Abstract

Pseudo-disordered structures enable additional design freedom for photon management. However, the optimization and interpretation is challenging when the large number of degrees of freedom encounters computationally intensive electromagnetic simulation method. Here we propose a novel one-dimensional multi-periodic pattern generation method to help us squeeze the disorder design space before performing rigorous calculation, by making use of the periodic attribute of the pattern. Consequently, thanks to the pre-filtered design space, it typically relieves us from computational burden and enables us to ‘globally’ optimize and study pseudo-disordered patterns. As an example, we show how this approach can be used to comprehensively optimize and systematically analyze generated disorder for broadband light trapping in thin film.

© 2016 Optical Society of America

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References

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2015 (4)

S. V. Boriskina, “Quasicrystals: Making invisible materials,” Nat. Photonics 9(7), 422–424 (2015).
[Crossref]

M.-C. van Lare and A. Polman, “Optimized scattering power spectral density of photovoltaic light-trapping patterns,” ACS Photonics 2(7), 822–831 (2015).
[Crossref]

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[Crossref] [PubMed]

L. C. Andreani, A. Bozzola, P. Kowalczewski, and M. Liscidini, “Photonic light trapping and electrical transport in thin-film silicon solar cells,” Sol. Energy Mater. Sol. Cells 135, 78–92 (2015).
[Crossref]

2014 (7)

C. Della Giovampaola and N. Engheta, “Digital metamaterials,” Nat. Mater. 13(12), 1115–1121 (2014).
[Crossref] [PubMed]

C. Kluge, J. Adam, N. Barié, P.-J. Jakobs, M. Guttmann, and M. Gerken, “Multi-periodic nanostructures for photon control,” Opt. Express 22(S5), A1363–A1371 (2014).
[Crossref] [PubMed]

A. Bozzola, M. Liscidini, and L. C. Andreani, “Broadband light trapping with disordered photonic structures in thin-film silicon solar cells,” Prog. Photovolt. Res. Appl. 22(12), 1237–1245 (2014).

J. Xavier, J. Probst, F. Back, P. Wyss, D. Eisenhauer, B. Löchel, E. Rudigier-Voigt, and C. Becker, “Quasicrystalline-structured light harvesting nanophotonic silicon films on nanoimprinted glass for ultra-thin photovoltaics,” Opt. Mater. Express 4(11), 2290–2299 (2014).
[Crossref]

S. Kasture, A. P. Ravishankar, V. J. Yallapragada, R. Patil, N. V. Valappil, G. Mulay, and V. G. Achanta, “Plasmonic quasicrystals with broadband transmission enhancement,” Sci. Rep. 4, 5257 (2014).
[Crossref] [PubMed]

F. Priolo, T. Gregorkiewicz, M. Galli, and T. F. Krauss, “Silicon nanostructures for photonics and photovoltaics,” Nat. Nanotechnol. 9(1), 19–32 (2014).
[Crossref] [PubMed]

V. Ganapati, O. D. Miller, and E. Yablonovitch, “Light trapping textures designed by electromagnetic optimization for sub-wavelength thick solar cells,” IEEE J. Photovoltaics 4(1), 175–182 (2014).
[Crossref]

2013 (5)

K. Jäger, M. Fischer, R. A. C. M. M. van Swaaij, and M. Zeman, “Designing optimized nano textures for thin-film silicon solar cells,” Opt. Express 21(S4), A656–A668 (2013).
[Crossref] [PubMed]

Z. Vardeny, A. Nahata, and A. Agrawal, “Optics of photonic quasicrystals,” Nat. Photonics 7(3), 177–187 (2013).
[Crossref]

R. Peretti, G. Gomard, L. Lalouat, C. Seassal, and E. Drouard, “Absorption control in pseudodisordered photonic-crystal thin films,” Phys. Rev. A 88(5), 053835 (2013).
[Crossref]

E. R. Martins, J. Li, Y. Liu, V. Depauw, Z. Chen, J. Zhou, and T. F. Krauss, “Deterministic quasi-random nanostructures for photon control,” Nat. Commun. 4, 2665 (2013).
[Crossref] [PubMed]

M. Burresi, F. Pratesi, K. Vynck, M. Prasciolu, M. Tormen, and D. S. Wiersma, “Two-dimensional disorder for broadband, omnidirectional and polarization-insensitive absorption,” Opt. Express 21(S2), A268–A275 (2013).
[Crossref] [PubMed]

2012 (5)

E. R. Martins, J. Li, Y. Liu, J. Zhou, and T. F. Krauss, “Engineering gratings for light trapping in photovoltaics: The supercell concept,” Phys. Rev. B . Condens, Matter Mater. Phys. 86(4), 041404 (2012).
[Crossref]

P. Kowalczewski, M. Liscidini, and L. C. Andreani, “Engineering Gaussian disorder at rough interfaces for light trapping in thin-film solar cells,” Opt. Lett. 37(23), 4868–4870 (2012).
[Crossref] [PubMed]

A. Oskooi, P. Favuzzi, Y. Tanaka, H. Shigeta, Y. Kawakami, and S. Noda, “Partially disordered photonic-crystal thin films for enhanced and robust photovoltaics,” Appl. Phys. Lett. 100(18), 181110 (2012).
[Crossref]

