Abstract

This report will present a generalized two-dimensional quasiperiodic (QP) tiling algorithm based on de Bruijn’s “cut and projection” method for use in plasmonic concentrator (PC) / photovoltaic hybrid devices to produce wide-angle, polarization-insensitive, and broadband light absorption enhancement. This algorithm can be employed with any PC consisting of point-like scattering objects, and can be fine-tuned to achieve a high spatial density of points and high orders of local and long-range rotational symmetry. Simulations and experimental data demonstrate this enhancement in ultra-thin layers of organic photovoltaic materials resting on metallic films etched with arrays of shallow sub-wavelength nanoholes. These devices work by coupling the incident light to surface plasmon polariton (SPP) modes that propagate along the dielectric / metal interface. This effectively increases the scale of light-matter interaction, and can also result in constructive interference between propagating SPP waves. By comparing PCs made with random, periodic, and QP arrangements, it is clear that QP is superior in intensifying the local fields and enhancing absorption in the active layer.

© 2013 OSA

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  28. E. Yablonovitch and G. D. Cody, “Intensity enhancement in textured optical sheets for solar cells,” IEEE Trans. Electron. Dev.29(2), 300–305 (1982).
    [CrossRef]
  29. E. Yablonovitch, “Statistical ray optics,” J. Opt. Soc. Am.72(7), 899–907 (1982).
    [CrossRef]
  30. T. Tiedje, E. Yablonovitch, G. D. Cody, and B. G. Brooks, “Limiting efficiency of silicon solar cells,” IEEE Trans. Electron. Dev.31(5), 711–716 (1984).
    [CrossRef]
  31. J. Feng, V. S. Siu, A. Roelke, V. Mehta, S. Y. Rhieu, G. T. R. Palmore, and D. Pacifici, “Nanoscale plasmonic interferometers for multispectral, high-throughput biochemical sensing,” Nano Lett.12(2), 602–609 (2012).
    [CrossRef] [PubMed]
  32. J. Gilot, I. Barbu, M. M. Wienk, and R. A. J. Janssen, “The use of ZnO as optical spacer in polymer solar cells: theoretical and experimental study,” Appl. Phys. Lett.91(11), 113520 (2007).
    [CrossRef]

2012 (2)

M. A. Green, K. Emery, Y. Hishikawa, W. Warta, and E. D. Dunlop, “Solar cell efficiency tables (version 39),” Prog. Photovolt. Res. Appl.20(1), 12–20 (2012).
[CrossRef]

J. Feng, V. S. Siu, A. Roelke, V. Mehta, S. Y. Rhieu, G. T. R. Palmore, and D. Pacifici, “Nanoscale plasmonic interferometers for multispectral, high-throughput biochemical sensing,” Nano Lett.12(2), 602–609 (2012).
[CrossRef] [PubMed]

2011 (4)

L. Dal Negro and S. V. Boriskina. “Deterministic aperiodic nanostructures for photonics and plasmonics applications.” Laser & Photonics Rev. 1–41 (2011).

Y. A. Akimov and W. S. Koh, “Design of plasmonic nanoparticles for efficient subwavelength light trapping in thin-film solar cells,” Photonics6, 155–161 (2011).

V. E. Ferry, M. A. Verschuuren, M. C. Lare, R. E. I. Schropp, H. A. Atwater, and A. Polman, “Optimized spatial correlations for broadband light trapping nanopatterns in high efficiency ultrathin film a-Si:H solar cells,” Nano Lett.11(10), 4239–4245 (2011).
[CrossRef] [PubMed]

A. E. Ostfeld and D. Pacifici, “Plasmonic concentrators for enhanced light absorption in ultra-thin film organic photovoltaics,” Appl. Phys. Lett.98(11), 113112 (2011).
[CrossRef]

2010 (3)

H. A. Atwater and A. Polman, “Plasmonics for improved photovoltaic devices,” Nat. Mater.9(3), 205–213 (2010).
[CrossRef] [PubMed]

S. Pillai and M. A. Green, “Plasmonics for photovoltaics applications,” Sol. Energy Mater. Sol. Cells94(9), 1481–1486 (2010).
[CrossRef]

V. E. Ferry, M. A. Verschuuren, H. B. T. Li, E. Verhagen, R. J. Walters, R. E. I. Schropp, H. A. Atwater, and A. Polman, “Light trapping in ultrathin plasmonic solar cells,” Opt. Express18(S2Suppl 2), A237–A245 (2010).
[CrossRef] [PubMed]

2009 (3)

V. E. Ferry, M. A. Vershuuren, H. B. T. Li, R. E. I. Schropp, H. A. Atwater, and A. Polman, “Improved red-response in thin film a-Si:H solar cells with soft-imprinted plasmonic back reflectors,” Appl. Phys. Lett.95(18), 183503 (2009).
[CrossRef]

R. A. Pala, J. White, E. Barnard, J. Liu, and M. L. Brongersma, “Design of plasmonic thin-film solar cells with broadband absorption enhancements,” Adv. Mater. (Deerfield Beach Fla.)21(34), 3504–3509 (2009).
[CrossRef]

G. Dennler, M. C. Scharber, and C. J. Brabec, “Polymer-fullerene bulk-heterojunction solar cells,” Adv. Mater. (Deerfield Beach Fla.)21(13), 1323–1338 (2009).
[CrossRef]

2008 (4)

K. Nakayama, K. Tanabe, and H. A. Atwater, “Plasmonic nanoparticle enhanced light absorption in GaAs solar cells,” Appl. Phys. Lett.93(12), 121904 (2008).
[CrossRef]

P. E. Shaw, A. Ruseckas, and I. D. W. Samuel, “Exciton diffusion measurements in poly(3-hexylthiophene),” Adv. Mater. (Deerfield Beach Fla.)20(18), 3516–3520 (2008).
[CrossRef]

D. Pacifici, H. J. Lezec, L. A. Sweatlock, R. J. Walters, and H. A. Atwater, “Universal optical transmission features in periodic and quasiperiodic hole arrays,” Opt. Express16(12), 9222–9238 (2008).
[CrossRef] [PubMed]

J. A. Dionne, E. Verhagen, A. Polman, and H. A. Atwater, “Are negative index materials achievable with surface plasmon waveguides? A case study of three plasmonic geometries,” Opt. Express16(23), 19001–19017 (2008).
[CrossRef] [PubMed]

2007 (4)

J. Gilot, I. Barbu, M. M. Wienk, and R. A. J. Janssen, “The use of ZnO as optical spacer in polymer solar cells: theoretical and experimental study,” Appl. Phys. Lett.91(11), 113520 (2007).
[CrossRef]

A. J. Moule and K. Meerholz, “Interference method for the determination of the complex refractive index of thin polymer layers,” Appl. Phys. Lett.91(6), 061901 (2007).
[CrossRef]

T. Matsui, A. Agrawal, A. Nahata, and Z. V. Vardeny, “Transmission resonances through aperiodic arrays of subwavelength apertures,” Nature446(7135), 517–521 (2007).
[CrossRef] [PubMed]

