Abstract

We show that materials made of scatterers distributed on a stealth hyperuniform point pattern can be transparent at densities for which an uncorrelated disordered material would be opaque due to multiple scattering. The conditions for transparency are analyzed using numerical simulations, and an explicit criterion is found based on a perturbative theory. The broad applicability of the concept offers perspectives for various applications in photonics and more generally in wave physics.

© 2016 Optical Society of America

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References

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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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2015 (2)

T. Amoah and M. Florescu, “High-Q optical cavities in hyperuniform disordered materials,” Phys. Rev. B 91, 020201(R) (2015).
[Crossref]

R. Dreyfus, Y. Xu, T. Still, L. A. Hough, A. G. Yodh, and S. Torquato, “Diagnosing hyperuniformity in two-dimensional, disordered, jammed packings of soft spheres,” Phys. Rev. E 91, 012302 (2015).
[Crossref]

2014 (2)

G. M. Conley, M. Burresi, F. Pratesi, K. Vynck, and D. S. Wiersma, “Light transport and localization in two-dimensional correlated disorder,” Phys. Rev. Lett. 112, 143901 (2014).
[Crossref]

O. Leseur, R. Pierrat, J. J. Sáenz, and R. Carminati, “Probing two-dimensional Anderson localization without statistics,” Phys. Rev. A 90, 053827 (2014).
[Crossref]

2013 (6)

J. Haberko and F. Scheffold, “Fabrication of mesoscale polymeric templates for three-dimensional disordered photonic materials,” Opt. Express 21, 1057 (2013).
[Crossref]

J. Haberko, N. Muller, and F. Scheffold, “Direct laser writing of three-dimensional network structures as templates for disordered photonic materials,” Phys. Rev. A 88, 043822 (2013).
[Crossref]

W. Man, M. Florescu, K. Matsuyama, P. Yadak, G. Nahal, S. Hashemizad, E. Williamson, P. Steinhardt, S. Torquato, and P. Chaikin, “Photonic band gap in isotropic hyperuniform disordered solids with low dielectric contrast,” Opt. Express 21, 19972 (2013).
[Crossref]

N. Muller, J. Haberko, C. Marichy, and F. Scheffold, “Silicon hyperuniform disordered photonic materials with a pronounced gap in the shortwave infrared,” Adv. Opt. Mater. 2, 115–119 (2013).
[Crossref]

M. Florescu, P. J. Steinhardt, and S. Torquato, “Optical cavities and waveguides in hyperuniform disordered photonic solids,” Phys. Rev. B 87, 165116 (2013).
[Crossref]

W. Man, M. Florescu, E. P. Williamson, Y. He, S. R. Hashemizad, B. Y. C. Leung, D. R. Liner, S. Torquato, P. M. Chaikin, and P. J. Steinhardt, “Isotropic band gaps and freeform waveguides observed in hyperuniform disordered photonic solids,” Proc. Natl. Acad. Sci. USA 110, 15886–15891 (2013).
[Crossref]

2012 (1)

A. P. Mosk, A. Lagendijk, G. Lerosey, and M. Fink, “Controlling waves in space and time for imaging and focusing in complex media,” Nat. Photonics 6, 283–292 (2012).
[Crossref]

2011 (3)

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

J.-H. Tian, J. Hu, S.-S. Li, F. Zhang, J. Liu, J. Shi, X. Li, Z.-Q. Tian, and Y. Chen, “Improved seedless hydrothermal synthesis of dense and ultralong ZnO nanowires,” Nanotechnology 22, 245601 (2011).
[Crossref]

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]

2010 (3)

J.-K. Yang, C. Schreck, H. Noh, S.-F. Liew, M. I. Guy, C. S. O’Hern, and H. Cao, “Photonic-band-gap effects in two-dimensional polycrystalline and amorphous structures,” Phys. Rev. A 82, 053838 (2010).
[Crossref]

S. M. Popoff, G. Lerosey, R. Carminati, M. Fink, A. C. Boccara, and S. Gigan, “Measuring the transmission matrix in optics: an approach to the study and control of light propagation in disordered media,” Phys. Rev. Lett. 104, 100601 (2010).
[Crossref]

P. D. García, R. Sapienza, and C. López, “Photonic glasses: a step beyond white paint,” Adv. Mater. 22, 12–19 (2010).
[Crossref]

2009 (1)

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

2008 (4)

R. D. Batten, F. H. Stillinger, and S. Torquato, “Classical disordered ground states: super-ideal gases and stealth and equi-luminous materials,” J. Appl. Phys. 104, 033504 (2008).
[Crossref]