K. Vynck, M. Burresi, F. Riboli, and D. S. Wiersma, “Photon management in two-dimensional disordered media,” Nat. Mater. 11(12), 1017–1022 (2012).
[PubMed]

A. David, H. Benisty, and C. Weisbuch, “Photonic crystal light-emitting sources,” Rep. Prog. Phys. 75(12), 126501 (2012).
[Crossref] [PubMed]

2011 (1)

S. Kocaman, M. S. Aras, P. Hsieh, J. F. McMillan, C. G. Biris, N. C. Panoiu, M. B. Yu, D. L. Kwong, A. Stein, and C. W. Wong, “Zero phase delay in negative-refractive-index photonic crystal superlattices,” Nat. Photonics 5(8), 499–505 (2011).
[Crossref]

2010 (1)

2009 (1)

2008 (2)

A. Lin and J. Phillips, “Optimization of random diffraction gratings in thin-film solar cells using genetic algorithms,” Sol. Energy Mater. Sol. Cells 92(12), 1689–1696 (2008).
[Crossref]

Q. Yu, P. Guan, D. Qin, G. Golden, and P. M. Wallace, “Inverted size-dependence of Surface-Enhanced Raman scattering on gold nanohole and nanodisk arrays,” Nano Lett. 8(7), 1923–1928 (2008).
[Crossref] [PubMed]

2007 (1)

2003 (2)

L. Shen, Z. Ye, and S. He, “Design of two-dimensional photonic crystals with large absolute band gaps using a genetic algorithm,” Phys. Rev. B 68(3), 035109 (2003).
[Crossref]

J. Sawada, “A fast algorithm to generate necklaces with fixed content,” Theor. Comput. Sci. 301(1–3), 477–489 (2003).
[Crossref]

2002 (1)

A. Chutinan, M. Okano, and S. Noda, “Wider bandwidth with high transmission through waveguide bends in two-dimensional photonic crystal slabs,” Appl. Phys. Lett. 80(10), 1698 (2002).
[Crossref]

1999 (1)

1996 (1)

1983 (1)

Achanta, V. G.

S. Kasture, A. P. Ravishankar, V. J. Yallapragada, R. Patil, N. V. Valappil, G. Mulay, and V. G. Achanta, “Plasmonic quasicrystals with broadband transmission enhancement,” Sci. Rep. 4, 5257 (2014).
[Crossref] [PubMed]

Adam, J.

Agrawal, A.

Z. Vardeny, A. Nahata, and A. Agrawal, “Optics of photonic quasicrystals,” Nat. Photonics 7(3), 177–187 (2013).
[Crossref]

Andreani, L. C.

L. C. Andreani, A. Bozzola, P. Kowalczewski, and M. Liscidini, “Photonic light trapping and electrical transport in thin-film silicon solar cells,” Sol. Energy Mater. Sol. Cells 135, 78–92 (2015).
[Crossref]

A. Bozzola, M. Liscidini, and L. C. Andreani, “Broadband light trapping with disordered photonic structures in thin-film silicon solar cells,” Prog. Photovolt. Res. Appl. 22(12), 1237–1245 (2014).

P. Kowalczewski, M. Liscidini, and L. C. Andreani, “Engineering Gaussian disorder at rough interfaces for light trapping in thin-film solar cells,” Opt. Lett. 37(23), 4868–4870 (2012).
[Crossref] [PubMed]

Aras, M. S.

S. Kocaman, M. S. Aras, P. Hsieh, J. F. McMillan, C. G. Biris, N. C. Panoiu, M. B. Yu, D. L. Kwong, A. Stein, and C. W. Wong, “Zero phase delay in negative-refractive-index photonic crystal superlattices,” Nat. Photonics 5(8), 499–505 (2011).
[Crossref]

Back, F.

Barié, N.

Becker, C.

Benisty, H.

A. David, H. Benisty, and C. Weisbuch, “Photonic crystal light-emitting sources,” Rep. Prog. Phys. 75(12), 126501 (2012).
[Crossref] [PubMed]

Biris, C. G.

S. Kocaman, M. S. Aras, P. Hsieh, J. F. McMillan, C. G. Biris, N. C. Panoiu, M. B. Yu, D. L. Kwong, A. Stein, and C. W. Wong, “Zero phase delay in negative-refractive-index photonic crystal superlattices,” Nat. Photonics 5(8), 499–505 (2011).
[Crossref]

Boriskina, S. V.

Bozzola, A.

L. C. Andreani, A. Bozzola, P. Kowalczewski, and M. Liscidini, “Photonic light trapping and electrical transport in thin-film silicon solar cells,” Sol. Energy Mater. Sol. Cells 135, 78–92 (2015).
[Crossref]

A. Bozzola, M. Liscidini, and L. C. Andreani, “Broadband light trapping with disordered photonic structures in thin-film silicon solar cells,” Prog. Photovolt. Res. Appl. 22(12), 1237–1245 (2014).

Burresi, M.

Chen, P. Y.

Chen, Z.

E. R. Martins, J. Li, Y. Liu, V. Depauw, Z. Chen, J. Zhou, and T. F. Krauss, “Deterministic quasi-random nanostructures for photon control,” Nat. Commun. 4, 2665 (2013).
[Crossref] [PubMed]

Chutinan, A.