D. Pacifici, H. J. Lezec, and H. A. Atwater, “All-optical modulation by plasmonic excitation of CdSe quantum dots,” Nat. Photonics1(7), 402–406 (2007).
[CrossRef]

2006 (3)

S. Mei, T. Jie, L. Zhi-Yuan, C. Bing-Ying, Z. Dao-Zhong, J. Ai-Zi, and Y. Hai-Fang, “The role of periodicity in enhanced transmission through subwavelength hole arrays,” Chin. Phys. Lett.23(2), 486–488 (2006).
[CrossRef]

F. Przybilla, C. Genet, and T. W. Ebbesen, “Enhanced transmission through Penrose subwavelength hole arrays,” Appl. Phys. Lett.89(12), 121115 (2006).
[CrossRef]

H. J. Snaith, L. Schmidt-Mende, M. Chiesa, and M. Grätzel, “Light intensity, temperature, and thickness dependence of the open-circuit voltage in solid-state dye-sensitized solar cells,” Phys. Rev. B74(4), 045306 (2006).
[CrossRef]

2005 (2)

M. Reyes-Reyes, K. Kim, and D. L. Carroll, “High-efficiency photovoltaic devices based on annealed poly(3-hexylthiophene) and 1-(3-methoxycarbonyl)-propyl-1-phenyl-(6,6)C61 blends,” Appl. Phys. Lett.87(8), 083506 (2005).
[CrossRef]

W. Ma, C. Yang, X. Gong, K. Lee, and A. J. Heeger, “Thermally stable, efficient polymer solar cells with nanoscale control of the interpenetrating network morphology,” Adv. Funct. Mater.15(10), 1617–1622 (2005).
[CrossRef]

2004 (1)

L. Lüer, H.-J. Egelhaaf, D. Oelkrug, G. Cerullo, G. Lanzani, B.-H. Huisman, and D. de Leeuw, “Oxygen-induced quenching of photoexcited states in polythiophene films,” Org. Electron.5(1-3), 83–89 (2004).
[CrossRef]

1984 (1)

T. Tiedje, E. Yablonovitch, G. D. Cody, and B. G. Brooks, “Limiting efficiency of silicon solar cells,” IEEE Trans. Electron. Dev.31(5), 711–716 (1984).
[CrossRef]

1982 (2)

E. Yablonovitch, “Statistical ray optics,” J. Opt. Soc. Am.72(7), 899–907 (1982).
[CrossRef]

E. Yablonovitch and G. D. Cody, “Intensity enhancement in textured optical sheets for solar cells,” IEEE Trans. Electron. Dev.29(2), 300–305 (1982).
[CrossRef]

1981 (1)

N. G. de Bruijn, “Algebraic theory of Penrose's non-periodic tilings of the plane, Pt. I & II,” Kon. Nederl. Akad. Wetensch. Proc. Ser. A84, 39–66 (1981).

1974 (1)

R. Penrose, “The role of aesthetics in pure and applied mathematical research,” Bull. Inst. Math. Appl.10, 266–271 (1974).

Agrawal, A.

T. Matsui, A. Agrawal, A. Nahata, and Z. V. Vardeny, “Transmission resonances through aperiodic arrays of subwavelength apertures,” Nature446(7135), 517–521 (2007).
[CrossRef] [PubMed]

Ai-Zi, J.

S. Mei, T. Jie, L. Zhi-Yuan, C. Bing-Ying, Z. Dao-Zhong, J. Ai-Zi, and Y. Hai-Fang, “The role of periodicity in enhanced transmission through subwavelength hole arrays,” Chin. Phys. Lett.23(2), 486–488 (2006).
[CrossRef]

Akimov, Y. A.

Y. A. Akimov and W. S. Koh, “Design of plasmonic nanoparticles for efficient subwavelength light trapping in thin-film solar cells,” Photonics6, 155–161 (2011).

Atwater, H. A.

V. E. Ferry, M. A. Verschuuren, M. C. Lare, R. E. I. Schropp, H. A. Atwater, and A. Polman, “Optimized spatial correlations for broadband light trapping nanopatterns in high efficiency ultrathin film a-Si:H solar cells,” Nano Lett.11(10), 4239–4245 (2011).
[CrossRef] [PubMed]

V. E. Ferry, M. A. Verschuuren, H. B. T. Li, E. Verhagen, R. J. Walters, R. E. I. Schropp, H. A. Atwater, and A. Polman, “Light trapping in ultrathin plasmonic solar cells,” Opt. Express18(S2Suppl 2), A237–A245 (2010).
[CrossRef] [PubMed]

H. A. Atwater and A. Polman, “Plasmonics for improved photovoltaic devices,” Nat. Mater.9(3), 205–213 (2010).
[CrossRef] [PubMed]

V. E. Ferry, M. A. Vershuuren, H. B. T. Li, R. E. I. Schropp, H. A. Atwater, and A. Polman, “Improved red-response in thin film a-Si:H solar cells with soft-imprinted plasmonic back reflectors,” Appl. Phys. Lett.95(18), 183503 (2009).
[CrossRef]

J. A. Dionne, E. Verhagen, A. Polman, and H. A. Atwater, “Are negative index materials achievable with surface plasmon waveguides? A case study of three plasmonic geometries,” Opt. Express16(23), 19001–19017 (2008).
[CrossRef] [PubMed]

D. Pacifici, H. J. Lezec, L. A. Sweatlock, R. J. Walters, and H. A. Atwater, “Universal optical transmission features in periodic and quasiperiodic hole arrays,” Opt. Express16(12), 9222–9238 (2008).
[CrossRef] [PubMed]

K. Nakayama, K. Tanabe, and H. A. Atwater, “Plasmonic nanoparticle enhanced light absorption in GaAs solar cells,” Appl. Phys. Lett.93(12), 121904 (2008).
[CrossRef]

D. Pacifici, H. J. Lezec, and H. A. Atwater, “All-optical modulation by plasmonic excitation of CdSe quantum dots,” Nat. Photonics1(7), 402–406 (2007).
[CrossRef]

Barbu, I.

J. Gilot, I. Barbu, M. M. Wienk, and R. A. J. Janssen, “The use of ZnO as optical spacer in polymer solar cells: theoretical and experimental study,” Appl. Phys. Lett.91(11), 113520 (2007).
[CrossRef]

Barnard, E.

R. A. Pala, J. White, E. Barnard, J. Liu, and M. L. Brongersma, “Design of plasmonic thin-film solar cells with broadband absorption enhancements,” Adv. Mater. (Deerfield Beach Fla.)21(34), 3504–3509 (2009).
[CrossRef]

Bing-Ying, C.

S. Mei, T. Jie, L. Zhi-Yuan, C. Bing-Ying, Z. Dao-Zhong, J. Ai-Zi, and Y. Hai-Fang, “The role of periodicity in enhanced transmission through subwavelength hole arrays,” Chin. Phys. Lett.23(2), 486–488 (2006).
[CrossRef]

Boriskina, S. V.

L. Dal Negro and S. V. Boriskina. “Deterministic aperiodic nanostructures for photonics and plasmonics applications.” Laser & Photonics Rev. 1–41 (2011).

