. Popescu, G. Deodatis, J. Prevost, “Simulation of homogeneous nonGaussian stochastic vector fields,” Probabilist. Eng. Mech. 13, 1–13 (1998).

Despeisse, M.

C. Battaglia, C.-M. Hsu, K. Söderström, J. Escarré, F.-J. Haug, M. Charrière, M. Boccard, M. Despeisse, D. T. L. Alexander, M. Cantoni, Y. Cui, C. Ballif, “Light trapping in solar cells: Can periodic beat random?” ACS Nano 6, 2790–2797 (2012).
[Crossref]

Divitt, S.

Dunlop, E. D.

M. A. Green, K. Emery, Y. Hishikawa, W. Warta, E. D. Dunlop, “Solar cell efficiency tables (version 43),” Prog. Photovoltaics 22, 1–9 (2014).
[Crossref]

Emery, K.

M. A. Green, K. Emery, Y. Hishikawa, W. Warta, E. D. Dunlop, “Solar cell efficiency tables (version 43),” Prog. Photovoltaics 22, 1–9 (2014).
[Crossref]

Escarré, J.

C. Battaglia, C.-M. Hsu, K. Söderström, J. Escarré, F.-J. Haug, M. Charrière, M. Boccard, M. Despeisse, D. T. L. Alexander, M. Cantoni, Y. Cui, C. Ballif, “Light trapping in solar cells: Can periodic beat random?” ACS Nano 6, 2790–2797 (2012).
[Crossref]

Fan, S.

M. L. Brongersma, Y. Cui, S. Fan, “Light management for photovoltaics using high-index nanostructures,” Nat. Mater. 13, 451–460 (2014).
[Crossref]

R. A. Pala, J. S. Liu, E. S. Barnard, D. Askarov, E. C. Garnett, S. Fan, M. L. Brongersma, “Optimization of non-periodic plasmonic light-trapping layers for thin-film solar cells,” Nat. Commun. 4, 2095 (2013).
[Crossref]

Fei Guo, C.

T. Sun, C. Fei Guo, F. Cao, E. Metin Akinoglu, Y. Wang, M. Giersig, Z. Ren, K. Kempa, “A broadband solar absorber with 12  nm thick ultrathin a-Si layer by using random metallic nanomeshes,” Appl. Phys. Lett. 104, 251119 (2014).
[Crossref]

Ferreira, I.

Ferry, V. E.

V. E. Ferry, M. A. Verschuuren, M. C. v. Lare, R. E. I. Schropp, H. A. Atwater, A. Polman, “Optimized spatial correlations for broadband light trapping nanopatterns in high efficiency ultrathin film a-Si:H solar cells,” Nano Lett. 11, 4239–4245 (2011).

Feuermann, D.

Filonovich, S. A.

Fortunato, E.

Friberg, A. T.

Garnett, E.

E. Garnett, P. Yang, “Light trapping in silicon nanowire solar cells,” Nano Lett. 10, 1082–1087 (2010).

Garnett, E. C.

R. A. Pala, J. S. Liu, E. S. Barnard, D. Askarov, E. C. Garnett, S. Fan, M. L. Brongersma, “Optimization of non-periodic plasmonic light-trapping layers for thin-film solar cells,” Nat. Commun. 4, 2095 (2013).
[Crossref]

Gbur, G.

Giersig, M.

T. Sun, C. Fei Guo, F. Cao, E. Metin Akinoglu, Y. Wang, M. Giersig, Z. Ren, K. Kempa, “A broadband solar absorber with 12  nm thick ultrathin a-Si layer by using random metallic nanomeshes,” Appl. Phys. Lett. 104, 251119 (2014).
[Crossref]

Goldstein, A.

Gordon, J. M.

Green, M. A.

M. A. Green, K. Emery, Y. Hishikawa, W. Warta, E. D. Dunlop, “Solar cell efficiency tables (version 43),” Prog. Photovoltaics 22, 1–9 (2014).
[Crossref]

Haug, F.-J.