A. Gabrielli, M. Joyce, and S. Torquato, “Tilings of space and superhomogeneous point processes,” Phys. Rev. E 77, 031125 (2008).
[Crossref]

L. Corté, P. M. Chaikin, J. P. Gollub, and D. J. Pine, “Random organization in periodically driven systems,” Nat. Phys. 4, 420–424 (2008).
[Crossref]

K. Edagawa, S. Kanoko, and M. Notomi, “Photonic amorphous diamond structure with a 3D photonic band gap,” Phys. Rev. Lett. 100, 013901 (2008).
[Crossref]

2007 (3)

M. Reufer, L. F. Rojas-Ochoa, S. Eiden, J. J. Sáenz, and F. Scheffold, “Transport of light in amorphous photonic materials,” Appl. Phys. Lett. 91, 171904 (2007).
[Crossref]

P. D. García, R. Sapienza, A. Blanco, and C. López, “Photonic glass: a novel random material for light,” Adv. Mater. 19, 2597–2602 (2007).
[Crossref]

I. M. Vellekoop and A. P. Mosk, “Focusing coherent light through opaque strongly scattering media,” Opt. Lett. 32, 2309 (2007).
[Crossref]

2006 (1)

O. U. Uche, S. Torquato, and F. H. Stillinger, “Collective coordinate control of density distributions,” Phys. Rev. E 74, 031104 (2006).
[Crossref]

2005 (1)

A. Donev, F. Stillinger, and S. Torquato, “Unexpected density fluctuations in jammed disordered sphere packings,” Phys. Rev. Lett. 95, 090604 (2005).
[Crossref]

2004 (2)

O. U. Uche, F. H. Stillinger, and S. Torquato, “Constraints on collective density variables: two dimensions,” Phys. Rev. E 70, 046122 (2004).
[Crossref]

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

2003 (2)

A. Yamilov and H. Cao, “Density of resonant states and a manifestation of photonic band structure in small clusters of spherical particles,” Phys. Rev. B 68, 085111 (2003).
[Crossref]

S. Torquato and F. H. Stillinger, “Local density fluctuations, hyperuniformity, and order metrics,” Phys. Rev. E 68, 041113 (2003).
[Crossref]

2002 (1)

A. Gabrielli, M. Joyce, and F. Sylos Labini, “Glass-like universe: real-space correlation properties of standard cosmological models,” Phys. Rev. D 65, 083523 (2002).
[Crossref]

2001 (1)

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

1990 (1)

S. Fraden and G. Maret, “Multiple light scattering from concentrated, interacting suspensions,” Phys. Rev. Lett. 65, 512–515 (1990).
[Crossref]

1976 (1)

1952 (1)

M. Lax, “Multiple scattering of waves. II. The effective field in dense systems,” Phys. Rev. 85, 621–629 (1952).
[Crossref]

Akkermans, E.

E. Akkermans and G. Montambaux, Mesoscopic Physics of Electrons and Photons (Cambridge University, 2007).

Amoah, T.

T. Amoah and M. Florescu, “High-Q optical cavities in hyperuniform disordered materials,” Phys. Rev. B 91, 020201(R) (2015).
[Crossref]

Batten, R. D.

R. D. Batten, F. H. Stillinger, and S. Torquato, “Classical disordered ground states: super-ideal gases and stealth and equi-luminous materials,” J. Appl. Phys. 104, 033504 (2008).
[Crossref]

Blanco, A.

P. D. García, R. Sapienza, A. Blanco, and C. López, “Photonic glass: a novel random material for light,” Adv. Mater. 19, 2597–2602 (2007).
[Crossref]

Boccara, A. C.

S. M. Popoff, G. Lerosey, R. Carminati, M. Fink, A. C. Boccara, and S. Gigan, “Measuring the transmission matrix in optics: an approach to the study and control of light propagation in disordered media,” Phys. Rev. Lett. 104, 100601 (2010).
[Crossref]

Burresi, M.

G. M. Conley, M. Burresi, F. Pratesi, K. Vynck, and D. S. Wiersma, “Light transport and localization in two-dimensional correlated disorder,” Phys. Rev. Lett. 112, 143901 (2014).
[Crossref]

Cao, H.

J.-K. Yang, C. Schreck, H. Noh, S.-F. Liew, M. I. Guy, C. S. O’Hern, and H. Cao, “Photonic-band-gap effects in two-dimensional polycrystalline and amorphous structures,” Phys. Rev. A 82, 053838 (2010).
[Crossref]

A. Yamilov and H. Cao, “Density of resonant states and a manifestation of photonic band structure in small clusters of spherical particles,” Phys. Rev. B 68, 085111 (2003).
[Crossref]

Carminati, R.