A. Chutinan, M. Okano, and S. Noda, “Wider bandwidth with high transmission through waveguide bends in two-dimensional photonic crystal slabs,” Appl. Phys. Lett. 80(10), 1698 (2002).
[Crossref]

Dal Negro, L.

David, A.

A. David, H. Benisty, and C. Weisbuch, “Photonic crystal light-emitting sources,” Rep. Prog. Phys. 75(12), 126501 (2012).
[Crossref] [PubMed]

Della Giovampaola, C.

C. Della Giovampaola and N. Engheta, “Digital metamaterials,” Nat. Mater. 13(12), 1115–1121 (2014).
[Crossref] [PubMed]

Depauw, V.

E. R. Martins, J. Li, Y. Liu, V. Depauw, Z. Chen, J. Zhou, and T. F. Krauss, “Deterministic quasi-random nanostructures for photon control,” Nat. Commun. 4, 2665 (2013).
[Crossref] [PubMed]

Donelli, M.

Drouard, E.

R. Peretti, G. Gomard, L. Lalouat, C. Seassal, and E. Drouard, “Absorption control in pseudodisordered photonic-crystal thin films,” Phys. Rev. A 88(5), 053835 (2013).
[Crossref]

Eberhart, R.

J. Kennedy and R. Eberhart, “Particle swarm optimization,” in Proceedings of ICNN’95 - International Conference on Neural Networks (IEEE, 1995), 4, pp. 1942–1948.
[Crossref]

Eisenhauer, D.

Engheta, N.

C. Della Giovampaola and N. Engheta, “Digital metamaterials,” Nat. Mater. 13(12), 1115–1121 (2014).
[Crossref] [PubMed]

Favuzzi, P.

A. Oskooi, P. Favuzzi, Y. Tanaka, H. Shigeta, Y. Kawakami, and S. Noda, “Partially disordered photonic-crystal thin films for enhanced and robust photovoltaics,” Appl. Phys. Lett. 100(18), 181110 (2012).
[Crossref]

Fischer, M.

Forestiere, C.

Fu, S. M.

Galli, M.

F. Priolo, T. Gregorkiewicz, M. Galli, and T. F. Krauss, “Silicon nanostructures for photonics and photovoltaics,” Nat. Nanotechnol. 9(1), 19–32 (2014).
[Crossref] [PubMed]

Ganapati, V.

V. Ganapati, O. D. Miller, and E. Yablonovitch, “Light trapping textures designed by electromagnetic optimization for sub-wavelength thick solar cells,” IEEE J. Photovoltaics 4(1), 175–182 (2014).
[Crossref]

Gaylord, T. K.

Gerken, M.

Golden, G.

Q. Yu, P. Guan, D. Qin, G. Golden, and P. M. Wallace, “Inverted size-dependence of Surface-Enhanced Raman scattering on gold nanohole and nanodisk arrays,” Nano Lett. 8(7), 1923–1928 (2008).
[Crossref] [PubMed]

Golmohammadi, S.

Gomard, G.

R. Peretti, G. Gomard, L. Lalouat, C. Seassal, and E. Drouard, “Absorption control in pseudodisordered photonic-crystal thin films,” Phys. Rev. A 88(5), 053835 (2013).
[Crossref]

Gopinath, A.

Gregorkiewicz, T.

F. Priolo, T. Gregorkiewicz, M. Galli, and T. F. Krauss, “Silicon nanostructures for photonics and photovoltaics,” Nat. Nanotechnol. 9(1), 19–32 (2014).
[Crossref] [PubMed]

Guan, P.

Q. Yu, P. Guan, D. Qin, G. Golden, and P. M. Wallace, “Inverted size-dependence of Surface-Enhanced Raman scattering on gold nanohole and nanodisk arrays,” Nano Lett. 8(7), 1923–1928 (2008).
[Crossref] [PubMed]

Guttmann, M.

He, S.

L. Shen, Z. Ye, and S. He, “Design of two-dimensional photonic crystals with large absolute band gaps using a genetic algorithm,” Phys. Rev. B 68(3), 035109 (2003).
[Crossref]

Hsieh, P.

S. Kocaman, M. S. Aras, P. Hsieh, J. F. McMillan, C. G. Biris, N. C. Panoiu, M. B. Yu, D. L. Kwong, A. Stein, and C. W. Wong, “Zero phase delay in negative-refractive-index photonic crystal superlattices,” Nat. Photonics 5(8), 499–505 (2011).
[Crossref]

Jäger, K.

Jakobs, P.-J.

Ju, N. P.

Kasture, S.

S. Kasture, A. P. Ravishankar, V. J. Yallapragada, R. Patil, N. V. Valappil, G. Mulay, and V. G. Achanta, “Plasmonic quasicrystals with broadband transmission enhancement,” Sci. Rep. 4, 5257 (2014).
[Crossref] [PubMed]

Kawakami, Y.

A. Oskooi, P. Favuzzi, Y. Tanaka, H. Shigeta, Y. Kawakami, and S. Noda, “Partially disordered photonic-crystal thin films for enhanced and robust photovoltaics,” Appl. Phys. Lett. 100(18), 181110 (2012).
[Crossref]

Kennedy, J.

