Abstract

We report on the mesoscale fabrication and characterization of polymeric templates for isotropic photonic materials derived from hyper-uniform point patterns using direct laser writing in a polymer photoresist. We study experimentally the microscopic structure by electron microscopy and small angle light scattering. Reducing the refractive index mismatch by liquid infiltration we find good agreement between the scattering data and numerical calculations in the single scattering limit. Our work thus demonstrates the feasibility of fabricating such random designer materials on technologically relevant length scales.

© 2013 OSA

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  1. J. D. Joannopoulos, Photonic Crystals: Molding the Flow of Light, 2nd ed. (Princeton University Press, 2008).
  2. W. H. Wang, C. Dong, and C. H. Shek, “Bulk metallic glasses,” Mat Sci Eng R44, 45–89 (2004).
    [CrossRef]
  3. E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys Rev Lett58, 2059–2062 (1987).
    [CrossRef] [PubMed]
  4. S. John, “Localization of photons in certain disordered dielectric superlattices,” Phys Rev Lett58, 2486–2489 (1987).
    [CrossRef] [PubMed]
  5. C. Lopez, “Materials aspects of photonic crystals,” Adv. Mater.15, 1679–1704 (2003).
    [CrossRef]
  6. M. Deubel, G. von Freymann, M. Wegener, S. Pereira, K. Busch, and C. M. Soukoulis, “Direct laser writing of three-dimensional photonic-crystal templates for telecommunications,” Nature Materials3, 444–447 (2004).
    [CrossRef] [PubMed]
  7. M. Florescu, S. Torquato, and P. J. Steinhardt, “Designer disordered materials with large, complete photonic band gaps,” Proc. Natl. Acad. Sci.106, 20658–20663 (2009).
    [CrossRef] [PubMed]
  8. S. F. Liew, J.-K. Yang, H. Noh, C. F. Schreck, E. R. Dufresne, C. S. OHern, and H. Cao, “Photonic band gaps in three-dimensional network structures with short-range order,” Phys. Rev. A.84, 063818 (2011).
    [CrossRef]
  9. M. Florescu, S. Torquato, and P. J. Steinhardt, “Complete band gaps in two-dimensional photonic quasicrystals,” Phys. Rev. B80, 155112 (2009).
    [CrossRef]
  10. W. N. Man, M. Megens, P. J. Steinhardt, and P. M. Chaikin, “Experimental measurement of the photonic properties of icosahedral quasicrystals,” Nature436, 993–996 (2005).
    [CrossRef] [PubMed]
  11. P. J. Steinhardt and D. P. Divincenzo, Quasicrystals : The State of the Art (World Scientific, 1999).
  12. C. J. Jin, X. D. Meng, B. Y. Cheng, Z. L. Li, and D. Z. Zhang, “Photonic gap in amorphous photonic materials,” Phys. Rev. B.63, 195107 (2001).
    [CrossRef]
  13. M. Rechtsman, A. Szameit, F. Dreisow, M. Heinrich, R. Keil, S. Nolte, and S. Mordechai, “Amorphous photonic lattices: band gaps, effective mass, and suppressed transport,” Phys. Rev. Lett.106, 193904 (2011)
    [CrossRef] [PubMed]
  14. L. F. Rojas-Ochoa, J. M. Mendez-Alcaraz, P. Schurtenberger, J. J. Saenz, and F. Scheffold, “Photonic properties of strongly correlated colloidal liquids,” Phys. Rev. Lett.93, 073903 (2004).
    [CrossRef] [PubMed]
  15. M. Reufer, L. F. Rojas-Ochoa, P. Schurtenberger, J. J. Saenz, and F. Scheffold, “Transport of light in amorphous photonic materials,” Appl. Phys. Lett.91, 171904 (2007).
    [CrossRef]
  16. J. F. Galisteo-Lopez, M. Ibisate, R. Sapienza, L. S. Froufe-Prez, A. Blanco, and C. Lopez, “Self-assembled photonic structures,” Adv Mater23, 30–69 (2011).
    [CrossRef]
  17. H. Noh, J.-K. Yang, S. F. Liew, M. J. Rooks, G. S. Solomon, and H. Cao, “Control of lasing in biomimetic structures with short-range order,” Phys Rev Lett106, 183901 (2011).
    [CrossRef] [PubMed]
  18. C. E. Zachary, Y. Jiao, and S. Torquato, “Hyperuniform long-range correlations are a signature of disordered jammed hard-particle packings,” Phys. Rev. Lett.106, 178001 (2011).
    [CrossRef] [PubMed]
  19. W. N. Man, M. Florescu, K. Matsuyama, P. Yadak, S. Torquato, P. J. Steinhardt, and P. Chaikin, “Experimental observation of photonic bandgaps in hyperuniform disordered material” in Proceedings of the Conference on Lasers and Electro-Optics (Cleo) and Quantum Electronics and Laser Science Conference (Qels) (2010).
  20. C. Song, P. Wang, and H. A. Makse, “A phase diagram for jammed matter,” Nature453, 629–632 (2008). Data taken from Hernán Makse’s web page, City College of New York (USA), http://lev.ccny.cuny.edu/hmakse/ .
    [CrossRef]
  21. A. Donev, S. Torquato, and F. H. Stillinger, “Pair correlation function characteristics of nearly jammed disordered and ordered hard-sphere packings,” Phys. Rev. E71, 011105 (2005).
    [CrossRef]
  22. J.-L. Barrat and J.-P. Hansen, Basic Concepts for Simple and Complex Liquids (Cambridge University Press, 2003).
    [CrossRef]
  23. F. Ferri, “Use of a charge coupled device camera for low-angle elastic light scattering,” Rev. Sci. Instrum.68, 2265–2274 (1997).
    [CrossRef]
  24. A. K. Jain, Fundamentals of Digital Image Processing (Prentice Hall, 1989).
  25. B.T. Draine and P.J. Flatau, “Discrete-dipole approximation for scattering calculations,” J. Opt. Soc. Am. A1, 1491–1499 (1994).
    [CrossRef]
  26. A. Ledermann, L. Cademartiri, M. Hermatschweiler, C. Toninelli, G. A. Ozin, D. S. Wiersma, M. Wegener, and G. von Freymann, “Three-dimensional silicon inverse photonic quasicrystals for infrared wavelengths,” Nat. Materials5, 942–945 (2006).
    [CrossRef]
  27. I. Staude, M. Thiel, S. Essig, C. Wolff, K. Busch, G. von Freymann, and M. Wegener, “Fabrication and characterization of silicon woodpile photonic crystals with a complete bandgap at telecom wavelengths,” Opt. Lett.35, 1094–1096 (2010).
    [CrossRef] [PubMed]