Brabec, C. J.

G. Dennler, M. C. Scharber, and C. J. Brabec, “Polymer-fullerene bulk-heterojunction solar cells,” Adv. Mater. (Deerfield Beach Fla.)21(13), 1323–1338 (2009).
[CrossRef]

Brongersma, M. L.

R. A. Pala, J. White, E. Barnard, J. Liu, and M. L. Brongersma, “Design of plasmonic thin-film solar cells with broadband absorption enhancements,” Adv. Mater. (Deerfield Beach Fla.)21(34), 3504–3509 (2009).
[CrossRef]

Brooks, B. G.

T. Tiedje, E. Yablonovitch, G. D. Cody, and B. G. Brooks, “Limiting efficiency of silicon solar cells,” IEEE Trans. Electron. Dev.31(5), 711–716 (1984).
[CrossRef]

Carroll, D. L.

M. Reyes-Reyes, K. Kim, and D. L. Carroll, “High-efficiency photovoltaic devices based on annealed poly(3-hexylthiophene) and 1-(3-methoxycarbonyl)-propyl-1-phenyl-(6,6)C61 blends,” Appl. Phys. Lett.87(8), 083506 (2005).
[CrossRef]

Cerullo, G.

L. Lüer, H.-J. Egelhaaf, D. Oelkrug, G. Cerullo, G. Lanzani, B.-H. Huisman, and D. de Leeuw, “Oxygen-induced quenching of photoexcited states in polythiophene films,” Org. Electron.5(1-3), 83–89 (2004).
[CrossRef]

Chiesa, M.

H. J. Snaith, L. Schmidt-Mende, M. Chiesa, and M. Grätzel, “Light intensity, temperature, and thickness dependence of the open-circuit voltage in solid-state dye-sensitized solar cells,” Phys. Rev. B74(4), 045306 (2006).
[CrossRef]

Cody, G. D.

T. Tiedje, E. Yablonovitch, G. D. Cody, and B. G. Brooks, “Limiting efficiency of silicon solar cells,” IEEE Trans. Electron. Dev.31(5), 711–716 (1984).
[CrossRef]

E. Yablonovitch and G. D. Cody, “Intensity enhancement in textured optical sheets for solar cells,” IEEE Trans. Electron. Dev.29(2), 300–305 (1982).
[CrossRef]

Dal Negro, L.

L. Dal Negro and S. V. Boriskina. “Deterministic aperiodic nanostructures for photonics and plasmonics applications.” Laser & Photonics Rev. 1–41 (2011).

Dao-Zhong, Z.

S. Mei, T. Jie, L. Zhi-Yuan, C. Bing-Ying, Z. Dao-Zhong, J. Ai-Zi, and Y. Hai-Fang, “The role of periodicity in enhanced transmission through subwavelength hole arrays,” Chin. Phys. Lett.23(2), 486–488 (2006).
[CrossRef]

de Bruijn, N. G.

N. G. de Bruijn, “Algebraic theory of Penrose's non-periodic tilings of the plane, Pt. I & II,” Kon. Nederl. Akad. Wetensch. Proc. Ser. A84, 39–66 (1981).

de Leeuw, D.

L. Lüer, H.-J. Egelhaaf, D. Oelkrug, G. Cerullo, G. Lanzani, B.-H. Huisman, and D. de Leeuw, “Oxygen-induced quenching of photoexcited states in polythiophene films,” Org. Electron.5(1-3), 83–89 (2004).
[CrossRef]

Dennler, G.

G. Dennler, M. C. Scharber, and C. J. Brabec, “Polymer-fullerene bulk-heterojunction solar cells,” Adv. Mater. (Deerfield Beach Fla.)21(13), 1323–1338 (2009).
[CrossRef]

Dionne, J. A.

Dunlop, E. D.

M. A. Green, K. Emery, Y. Hishikawa, W. Warta, and E. D. Dunlop, “Solar cell efficiency tables (version 39),” Prog. Photovolt. Res. Appl.20(1), 12–20 (2012).
[CrossRef]

Ebbesen, T. W.

F. Przybilla, C. Genet, and T. W. Ebbesen, “Enhanced transmission through Penrose subwavelength hole arrays,” Appl. Phys. Lett.89(12), 121115 (2006).
[CrossRef]

Egelhaaf, H.-J.

L. Lüer, H.-J. Egelhaaf, D. Oelkrug, G. Cerullo, G. Lanzani, B.-H. Huisman, and D. de Leeuw, “Oxygen-induced quenching of photoexcited states in polythiophene films,” Org. Electron.5(1-3), 83–89 (2004).
[CrossRef]

Emery, K.

M. A. Green, K. Emery, Y. Hishikawa, W. Warta, and E. D. Dunlop, “Solar cell efficiency tables (version 39),” Prog. Photovolt. Res. Appl.20(1), 12–20 (2012).
[CrossRef]

Feng, J.

J. Feng, V. S. Siu, A. Roelke, V. Mehta, S. Y. Rhieu, G. T. R. Palmore, and D. Pacifici, “Nanoscale plasmonic interferometers for multispectral, high-throughput biochemical sensing,” Nano Lett.12(2), 602–609 (2012).
[CrossRef] [PubMed]

Ferry, V. E.

V. E. Ferry, M. A. Verschuuren, M. C. Lare, R. E. I. Schropp, H. A. Atwater, and A. Polman, “Optimized spatial correlations for broadband light trapping nanopatterns in high efficiency ultrathin film a-Si:H solar cells,” Nano Lett.11(10), 4239–4245 (2011).
[CrossRef] [PubMed]

V. E. Ferry, M. A. Verschuuren, H. B. T. Li, E. Verhagen, R. J. Walters, R. E. I. Schropp, H. A. Atwater, and A. Polman, “Light trapping in ultrathin plasmonic solar cells,” Opt. Express18(S2Suppl 2), A237–A245 (2010).
[CrossRef] [PubMed]

V. E. Ferry, M. A. Vershuuren, H. B. T. Li, R. E. I. Schropp, H. A. Atwater, and A. Polman, “Improved red-response in thin film a-Si:H solar cells with soft-imprinted plasmonic back reflectors,” Appl. Phys. Lett.95(18), 183503 (2009).
[CrossRef]

Genet, C.

F. Przybilla, C. Genet, and T. W. Ebbesen, “Enhanced transmission through Penrose subwavelength hole arrays,” Appl. Phys. Lett.89(12), 121115 (2006).
[CrossRef]

Gilot, J.

J. Gilot, I. Barbu, M. M. Wienk, and R. A. J. Janssen, “The use of ZnO as optical spacer in polymer solar cells: theoretical and experimental study,” Appl. Phys. Lett.91(11), 113520 (2007).
[CrossRef]

Gong, X.

W. Ma, C. Yang, X. Gong, K. Lee, and A. J. Heeger, “Thermally stable, efficient polymer solar cells with nanoscale control of the interpenetrating network morphology,” Adv. Funct. Mater.15(10), 1617–1622 (2005).
[CrossRef]

Grätzel, M.