O. Leseur, R. Pierrat, J. J. Sáenz, and R. Carminati, “Probing two-dimensional Anderson localization without statistics,” Phys. Rev. A 90, 053827 (2014).
[Crossref]

S. M. Popoff, G. Lerosey, R. Carminati, M. Fink, A. C. Boccara, and S. Gigan, “Measuring the transmission matrix in optics: an approach to the study and control of light propagation in disordered media,” Phys. Rev. Lett. 104, 100601 (2010).
[Crossref]

Chaikin, P.

Chaikin, P. M.

W. Man, M. Florescu, E. P. Williamson, Y. He, S. R. Hashemizad, B. Y. C. Leung, D. R. Liner, S. Torquato, P. M. Chaikin, and P. J. Steinhardt, “Isotropic band gaps and freeform waveguides observed in hyperuniform disordered photonic solids,” Proc. Natl. Acad. Sci. USA 110, 15886–15891 (2013).
[Crossref]

L. Corté, P. M. Chaikin, J. P. Gollub, and D. J. Pine, “Random organization in periodically driven systems,” Nat. Phys. 4, 420–424 (2008).
[Crossref]

Chandrasekhar, S.

S. Chandrasekhar, Radiative Transfer (Dover, 1950).

Chen, Y.

J.-H. Tian, J. Hu, S.-S. Li, F. Zhang, J. Liu, J. Shi, X. Li, Z.-Q. Tian, and Y. Chen, “Improved seedless hydrothermal synthesis of dense and ultralong ZnO nanowires,” Nanotechnology 22, 245601 (2011).
[Crossref]

Cheng, B.

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

Conley, G. M.

G. M. Conley, M. Burresi, F. Pratesi, K. Vynck, and D. S. Wiersma, “Light transport and localization in two-dimensional correlated disorder,” Phys. Rev. Lett. 112, 143901 (2014).
[Crossref]

Corté, L.

L. Corté, P. M. Chaikin, J. P. Gollub, and D. J. Pine, “Random organization in periodically driven systems,” Nat. Phys. 4, 420–424 (2008).
[Crossref]

Damasceno, P. F.

L. S. Froufe-Pérez, M. Engel, P. F. Damasceno, N. Muller, J. Haberko, S. C. Glotzer, and F. Scheffold, “The role of short-range order and hyperuniformity in the formation of band gaps in disordered photonic materials,” arXiv:1602.01002 (2016).

Donev, A.

A. Donev, F. Stillinger, and S. Torquato, “Unexpected density fluctuations in jammed disordered sphere packings,” Phys. Rev. Lett. 95, 090604 (2005).
[Crossref]

Dreisow, F.

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

Dreyfus, R.

R. Dreyfus, Y. Xu, T. Still, L. A. Hough, A. G. Yodh, and S. Torquato, “Diagnosing hyperuniformity in two-dimensional, disordered, jammed packings of soft spheres,” Phys. Rev. E 91, 012302 (2015).
[Crossref]

Edagawa, K.

K. Edagawa, S. Kanoko, and M. Notomi, “Photonic amorphous diamond structure with a 3D photonic band gap,” Phys. Rev. Lett. 100, 013901 (2008).
[Crossref]

Eiden, S.

M. Reufer, L. F. Rojas-Ochoa, S. Eiden, J. J. Sáenz, and F. Scheffold, “Transport of light in amorphous photonic materials,” Appl. Phys. Lett. 91, 171904 (2007).
[Crossref]

Engel, M.

L. S. Froufe-Pérez, M. Engel, P. F. Damasceno, N. Muller, J. Haberko, S. C. Glotzer, and F. Scheffold, “The role of short-range order and hyperuniformity in the formation of band gaps in disordered photonic materials,” arXiv:1602.01002 (2016).

Farrell, R. A.

Fink, M.

A. P. Mosk, A. Lagendijk, G. Lerosey, and M. Fink, “Controlling waves in space and time for imaging and focusing in complex media,” Nat. Photonics 6, 283–292 (2012).
[Crossref]

S. M. Popoff, G. Lerosey, R. Carminati, M. Fink, A. C. Boccara, and S. Gigan, “Measuring the transmission matrix in optics: an approach to the study and control of light propagation in disordered media,” Phys. Rev. Lett. 104, 100601 (2010).
[Crossref]

Florescu, M.