2011 (5)

S. F. Liew, J.-K. Yang, H. Noh, C. F. Schreck, E. R. Dufresne, C. S. OHern, and H. Cao, “Photonic band gaps in three-dimensional network structures with short-range order,” Phys. Rev. A.84, 063818 (2011).
[CrossRef]

M. Rechtsman, A. Szameit, F. Dreisow, M. Heinrich, R. Keil, S. Nolte, and S. Mordechai, “Amorphous photonic lattices: band gaps, effective mass, and suppressed transport,” Phys. Rev. Lett.106, 193904 (2011)
[CrossRef] [PubMed]

J. F. Galisteo-Lopez, M. Ibisate, R. Sapienza, L. S. Froufe-Prez, A. Blanco, and C. Lopez, “Self-assembled photonic structures,” Adv Mater23, 30–69 (2011).
[CrossRef]

H. Noh, J.-K. Yang, S. F. Liew, M. J. Rooks, G. S. Solomon, and H. Cao, “Control of lasing in biomimetic structures with short-range order,” Phys Rev Lett106, 183901 (2011).
[CrossRef] [PubMed]

C. E. Zachary, Y. Jiao, and S. Torquato, “Hyperuniform long-range correlations are a signature of disordered jammed hard-particle packings,” Phys. Rev. Lett.106, 178001 (2011).
[CrossRef] [PubMed]

2010 (1)

2009 (2)

M. Florescu, S. Torquato, and P. J. Steinhardt, “Designer disordered materials with large, complete photonic band gaps,” Proc. Natl. Acad. Sci.106, 20658–20663 (2009).
[CrossRef] [PubMed]

M. Florescu, S. Torquato, and P. J. Steinhardt, “Complete band gaps in two-dimensional photonic quasicrystals,” Phys. Rev. B80, 155112 (2009).
[CrossRef]

2008 (1)

C. Song, P. Wang, and H. A. Makse, “A phase diagram for jammed matter,” Nature453, 629–632 (2008). Data taken from Hernán Makse’s web page, City College of New York (USA), http://lev.ccny.cuny.edu/hmakse/ .
[CrossRef]

2007 (1)

M. Reufer, L. F. Rojas-Ochoa, P. Schurtenberger, J. J. Saenz, and F. Scheffold, “Transport of light in amorphous photonic materials,” Appl. Phys. Lett.91, 171904 (2007).
[CrossRef]

2006 (1)

A. Ledermann, L. Cademartiri, M. Hermatschweiler, C. Toninelli, G. A. Ozin, D. S. Wiersma, M. Wegener, and G. von Freymann, “Three-dimensional silicon inverse photonic quasicrystals for infrared wavelengths,” Nat. Materials5, 942–945 (2006).
[CrossRef]

2005 (2)

A. Donev, S. Torquato, and F. H. Stillinger, “Pair correlation function characteristics of nearly jammed disordered and ordered hard-sphere packings,” Phys. Rev. E71, 011105 (2005).
[CrossRef]

W. N. Man, M. Megens, P. J. Steinhardt, and P. M. Chaikin, “Experimental measurement of the photonic properties of icosahedral quasicrystals,” Nature436, 993–996 (2005).
[CrossRef] [PubMed]

2004 (3)

W. H. Wang, C. Dong, and C. H. Shek, “Bulk metallic glasses,” Mat Sci Eng R44, 45–89 (2004).
[CrossRef]

M. Deubel, G. von Freymann, M. Wegener, S. Pereira, K. Busch, and C. M. Soukoulis, “Direct laser writing of three-dimensional photonic-crystal templates for telecommunications,” Nature Materials3, 444–447 (2004).
[CrossRef] [PubMed]

L. F. Rojas-Ochoa, J. M. Mendez-Alcaraz, P. Schurtenberger, J. J. Saenz, and F. Scheffold, “Photonic properties of strongly correlated colloidal liquids,” Phys. Rev. Lett.93, 073903 (2004).
[CrossRef] [PubMed]

2003 (1)

C. Lopez, “Materials aspects of photonic crystals,” Adv. Mater.15, 1679–1704 (2003).
[CrossRef]

2001 (1)

C. J. Jin, X. D. Meng, B. Y. Cheng, Z. L. Li, and D. Z. Zhang, “Photonic gap in amorphous photonic materials,” Phys. Rev. B.63, 195107 (2001).
[CrossRef]

1997 (1)

F. Ferri, “Use of a charge coupled device camera for low-angle elastic light scattering,” Rev. Sci. Instrum.68, 2265–2274 (1997).
[CrossRef]

1994 (1)

B.T. Draine and P.J. Flatau, “Discrete-dipole approximation for scattering calculations,” J. Opt. Soc. Am. A1, 1491–1499 (1994).
[CrossRef]

1987 (2)

E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys Rev Lett58, 2059–2062 (1987).
[CrossRef] [PubMed]

S. John, “Localization of photons in certain disordered dielectric superlattices,” Phys Rev Lett58, 2486–2489 (1987).
[CrossRef] [PubMed]

Barrat, J.-L.