H. J. Snaith, L. Schmidt-Mende, M. Chiesa, and M. Grätzel, “Light intensity, temperature, and thickness dependence of the open-circuit voltage in solid-state dye-sensitized solar cells,” Phys. Rev. B74(4), 045306 (2006).
[CrossRef]

Green, M. A.

M. A. Green, K. Emery, Y. Hishikawa, W. Warta, and E. D. Dunlop, “Solar cell efficiency tables (version 39),” Prog. Photovolt. Res. Appl.20(1), 12–20 (2012).
[CrossRef]

S. Pillai and M. A. Green, “Plasmonics for photovoltaics applications,” Sol. Energy Mater. Sol. Cells94(9), 1481–1486 (2010).
[CrossRef]

Hai-Fang, Y.

S. Mei, T. Jie, L. Zhi-Yuan, C. Bing-Ying, Z. Dao-Zhong, J. Ai-Zi, and Y. Hai-Fang, “The role of periodicity in enhanced transmission through subwavelength hole arrays,” Chin. Phys. Lett.23(2), 486–488 (2006).
[CrossRef]

Heeger, A. J.

W. Ma, C. Yang, X. Gong, K. Lee, and A. J. Heeger, “Thermally stable, efficient polymer solar cells with nanoscale control of the interpenetrating network morphology,” Adv. Funct. Mater.15(10), 1617–1622 (2005).
[CrossRef]

Hishikawa, Y.

M. A. Green, K. Emery, Y. Hishikawa, W. Warta, and E. D. Dunlop, “Solar cell efficiency tables (version 39),” Prog. Photovolt. Res. Appl.20(1), 12–20 (2012).
[CrossRef]

Huisman, B.-H.

L. Lüer, H.-J. Egelhaaf, D. Oelkrug, G. Cerullo, G. Lanzani, B.-H. Huisman, and D. de Leeuw, “Oxygen-induced quenching of photoexcited states in polythiophene films,” Org. Electron.5(1-3), 83–89 (2004).
[CrossRef]

Janssen, R. A. J.

J. Gilot, I. Barbu, M. M. Wienk, and R. A. J. Janssen, “The use of ZnO as optical spacer in polymer solar cells: theoretical and experimental study,” Appl. Phys. Lett.91(11), 113520 (2007).
[CrossRef]

Jie, T.

S. Mei, T. Jie, L. Zhi-Yuan, C. Bing-Ying, Z. Dao-Zhong, J. Ai-Zi, and Y. Hai-Fang, “The role of periodicity in enhanced transmission through subwavelength hole arrays,” Chin. Phys. Lett.23(2), 486–488 (2006).
[CrossRef]

Kim, K.

M. Reyes-Reyes, K. Kim, and D. L. Carroll, “High-efficiency photovoltaic devices based on annealed poly(3-hexylthiophene) and 1-(3-methoxycarbonyl)-propyl-1-phenyl-(6,6)C61 blends,” Appl. Phys. Lett.87(8), 083506 (2005).
[CrossRef]

Koh, W. S.

Y. A. Akimov and W. S. Koh, “Design of plasmonic nanoparticles for efficient subwavelength light trapping in thin-film solar cells,” Photonics6, 155–161 (2011).

Lanzani, G.

L. Lüer, H.-J. Egelhaaf, D. Oelkrug, G. Cerullo, G. Lanzani, B.-H. Huisman, and D. de Leeuw, “Oxygen-induced quenching of photoexcited states in polythiophene films,” Org. Electron.5(1-3), 83–89 (2004).
[CrossRef]

Lare, M. C.

V. E. Ferry, M. A. Verschuuren, M. C. Lare, R. E. I. Schropp, H. A. Atwater, and A. Polman, “Optimized spatial correlations for broadband light trapping nanopatterns in high efficiency ultrathin film a-Si:H solar cells,” Nano Lett.11(10), 4239–4245 (2011).
[CrossRef] [PubMed]

Lee, K.

W. Ma, C. Yang, X. Gong, K. Lee, and A. J. Heeger, “Thermally stable, efficient polymer solar cells with nanoscale control of the interpenetrating network morphology,” Adv. Funct. Mater.15(10), 1617–1622 (2005).
[CrossRef]

Lezec, H. J.

D. Pacifici, H. J. Lezec, L. A. Sweatlock, R. J. Walters, and H. A. Atwater, “Universal optical transmission features in periodic and quasiperiodic hole arrays,” Opt. Express16(12), 9222–9238 (2008).
[CrossRef] [PubMed]

D. Pacifici, H. J. Lezec, and H. A. Atwater, “All-optical modulation by plasmonic excitation of CdSe quantum dots,” Nat. Photonics1(7), 402–406 (2007).
[CrossRef]

Li, H. B. T.

V. E. Ferry, M. A. Verschuuren, H. B. T. Li, E. Verhagen, R. J. Walters, R. E. I. Schropp, H. A. Atwater, and A. Polman, “Light trapping in ultrathin plasmonic solar cells,” Opt. Express18(S2Suppl 2), A237–A245 (2010).
[CrossRef] [PubMed]

V. E. Ferry, M. A. Vershuuren, H. B. T. Li, R. E. I. Schropp, H. A. Atwater, and A. Polman, “Improved red-response in thin film a-Si:H solar cells with soft-imprinted plasmonic back reflectors,” Appl. Phys. Lett.95(18), 183503 (2009).
[CrossRef]

Liu, J.

R. A. Pala, J. White, E. Barnard, J. Liu, and M. L. Brongersma, “Design of plasmonic thin-film solar cells with broadband absorption enhancements,” Adv. Mater. (Deerfield Beach Fla.)21(34), 3504–3509 (2009).
[CrossRef]

Lüer, L.

L. Lüer, H.-J. Egelhaaf, D. Oelkrug, G. Cerullo, G. Lanzani, B.-H. Huisman, and D. de Leeuw, “Oxygen-induced quenching of photoexcited states in polythiophene films,” Org. Electron.5(1-3), 83–89 (2004).
[CrossRef]

Ma, W.

W. Ma, C. Yang, X. Gong, K. Lee, and A. J. Heeger, “Thermally stable, efficient polymer solar cells with nanoscale control of the interpenetrating network morphology,” Adv. Funct. Mater.15(10), 1617–1622 (2005).
[CrossRef]

Matsui, T.

T. Matsui, A. Agrawal, A. Nahata, and Z. V. Vardeny, “Transmission resonances through aperiodic arrays of subwavelength apertures,” Nature446(7135), 517–521 (2007).
[CrossRef] [PubMed]

Meerholz, K.

A. J. Moule and K. Meerholz, “Interference method for the determination of the complex refractive index of thin polymer layers,” Appl. Phys. Lett.91(6), 061901 (2007).
[CrossRef]

Mehta, V.

J. Feng, V. S. Siu, A. Roelke, V. Mehta, S. Y. Rhieu, G. T. R. Palmore, and D. Pacifici, “Nanoscale plasmonic interferometers for multispectral, high-throughput biochemical sensing,” Nano Lett.12(2), 602–609 (2012).
[CrossRef] [PubMed]

Mei, S.