C. Battaglia, C.-M. Hsu, K. Söderström, J. Escarré, F.-J. Haug, M. Charrière, M. Boccard, M. Despeisse, D. T. L. Alexander, M. Cantoni, Y. Cui, C. Ballif, “Light trapping in solar cells: Can periodic beat random?” ACS Nano 6, 2790–2797 (2012).
[Crossref]

Hecht, B.

L. Novotny, B. Hecht, Principles of Nano-Optics, 2nd ed. (Cambridge University, 2012).

Hishikawa, Y.

M. A. Green, K. Emery, Y. Hishikawa, W. Warta, E. D. Dunlop, “Solar cell efficiency tables (version 43),” Prog. Photovoltaics 22, 1–9 (2014).
[Crossref]

Hsu, C.-M.

C. Battaglia, C.-M. Hsu, K. Söderström, J. Escarré, F.-J. Haug, M. Charrière, M. Boccard, M. Despeisse, D. T. L. Alexander, M. Cantoni, Y. Cui, C. Ballif, “Light trapping in solar cells: Can periodic beat random?” ACS Nano 6, 2790–2797 (2012).
[Crossref]

Jensen, J.

J. Jensen, A. R. Mackintosh, Rare Earth Magnetism: Structures and Excitations (Clarendon, 1991).

Kaivola, M.

Kempa, K.

T. Sun, C. Fei Guo, F. Cao, E. Metin Akinoglu, Y. Wang, M. Giersig, Z. Ren, K. Kempa, “A broadband solar absorber with 12  nm thick ultrathin a-Si layer by using random metallic nanomeshes,” Appl. Phys. Lett. 104, 251119 (2014).
[Crossref]

Korotkova, O.

Kuang, Y.

Y. Kuang, M. D. Vece, J. K. Rath, L. van Dijk, R. E. I. Schropp, “Elongated nanostructures for radial junction solar cells,” Rep. Prog. Phys. 76, 106502 (2013).
[Crossref]

Labs, D.

H. Neckel, D. Labs, “Solar limb darkening 1986–1990 (λλ303 to 1099  nm),” Sol. Phys. 153, 91–114 (1994).
[Crossref]

Lahiri, M.

Lapin, Z. J.

Lare, M. C. v.

V. E. Ferry, M. A. Verschuuren, M. C. v. Lare, R. E. I. Schropp, H. A. Atwater, A. Polman, “Optimized spatial correlations for broadband light trapping nanopatterns in high efficiency ultrathin film a-Si:H solar cells,” Nano Lett. 11, 4239–4245 (2011).

Lenzmann, F.

Liu, J. S.

R. A. Pala, J. S. Liu, E. S. Barnard, D. Askarov, E. C. Garnett, S. Fan, M. L. Brongersma, “Optimization of non-periodic plasmonic light-trapping layers for thin-film solar cells,” Nat. Commun. 4, 2095 (2013).
[Crossref]

Mackintosh, A. R.

J. Jensen, A. R. Mackintosh, Rare Earth Magnetism: Structures and Excitations (Clarendon, 1991).

Mandel, L.

L. Mandel, E. Wolf, Optical Coherence and Quantum Optics (Cambridge University Press, 1995).

Martins, R.

Mashaal, H.

Mateus, T.

Mehta, C. L.

C. L. Mehta, E. Wolf, “Coherence properties of blackbody radiation. III. Cross-spectral tensors,” Phys. Rev. 161, 1328–1334 (1967).
[Crossref]

Mendes, M. J.

Metin Akinoglu, E.

T. Sun, C. Fei Guo, F. Cao, E. Metin Akinoglu, Y. Wang, M. Giersig, Z. Ren, K. Kempa, “A broadband solar absorber with 12  nm thick ultrathin a-Si layer by using random metallic nanomeshes,” Appl. Phys. Lett. 104, 251119 (2014).
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Mirabella, S.