J.-L. Barrat and J.-P. Hansen, Basic Concepts for Simple and Complex Liquids (Cambridge University Press, 2003).
[CrossRef]

Blanco, A.

J. F. Galisteo-Lopez, M. Ibisate, R. Sapienza, L. S. Froufe-Prez, A. Blanco, and C. Lopez, “Self-assembled photonic structures,” Adv Mater23, 30–69 (2011).
[CrossRef]

Busch, K.

I. Staude, M. Thiel, S. Essig, C. Wolff, K. Busch, G. von Freymann, and M. Wegener, “Fabrication and characterization of silicon woodpile photonic crystals with a complete bandgap at telecom wavelengths,” Opt. Lett.35, 1094–1096 (2010).
[CrossRef] [PubMed]

M. Deubel, G. von Freymann, M. Wegener, S. Pereira, K. Busch, and C. M. Soukoulis, “Direct laser writing of three-dimensional photonic-crystal templates for telecommunications,” Nature Materials3, 444–447 (2004).
[CrossRef] [PubMed]

Cademartiri, L.

A. Ledermann, L. Cademartiri, M. Hermatschweiler, C. Toninelli, G. A. Ozin, D. S. Wiersma, M. Wegener, and G. von Freymann, “Three-dimensional silicon inverse photonic quasicrystals for infrared wavelengths,” Nat. Materials5, 942–945 (2006).
[CrossRef]

Cao, H.

S. F. Liew, J.-K. Yang, H. Noh, C. F. Schreck, E. R. Dufresne, C. S. OHern, and H. Cao, “Photonic band gaps in three-dimensional network structures with short-range order,” Phys. Rev. A.84, 063818 (2011).
[CrossRef]

H. Noh, J.-K. Yang, S. F. Liew, M. J. Rooks, G. S. Solomon, and H. Cao, “Control of lasing in biomimetic structures with short-range order,” Phys Rev Lett106, 183901 (2011).
[CrossRef] [PubMed]

Chaikin, P.

W. N. Man, M. Florescu, K. Matsuyama, P. Yadak, S. Torquato, P. J. Steinhardt, and P. Chaikin, “Experimental observation of photonic bandgaps in hyperuniform disordered material” in Proceedings of the Conference on Lasers and Electro-Optics (Cleo) and Quantum Electronics and Laser Science Conference (Qels) (2010).

Chaikin, P. M.

W. N. Man, M. Megens, P. J. Steinhardt, and P. M. Chaikin, “Experimental measurement of the photonic properties of icosahedral quasicrystals,” Nature436, 993–996 (2005).
[CrossRef] [PubMed]

Cheng, B. Y.

C. J. Jin, X. D. Meng, B. Y. Cheng, Z. L. Li, and D. Z. Zhang, “Photonic gap in amorphous photonic materials,” Phys. Rev. B.63, 195107 (2001).
[CrossRef]

Deubel, M.

M. Deubel, G. von Freymann, M. Wegener, S. Pereira, K. Busch, and C. M. Soukoulis, “Direct laser writing of three-dimensional photonic-crystal templates for telecommunications,” Nature Materials3, 444–447 (2004).
[CrossRef] [PubMed]

Divincenzo, D. P.

P. J. Steinhardt and D. P. Divincenzo, Quasicrystals : The State of the Art (World Scientific, 1999).

Donev, A.

A. Donev, S. Torquato, and F. H. Stillinger, “Pair correlation function characteristics of nearly jammed disordered and ordered hard-sphere packings,” Phys. Rev. E71, 011105 (2005).
[CrossRef]

Dong, C.

W. H. Wang, C. Dong, and C. H. Shek, “Bulk metallic glasses,” Mat Sci Eng R44, 45–89 (2004).
[CrossRef]

Draine, B.T.

B.T. Draine and P.J. Flatau, “Discrete-dipole approximation for scattering calculations,” J. Opt. Soc. Am. A1, 1491–1499 (1994).
[CrossRef]

Dreisow, F.

M. Rechtsman, A. Szameit, F. Dreisow, M. Heinrich, R. Keil, S. Nolte, and S. Mordechai, “Amorphous photonic lattices: band gaps, effective mass, and suppressed transport,” Phys. Rev. Lett.106, 193904 (2011)
[CrossRef] [PubMed]

Dufresne, E. R.

S. F. Liew, J.-K. Yang, H. Noh, C. F. Schreck, E. R. Dufresne, C. S. OHern, and H. Cao, “Photonic band gaps in three-dimensional network structures with short-range order,” Phys. Rev. A.84, 063818 (2011).
[CrossRef]

Essig, S.

Ferri, F.

F. Ferri, “Use of a charge coupled device camera for low-angle elastic light scattering,” Rev. Sci. Instrum.68, 2265–2274 (1997).
[CrossRef]

Flatau, P.J.