S. Mei, T. Jie, L. Zhi-Yuan, C. Bing-Ying, Z. Dao-Zhong, J. Ai-Zi, and Y. Hai-Fang, “The role of periodicity in enhanced transmission through subwavelength hole arrays,” Chin. Phys. Lett.23(2), 486–488 (2006).
[CrossRef]

Moule, A. J.

A. J. Moule and K. Meerholz, “Interference method for the determination of the complex refractive index of thin polymer layers,” Appl. Phys. Lett.91(6), 061901 (2007).
[CrossRef]

Nahata, A.

T. Matsui, A. Agrawal, A. Nahata, and Z. V. Vardeny, “Transmission resonances through aperiodic arrays of subwavelength apertures,” Nature446(7135), 517–521 (2007).
[CrossRef] [PubMed]

Nakayama, K.

K. Nakayama, K. Tanabe, and H. A. Atwater, “Plasmonic nanoparticle enhanced light absorption in GaAs solar cells,” Appl. Phys. Lett.93(12), 121904 (2008).
[CrossRef]

Oelkrug, D.

L. Lüer, H.-J. Egelhaaf, D. Oelkrug, G. Cerullo, G. Lanzani, B.-H. Huisman, and D. de Leeuw, “Oxygen-induced quenching of photoexcited states in polythiophene films,” Org. Electron.5(1-3), 83–89 (2004).
[CrossRef]

Ostfeld, A. E.

A. E. Ostfeld and D. Pacifici, “Plasmonic concentrators for enhanced light absorption in ultra-thin film organic photovoltaics,” Appl. Phys. Lett.98(11), 113112 (2011).
[CrossRef]

Pacifici, D.

J. Feng, V. S. Siu, A. Roelke, V. Mehta, S. Y. Rhieu, G. T. R. Palmore, and D. Pacifici, “Nanoscale plasmonic interferometers for multispectral, high-throughput biochemical sensing,” Nano Lett.12(2), 602–609 (2012).
[CrossRef] [PubMed]

A. E. Ostfeld and D. Pacifici, “Plasmonic concentrators for enhanced light absorption in ultra-thin film organic photovoltaics,” Appl. Phys. Lett.98(11), 113112 (2011).
[CrossRef]

D. Pacifici, H. J. Lezec, L. A. Sweatlock, R. J. Walters, and H. A. Atwater, “Universal optical transmission features in periodic and quasiperiodic hole arrays,” Opt. Express16(12), 9222–9238 (2008).
[CrossRef] [PubMed]

D. Pacifici, H. J. Lezec, and H. A. Atwater, “All-optical modulation by plasmonic excitation of CdSe quantum dots,” Nat. Photonics1(7), 402–406 (2007).
[CrossRef]

Pala, R. A.

R. A. Pala, J. White, E. Barnard, J. Liu, and M. L. Brongersma, “Design of plasmonic thin-film solar cells with broadband absorption enhancements,” Adv. Mater. (Deerfield Beach Fla.)21(34), 3504–3509 (2009).
[CrossRef]

Palmore, G. T. R.

J. Feng, V. S. Siu, A. Roelke, V. Mehta, S. Y. Rhieu, G. T. R. Palmore, and D. Pacifici, “Nanoscale plasmonic interferometers for multispectral, high-throughput biochemical sensing,” Nano Lett.12(2), 602–609 (2012).
[CrossRef] [PubMed]

Penrose, R.

R. Penrose, “The role of aesthetics in pure and applied mathematical research,” Bull. Inst. Math. Appl.10, 266–271 (1974).

Pillai, S.

S. Pillai and M. A. Green, “Plasmonics for photovoltaics applications,” Sol. Energy Mater. Sol. Cells94(9), 1481–1486 (2010).
[CrossRef]

Polman, A.

V. E. Ferry, M. A. Verschuuren, M. C. Lare, R. E. I. Schropp, H. A. Atwater, and A. Polman, “Optimized spatial correlations for broadband light trapping nanopatterns in high efficiency ultrathin film a-Si:H solar cells,” Nano Lett.11(10), 4239–4245 (2011).
[CrossRef] [PubMed]

V. E. Ferry, M. A. Verschuuren, H. B. T. Li, E. Verhagen, R. J. Walters, R. E. I. Schropp, H. A. Atwater, and A. Polman, “Light trapping in ultrathin plasmonic solar cells,” Opt. Express18(S2Suppl 2), A237–A245 (2010).
[CrossRef] [PubMed]

H. A. Atwater and A. Polman, “Plasmonics for improved photovoltaic devices,” Nat. Mater.9(3), 205–213 (2010).
[CrossRef] [PubMed]

V. E. Ferry, M. A. Vershuuren, H. B. T. Li, R. E. I. Schropp, H. A. Atwater, and A. Polman, “Improved red-response in thin film a-Si:H solar cells with soft-imprinted plasmonic back reflectors,” Appl. Phys. Lett.95(18), 183503 (2009).
[CrossRef]

J. A. Dionne, E. Verhagen, A. Polman, and H. A. Atwater, “Are negative index materials achievable with surface plasmon waveguides? A case study of three plasmonic geometries,” Opt. Express16(23), 19001–19017 (2008).
[CrossRef] [PubMed]

Przybilla, F.

F. Przybilla, C. Genet, and T. W. Ebbesen, “Enhanced transmission through Penrose subwavelength hole arrays,” Appl. Phys. Lett.89(12), 121115 (2006).
[CrossRef]

Reyes-Reyes, M.

M. Reyes-Reyes, K. Kim, and D. L. Carroll, “High-efficiency photovoltaic devices based on annealed poly(3-hexylthiophene) and 1-(3-methoxycarbonyl)-propyl-1-phenyl-(6,6)C61 blends,” Appl. Phys. Lett.87(8), 083506 (2005).
[CrossRef]

Rhieu, S. Y.

J. Feng, V. S. Siu, A. Roelke, V. Mehta, S. Y. Rhieu, G. T. R. Palmore, and D. Pacifici, “Nanoscale plasmonic interferometers for multispectral, high-throughput biochemical sensing,” Nano Lett.12(2), 602–609 (2012).
[CrossRef] [PubMed]

Roelke, A.

J. Feng, V. S. Siu, A. Roelke, V. Mehta, S. Y. Rhieu, G. T. R. Palmore, and D. Pacifici, “Nanoscale plasmonic interferometers for multispectral, high-throughput biochemical sensing,” Nano Lett.12(2), 602–609 (2012).
[CrossRef] [PubMed]

Ruseckas, A.

P. E. Shaw, A. Ruseckas, and I. D. W. Samuel, “Exciton diffusion measurements in poly(3-hexylthiophene),” Adv. Mater. (Deerfield Beach Fla.)20(18), 3516–3520 (2008).
[CrossRef]

Samuel, I. D. W.

P. E. Shaw, A. Ruseckas, and I. D. W. Samuel, “Exciton diffusion measurements in poly(3-hexylthiophene),” Adv. Mater. (Deerfield Beach Fla.)20(18), 3516–3520 (2008).
[CrossRef]

Scharber, M. C.