Moddel, G.

G. Moddel, “Will rectenna solar cells be practical?” in Rectenna Solar Cells, G. Moddel, S. Grover, eds. (Springer, 2013), pp. 3–24.

Morawiec, S.

Neckel, H.

H. Neckel, D. Labs, “Solar limb darkening 1986–1990 (λλ303 to 1099  nm),” Sol. Phys. 153, 91–114 (1994).
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Novotny, L.

Office, U. S. N. A.

U. S. N. A. Office, Astronomical Almanac for the Year 2013 (United States Naval Observatory/Nautical Almanac Office, 2012).

Pala, R. A.

R. A. Pala, J. S. Liu, E. S. Barnard, D. Askarov, E. C. Garnett, S. Fan, M. L. Brongersma, “Optimization of non-periodic plasmonic light-trapping layers for thin-film solar cells,” Nat. Commun. 4, 2095 (2013).
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Parrent, G.

M. Beran, G. Parrent, Theory of Partial Coherence (The Society of Photo-optical Instrumentation Engineers, 1974).

Pattnaik, S.

S. Pattnaik, N. Chakravarty, R. Biswas, V. Dalal, D. Slafer, “Nano-photonic and nano-plasmonic enhancements in thin film silicon solar cells,” Sol. Energ. Mat. Sol. C. 129, 115–123 (2014).

Polman, A.

M. van Lare, F. Lenzmann, A. Polman, “Dielectric back scattering patterns for light trapping in thin-film Si solar cells,” Opt. Express 21, 20738–20746 (2013).
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A. Polman, H. A. Atwater, “Photonic design principles for ultrahigh-efficiency photovoltaics,” Nat. Mater. 11, 174–177 (2012).
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V. E. Ferry, M. A. Verschuuren, M. C. v. Lare, R. E. I. Schropp, H. A. Atwater, A. Polman, “Optimized spatial correlations for broadband light trapping nanopatterns in high efficiency ultrathin film a-Si:H solar cells,” Nano Lett. 11, 4239–4245 (2011).

Popescu, R.

R. Popescu, G. Deodatis, J. Prevost, “Simulation of homogeneous nonGaussian stochastic vector fields,” Probabilist. Eng. Mech. 13, 1–13 (1998).

Prevost, J.

R. Popescu, G. Deodatis, J. Prevost, “Simulation of homogeneous nonGaussian stochastic vector fields,” Probabilist. Eng. Mech. 13, 1–13 (1998).

Priolo, F.

Rath, J. K.

Y. Kuang, M. D. Vece, J. K. Rath, L. van Dijk, R. E. I. Schropp, “Elongated nanostructures for radial junction solar cells,” Rep. Prog. Phys. 76, 106502 (2013).
[Crossref]

Ren, Z.

T. Sun, C. Fei Guo, F. Cao, E. Metin Akinoglu, Y. Wang, M. Giersig, Z. Ren, K. Kempa, “A broadband solar absorber with 12  nm thick ultrathin a-Si layer by using random metallic nanomeshes,” Appl. Phys. Lett. 104, 251119 (2014).
[Crossref]

Schropp, R. E. I.

Y. Kuang, M. D. Vece, J. K. Rath, L. van Dijk, R. E. I. Schropp, “Elongated nanostructures for radial junction solar cells,” Rep. Prog. Phys. 76, 106502 (2013).
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V. E. Ferry, M. A. Verschuuren, M. C. v. Lare, R. E. I. Schropp, H. A. Atwater, A. Polman, “Optimized spatial correlations for broadband light trapping nanopatterns in high efficiency ultrathin film a-Si:H solar cells,” Nano Lett. 11, 4239–4245 (2011).

Setälä, T.

Simone, F.

Slafer, D.

S. Pattnaik, N. Chakravarty, R. Biswas, V. Dalal, D. Slafer, “Nano-photonic and nano-plasmonic enhancements in thin film silicon solar cells,” Sol. Energ. Mat. Sol. C. 129, 115–123 (2014).