B.T. Draine and P.J. Flatau, “Discrete-dipole approximation for scattering calculations,” J. Opt. Soc. Am. A1, 1491–1499 (1994).
[CrossRef]

Florescu, M.

M. Florescu, S. Torquato, and P. J. Steinhardt, “Complete band gaps in two-dimensional photonic quasicrystals,” Phys. Rev. B80, 155112 (2009).
[CrossRef]

M. Florescu, S. Torquato, and P. J. Steinhardt, “Designer disordered materials with large, complete photonic band gaps,” Proc. Natl. Acad. Sci.106, 20658–20663 (2009).
[CrossRef] [PubMed]

W. N. Man, M. Florescu, K. Matsuyama, P. Yadak, S. Torquato, P. J. Steinhardt, and P. Chaikin, “Experimental observation of photonic bandgaps in hyperuniform disordered material” in Proceedings of the Conference on Lasers and Electro-Optics (Cleo) and Quantum Electronics and Laser Science Conference (Qels) (2010).

Froufe-Prez, L. S.

J. F. Galisteo-Lopez, M. Ibisate, R. Sapienza, L. S. Froufe-Prez, A. Blanco, and C. Lopez, “Self-assembled photonic structures,” Adv Mater23, 30–69 (2011).
[CrossRef]

Galisteo-Lopez, J. F.

J. F. Galisteo-Lopez, M. Ibisate, R. Sapienza, L. S. Froufe-Prez, A. Blanco, and C. Lopez, “Self-assembled photonic structures,” Adv Mater23, 30–69 (2011).
[CrossRef]

Hansen, J.-P.

J.-L. Barrat and J.-P. Hansen, Basic Concepts for Simple and Complex Liquids (Cambridge University Press, 2003).
[CrossRef]

Heinrich, M.

M. Rechtsman, A. Szameit, F. Dreisow, M. Heinrich, R. Keil, S. Nolte, and S. Mordechai, “Amorphous photonic lattices: band gaps, effective mass, and suppressed transport,” Phys. Rev. Lett.106, 193904 (2011)
[CrossRef] [PubMed]

Hermatschweiler, M.

A. Ledermann, L. Cademartiri, M. Hermatschweiler, C. Toninelli, G. A. Ozin, D. S. Wiersma, M. Wegener, and G. von Freymann, “Three-dimensional silicon inverse photonic quasicrystals for infrared wavelengths,” Nat. Materials5, 942–945 (2006).
[CrossRef]

Ibisate, M.

J. F. Galisteo-Lopez, M. Ibisate, R. Sapienza, L. S. Froufe-Prez, A. Blanco, and C. Lopez, “Self-assembled photonic structures,” Adv Mater23, 30–69 (2011).
[CrossRef]

Jain, A. K.

A. K. Jain, Fundamentals of Digital Image Processing (Prentice Hall, 1989).

Jiao, Y.

C. E. Zachary, Y. Jiao, and S. Torquato, “Hyperuniform long-range correlations are a signature of disordered jammed hard-particle packings,” Phys. Rev. Lett.106, 178001 (2011).
[CrossRef] [PubMed]

Jin, C. J.

C. J. Jin, X. D. Meng, B. Y. Cheng, Z. L. Li, and D. Z. Zhang, “Photonic gap in amorphous photonic materials,” Phys. Rev. B.63, 195107 (2001).
[CrossRef]

Joannopoulos, J. D.

J. D. Joannopoulos, Photonic Crystals: Molding the Flow of Light, 2nd ed. (Princeton University Press, 2008).

John, S.

S. John, “Localization of photons in certain disordered dielectric superlattices,” Phys Rev Lett58, 2486–2489 (1987).
[CrossRef] [PubMed]

Keil, R.

M. Rechtsman, A. Szameit, F. Dreisow, M. Heinrich, R. Keil, S. Nolte, and S. Mordechai, “Amorphous photonic lattices: band gaps, effective mass, and suppressed transport,” Phys. Rev. Lett.106, 193904 (2011)
[CrossRef] [PubMed]

Ledermann, A.

A. Ledermann, L. Cademartiri, M. Hermatschweiler, C. Toninelli, G. A. Ozin, D. S. Wiersma, M. Wegener, and G. von Freymann, “Three-dimensional silicon inverse photonic quasicrystals for infrared wavelengths,” Nat. Materials5, 942–945 (2006).
[CrossRef]

Li, Z. L.

C. J. Jin, X. D. Meng, B. Y. Cheng, Z. L. Li, and D. Z. Zhang, “Photonic gap in amorphous photonic materials,” Phys. Rev. B.63, 195107 (2001).
[CrossRef]

Liew, S. F.

S. F. Liew, J.-K. Yang, H. Noh, C. F. Schreck, E. R. Dufresne, C. S. OHern, and H. Cao, “Photonic band gaps in three-dimensional network structures with short-range order,” Phys. Rev. A.84, 063818 (2011).
[CrossRef]

H. Noh, J.-K. Yang, S. F. Liew, M. J. Rooks, G. S. Solomon, and H. Cao, “Control of lasing in biomimetic structures with short-range order,” Phys Rev Lett106, 183901 (2011).
[CrossRef] [PubMed]

Lopez, C.

J. F. Galisteo-Lopez, M. Ibisate, R. Sapienza, L. S. Froufe-Prez, A. Blanco, and C. Lopez, “Self-assembled photonic structures,” Adv Mater23, 30–69 (2011).
[CrossRef]

C. Lopez, “Materials aspects of photonic crystals,” Adv. Mater.15, 1679–1704 (2003).
[CrossRef]

Makse, H. A.