T. Amoah and M. Florescu, “High-Q optical cavities in hyperuniform disordered materials,” Phys. Rev. B 91, 020201(R) (2015).
[Crossref]

M. Florescu, P. J. Steinhardt, and S. Torquato, “Optical cavities and waveguides in hyperuniform disordered photonic solids,” Phys. Rev. B 87, 165116 (2013).
[Crossref]

W. Man, M. Florescu, E. P. Williamson, Y. He, S. R. Hashemizad, B. Y. C. Leung, D. R. Liner, S. Torquato, P. M. Chaikin, and P. J. Steinhardt, “Isotropic band gaps and freeform waveguides observed in hyperuniform disordered photonic solids,” Proc. Natl. Acad. Sci. USA 110, 15886–15891 (2013).
[Crossref]

W. Man, M. Florescu, K. Matsuyama, P. Yadak, G. Nahal, S. Hashemizad, E. Williamson, P. Steinhardt, S. Torquato, and P. Chaikin, “Photonic band gap in isotropic hyperuniform disordered solids with low dielectric contrast,” Opt. Express 21, 19972 (2013).
[Crossref]

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

Fraden, S.

S. Fraden and G. Maret, “Multiple light scattering from concentrated, interacting suspensions,” Phys. Rev. Lett. 65, 512–515 (1990).
[Crossref]

Froufe-Pérez, L. S.

L. S. Froufe-Pérez, M. Engel, P. F. Damasceno, N. Muller, J. Haberko, S. C. Glotzer, and F. Scheffold, “The role of short-range order and hyperuniformity in the formation of band gaps in disordered photonic materials,” arXiv:1602.01002 (2016).

Gabrielli, A.

A. Gabrielli, M. Joyce, and S. Torquato, “Tilings of space and superhomogeneous point processes,” Phys. Rev. E 77, 031125 (2008).
[Crossref]

A. Gabrielli, M. Joyce, and F. Sylos Labini, “Glass-like universe: real-space correlation properties of standard cosmological models,” Phys. Rev. D 65, 083523 (2002).
[Crossref]

García, P. D.

P. D. García, R. Sapienza, and C. López, “Photonic glasses: a step beyond white paint,” Adv. Mater. 22, 12–19 (2010).
[Crossref]

P. D. García, R. Sapienza, A. Blanco, and C. López, “Photonic glass: a novel random material for light,” Adv. Mater. 19, 2597–2602 (2007).
[Crossref]

Gigan, S.

S. M. Popoff, G. Lerosey, R. Carminati, M. Fink, A. C. Boccara, and S. Gigan, “Measuring the transmission matrix in optics: an approach to the study and control of light propagation in disordered media,” Phys. Rev. Lett. 104, 100601 (2010).
[Crossref]

Glotzer, S. C.

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L. S. Froufe-Pérez, M. Engel, P. F. Damasceno, N. Muller, J. Haberko, S. C. Glotzer, and F. Scheffold, “The role of short-range order and hyperuniformity in the formation of band gaps in disordered photonic materials,” arXiv:1602.01002 (2016).