Söderström, K.

C. Battaglia, C.-M. Hsu, K. Söderström, J. Escarré, F.-J. Haug, M. Charrière, M. Boccard, M. Despeisse, D. T. L. Alexander, M. Cantoni, Y. Cui, C. Ballif, “Light trapping in solar cells: Can periodic beat random?” ACS Nano 6, 2790–2797 (2012).
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T. Sun, C. Fei Guo, F. Cao, E. Metin Akinoglu, Y. Wang, M. Giersig, Z. Ren, K. Kempa, “A broadband solar absorber with 12  nm thick ultrathin a-Si layer by using random metallic nanomeshes,” Appl. Phys. Lett. 104, 251119 (2014).
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Turunen, J.

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[Crossref]

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Y. Kuang, M. D. Vece, J. K. Rath, L. van Dijk, R. E. I. Schropp, “Elongated nanostructures for radial junction solar cells,” Rep. Prog. Phys. 76, 106502 (2013).
[Crossref]

van Lare, M.

Vece, M. D.

Y. Kuang, M. D. Vece, J. K. Rath, L. van Dijk, R. E. I. Schropp, “Elongated nanostructures for radial junction solar cells,” Rep. Prog. Phys. 76, 106502 (2013).
[Crossref]

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V. E. Ferry, M. A. Verschuuren, M. C. v. Lare, R. E. I. Schropp, H. A. Atwater, A. Polman, “Optimized spatial correlations for broadband light trapping nanopatterns in high efficiency ultrathin film a-Si:H solar cells,” Nano Lett. 11, 4239–4245 (2011).

Wang, Y.

T. Sun, C. Fei Guo, F. Cao, E. Metin Akinoglu, Y. Wang, M. Giersig, Z. Ren, K. Kempa, “A broadband solar absorber with 12  nm thick ultrathin a-Si layer by using random metallic nanomeshes,” Appl. Phys. Lett. 104, 251119 (2014).
[Crossref]

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M. A. Green, K. Emery, Y. Hishikawa, W. Warta, E. D. Dunlop, “Solar cell efficiency tables (version 43),” Prog. Photovoltaics 22, 1–9 (2014).
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ACS Nano (1)

C. Battaglia, C.-M. Hsu, K. Söderström, J. Escarré, F.-J. Haug, M. Charrière, M. Boccard, M. Despeisse, D. T. L. Alexander, M. Cantoni, Y. Cui, C. Ballif, “Light trapping in solar cells: Can periodic beat random?” ACS Nano 6, 2790–2797 (2012).
[Crossref]

Appl. Phys. Lett. (1)

T. Sun, C. Fei Guo, F. Cao, E. Metin Akinoglu, Y. Wang, M. Giersig, Z. Ren, K. Kempa, “A broadband solar absorber with 12  nm thick ultrathin a-Si layer by using random metallic nanomeshes,” Appl. Phys. Lett. 104, 251119 (2014).
[Crossref]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (2)

Nano Lett. (2)

E. Garnett, P. Yang, “Light trapping in silicon nanowire solar cells,” Nano Lett. 10, 1082–1087 (2010).

V. E. Ferry, M. A. Verschuuren, M. C. v. Lare, R. E. I. Schropp, H. A. Atwater, A. Polman, “Optimized spatial correlations for broadband light trapping nanopatterns in high efficiency ultrathin film a-Si:H solar cells,” Nano Lett. 11, 4239–4245 (2011).