C. Song, P. Wang, and H. A. Makse, “A phase diagram for jammed matter,” Nature453, 629–632 (2008). Data taken from Hernán Makse’s web page, City College of New York (USA), http://lev.ccny.cuny.edu/hmakse/ .
[CrossRef]

Man, W. N.

W. N. Man, M. Megens, P. J. Steinhardt, and P. M. Chaikin, “Experimental measurement of the photonic properties of icosahedral quasicrystals,” Nature436, 993–996 (2005).
[CrossRef] [PubMed]

W. N. Man, M. Florescu, K. Matsuyama, P. Yadak, S. Torquato, P. J. Steinhardt, and P. Chaikin, “Experimental observation of photonic bandgaps in hyperuniform disordered material” in Proceedings of the Conference on Lasers and Electro-Optics (Cleo) and Quantum Electronics and Laser Science Conference (Qels) (2010).

Matsuyama, K.

W. N. Man, M. Florescu, K. Matsuyama, P. Yadak, S. Torquato, P. J. Steinhardt, and P. Chaikin, “Experimental observation of photonic bandgaps in hyperuniform disordered material” in Proceedings of the Conference on Lasers and Electro-Optics (Cleo) and Quantum Electronics and Laser Science Conference (Qels) (2010).

Megens, M.

W. N. Man, M. Megens, P. J. Steinhardt, and P. M. Chaikin, “Experimental measurement of the photonic properties of icosahedral quasicrystals,” Nature436, 993–996 (2005).
[CrossRef] [PubMed]

Mendez-Alcaraz, J. M.

L. F. Rojas-Ochoa, J. M. Mendez-Alcaraz, P. Schurtenberger, J. J. Saenz, and F. Scheffold, “Photonic properties of strongly correlated colloidal liquids,” Phys. Rev. Lett.93, 073903 (2004).
[CrossRef] [PubMed]

Meng, X. D.

C. J. Jin, X. D. Meng, B. Y. Cheng, Z. L. Li, and D. Z. Zhang, “Photonic gap in amorphous photonic materials,” Phys. Rev. B.63, 195107 (2001).
[CrossRef]

Mordechai, S.

M. Rechtsman, A. Szameit, F. Dreisow, M. Heinrich, R. Keil, S. Nolte, and S. Mordechai, “Amorphous photonic lattices: band gaps, effective mass, and suppressed transport,” Phys. Rev. Lett.106, 193904 (2011)
[CrossRef] [PubMed]

Noh, H.

H. Noh, J.-K. Yang, S. F. Liew, M. J. Rooks, G. S. Solomon, and H. Cao, “Control of lasing in biomimetic structures with short-range order,” Phys Rev Lett106, 183901 (2011).
[CrossRef] [PubMed]

S. F. Liew, J.-K. Yang, H. Noh, C. F. Schreck, E. R. Dufresne, C. S. OHern, and H. Cao, “Photonic band gaps in three-dimensional network structures with short-range order,” Phys. Rev. A.84, 063818 (2011).
[CrossRef]

Nolte, S.

M. Rechtsman, A. Szameit, F. Dreisow, M. Heinrich, R. Keil, S. Nolte, and S. Mordechai, “Amorphous photonic lattices: band gaps, effective mass, and suppressed transport,” Phys. Rev. Lett.106, 193904 (2011)
[CrossRef] [PubMed]

OHern, C. S.

S. F. Liew, J.-K. Yang, H. Noh, C. F. Schreck, E. R. Dufresne, C. S. OHern, and H. Cao, “Photonic band gaps in three-dimensional network structures with short-range order,” Phys. Rev. A.84, 063818 (2011).
[CrossRef]

Ozin, G. A.

A. Ledermann, L. Cademartiri, M. Hermatschweiler, C. Toninelli, G. A. Ozin, D. S. Wiersma, M. Wegener, and G. von Freymann, “Three-dimensional silicon inverse photonic quasicrystals for infrared wavelengths,” Nat. Materials5, 942–945 (2006).
[CrossRef]

Pereira, S.

M. Deubel, G. von Freymann, M. Wegener, S. Pereira, K. Busch, and C. M. Soukoulis, “Direct laser writing of three-dimensional photonic-crystal templates for telecommunications,” Nature Materials3, 444–447 (2004).
[CrossRef] [PubMed]

Rechtsman, M.

M. Rechtsman, A. Szameit, F. Dreisow, M. Heinrich, R. Keil, S. Nolte, and S. Mordechai, “Amorphous photonic lattices: band gaps, effective mass, and suppressed transport,” Phys. Rev. Lett.106, 193904 (2011)
[CrossRef] [PubMed]

Reufer, M.

M. Reufer, L. F. Rojas-Ochoa, P. Schurtenberger, J. J. Saenz, and F. Scheffold, “Transport of light in amorphous photonic materials,” Appl. Phys. Lett.91, 171904 (2007).
[CrossRef]

Rojas-Ochoa, L. F.

M. Reufer, L. F. Rojas-Ochoa, P. Schurtenberger, J. J. Saenz, and F. Scheffold, “Transport of light in amorphous photonic materials,” Appl. Phys. Lett.91, 171904 (2007).
[CrossRef]

L. F. Rojas-Ochoa, J. M. Mendez-Alcaraz, P. Schurtenberger, J. J. Saenz, and F. Scheffold, “Photonic properties of strongly correlated colloidal liquids,” Phys. Rev. Lett.93, 073903 (2004).
[CrossRef] [PubMed]

Rooks, M. J.