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W. Man, M. Florescu, E. P. Williamson, Y. He, S. R. Hashemizad, B. Y. C. Leung, D. R. Liner, S. Torquato, P. M. Chaikin, and P. J. Steinhardt, “Isotropic band gaps and freeform waveguides observed in hyperuniform disordered photonic solids,” Proc. Natl. Acad. Sci. USA 110, 15886–15891 (2013).
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R. Dreyfus, Y. Xu, T. Still, L. A. Hough, A. G. Yodh, and S. Torquato, “Diagnosing hyperuniformity in two-dimensional, disordered, jammed packings of soft spheres,” Phys. Rev. E 91, 012302 (2015).
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W. Man, M. Florescu, E. P. Williamson, Y. He, S. R. Hashemizad, B. Y. C. Leung, D. R. Liner, S. Torquato, P. M. Chaikin, and P. J. Steinhardt, “Isotropic band gaps and freeform waveguides observed in hyperuniform disordered photonic solids,” Proc. Natl. Acad. Sci. USA 110, 15886–15891 (2013).
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J.-H. Tian, J. Hu, S.-S. Li, F. Zhang, J. Liu, J. Shi, X. Li, Z.-Q. Tian, and Y. Chen, “Improved seedless hydrothermal synthesis of dense and ultralong ZnO nanowires,” Nanotechnology 22, 245601 (2011).
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W. Man, M. Florescu, E. P. Williamson, Y. He, S. R. Hashemizad, B. Y. C. Leung, D. R. Liner, S. Torquato, P. M. Chaikin, and P. J. Steinhardt, “Isotropic band gaps and freeform waveguides observed in hyperuniform disordered photonic solids,” Proc. Natl. Acad. Sci. USA 110, 15886–15891 (2013).
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J.-H. Tian, J. Hu, S.-S. Li, F. Zhang, J. Liu, J. Shi, X. Li, Z.-Q. Tian, and Y. Chen, “Improved seedless hydrothermal synthesis of dense and ultralong ZnO nanowires,” Nanotechnology 22, 245601 (2011).
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W. Man, M. Florescu, E. P. Williamson, Y. He, S. R. Hashemizad, B. Y. C. Leung, D. R. Liner, S. Torquato, P. M. Chaikin, and P. J. Steinhardt, “Isotropic band gaps and freeform waveguides observed in hyperuniform disordered photonic solids,” Proc. Natl. Acad. Sci. USA 110, 15886–15891 (2013).
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W. Man, M. Florescu, K. Matsuyama, P. Yadak, G. Nahal, S. Hashemizad, E. Williamson, P. Steinhardt, S. Torquato, and P. Chaikin, “Photonic band gap in isotropic hyperuniform disordered solids with low dielectric contrast,” Opt. Express 21, 19972 (2013).
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L. F. Rojas-Ochoa, J. M. Mendez-Alcaraz, J. J. Sáenz, P. Schurtenberger, and F. Scheffold, “Photonic properties of strongly correlated colloidal liquids,” Phys. Rev. Lett. 93, 073903 (2004).
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J. Haberko, N. Muller, and F. Scheffold, “Direct laser writing of three-dimensional network structures as templates for disordered photonic materials,” Phys. Rev. A 88, 043822 (2013).
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N. Muller, J. Haberko, C. Marichy, and F. Scheffold, “Silicon hyperuniform disordered photonic materials with a pronounced gap in the shortwave infrared,” Adv. Opt. Mater. 2, 115–119 (2013).
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L. S. Froufe-Pérez, M. Engel, P. F. Damasceno, N. Muller, J. Haberko, S. C. Glotzer, and F. Scheffold, “The role of short-range order and hyperuniformity in the formation of band gaps in disordered photonic materials,” arXiv:1602.01002 (2016).

Nahal, G.

Noh, H.

J.-K. Yang, C. Schreck, H. Noh, S.-F. Liew, M. I. Guy, C. S. O’Hern, and H. Cao, “Photonic-band-gap effects in two-dimensional polycrystalline and amorphous structures,” Phys. Rev. A 82, 053838 (2010).
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M. Rechtsman, A. Szameit, F. Dreisow, M. Heinrich, R. Keil, S. Nolte, and M. Segev, “Amorphous photonic lattices: band gaps, effective mass, and suppressed transport,” Phys. Rev. Lett. 106, 193904 (2011).
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O. Leseur, R. Pierrat, J. J. Sáenz, and R. Carminati, “Probing two-dimensional Anderson localization without statistics,” Phys. Rev. A 90, 053827 (2014).
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L. Corté, P. M. Chaikin, J. P. Gollub, and D. J. Pine, “Random organization in periodically driven systems,” Nat. Phys. 4, 420–424 (2008).
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G. M. Conley, M. Burresi, F. Pratesi, K. Vynck, and D. S. Wiersma, “Light transport and localization in two-dimensional correlated disorder,” Phys. Rev. Lett. 112, 143901 (2014).
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O. Leseur, R. Pierrat, J. J. Sáenz, and R. Carminati, “Probing two-dimensional Anderson localization without statistics,” Phys. Rev. A 90, 053827 (2014).
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M. Reufer, L. F. Rojas-Ochoa, S. Eiden, J. J. Sáenz, and F. Scheffold, “Transport of light in amorphous photonic materials,” Appl. Phys. Lett. 91, 171904 (2007).
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L. F. Rojas-Ochoa, J. M. Mendez-Alcaraz, J. J. Sáenz, P. Schurtenberger, and F. Scheffold, “Photonic properties of strongly correlated colloidal liquids,” Phys. Rev. Lett. 93, 073903 (2004).
[Crossref]

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P. D. García, R. Sapienza, and C. López, “Photonic glasses: a step beyond white paint,” Adv. Mater. 22, 12–19 (2010).
[Crossref]

P. D. García, R. Sapienza, A. Blanco, and C. López, “Photonic glass: a novel random material for light,” Adv. Mater. 19, 2597–2602 (2007).
[Crossref]