Nat. Commun. (1)

R. A. Pala, J. S. Liu, E. S. Barnard, D. Askarov, E. C. Garnett, S. Fan, M. L. Brongersma, “Optimization of non-periodic plasmonic light-trapping layers for thin-film solar cells,” Nat. Commun. 4, 2095 (2013).
[Crossref]

Nat. Mater. (2)

A. Polman, H. A. Atwater, “Photonic design principles for ultrahigh-efficiency photovoltaics,” Nat. Mater. 11, 174–177 (2012).
[Crossref]

M. L. Brongersma, Y. Cui, S. Fan, “Light management for photovoltaics using high-index nanostructures,” Nat. Mater. 13, 451–460 (2014).
[Crossref]

Opt. Express (3)

Opt. Lett. (7)

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[Crossref]

Phys. Rev. A (1)

K. Blomstedt, T. Setälä, J. Tervo, J. Turunen, A. T. Friberg, “Partial polarization and electromagnetic spatial coherence of blackbody radiation emanating from an aperture,” Phys. Rev. A 88, 013824 (2013).
[Crossref]

Probabilist. Eng. Mech. (1)

R. Popescu, G. Deodatis, J. Prevost, “Simulation of homogeneous nonGaussian stochastic vector fields,” Probabilist. Eng. Mech. 13, 1–13 (1998).

Prog. Photovoltaics (1)

M. A. Green, K. Emery, Y. Hishikawa, W. Warta, E. D. Dunlop, “Solar cell efficiency tables (version 43),” Prog. Photovoltaics 22, 1–9 (2014).
[Crossref]

Rep. Prog. Phys. (1)

Y. Kuang, M. D. Vece, J. K. Rath, L. van Dijk, R. E. I. Schropp, “Elongated nanostructures for radial junction solar cells,” Rep. Prog. Phys. 76, 106502 (2013).
[Crossref]

Sol. Energ. Mat. Sol. C. (1)

S. Pattnaik, N. Chakravarty, R. Biswas, V. Dalal, D. Slafer, “Nano-photonic and nano-plasmonic enhancements in thin film silicon solar cells,” Sol. Energ. Mat. Sol. C. 129, 115–123 (2014).

Sol. Phys. (1)

H. Neckel, D. Labs, “Solar limb darkening 1986–1990 (λλ303 to 1099  nm),” Sol. Phys. 153, 91–114 (1994).
[Crossref]

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L. Novotny, B. Hecht, Principles of Nano-Optics, 2nd ed. (Cambridge University, 2012).

M. Beran, G. Parrent, Theory of Partial Coherence (The Society of Photo-optical Instrumentation Engineers, 1974).

E. Wolf, Introduction to the Theory of Coherence and Polarization of Light (Cambridge University, 2007).

The statistical correlations of light obey precise propagation laws as given in Ref. (24) p. 182–183. Specifically, the ensemble average behavior of an optical system depends on the cross-spectral density of incident light, which is a measure for the spectral dependence of the spatial coherence.

G. Moddel, “Will rectenna solar cells be practical?” in Rectenna Solar Cells, G. Moddel, S. Grover, eds. (Springer, 2013), pp. 3–24.

R. E. Collin, F. J. Zucker, Antenna Theory Part 1 (McGraw-Hill, 1969).

M. E. Verdet, Leçons d’Optique Physique, vol. 1 (L’Imprimerie Impériale, 1869).

J. Jensen, A. R. Mackintosh, Rare Earth Magnetism: Structures and Excitations (Clarendon, 1991).

C. F. Bohren, “Atmospheric optics,” in The Optics Encyclopedia (Wiley-VCH Verlag GmbH and Co. KGaA, 2007).

M. Born, E. Wolf, Principles of Optics, 7th ed. (Cambridge University, 1999).

U. S. N. A. Office, Astronomical Almanac for the Year 2013 (United States Naval Observatory/Nautical Almanac Office, 2012).

ASTM G173-03(2012), “Standard tables for reference solar spectral irradiances: Direct normal and hemispherical on 37° tilted surface,” (2012). ASTM International.

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Figures (5)

Fig. 1.
Fig. 1.

Illustration of the experimental measurement procedure. Broadband light from the source passes through a pair of non-parallel slits creating an interference pattern on a detector.

Fig. 2.
Fig. 2.