G. Dennler, M. C. Scharber, and C. J. Brabec, “Polymer-fullerene bulk-heterojunction solar cells,” Adv. Mater. (Deerfield Beach Fla.)21(13), 1323–1338 (2009).
[CrossRef]

Schmidt-Mende, L.

H. J. Snaith, L. Schmidt-Mende, M. Chiesa, and M. Grätzel, “Light intensity, temperature, and thickness dependence of the open-circuit voltage in solid-state dye-sensitized solar cells,” Phys. Rev. B74(4), 045306 (2006).
[CrossRef]

Schropp, R. E. I.

V. E. Ferry, M. A. Verschuuren, M. C. Lare, R. E. I. Schropp, H. A. Atwater, and A. Polman, “Optimized spatial correlations for broadband light trapping nanopatterns in high efficiency ultrathin film a-Si:H solar cells,” Nano Lett.11(10), 4239–4245 (2011).
[CrossRef] [PubMed]

V. E. Ferry, M. A. Verschuuren, H. B. T. Li, E. Verhagen, R. J. Walters, R. E. I. Schropp, H. A. Atwater, and A. Polman, “Light trapping in ultrathin plasmonic solar cells,” Opt. Express18(S2Suppl 2), A237–A245 (2010).
[CrossRef] [PubMed]

V. E. Ferry, M. A. Vershuuren, H. B. T. Li, R. E. I. Schropp, H. A. Atwater, and A. Polman, “Improved red-response in thin film a-Si:H solar cells with soft-imprinted plasmonic back reflectors,” Appl. Phys. Lett.95(18), 183503 (2009).
[CrossRef]

Shaw, P. E.

P. E. Shaw, A. Ruseckas, and I. D. W. Samuel, “Exciton diffusion measurements in poly(3-hexylthiophene),” Adv. Mater. (Deerfield Beach Fla.)20(18), 3516–3520 (2008).
[CrossRef]

Siu, V. S.

J. Feng, V. S. Siu, A. Roelke, V. Mehta, S. Y. Rhieu, G. T. R. Palmore, and D. Pacifici, “Nanoscale plasmonic interferometers for multispectral, high-throughput biochemical sensing,” Nano Lett.12(2), 602–609 (2012).
[CrossRef] [PubMed]

Snaith, H. J.

H. J. Snaith, L. Schmidt-Mende, M. Chiesa, and M. Grätzel, “Light intensity, temperature, and thickness dependence of the open-circuit voltage in solid-state dye-sensitized solar cells,” Phys. Rev. B74(4), 045306 (2006).
[CrossRef]

Sweatlock, L. A.

Tanabe, K.

K. Nakayama, K. Tanabe, and H. A. Atwater, “Plasmonic nanoparticle enhanced light absorption in GaAs solar cells,” Appl. Phys. Lett.93(12), 121904 (2008).
[CrossRef]

Tiedje, T.

T. Tiedje, E. Yablonovitch, G. D. Cody, and B. G. Brooks, “Limiting efficiency of silicon solar cells,” IEEE Trans. Electron. Dev.31(5), 711–716 (1984).
[CrossRef]

Vardeny, Z. V.

T. Matsui, A. Agrawal, A. Nahata, and Z. V. Vardeny, “Transmission resonances through aperiodic arrays of subwavelength apertures,” Nature446(7135), 517–521 (2007).
[CrossRef] [PubMed]

Verhagen, E.

Verschuuren, M. A.

V. E. Ferry, M. A. Verschuuren, M. C. Lare, R. E. I. Schropp, H. A. Atwater, and A. Polman, “Optimized spatial correlations for broadband light trapping nanopatterns in high efficiency ultrathin film a-Si:H solar cells,” Nano Lett.11(10), 4239–4245 (2011).
[CrossRef] [PubMed]

V. E. Ferry, M. A. Verschuuren, H. B. T. Li, E. Verhagen, R. J. Walters, R. E. I. Schropp, H. A. Atwater, and A. Polman, “Light trapping in ultrathin plasmonic solar cells,” Opt. Express18(S2Suppl 2), A237–A245 (2010).
[CrossRef] [PubMed]

Vershuuren, M. A.

V. E. Ferry, M. A. Vershuuren, H. B. T. Li, R. E. I. Schropp, H. A. Atwater, and A. Polman, “Improved red-response in thin film a-Si:H solar cells with soft-imprinted plasmonic back reflectors,” Appl. Phys. Lett.95(18), 183503 (2009).
[CrossRef]

Walters, R. J.

Warta, W.

M. A. Green, K. Emery, Y. Hishikawa, W. Warta, and E. D. Dunlop, “Solar cell efficiency tables (version 39),” Prog. Photovolt. Res. Appl.20(1), 12–20 (2012).
[CrossRef]

White, J.

R. A. Pala, J. White, E. Barnard, J. Liu, and M. L. Brongersma, “Design of plasmonic thin-film solar cells with broadband absorption enhancements,” Adv. Mater. (Deerfield Beach Fla.)21(34), 3504–3509 (2009).
[CrossRef]

Wienk, M. M.

J. Gilot, I. Barbu, M. M. Wienk, and R. A. J. Janssen, “The use of ZnO as optical spacer in polymer solar cells: theoretical and experimental study,” Appl. Phys. Lett.91(11), 113520 (2007).
[CrossRef]

Yablonovitch, E.

T. Tiedje, E. Yablonovitch, G. D. Cody, and B. G. Brooks, “Limiting efficiency of silicon solar cells,” IEEE Trans. Electron. Dev.31(5), 711–716 (1984).
[CrossRef]

E. Yablonovitch, “Statistical ray optics,” J. Opt. Soc. Am.72(7), 899–907 (1982).
[CrossRef]

E. Yablonovitch and G. D. Cody, “Intensity enhancement in textured optical sheets for solar cells,” IEEE Trans. Electron. Dev.29(2), 300–305 (1982).
[CrossRef]

Yang, C.

W. Ma, C. Yang, X. Gong, K. Lee, and A. J. Heeger, “Thermally stable, efficient polymer solar cells with nanoscale control of the interpenetrating network morphology,” Adv. Funct. Mater.15(10), 1617–1622 (2005).
[CrossRef]

Zhi-Yuan, L.