J. Kennedy and R. Eberhart, “Particle swarm optimization,” in Proceedings of ICNN’95 - International Conference on Neural Networks (IEEE, 1995), 4, pp. 1942–1948.
[Crossref]

Kluge, C.

Kocaman, S.

S. Kocaman, M. S. Aras, P. Hsieh, J. F. McMillan, C. G. Biris, N. C. Panoiu, M. B. Yu, D. L. Kwong, A. Stein, and C. W. Wong, “Zero phase delay in negative-refractive-index photonic crystal superlattices,” Nat. Photonics 5(8), 499–505 (2011).
[Crossref]

Kowalczewski, P.

L. C. Andreani, A. Bozzola, P. Kowalczewski, and M. Liscidini, “Photonic light trapping and electrical transport in thin-film silicon solar cells,” Sol. Energy Mater. Sol. Cells 135, 78–92 (2015).
[Crossref]

P. Kowalczewski, M. Liscidini, and L. C. Andreani, “Engineering Gaussian disorder at rough interfaces for light trapping in thin-film solar cells,” Opt. Lett. 37(23), 4868–4870 (2012).
[Crossref] [PubMed]

Krauss, T. F.

F. Priolo, T. Gregorkiewicz, M. Galli, and T. F. Krauss, “Silicon nanostructures for photonics and photovoltaics,” Nat. Nanotechnol. 9(1), 19–32 (2014).
[Crossref] [PubMed]

E. R. Martins, J. Li, Y. Liu, V. Depauw, Z. Chen, J. Zhou, and T. F. Krauss, “Deterministic quasi-random nanostructures for photon control,” Nat. Commun. 4, 2665 (2013).
[Crossref] [PubMed]

E. R. Martins, J. Li, Y. Liu, J. Zhou, and T. F. Krauss, “Engineering gratings for light trapping in photovoltaics: The supercell concept,” Phys. Rev. B . Condens, Matter Mater. Phys. 86(4), 041404 (2012).
[Crossref]

Kwong, D. L.

S. Kocaman, M. S. Aras, P. Hsieh, J. F. McMillan, C. G. Biris, N. C. Panoiu, M. B. Yu, D. L. Kwong, A. Stein, and C. W. Wong, “Zero phase delay in negative-refractive-index photonic crystal superlattices,” Nat. Photonics 5(8), 499–505 (2011).
[Crossref]

Lalanne, P.

Lalouat, L.

R. Peretti, G. Gomard, L. Lalouat, C. Seassal, and E. Drouard, “Absorption control in pseudodisordered photonic-crystal thin films,” Phys. Rev. A 88(5), 053835 (2013).
[Crossref]

Lee, R. K.

Li, J.

E. R. Martins, J. Li, Y. Liu, V. Depauw, Z. Chen, J. Zhou, and T. F. Krauss, “Deterministic quasi-random nanostructures for photon control,” Nat. Commun. 4, 2665 (2013).
[Crossref] [PubMed]

E. R. Martins, J. Li, Y. Liu, J. Zhou, and T. F. Krauss, “Engineering gratings for light trapping in photovoltaics: The supercell concept,” Phys. Rev. B . Condens, Matter Mater. Phys. 86(4), 041404 (2012).
[Crossref]

Lin, A.

Y. K. Zhong, S. M. Fu, N. P. Ju, P. Y. Chen, and A. Lin, “Experimentally-implemented genetic algorithm (Exp-GA): toward fully optimal photovoltaics,” Opt. Express 23(19), A1324–A1333 (2015).
[Crossref] [PubMed]

A. Lin and J. Phillips, “Optimization of random diffraction gratings in thin-film solar cells using genetic algorithms,” Sol. Energy Mater. Sol. Cells 92(12), 1689–1696 (2008).
[Crossref]

Liscidini, M.

L. C. Andreani, A. Bozzola, P. Kowalczewski, and M. Liscidini, “Photonic light trapping and electrical transport in thin-film silicon solar cells,” Sol. Energy Mater. Sol. Cells 135, 78–92 (2015).
[Crossref]

A. Bozzola, M. Liscidini, and L. C. Andreani, “Broadband light trapping with disordered photonic structures in thin-film silicon solar cells,” Prog. Photovolt. Res. Appl. 22(12), 1237–1245 (2014).

P. Kowalczewski, M. Liscidini, and L. C. Andreani, “Engineering Gaussian disorder at rough interfaces for light trapping in thin-film solar cells,” Opt. Lett. 37(23), 4868–4870 (2012).
[Crossref] [PubMed]

Liu, Y.

E. R. Martins, J. Li, Y. Liu, V. Depauw, Z. Chen, J. Zhou, and T. F. Krauss, “Deterministic quasi-random nanostructures for photon control,” Nat. Commun. 4, 2665 (2013).
[Crossref] [PubMed]

E. R. Martins, J. Li, Y. Liu, J. Zhou, and T. F. Krauss, “Engineering gratings for light trapping in photovoltaics: The supercell concept,” Phys. Rev. B . Condens, Matter Mater. Phys. 86(4), 041404 (2012).
[Crossref]

Löchel, B.