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N. Muller, J. Haberko, C. Marichy, and F. Scheffold, “Silicon hyperuniform disordered photonic materials with a pronounced gap in the shortwave infrared,” Adv. Opt. Mater. 2, 115–119 (2013).
[Crossref]

J. Haberko, N. Muller, and F. Scheffold, “Direct laser writing of three-dimensional network structures as templates for disordered photonic materials,” Phys. Rev. A 88, 043822 (2013).
[Crossref]

J. Haberko and F. Scheffold, “Fabrication of mesoscale polymeric templates for three-dimensional disordered photonic materials,” Opt. Express 21, 1057 (2013).
[Crossref]

M. Reufer, L. F. Rojas-Ochoa, S. Eiden, J. J. Sáenz, 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, J. J. Sáenz, P. Schurtenberger, and F. Scheffold, “Photonic properties of strongly correlated colloidal liquids,” Phys. Rev. Lett. 93, 073903 (2004).
[Crossref]

L. S. Froufe-Pérez, M. Engel, P. F. Damasceno, N. Muller, J. Haberko, S. C. Glotzer, and F. Scheffold, “The role of short-range order and hyperuniformity in the formation of band gaps in disordered photonic materials,” arXiv:1602.01002 (2016).

Schreck, C.

J.-K. Yang, C. Schreck, H. Noh, S.-F. Liew, M. I. Guy, C. S. O’Hern, and H. Cao, “Photonic-band-gap effects in two-dimensional polycrystalline and amorphous structures,” Phys. Rev. A 82, 053838 (2010).
[Crossref]

Schurtenberger, P.

L. F. Rojas-Ochoa, J. M. Mendez-Alcaraz, J. J. Sáenz, P. Schurtenberger, and F. Scheffold, “Photonic properties of strongly correlated colloidal liquids,” Phys. Rev. Lett. 93, 073903 (2004).
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M. Rechtsman, A. Szameit, F. Dreisow, M. Heinrich, R. Keil, S. Nolte, and M. Segev, “Amorphous photonic lattices: band gaps, effective mass, and suppressed transport,” Phys. Rev. Lett. 106, 193904 (2011).
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J.-H. Tian, J. Hu, S.-S. Li, F. Zhang, J. Liu, J. Shi, X. Li, Z.-Q. Tian, and Y. Chen, “Improved seedless hydrothermal synthesis of dense and ultralong ZnO nanowires,” Nanotechnology 22, 245601 (2011).
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Steinhardt, P.

Steinhardt, P. J.

W. Man, M. Florescu, E. P. Williamson, Y. He, S. R. Hashemizad, B. Y. C. Leung, D. R. Liner, S. Torquato, P. M. Chaikin, and P. J. Steinhardt, “Isotropic band gaps and freeform waveguides observed in hyperuniform disordered photonic solids,” Proc. Natl. Acad. Sci. USA 110, 15886–15891 (2013).
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M. Florescu, P. J. Steinhardt, and S. Torquato, “Optical cavities and waveguides in hyperuniform disordered photonic solids,” Phys. Rev. B 87, 165116 (2013).
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M. Florescu, S. Torquato, and P. J. Steinhardt, “Designer disordered materials with large, complete photonic band gaps,” Proc. Natl. Acad. Sci. USA 106, 20658–20663 (2009).
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Still, T.

R. Dreyfus, Y. Xu, T. Still, L. A. Hough, A. G. Yodh, and S. Torquato, “Diagnosing hyperuniformity in two-dimensional, disordered, jammed packings of soft spheres,” Phys. Rev. E 91, 012302 (2015).
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A. Donev, F. Stillinger, and S. Torquato, “Unexpected density fluctuations in jammed disordered sphere packings,” Phys. Rev. Lett. 95, 090604 (2005).
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Stillinger, F. H.

R. D. Batten, F. H. Stillinger, and S. Torquato, “Classical disordered ground states: super-ideal gases and stealth and equi-luminous materials,” J. Appl. Phys. 104, 033504 (2008).
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O. U. Uche, S. Torquato, and F. H. Stillinger, “Collective coordinate control of density distributions,” Phys. Rev. E 74, 031104 (2006).
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O. U. Uche, F. H. Stillinger, and S. Torquato, “Constraints on collective density variables: two dimensions,” Phys. Rev. E 70, 046122 (2004).
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S. Torquato and F. H. Stillinger, “Local density fluctuations, hyperuniformity, and order metrics,” Phys. Rev. E 68, 041113 (2003).
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Sylos Labini, F.