H. Noh, J.-K. Yang, S. F. Liew, M. J. Rooks, G. S. Solomon, and H. Cao, “Control of lasing in biomimetic structures with short-range order,” Phys Rev Lett106, 183901 (2011).
[CrossRef] [PubMed]

Saenz, J. J.

M. Reufer, L. F. Rojas-Ochoa, P. Schurtenberger, J. J. Saenz, and F. Scheffold, “Transport of light in amorphous photonic materials,” Appl. Phys. Lett.91, 171904 (2007).
[CrossRef]

L. F. Rojas-Ochoa, J. M. Mendez-Alcaraz, P. Schurtenberger, J. J. Saenz, and F. Scheffold, “Photonic properties of strongly correlated colloidal liquids,” Phys. Rev. Lett.93, 073903 (2004).
[CrossRef] [PubMed]

Sapienza, R.

J. F. Galisteo-Lopez, M. Ibisate, R. Sapienza, L. S. Froufe-Prez, A. Blanco, and C. Lopez, “Self-assembled photonic structures,” Adv Mater23, 30–69 (2011).
[CrossRef]

Scheffold, F.

M. Reufer, L. F. Rojas-Ochoa, P. Schurtenberger, J. J. Saenz, and F. Scheffold, “Transport of light in amorphous photonic materials,” Appl. Phys. Lett.91, 171904 (2007).
[CrossRef]

L. F. Rojas-Ochoa, J. M. Mendez-Alcaraz, P. Schurtenberger, J. J. Saenz, and F. Scheffold, “Photonic properties of strongly correlated colloidal liquids,” Phys. Rev. Lett.93, 073903 (2004).
[CrossRef] [PubMed]

Schreck, C. F.

S. F. Liew, J.-K. Yang, H. Noh, C. F. Schreck, E. R. Dufresne, C. S. OHern, and H. Cao, “Photonic band gaps in three-dimensional network structures with short-range order,” Phys. Rev. A.84, 063818 (2011).
[CrossRef]

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M. Reufer, L. F. Rojas-Ochoa, P. Schurtenberger, J. J. Saenz, and F. Scheffold, “Transport of light in amorphous photonic materials,” Appl. Phys. Lett.91, 171904 (2007).
[CrossRef]

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W. H. Wang, C. Dong, and C. H. Shek, “Bulk metallic glasses,” Mat Sci Eng R44, 45–89 (2004).
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H. Noh, J.-K. Yang, S. F. Liew, M. J. Rooks, G. S. Solomon, and H. Cao, “Control of lasing in biomimetic structures with short-range order,” Phys Rev Lett106, 183901 (2011).
[CrossRef] [PubMed]

Song, C.

C. Song, P. Wang, and H. A. Makse, “A phase diagram for jammed matter,” Nature453, 629–632 (2008). Data taken from Hernán Makse’s web page, City College of New York (USA), http://lev.ccny.cuny.edu/hmakse/ .
[CrossRef]

Soukoulis, C. M.

M. Deubel, G. von Freymann, M. Wegener, S. Pereira, K. Busch, and C. M. Soukoulis, “Direct laser writing of three-dimensional photonic-crystal templates for telecommunications,” Nature Materials3, 444–447 (2004).
[CrossRef] [PubMed]

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Steinhardt, P. J.

M. Florescu, S. Torquato, and P. J. Steinhardt, “Designer disordered materials with large, complete photonic band gaps,” Proc. Natl. Acad. Sci.106, 20658–20663 (2009).
[CrossRef] [PubMed]

M. Florescu, S. Torquato, and P. J. Steinhardt, “Complete band gaps in two-dimensional photonic quasicrystals,” Phys. Rev. B80, 155112 (2009).
[CrossRef]

W. N. Man, M. Megens, P. J. Steinhardt, and P. M. Chaikin, “Experimental measurement of the photonic properties of icosahedral quasicrystals,” Nature436, 993–996 (2005).
[CrossRef] [PubMed]

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W. N. Man, M. Florescu, K. Matsuyama, P. Yadak, S. Torquato, P. J. Steinhardt, and P. Chaikin, “Experimental observation of photonic bandgaps in hyperuniform disordered material” in Proceedings of the Conference on Lasers and Electro-Optics (Cleo) and Quantum Electronics and Laser Science Conference (Qels) (2010).

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A. Donev, S. Torquato, and F. H. Stillinger, “Pair correlation function characteristics of nearly jammed disordered and ordered hard-sphere packings,” Phys. Rev. E71, 011105 (2005).
[CrossRef]

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M. Rechtsman, A. Szameit, F. Dreisow, M. Heinrich, R. Keil, S. Nolte, and S. Mordechai, “Amorphous photonic lattices: band gaps, effective mass, and suppressed transport,” Phys. Rev. Lett.106, 193904 (2011)
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A. Ledermann, L. Cademartiri, M. Hermatschweiler, C. Toninelli, G. A. Ozin, D. S. Wiersma, M. Wegener, and G. von Freymann, “Three-dimensional silicon inverse photonic quasicrystals for infrared wavelengths,” Nat. Materials5, 942–945 (2006).
[CrossRef]

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C. E. Zachary, Y. Jiao, and S. Torquato, “Hyperuniform long-range correlations are a signature of disordered jammed hard-particle packings,” Phys. Rev. Lett.106, 178001 (2011).
[CrossRef] [PubMed]

M. Florescu, S. Torquato, and P. J. Steinhardt, “Complete band gaps in two-dimensional photonic quasicrystals,” Phys. Rev. B80, 155112 (2009).
[CrossRef]

M. Florescu, S. Torquato, and P. J. Steinhardt, “Designer disordered materials with large, complete photonic band gaps,” Proc. Natl. Acad. Sci.106, 20658–20663 (2009).
[CrossRef] [PubMed]

A. Donev, S. Torquato, and F. H. Stillinger, “Pair correlation function characteristics of nearly jammed disordered and ordered hard-sphere packings,” Phys. Rev. E71, 011105 (2005).
[CrossRef]

W. N. Man, M. Florescu, K. Matsuyama, P. Yadak, S. Torquato, P. J. Steinhardt, and P. Chaikin, “Experimental observation of photonic bandgaps in hyperuniform disordered material” in Proceedings of the Conference on Lasers and Electro-Optics (Cleo) and Quantum Electronics and Laser Science Conference (Qels) (2010).