Martins, E. R.

E. R. Martins, J. Li, Y. Liu, V. Depauw, Z. Chen, J. Zhou, and T. F. Krauss, “Deterministic quasi-random nanostructures for photon control,” Nat. Commun. 4, 2665 (2013).
[Crossref] [PubMed]

E. R. Martins, J. Li, Y. Liu, J. Zhou, and T. F. Krauss, “Engineering gratings for light trapping in photovoltaics: The supercell concept,” Phys. Rev. B . Condens, Matter Mater. Phys. 86(4), 041404 (2012).
[Crossref]

McMillan, J. F.

S. Kocaman, M. S. Aras, P. Hsieh, J. F. McMillan, C. G. Biris, N. C. Panoiu, M. B. Yu, D. L. Kwong, A. Stein, and C. W. Wong, “Zero phase delay in negative-refractive-index photonic crystal superlattices,” Nat. Photonics 5(8), 499–505 (2011).
[Crossref]

Miano, G.

Miller, O. D.

V. Ganapati, O. D. Miller, and E. Yablonovitch, “Light trapping textures designed by electromagnetic optimization for sub-wavelength thick solar cells,” IEEE J. Photovoltaics 4(1), 175–182 (2014).
[Crossref]

Moharam, M. G.

Moravvej-Farshi, M. K.

Morris, G. M.

Mulay, G.

S. Kasture, A. P. Ravishankar, V. J. Yallapragada, R. Patil, N. V. Valappil, G. Mulay, and V. G. Achanta, “Plasmonic quasicrystals with broadband transmission enhancement,” Sci. Rep. 4, 5257 (2014).
[Crossref] [PubMed]

Nahata, A.

Z. Vardeny, A. Nahata, and A. Agrawal, “Optics of photonic quasicrystals,” Nat. Photonics 7(3), 177–187 (2013).
[Crossref]

Noda, S.

A. Oskooi, P. Favuzzi, Y. Tanaka, H. Shigeta, Y. Kawakami, and S. Noda, “Partially disordered photonic-crystal thin films for enhanced and robust photovoltaics,” Appl. Phys. Lett. 100(18), 181110 (2012).
[Crossref]

A. Chutinan, M. Okano, and S. Noda, “Wider bandwidth with high transmission through waveguide bends in two-dimensional photonic crystal slabs,” Appl. Phys. Lett. 80(10), 1698 (2002).
[Crossref]

Okano, M.

A. Chutinan, M. Okano, and S. Noda, “Wider bandwidth with high transmission through waveguide bends in two-dimensional photonic crystal slabs,” Appl. Phys. Lett. 80(10), 1698 (2002).
[Crossref]

Oskooi, A.

A. Oskooi, P. Favuzzi, Y. Tanaka, H. Shigeta, Y. Kawakami, and S. Noda, “Partially disordered photonic-crystal thin films for enhanced and robust photovoltaics,” Appl. Phys. Lett. 100(18), 181110 (2012).
[Crossref]

Panoiu, N. C.

S. Kocaman, M. S. Aras, P. Hsieh, J. F. McMillan, C. G. Biris, N. C. Panoiu, M. B. Yu, D. L. Kwong, A. Stein, and C. W. Wong, “Zero phase delay in negative-refractive-index photonic crystal superlattices,” Nat. Photonics 5(8), 499–505 (2011).
[Crossref]

Patil, R.

S. Kasture, A. P. Ravishankar, V. J. Yallapragada, R. Patil, N. V. Valappil, G. Mulay, and V. G. Achanta, “Plasmonic quasicrystals with broadband transmission enhancement,” Sci. Rep. 4, 5257 (2014).
[Crossref] [PubMed]

Peretti, R.

R. Peretti, G. Gomard, L. Lalouat, C. Seassal, and E. Drouard, “Absorption control in pseudodisordered photonic-crystal thin films,” Phys. Rev. A 88(5), 053835 (2013).
[Crossref]

Phillips, J.

A. Lin and J. Phillips, “Optimization of random diffraction gratings in thin-film solar cells using genetic algorithms,” Sol. Energy Mater. Sol. Cells 92(12), 1689–1696 (2008).
[Crossref]

Polman, A.

M.-C. van Lare and A. Polman, “Optimized scattering power spectral density of photovoltaic light-trapping patterns,” ACS Photonics 2(7), 822–831 (2015).
[Crossref]

Prasciolu, M.

Pratesi, F.

Priolo, F.

F. Priolo, T. Gregorkiewicz, M. Galli, and T. F. Krauss, “Silicon nanostructures for photonics and photovoltaics,” Nat. Nanotechnol. 9(1), 19–32 (2014).
[Crossref] [PubMed]

Probst, J.

Qin, D.

Q. Yu, P. Guan, D. Qin, G. Golden, and P. M. Wallace, “Inverted size-dependence of Surface-Enhanced Raman scattering on gold nanohole and nanodisk arrays,” Nano Lett. 8(7), 1923–1928 (2008).
[Crossref] [PubMed]

Ravishankar, A. P.