A. Gabrielli, M. Joyce, and F. Sylos Labini, “Glass-like universe: real-space correlation properties of standard cosmological models,” Phys. Rev. D 65, 083523 (2002).
[Crossref]

Szameit, A.

M. Rechtsman, A. Szameit, F. Dreisow, M. Heinrich, R. Keil, S. Nolte, and M. Segev, “Amorphous photonic lattices: band gaps, effective mass, and suppressed transport,” Phys. Rev. Lett. 106, 193904 (2011).
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S. M. Rytov, Y. A. Kravtsov, and V. I. Tatarskii, Principles of Statistical Radiophysics (Springer-Verlag, 1989), Vol. 4.

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J.-H. Tian, J. Hu, S.-S. Li, F. Zhang, J. Liu, J. Shi, X. Li, Z.-Q. Tian, and Y. Chen, “Improved seedless hydrothermal synthesis of dense and ultralong ZnO nanowires,” Nanotechnology 22, 245601 (2011).
[Crossref]

Tian, Z.-Q.

J.-H. Tian, J. Hu, S.-S. Li, F. Zhang, J. Liu, J. Shi, X. Li, Z.-Q. Tian, and Y. Chen, “Improved seedless hydrothermal synthesis of dense and ultralong ZnO nanowires,” Nanotechnology 22, 245601 (2011).
[Crossref]

Torquato, S.

R. Dreyfus, Y. Xu, T. Still, L. A. Hough, A. G. Yodh, and S. Torquato, “Diagnosing hyperuniformity in two-dimensional, disordered, jammed packings of soft spheres,” Phys. Rev. E 91, 012302 (2015).
[Crossref]

W. Man, M. Florescu, K. Matsuyama, P. Yadak, G. Nahal, S. Hashemizad, E. Williamson, P. Steinhardt, S. Torquato, and P. Chaikin, “Photonic band gap in isotropic hyperuniform disordered solids with low dielectric contrast,” Opt. Express 21, 19972 (2013).
[Crossref]

M. Florescu, P. J. Steinhardt, and S. Torquato, “Optical cavities and waveguides in hyperuniform disordered photonic solids,” Phys. Rev. B 87, 165116 (2013).
[Crossref]

W. Man, M. Florescu, E. P. Williamson, Y. He, S. R. Hashemizad, B. Y. C. Leung, D. R. Liner, S. Torquato, P. M. Chaikin, and P. J. Steinhardt, “Isotropic band gaps and freeform waveguides observed in hyperuniform disordered photonic solids,” Proc. Natl. Acad. Sci. USA 110, 15886–15891 (2013).
[Crossref]

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]

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

A. Gabrielli, M. Joyce, and S. Torquato, “Tilings of space and superhomogeneous point processes,” Phys. Rev. E 77, 031125 (2008).
[Crossref]

R. D. Batten, F. H. Stillinger, and S. Torquato, “Classical disordered ground states: super-ideal gases and stealth and equi-luminous materials,” J. Appl. Phys. 104, 033504 (2008).
[Crossref]

O. U. Uche, S. Torquato, and F. H. Stillinger, “Collective coordinate control of density distributions,” Phys. Rev. E 74, 031104 (2006).
[Crossref]

A. Donev, F. Stillinger, and S. Torquato, “Unexpected density fluctuations in jammed disordered sphere packings,” Phys. Rev. Lett. 95, 090604 (2005).
[Crossref]

O. U. Uche, F. H. Stillinger, and S. Torquato, “Constraints on collective density variables: two dimensions,” Phys. Rev. E 70, 046122 (2004).
[Crossref]

S. Torquato and F. H. Stillinger, “Local density fluctuations, hyperuniformity, and order metrics,” Phys. Rev. E 68, 041113 (2003).
[Crossref]

Uche, O. U.

O. U. Uche, S. Torquato, and F. H. Stillinger, “Collective coordinate control of density distributions,” Phys. Rev. E 74, 031104 (2006).
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O. U. Uche, F. H. Stillinger, and S. Torquato, “Constraints on collective density variables: two dimensions,” Phys. Rev. E 70, 046122 (2004).
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Vynck, K.

G. M. Conley, M. Burresi, F. Pratesi, K. Vynck, and D. S. Wiersma, “Light transport and localization in two-dimensional correlated disorder,” Phys. Rev. Lett. 112, 143901 (2014).
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G. M. Conley, M. Burresi, F. Pratesi, K. Vynck, and D. S. Wiersma, “Light transport and localization in two-dimensional correlated disorder,” Phys. Rev. Lett. 112, 143901 (2014).
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Williamson, E.

Williamson, E. P.