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I. Staude, M. Thiel, S. Essig, C. Wolff, K. Busch, G. von Freymann, and M. Wegener, “Fabrication and characterization of silicon woodpile photonic crystals with a complete bandgap at telecom wavelengths,” Opt. Lett.35, 1094–1096 (2010).
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[CrossRef]

M. Deubel, G. von Freymann, M. Wegener, S. Pereira, K. Busch, and C. M. Soukoulis, “Direct laser writing of three-dimensional photonic-crystal templates for telecommunications,” Nature Materials3, 444–447 (2004).
[CrossRef] [PubMed]

Wang, P.

C. Song, P. Wang, and H. A. Makse, “A phase diagram for jammed matter,” Nature453, 629–632 (2008). Data taken from Hernán Makse’s web page, City College of New York (USA), http://lev.ccny.cuny.edu/hmakse/ .
[CrossRef]

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W. H. Wang, C. Dong, and C. H. Shek, “Bulk metallic glasses,” Mat Sci Eng R44, 45–89 (2004).
[CrossRef]

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I. Staude, M. Thiel, S. Essig, C. Wolff, K. Busch, G. von Freymann, and M. Wegener, “Fabrication and characterization of silicon woodpile photonic crystals with a complete bandgap at telecom wavelengths,” Opt. Lett.35, 1094–1096 (2010).
[CrossRef] [PubMed]

A. Ledermann, L. Cademartiri, M. Hermatschweiler, C. Toninelli, G. A. Ozin, D. S. Wiersma, M. Wegener, and G. von Freymann, “Three-dimensional silicon inverse photonic quasicrystals for infrared wavelengths,” Nat. Materials5, 942–945 (2006).
[CrossRef]

M. Deubel, G. von Freymann, M. Wegener, S. Pereira, K. Busch, and C. M. Soukoulis, “Direct laser writing of three-dimensional photonic-crystal templates for telecommunications,” Nature Materials3, 444–447 (2004).
[CrossRef] [PubMed]

Wiersma, D. S.

A. Ledermann, L. Cademartiri, M. Hermatschweiler, C. Toninelli, G. A. Ozin, D. S. Wiersma, M. Wegener, and G. von Freymann, “Three-dimensional silicon inverse photonic quasicrystals for infrared wavelengths,” Nat. Materials5, 942–945 (2006).
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W. N. Man, M. Florescu, K. Matsuyama, P. Yadak, S. Torquato, P. J. Steinhardt, and P. Chaikin, “Experimental observation of photonic bandgaps in hyperuniform disordered material” in Proceedings of the Conference on Lasers and Electro-Optics (Cleo) and Quantum Electronics and Laser Science Conference (Qels) (2010).

Yang, J.-K.

H. Noh, J.-K. Yang, S. F. Liew, M. J. Rooks, G. S. Solomon, and H. Cao, “Control of lasing in biomimetic structures with short-range order,” Phys Rev Lett106, 183901 (2011).
[CrossRef] [PubMed]

S. F. Liew, J.-K. Yang, H. Noh, C. F. Schreck, E. R. Dufresne, C. S. OHern, and H. Cao, “Photonic band gaps in three-dimensional network structures with short-range order,” Phys. Rev. A.84, 063818 (2011).
[CrossRef]

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C. E. Zachary, Y. Jiao, and S. Torquato, “Hyperuniform long-range correlations are a signature of disordered jammed hard-particle packings,” Phys. Rev. Lett.106, 178001 (2011).
[CrossRef] [PubMed]

Zhang, D. Z.

C. J. Jin, X. D. Meng, B. Y. Cheng, Z. L. Li, and D. Z. Zhang, “Photonic gap in amorphous photonic materials,” Phys. Rev. B.63, 195107 (2001).
[CrossRef]

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J. F. Galisteo-Lopez, M. Ibisate, R. Sapienza, L. S. Froufe-Prez, A. Blanco, and C. Lopez, “Self-assembled photonic structures,” Adv Mater23, 30–69 (2011).
[CrossRef]

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[CrossRef]

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M. Reufer, L. F. Rojas-Ochoa, P. Schurtenberger, J. J. Saenz, and F. Scheffold, “Transport of light in amorphous photonic materials,” Appl. Phys. Lett.91, 171904 (2007).
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[CrossRef]

Mat Sci Eng R (1)

W. H. Wang, C. Dong, and C. H. Shek, “Bulk metallic glasses,” Mat Sci Eng R44, 45–89 (2004).
[CrossRef]

Nat. Materials (1)

A. Ledermann, L. Cademartiri, M. Hermatschweiler, C. Toninelli, G. A. Ozin, D. S. Wiersma, M. Wegener, and G. von Freymann, “Three-dimensional silicon inverse photonic quasicrystals for infrared wavelengths,” Nat. Materials5, 942–945 (2006).
[CrossRef]