S. Kasture, A. P. Ravishankar, V. J. Yallapragada, R. Patil, N. V. Valappil, G. Mulay, and V. G. Achanta, “Plasmonic quasicrystals with broadband transmission enhancement,” Sci. Rep. 4, 5257 (2014).
[Crossref] [PubMed]

Reinhard, B. M.

Riboli, F.

K. Vynck, M. Burresi, F. Riboli, and D. S. Wiersma, “Photon management in two-dimensional disordered media,” Nat. Mater. 11(12), 1017–1022 (2012).
[PubMed]

Rostami, A.

Rudigier-Voigt, E.

Sawada, J.

J. Sawada, “A fast algorithm to generate necklaces with fixed content,” Theor. Comput. Sci. 301(1–3), 477–489 (2003).
[Crossref]

Scherer, A.

Seassal, C.

R. Peretti, G. Gomard, L. Lalouat, C. Seassal, and E. Drouard, “Absorption control in pseudodisordered photonic-crystal thin films,” Phys. Rev. A 88(5), 053835 (2013).
[Crossref]

Shen, L.

L. Shen, Z. Ye, and S. He, “Design of two-dimensional photonic crystals with large absolute band gaps using a genetic algorithm,” Phys. Rev. B 68(3), 035109 (2003).
[Crossref]

Shigeta, H.

A. Oskooi, P. Favuzzi, Y. Tanaka, H. Shigeta, Y. Kawakami, and S. Noda, “Partially disordered photonic-crystal thin films for enhanced and robust photovoltaics,” Appl. Phys. Lett. 100(18), 181110 (2012).
[Crossref]

Stein, A.

S. Kocaman, M. S. Aras, P. Hsieh, J. F. McMillan, C. G. Biris, N. C. Panoiu, M. B. Yu, D. L. Kwong, A. Stein, and C. W. Wong, “Zero phase delay in negative-refractive-index photonic crystal superlattices,” Nat. Photonics 5(8), 499–505 (2011).
[Crossref]

Tanaka, Y.

A. Oskooi, P. Favuzzi, Y. Tanaka, H. Shigeta, Y. Kawakami, and S. Noda, “Partially disordered photonic-crystal thin films for enhanced and robust photovoltaics,” Appl. Phys. Lett. 100(18), 181110 (2012).
[Crossref]

Tormen, M.

Valappil, N. V.

S. Kasture, A. P. Ravishankar, V. J. Yallapragada, R. Patil, N. V. Valappil, G. Mulay, and V. G. Achanta, “Plasmonic quasicrystals with broadband transmission enhancement,” Sci. Rep. 4, 5257 (2014).
[Crossref] [PubMed]

van Lare, M.-C.

M.-C. van Lare and A. Polman, “Optimized scattering power spectral density of photovoltaic light-trapping patterns,” ACS Photonics 2(7), 822–831 (2015).
[Crossref]

van Swaaij, R. A. C. M. M.

Vardeny, Z.

Z. Vardeny, A. Nahata, and A. Agrawal, “Optics of photonic quasicrystals,” Nat. Photonics 7(3), 177–187 (2013).
[Crossref]

Vynck, K.

Wallace, P. M.

Q. Yu, P. Guan, D. Qin, G. Golden, and P. M. Wallace, “Inverted size-dependence of Surface-Enhanced Raman scattering on gold nanohole and nanodisk arrays,” Nano Lett. 8(7), 1923–1928 (2008).
[Crossref] [PubMed]

Walsh, G. F.

Weisbuch, C.

A. David, H. Benisty, and C. Weisbuch, “Photonic crystal light-emitting sources,” Rep. Prog. Phys. 75(12), 126501 (2012).
[Crossref] [PubMed]

Wiersma, D. S.

Wong, C. W.

S. Kocaman, M. S. Aras, P. Hsieh, J. F. McMillan, C. G. Biris, N. C. Panoiu, M. B. Yu, D. L. Kwong, A. Stein, and C. W. Wong, “Zero phase delay in negative-refractive-index photonic crystal superlattices,” Nat. Photonics 5(8), 499–505 (2011).
[Crossref]

Wyss, P.

Xavier, J.

Xu, Y.

Yablonovitch, E.

V. Ganapati, O. D. Miller, and E. Yablonovitch, “Light trapping textures designed by electromagnetic optimization for sub-wavelength thick solar cells,” IEEE J. Photovoltaics 4(1), 175–182 (2014).
[Crossref]

Yallapragada, V. J.

S. Kasture, A. P. Ravishankar, V. J. Yallapragada, R. Patil, N. V. Valappil, G. Mulay, and V. G. Achanta, “Plasmonic quasicrystals with broadband transmission enhancement,” Sci. Rep. 4, 5257 (2014).
[Crossref] [PubMed]

Yariv, A.

Ye, Z.

L. Shen, Z. Ye, and S. He, “Design of two-dimensional photonic crystals with large absolute band gaps using a genetic algorithm,” Phys. Rev. B 68(3), 035109 (2003).
[Crossref]

Yu, M. B.

S. Kocaman, M. S. Aras, P. Hsieh, J. F. McMillan, C. G. Biris, N. C. Panoiu, M. B. Yu, D. L. Kwong, A. Stein, and C. W. Wong, “Zero phase delay in negative-refractive-index photonic crystal superlattices,” Nat. Photonics 5(8), 499–505 (2011).
[Crossref]

Yu, Q.