S. Mei, T. Jie, L. Zhi-Yuan, C. Bing-Ying, Z. Dao-Zhong, J. Ai-Zi, and Y. Hai-Fang, “The role of periodicity in enhanced transmission through subwavelength hole arrays,” Chin. Phys. Lett.23(2), 486–488 (2006).
[CrossRef]

Adv. Funct. Mater. (1)

W. Ma, C. Yang, X. Gong, K. Lee, and A. J. Heeger, “Thermally stable, efficient polymer solar cells with nanoscale control of the interpenetrating network morphology,” Adv. Funct. Mater.15(10), 1617–1622 (2005).
[CrossRef]

Adv. Mater. (Deerfield Beach Fla.) (3)

R. A. Pala, J. White, E. Barnard, J. Liu, and M. L. Brongersma, “Design of plasmonic thin-film solar cells with broadband absorption enhancements,” Adv. Mater. (Deerfield Beach Fla.)21(34), 3504–3509 (2009).
[CrossRef]

G. Dennler, M. C. Scharber, and C. J. Brabec, “Polymer-fullerene bulk-heterojunction solar cells,” Adv. Mater. (Deerfield Beach Fla.)21(13), 1323–1338 (2009).
[CrossRef]

P. E. Shaw, A. Ruseckas, and I. D. W. Samuel, “Exciton diffusion measurements in poly(3-hexylthiophene),” Adv. Mater. (Deerfield Beach Fla.)20(18), 3516–3520 (2008).
[CrossRef]

Appl. Phys. Lett. (7)

A. J. Moule and K. Meerholz, “Interference method for the determination of the complex refractive index of thin polymer layers,” Appl. Phys. Lett.91(6), 061901 (2007).
[CrossRef]

M. Reyes-Reyes, K. Kim, and D. L. Carroll, “High-efficiency photovoltaic devices based on annealed poly(3-hexylthiophene) and 1-(3-methoxycarbonyl)-propyl-1-phenyl-(6,6)C61 blends,” Appl. Phys. Lett.87(8), 083506 (2005).
[CrossRef]

A. E. Ostfeld and D. Pacifici, “Plasmonic concentrators for enhanced light absorption in ultra-thin film organic photovoltaics,” Appl. Phys. Lett.98(11), 113112 (2011).
[CrossRef]

F. Przybilla, C. Genet, and T. W. Ebbesen, “Enhanced transmission through Penrose subwavelength hole arrays,” Appl. Phys. Lett.89(12), 121115 (2006).
[CrossRef]

K. Nakayama, K. Tanabe, and H. A. Atwater, “Plasmonic nanoparticle enhanced light absorption in GaAs solar cells,” Appl. Phys. Lett.93(12), 121904 (2008).
[CrossRef]

V. E. Ferry, M. A. Vershuuren, H. B. T. Li, R. E. I. Schropp, H. A. Atwater, and A. Polman, “Improved red-response in thin film a-Si:H solar cells with soft-imprinted plasmonic back reflectors,” Appl. Phys. Lett.95(18), 183503 (2009).
[CrossRef]

J. Gilot, I. Barbu, M. M. Wienk, and R. A. J. Janssen, “The use of ZnO as optical spacer in polymer solar cells: theoretical and experimental study,” Appl. Phys. Lett.91(11), 113520 (2007).
[CrossRef]

Bull. Inst. Math. Appl. (1)

R. Penrose, “The role of aesthetics in pure and applied mathematical research,” Bull. Inst. Math. Appl.10, 266–271 (1974).

Chin. Phys. Lett. (1)

S. Mei, T. Jie, L. Zhi-Yuan, C. Bing-Ying, Z. Dao-Zhong, J. Ai-Zi, and Y. Hai-Fang, “The role of periodicity in enhanced transmission through subwavelength hole arrays,” Chin. Phys. Lett.23(2), 486–488 (2006).
[CrossRef]

IEEE Trans. Electron. Dev. (2)

E. Yablonovitch and G. D. Cody, “Intensity enhancement in textured optical sheets for solar cells,” IEEE Trans. Electron. Dev.29(2), 300–305 (1982).
[CrossRef]

T. Tiedje, E. Yablonovitch, G. D. Cody, and B. G. Brooks, “Limiting efficiency of silicon solar cells,” IEEE Trans. Electron. Dev.31(5), 711–716 (1984).
[CrossRef]

J. Opt. Soc. Am. (1)

Kon. Nederl. Akad. Wetensch. Proc. Ser. A (1)

N. G. de Bruijn, “Algebraic theory of Penrose's non-periodic tilings of the plane, Pt. I & II,” Kon. Nederl. Akad. Wetensch. Proc. Ser. A84, 39–66 (1981).

Nano Lett. (2)

V. E. Ferry, M. A. Verschuuren, M. C. Lare, R. E. I. Schropp, H. A. Atwater, and A. Polman, “Optimized spatial correlations for broadband light trapping nanopatterns in high efficiency ultrathin film a-Si:H solar cells,” Nano Lett.11(10), 4239–4245 (2011).
[CrossRef] [PubMed]

J. Feng, V. S. Siu, A. Roelke, V. Mehta, S. Y. Rhieu, G. T. R. Palmore, and D. Pacifici, “Nanoscale plasmonic interferometers for multispectral, high-throughput biochemical sensing,” Nano Lett.12(2), 602–609 (2012).
[CrossRef] [PubMed]

Nat. Mater. (1)

H. A. Atwater and A. Polman, “Plasmonics for improved photovoltaic devices,” Nat. Mater.9(3), 205–213 (2010).
[CrossRef] [PubMed]

Nat. Photonics (1)

D. Pacifici, H. J. Lezec, and H. A. Atwater, “All-optical modulation by plasmonic excitation of CdSe quantum dots,” Nat. Photonics1(7), 402–406 (2007).
[CrossRef]

Nature (1)

T. Matsui, A. Agrawal, A. Nahata, and Z. V. Vardeny, “Transmission resonances through aperiodic arrays of subwavelength apertures,” Nature446(7135), 517–521 (2007).
[CrossRef] [PubMed]

Opt. Express (3)

Org. Electron. (1)

L. Lüer, H.-J. Egelhaaf, D. Oelkrug, G. Cerullo, G. Lanzani, B.-H. Huisman, and D. de Leeuw, “Oxygen-induced quenching of photoexcited states in polythiophene films,” Org. Electron.5(1-3), 83–89 (2004).
[CrossRef]

Photonics (1)

Y. A. Akimov and W. S. Koh, “Design of plasmonic nanoparticles for efficient subwavelength light trapping in thin-film solar cells,” Photonics6, 155–161 (2011).

Phys. Rev. B (1)

H. J. Snaith, L. Schmidt-Mende, M. Chiesa, and M. Grätzel, “Light intensity, temperature, and thickness dependence of the open-circuit voltage in solid-state dye-sensitized solar cells,” Phys. Rev. B74(4), 045306 (2006).
[CrossRef]

Prog. Photovolt. Res. Appl. (1)

M. A. Green, K. Emery, Y. Hishikawa, W. Warta, and E. D. Dunlop, “Solar cell efficiency tables (version 39),” Prog. Photovolt. Res. Appl.20(1), 12–20 (2012).
[CrossRef]

Sol. Energy Mater. Sol. Cells (1)

S. Pillai and M. A. Green, “Plasmonics for photovoltaics applications,” Sol. Energy Mater. Sol. Cells94(9), 1481–1486 (2010).
[CrossRef]

Other (2)

L. Dal Negro and S. V. Boriskina. “Deterministic aperiodic nanostructures for photonics and plasmonics applications.” Laser & Photonics Rev. 1–41 (2011).