W. Man, M. Florescu, E. P. Williamson, Y. He, S. R. Hashemizad, B. Y. C. Leung, D. R. Liner, S. Torquato, P. M. Chaikin, and P. J. Steinhardt, “Isotropic band gaps and freeform waveguides observed in hyperuniform disordered photonic solids,” Proc. Natl. Acad. Sci. USA 110, 15886–15891 (2013).
[Crossref]

Xu, Y.

R. Dreyfus, Y. Xu, T. Still, L. A. Hough, A. G. Yodh, and S. Torquato, “Diagnosing hyperuniformity in two-dimensional, disordered, jammed packings of soft spheres,” Phys. Rev. E 91, 012302 (2015).
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Yamilov, A.

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R. Dreyfus, Y. Xu, T. Still, L. A. Hough, A. G. Yodh, and S. Torquato, “Diagnosing hyperuniformity in two-dimensional, disordered, jammed packings of soft spheres,” Phys. Rev. E 91, 012302 (2015).
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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).
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J. Opt. Soc. Am. (1)

Nanotechnology (1)

J.-H. Tian, J. Hu, S.-S. Li, F. Zhang, J. Liu, J. Shi, X. Li, Z.-Q. Tian, and Y. Chen, “Improved seedless hydrothermal synthesis of dense and ultralong ZnO nanowires,” Nanotechnology 22, 245601 (2011).
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J.-K. Yang, C. Schreck, H. Noh, S.-F. Liew, M. I. Guy, C. S. O’Hern, and H. Cao, “Photonic-band-gap effects in two-dimensional polycrystalline and amorphous structures,” Phys. Rev. A 82, 053838 (2010).
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S. Torquato and F. H. Stillinger, “Local density fluctuations, hyperuniformity, and order metrics,” Phys. Rev. E 68, 041113 (2003).
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Supplementary Material (1)

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» Supplement 1: PDF (1041 KB)      Document with supplemental technical information

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Figures (3)

Fig. 1.
Fig. 1. (a) Hyperuniform medium generated with N = 90000 and χ = 0.222 . (b) Structure factor of the hyperuniform medium averaged over 20 configurations. (c) Uncorrelated medium generated with N = 90000 and χ = 0 . (d) Structure factor of the uncorrelated medium.
Fig. 2.
Fig. 2. (a) Scattering geometry. The 2D medium is illuminated by a Gaussian beam at normal incidence (beam waist w = 60 / k 0 ), and the diffuse intensity is calculated in direction θ . (b) Schematic view of the domain described by the scattered wavevector q = k s k i in Fourier space. For a hyperuniform material, the structure factor vanishes in the square domain Ω . (c) Angular pattern of the average diffuse intensity in the single scattering regime ( b B = 0.5 ) for a hyperuniform medium with k 0 = K / 8 (blue line) and for uncorrelated disorder (red dashed line). The same scatterers and the same density are used in both cases, the intensity is averaged over 20 configurations, and k 0 B = 444 . (d) Same as (c) with k 0 = K / 3.5 and k 0 B = 1015 .
Fig. 3.
Fig. 3. (a) Angular pattern of the average diffuse intensity in the multiple-scattering regime ( b B = 5 ) for a hyperuniform medium with k 0 = K / 8 (blue line) and for uncorrelated disorder (red dashed line). The same scatterers and the same density are used in both cases, the intensity is averaged over 20 configurations, and k 0 B = 44.4 . (b) Zoom on the central part of the polar plot.

Equations (8)

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S ( q ) = 1 N | j = 1 N exp [ i q · r j ] | 2 ,
E sca ( r , ω ) = i ( 1 i ) 4 π k 0 r exp [ i k 0 r ] E sca ( θ , ω ) ,
I diff ( θ , ω ) = | E sca ( θ , ω ) | 2 | E sca ( θ , ω ) | 2 ,
I diff ( θ , ω ) N S ( q ) | E 0 | 2 N 2 V 2 | Θ ( q ) | 2 | E 0 | 2 ,
p ( u , u ) S [ k 0 ( u u ) ] N 1 V 2 | Θ [ k 0 ( u u ) ] | 2 ,
1 = 8 π ρ k 0 2 B 0 R [ α ( ω ) G 0 ( r ) ] h ( r ) F ( k 0 r ) r d 1 d r ,
Σ = ρ k 0 2 α ( ω ) [ 1 + 2 π ρ k 0 2 α ( ω ) 0 G 0 ( r ) h ( r ) F ( k 0 r ) r d 1 d r ] .
b B k 0 B .

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