Q. Yu, P. Guan, D. Qin, G. Golden, and P. M. Wallace, “Inverted size-dependence of Surface-Enhanced Raman scattering on gold nanohole and nanodisk arrays,” Nano Lett. 8(7), 1923–1928 (2008).
[Crossref] [PubMed]

Zarifkar, A.

Zeman, M.

Zeni, E.

Zhong, Y. K.

Zhou, J.

E. R. Martins, J. Li, Y. Liu, V. Depauw, Z. Chen, J. Zhou, and T. F. Krauss, “Deterministic quasi-random nanostructures for photon control,” Nat. Commun. 4, 2665 (2013).
[Crossref] [PubMed]

E. R. Martins, J. Li, Y. Liu, J. Zhou, and T. F. Krauss, “Engineering gratings for light trapping in photovoltaics: The supercell concept,” Phys. Rev. B . Condens, Matter Mater. Phys. 86(4), 041404 (2012).
[Crossref]

ACS Photonics (1)

M.-C. van Lare and A. Polman, “Optimized scattering power spectral density of photovoltaic light-trapping patterns,” ACS Photonics 2(7), 822–831 (2015).
[Crossref]

Appl. Phys. Lett. (2)

A. Oskooi, P. Favuzzi, Y. Tanaka, H. Shigeta, Y. Kawakami, and S. Noda, “Partially disordered photonic-crystal thin films for enhanced and robust photovoltaics,” Appl. Phys. Lett. 100(18), 181110 (2012).
[Crossref]

A. Chutinan, M. Okano, and S. Noda, “Wider bandwidth with high transmission through waveguide bends in two-dimensional photonic crystal slabs,” Appl. Phys. Lett. 80(10), 1698 (2002).
[Crossref]

IEEE J. Photovoltaics (1)

V. Ganapati, O. D. Miller, and E. Yablonovitch, “Light trapping textures designed by electromagnetic optimization for sub-wavelength thick solar cells,” IEEE J. Photovoltaics 4(1), 175–182 (2014).
[Crossref]

J. Opt. Soc. Am. (1)

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

Nano Lett. (1)

Q. Yu, P. Guan, D. Qin, G. Golden, and P. M. Wallace, “Inverted size-dependence of Surface-Enhanced Raman scattering on gold nanohole and nanodisk arrays,” Nano Lett. 8(7), 1923–1928 (2008).
[Crossref] [PubMed]

Nat. Commun. (1)

E. R. Martins, J. Li, Y. Liu, V. Depauw, Z. Chen, J. Zhou, and T. F. Krauss, “Deterministic quasi-random nanostructures for photon control,” Nat. Commun. 4, 2665 (2013).
[Crossref] [PubMed]

Nat. Mater. (2)

C. Della Giovampaola and N. Engheta, “Digital metamaterials,” Nat. Mater. 13(12), 1115–1121 (2014).
[Crossref] [PubMed]

K. Vynck, M. Burresi, F. Riboli, and D. S. Wiersma, “Photon management in two-dimensional disordered media,” Nat. Mater. 11(12), 1017–1022 (2012).
[PubMed]

Nat. Nanotechnol. (1)

F. Priolo, T. Gregorkiewicz, M. Galli, and T. F. Krauss, “Silicon nanostructures for photonics and photovoltaics,” Nat. Nanotechnol. 9(1), 19–32 (2014).
[Crossref] [PubMed]

Nat. Photonics (3)

Z. Vardeny, A. Nahata, and A. Agrawal, “Optics of photonic quasicrystals,” Nat. Photonics 7(3), 177–187 (2013).
[Crossref]

S. Kocaman, M. S. Aras, P. Hsieh, J. F. McMillan, C. G. Biris, N. C. Panoiu, M. B. Yu, D. L. Kwong, A. Stein, and C. W. Wong, “Zero phase delay in negative-refractive-index photonic crystal superlattices,” Nat. Photonics 5(8), 499–505 (2011).
[Crossref]

S. V. Boriskina, “Quasicrystals: Making invisible materials,” Nat. Photonics 9(7), 422–424 (2015).
[Crossref]

Opt. Express (6)

Opt. Lett. (3)

Opt. Mater. Express (1)

Phys. Rev. A (1)

R. Peretti, G. Gomard, L. Lalouat, C. Seassal, and E. Drouard, “Absorption control in pseudodisordered photonic-crystal thin films,” Phys. Rev. A 88(5), 053835 (2013).
[Crossref]

Phys. Rev. B (1)

L. Shen, Z. Ye, and S. He, “Design of two-dimensional photonic crystals with large absolute band gaps using a genetic algorithm,” Phys. Rev. B 68(3), 035109 (2003).
[Crossref]

Phys. Rev. B . Condens, Matter Mater. Phys. (1)

E. R. Martins, J. Li, Y. Liu, J. Zhou, and T. F. Krauss, “Engineering gratings for light trapping in photovoltaics: The supercell concept,” Phys. Rev. B . Condens, Matter Mater. Phys. 86(4), 041404 (2012).
[Crossref]

Prog. Photovolt. Res. Appl. (1)

A. Bozzola, M. Liscidini, and L. C. Andreani, “Broadband light trapping with disordered photonic structures in thin-film silicon solar cells,” Prog. Photovolt. Res. Appl. 22(12), 1237–1245 (2014).