H. Raether, Surface Plasmons on Smooth and Rough Surfaces and on Gratings (Springer-Verlag, 1988).

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Figures (9)

Fig. 1
Fig. 1

Visual representation of the generalized cut and projection algorithm, starting in complex “grid space”, then moving to the real “array space” (which contains the actual pattern), then ending in reciprocal space (for analytical purposes). The algorithm works by mapping – via the function f(z) – domains in the complex plane to points in real space, thus determining the position of points in the array. Corresponding domain-hole pairs are identified by the same color (colors are based on the distance from the central point of symmetry; 18 shown here). The examples of planar tilings provided have the same scaling factor (a) and hole diameter (D), but are made with different grid numbers (N). The top two examples are periodic: tri-grid (N = 3, a.k.a. honeycomb) and quad-grid (N = 4, a.k.a. square). The bottom two examples are quasiperiodic: penta-grid (N = 5, a.k.a. Penrose) and octo-grid (N = 8). The figures in the right column were obtained by performing a 2-D discrete fast Fourier transform (DFFT) on the real space array; the scale bar in those figures is 2π / a. The insets in the right column show the first Brillouin zones of the Fourier power spectrum of each pattern; the scale bar in those inset figures is π / a.

Fig. 2
Fig. 2

(a) Order of rotational symmetry as a function of “grid number” N (equivalent to the dimension of the hypercube used in the “cut and projection” algorithm). If a pattern is made with an even number of grids, it has N-fold symmetry; if a pattern is made with an odd number of grids, if has 2N-fold symmetry. (b) Planar density of holes as a function of N, with the scaling factor held constant at a = 400 nm. (c) Planar density of holes as a function of a, with the grid number set at N = 17 (heptadeca-grid).

Fig. 3
Fig. 3

Schematic detailing the process of absorption enhancement in a plasmonic concentrator (PC) realized using a nanohole array (NHA). (a) Light normally incident on a flat metal surface is mostly reflected back. (b) If light is normally incident on a nanocorrugated metal / dielectric interface, some fraction of the incident radiation can be converted to a propagating SPP mode (with amplitude scattering efficiency β). Constructive interference between SPP modes originating from neighboring holes can significantly increase the light intensity at the metal / dielectric interface, thus contributing to enhanced light absorption if the dielectric material is an optical absorber.

Fig. 4
Fig. 4

(a) Calculated SPP mode dispersion relation (incident wavelength vs. real part of the in-plane SPP wavevector), shown for four different P3HT:PCBM thicknesses. The dielectric function for silver was determined via spectroscopic ellipsometry; the values for P3HT:PCBM came from Moule and Meerholz [27]. (b) SPP propagation length as a function of incident wavelength, parameterized by d. Inset: component of the SPP electric field parallel to the metal / dielectric interface (Ex) for the same four P3HT:PCBM thicknesses, calculated at an incident wavelength of λ = 700 nm. The field profiles are to scale and normalized to the highest value in each curve.

Fig. 5
Fig. 5

Simulations of the normalized field intensity I(r,λ) in square (periodic, N = 4) and heptadeca-grid (QP, N = 17) NHAs at four different incident wavelengths. In all cases, the array scaling factor is a = 400 nm and the organic layer is 24 nm thick. The scale bars seen in the square, λ = 500 nm case (both in the main figure and the inset) apply to all other images. Note that the color bar has been rescaled from 0 to 10 for clarity; the color seen on the map does not necessarily correspond to the actual value of I(r,λ) (the zero value stays the same after the rescale). The calculated SPP propagation length is included for each of the four wavelengths studied (obtained from Fig. 4(b)).

Fig. 6
Fig. 6

(a) Experimental spectral absorptance (A) in a P3HT:PCBM film for different thicknesses (d) and NHAs [11]. The d = 0 case refers to just a vacuum / Ag interface. The equivalent lattice constant is a = 400 nm in all cases. (b) Spectral absorption enhancement when comparing a corrugated structure to an uncorrugated structure. The curves shown here are found by taking the “corrugated” curves from part (a) and dividing by an “uncorrugated” curve of the same thickness. (c) Comparison of heptadeca-grid to square in two different contexts (both at d = 24 nm). Left axis (solid magenta line): ratio of experimental absorptance (from panel (a)). Right axis (orange spheres): ratio of simulated normalized spatially-averaged field intensities (from simulations similar to those reported in Fig. 5).

Fig. 7
Fig. 7

Simulations of the normalized field intensity (I(r,λ)) in PCs consisting of various NHAs with a = 200 or 850 nm, at three different incident wavelengths. In all cases, the grid number is N = 17 and the organic layer is d = 24 nm. The scale bars seen in the a = 200 nm, λ = 450 nm case (both in the main figure and the inset) apply to all other images. As with Fig. 5, the color bar has been rescaled from 0 to 10, with the zero point same after rescale). The calculated SPP propagation length is included for each of the three wavelengths studied (obtained from Fig. 4(b)).

Fig. 8
Fig. 8

(a) Experimental spectral absorptance of a 24-nm-thick P3HT:PCBM film in the presence of several PCs consisting of various quasiperiodic NHAs with the same order of rotational symmetry (heptadeca-grid, N = 17) but different equivalent lattice constants (a, in nm), as well as an uncorrugated structure (to serve as a reference for the absorption enhancement). (b) Absorptance enhancement in the specific NHAs, defined as that device’s absorptance curve divided by the uncorrugated curve.

Fig. 9
Fig. 9

Calculated short-circuit current (Jsc) as a function of NHA scaling factor, as well as the percent increase with respect to an uncorrugated device (Jsc = 4.09 mA / cm2), as calculated using the data in Fig. 8 and assuming AM1.5G illumination conditions. In all cases, d = 24 nm, and IQE = 95%. The two curves refer to patterns with the same planar density of holes, but one is QP (N = 17) and the other is purely random. Insets: Scanning Electron Microscope images of heptadeca-grid NHAs (one at a = 200 nm, the other at a = 850 nm) etched on a 300-nm-thick Ag film.

Tables (3)

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Table 1 Summary of maps from Fig. 5 (a comparison of N = 17 vs. N = 4 when a = 400 nm): space-averaged SPP field intensity (<I(λ)>) and highest intensity that is observed on a given map (max[I(r,λ)]).

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Table 2 Calculated short-circuit current density based on the measured absorptance spectra as reported in [11].

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Table 3 Summary of simulated intensity maps from Fig. 7 (a comparison of a = 200 nm vs. a = 850 nm when N = 17): space-averaged SPP field (<I(λ)>) and highest intensity that is observed on a given map (max[I(r,λ)]).

Equations (7)

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f( z )= j=1 N κ j ( z ) ζ j1 ,
κ j = Re[ z ζ 1j ]+ γ j
k x ( ω )= ω c ε 1 ε 2 ε 1 + ε 2 = ω c n SPP
k z,i ( ω )= ε i ( ω c ) 2 k x 2
H j ( r )= H 0 β j | r r j | 1/2 exp[ i( k SPP (r r j )+ φ j ) ]
I( r,λ )= 1 H 0 2 | j H j ( r ) | 2 ,
J sc =e η IQE ( λ )A( λ )( d J γ dλ )dλ

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