Illustration of the theoretical model. (a) An plane wave propagating along the u^ direction is emitted from the corresponding position on a distant source σ. Positions r⃗1 and r⃗2 lie in the device (x,y) plane. (b) A cutaway illustration of a combined disk-shell source. The device plane is illuminated by diffuse light (half-shell source) with spectral density as(u^,ω) and by direct sunlight (disk source centered at r⃗0) with spectral density ad(u^,ω). The front portion of the half-shell has been removed to reveal the origin.

Fig. 3.
Fig. 3.

Measured and calculated transverse spectral degrees of coherence η of direct sunshine. Amplitude (a) and phase (b) of the transverse spectral degree of coherence measured by the double slit apparatus. Amplitude (c) and phase (d) of the spectral degree of coherence calculated by Eqs. (1) and (2) as applied to hyperspectral images of the Sun.

Fig. 4.
Fig. 4.

Transverse spectral degree of coherence η at 510 nm for various sources. The amplitude of η is shown in (a) and the phase in (b). The inset in (a) shows |η| on a logarithmic scale. The measured and calculated curves relating to sunshine in both (a) and (b) correspond to cross sections along the respective lines given in Figs. 3(a-d).

Fig. 5.
Fig. 5.

Amplitude of the transverse spectral degree of coherence (|η|) at 510 nm for different weather conditions. The inset shows |η| on a logarithmic sale. The direct sunshine case corresponds to the measured curve given in Fig. 4(a).

Equations (18)

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

η(r⃗1,r⃗2,ω)Tr[W(r⃗1,r⃗2,ω)]Tr[W(r⃗1,r⃗1,ω)]Tr[W(r⃗2,r⃗2,ω)],
W(r⃗1,r⃗2,ω)E⃗*(r⃗1,ω)E⃗(r⃗2,ω)=σa(u^,ω)(U3u^u^)exp(iku^·r⃗)dΩ,
u^=sinθcosϕx^sinθsinϕy^cosθz^
ηs(r⃗,ω)=sin(k|r⃗|)k|r⃗|.
η(r⃗,ω)=sdsd+ssηd(r⃗,ω)+sssd+ssηs(r⃗,ω),
η(r⃗,ω)=γηd(r⃗,ω)+(1γ)ηs(r⃗,ω).
Wd(r⃗1,r⃗2,ω)MW(Mr⃗,ω)Mexp(ikrp),
ηd(r⃗1,r⃗2,ω)η(r1p2,ω)exp(ikrp),
W(r⃗1,r⃗2,ω)Wd(r⃗1,r⃗2,ω)+Ws(r⃗1,r⃗2,ω),
η(r⃗1,r⃗2,ω)γη(r1p2,ω)eikrp+(1γ)sin(kr)kr,
B(ω)=σa(u^,ω)χ(u^,ω)dΩ,
ψ(θ)sin2θdsin2θsinθd
W(r⃗1,r⃗2,ω)exp(ikz^r⃗)0θd02πaθ(θ,ω)(U3u^u^)×exp(ikσ⃗·ρ⃗)sinθdϕdθ,
W(r⃗,ω)0θd02πaθ(θ,ω)(U3u^u^)×exp(ikσ⃗·ρ⃗)sinθdϕdθ,
W(r⃗1,r⃗2,ω)exp(ikz^r⃗)W(r⃗,ω).
M(θ,ϕ)Rz(ϕ)Ry(θ)=(cosϕcosθsinϕcosϕsinθcosθsinϕcosϕsinϕsinθsinθ0cosθ).
W(r⃗,ω)2πad(ω){[θdJ1(α)βθd2J2(α)β2]U2+2θd2J2(α)β2z^z^+iθd2J2(α)β[ρ^z^+z^ρ^]},
Ws(r⃗1,r⃗2,ω)=2πas(ω){[j0(β)j1(β)β]U3+j2(β)ρ^ρ^+iJ2(β)β[ρ^z^+z^ρ^]},

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