Rep. Prog. Phys. (1)

A. David, H. Benisty, and C. Weisbuch, “Photonic crystal light-emitting sources,” Rep. Prog. Phys. 75(12), 126501 (2012).
[Crossref] [PubMed]

Sci. Rep. (1)

S. Kasture, A. P. Ravishankar, V. J. Yallapragada, R. Patil, N. V. Valappil, G. Mulay, and V. G. Achanta, “Plasmonic quasicrystals with broadband transmission enhancement,” Sci. Rep. 4, 5257 (2014).
[Crossref] [PubMed]

Sol. Energy Mater. Sol. Cells (2)

A. Lin and J. Phillips, “Optimization of random diffraction gratings in thin-film solar cells using genetic algorithms,” Sol. Energy Mater. Sol. Cells 92(12), 1689–1696 (2008).
[Crossref]

L. C. Andreani, A. Bozzola, P. Kowalczewski, and M. Liscidini, “Photonic light trapping and electrical transport in thin-film silicon solar cells,” Sol. Energy Mater. Sol. Cells 135, 78–92 (2015).
[Crossref]

Theor. Comput. Sci. (1)

J. Sawada, “A fast algorithm to generate necklaces with fixed content,” Theor. Comput. Sci. 301(1–3), 477–489 (2003).
[Crossref]

Other (2)

OEIS Foundation Inc, “The On-Line Encyclopedia of Integer Sequences,” (2011). http://oeis.org/A000029

J. Kennedy and R. Eberhart, “Particle swarm optimization,” in Proceedings of ICNN’95 - International Conference on Neural Networks (IEEE, 1995), 4, pp. 1942–1948.
[Crossref]

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Figures (6)

Fig. 1
Fig. 1 Absorption spectra of a 1 μm thick c-Si layer under un-polarized normal incident light, (a) for the optimized mono-periodic PC with lattice length of 300 nm (inset shows a typical cell) and (b) for the optimized multi-periodic PC with lattice length of 2550 nm (inset shows a typical cell).
Fig. 2
Fig. 2 Integrated absorption achieved for all the unrepeated representations of multi-period patterns with lattice length of 2550 nm. Block numbers are represented by different colors. The horizontal dashed line shows the Iabs of the optimized mono-periodic pattern under un-polarized illumination.
Fig. 3
Fig. 3 Integrated absorption for all different multi-periodic patterns with lattice length of 2550 nm and number of ridges of 8. The horizontal dashed line shows the Iabs of the optimized mono-periodic pattern under un-polarized illumination.
Fig. 4
Fig. 4 Fourier analysis of all the patterns with lattice length of 2550 nm and number of ridges of 8. Fourier transform of the PCs code sequences sorted by increasing absorption for (a) TE mode, and (c) TM mode. The magnitude of Fourier components lying in the leakage range (from 0 to 10.5 μm−1 in blue) and in the light trapping range (from 10.5 to 31.4 μm−1 in red). To compare the Fourier coefficients of different patterns, the Fourier amplitudes are normalized with respect to the constant zeroth order coefficient. High orders are not taken into account.
Fig. 5
Fig. 5 Analysis of the optical mode decomposition in Fourier space. Fourier transforms of the PC code sequences and electromagnetic fields (TE-TM averaged) for (a) the optimized mono-periodic pattern, (b) the optimized multi-periodic pattern, and (c) the mono-periodic pattern with the same lattice length and ff as the best performed multi-periodic pattern (code sequence: 11111111000000000). The Fourier transforms of the electromagnetic field is calculated by integrating the Fourier components of the electromagnetic field from 600 to 1100 nm. For easier comparison, the Fourier amplitudes of the PCs code sequences and the fields are normalized according to the strength of zeroth order. As such, the zeroth order is not taken into account. Decomposition of the electromagnetic fields in Fourier space associated to the three selected structures (d, e and f) from 600 to 1100 nm.
Fig. 6
Fig. 6 TE-TM averaged angular absorption spectra for (a) the optimized mono-periodic pattern, and (b) the optimized multi-periodic pattern. (c) Comparison of integrated absorption between the optimized mono-periodic pattern (red line) and the optimized multi-periodic pattern (blue line) for different angles of un-polarized incident light.

Tables (3)

Tables Icon

Table 1 Construction of strings and bracelets for a binary quadruple.

Tables Icon

Table 2 Comparison of the number of strings (S2(N)) and bracelets (B2(N)) for different lengths of binary code sequences (N).

Tables Icon

Table 3 The optimized code sequences with different lengths of binary code sequences (N). The all-zero code sequences were excluded. Patterns with lattice length of 2700 nm and 3000 nm were optimized with constraint to 50% filling fraction because of the heavy computational burden.

Equations (3)

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S k (n)= n k
N k (n)= 1 n i=1 v(n) φ( d i ) k n/ d i
B k (n)={ 1 2 N k (n)+ 1 4 (k+1) k n/2 n even 1 2 N k (n)+ 1 2 k (n+1)/2 n odd

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