Nature (2)

C. Song, P. Wang, and H. A. Makse, “A phase diagram for jammed matter,” Nature453, 629–632 (2008). Data taken from Hernán Makse’s web page, City College of New York (USA), http://lev.ccny.cuny.edu/hmakse/ .
[CrossRef]

W. N. Man, M. Megens, P. J. Steinhardt, and P. M. Chaikin, “Experimental measurement of the photonic properties of icosahedral quasicrystals,” Nature436, 993–996 (2005).
[CrossRef] [PubMed]

Nature Materials (1)

M. Deubel, G. von Freymann, M. Wegener, S. Pereira, K. Busch, and C. M. Soukoulis, “Direct laser writing of three-dimensional photonic-crystal templates for telecommunications,” Nature Materials3, 444–447 (2004).
[CrossRef] [PubMed]

Opt. Lett. (1)

Phys Rev Lett (3)

E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys Rev Lett58, 2059–2062 (1987).
[CrossRef] [PubMed]

S. John, “Localization of photons in certain disordered dielectric superlattices,” Phys Rev Lett58, 2486–2489 (1987).
[CrossRef] [PubMed]

H. Noh, J.-K. Yang, S. F. Liew, M. J. Rooks, G. S. Solomon, and H. Cao, “Control of lasing in biomimetic structures with short-range order,” Phys Rev Lett106, 183901 (2011).
[CrossRef] [PubMed]

Phys. Rev. A. (1)

S. F. Liew, J.-K. Yang, H. Noh, C. F. Schreck, E. R. Dufresne, C. S. OHern, and H. Cao, “Photonic band gaps in three-dimensional network structures with short-range order,” Phys. Rev. A.84, 063818 (2011).
[CrossRef]

Phys. Rev. B (1)

M. Florescu, S. Torquato, and P. J. Steinhardt, “Complete band gaps in two-dimensional photonic quasicrystals,” Phys. Rev. B80, 155112 (2009).
[CrossRef]

Phys. Rev. B. (1)

C. J. Jin, X. D. Meng, B. Y. Cheng, Z. L. Li, and D. Z. Zhang, “Photonic gap in amorphous photonic materials,” Phys. Rev. B.63, 195107 (2001).
[CrossRef]

Phys. Rev. E (1)

A. Donev, S. Torquato, and F. H. Stillinger, “Pair correlation function characteristics of nearly jammed disordered and ordered hard-sphere packings,” Phys. Rev. E71, 011105 (2005).
[CrossRef]

Phys. Rev. Lett. (3)

M. Rechtsman, A. Szameit, F. Dreisow, M. Heinrich, R. Keil, S. Nolte, and S. Mordechai, “Amorphous photonic lattices: band gaps, effective mass, and suppressed transport,” Phys. Rev. Lett.106, 193904 (2011)
[CrossRef] [PubMed]

L. F. Rojas-Ochoa, J. M. Mendez-Alcaraz, P. Schurtenberger, J. J. Saenz, and F. Scheffold, “Photonic properties of strongly correlated colloidal liquids,” Phys. Rev. Lett.93, 073903 (2004).
[CrossRef] [PubMed]

C. E. Zachary, Y. Jiao, and S. Torquato, “Hyperuniform long-range correlations are a signature of disordered jammed hard-particle packings,” Phys. Rev. Lett.106, 178001 (2011).
[CrossRef] [PubMed]

Proc. Natl. Acad. Sci. (1)

M. Florescu, S. Torquato, and P. J. Steinhardt, “Designer disordered materials with large, complete photonic band gaps,” Proc. Natl. Acad. Sci.106, 20658–20663 (2009).
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[CrossRef]

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W. N. Man, M. Florescu, K. Matsuyama, P. Yadak, S. Torquato, P. J. Steinhardt, and P. Chaikin, “Experimental observation of photonic bandgaps in hyperuniform disordered material” in Proceedings of the Conference on Lasers and Electro-Optics (Cleo) and Quantum Electronics and Laser Science Conference (Qels) (2010).

J. D. Joannopoulos, Photonic Crystals: Molding the Flow of Light, 2nd ed. (Princeton University Press, 2008).

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Figures (4)

Fig. 1
Fig. 1

Design of amorphous photonic structures based upon a tetrahedral network of elliptical rods. (a) Enlarged view of part of the network obtained by tessellation of a hyperuniform seed pattern, rod cross section 840 × 280nm2. (b) close-up showing also the grid points lying inside or at the surface of the rods used for the numerical analysis of the scattering pattern.

Fig. 2
Fig. 2

Electron micrographs of fabricated hyperuniform three-dimensional disordered structures. (a) Normal view of a structure with height h = 8μm and inner diameter d = 65μm (b) close-up view (c) focused ion beam cut of the same structure (oblique view).

Fig. 3
Fig. 3

Small angle light scattering pattern using a λ = 632.8nm laser. (a),(b),(c), scattering pattern for a structure of thickness h = 4μm in air, infiltrated with isopropanol (n = 1.377) and with toluene (n = 1.496). (d) calculated scattering pattern in the single scattering limit for the same structure based on a discrete dipole approximation (DDA).

Fig. 4
Fig. 4

Radially averaged scattering intensity. Symbols: experimental data I(q) for h = 4μm, immersed in toluene (n = 1.496), and h = 8μm, immersed in toluene/chlorobenzene 1:2 (n = 1.517). Solid lines: theoretical calculations for the same heights.

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