Abstract

We report the first experimental demonstration of a TE-polarization photonic band gap (PBG) in a 2D isotropic hyperuniform disordered solid (HUDS) made of dielectric media with a dielectric index contrast of 1.6:1, very low for PBG formation. The solid is composed of a connected network of dielectric walls enclosing air-filled cells. Direct comparison with photonic crystals and quasicrystals permitted us to investigate band-gap properties as a function of increasing rotational isotropy. We present results from numerical simulations proving that the PBG observed experimentally for HUDS at low index contrast has zero density of states. The PBG is associated with the energy difference between complementary resonant modes above and below the gap, with the field predominantly concentrated in the air or in the dielectric. The intrinsic isotropy of HUDS may offer unprecedented flexibilities and freedom in applications (i. e. defect architecture design) not limited by crystalline symmetries.

© 2013 OSA

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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]

2013 (2)

M. Florescu, P. J. Steinhardt, and S. Torquato, “Optical cavities and waveguides in hyperuniform disordered photonic solids,” Phys. Rev. B87(16), 165116 (2013).
[CrossRef]

K. Ishizaki, M. Koumura, K. Suzuki, K. Gondaira, and S. Noda, “Realization of three-dimensional guiding of photons in photonic crystals,” Nat. Photonics7(2), 133–137 (2013).
[CrossRef]

2012 (1)

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]

2011 (3)

J. Duplat, B. Bossa, and E. Villermaux, “On two-dimensional foam ageing,” J. Fluid Mech.673, 147–179 (2011).
[CrossRef]

Y. Su, G. T. Fei, Y. Zhang, H. Li, P. Yan, G. L. Shang, and L. D. Zhang, “Anodic alumina photonic crystal heterostructures,” J. Opt. Soc. Am. B28(12), 2931–2933 (2011).
[CrossRef]

M. M. Rahman, J. Ferré-Borrull, J. Pallarès, and L. F. Marsal, “Photonic stop bands of two-dimensional quasi-random structures based on macroporous silicon,” Phys. Status Solidi. C8(3), 1066–1070 (2011).
[CrossRef]

2010 (2)

S. Imagawa, K. Edagawa, K. Morita, T. Niino, Y. Kagawa, and M. Notomi, “Photonic band-gap formation, light diffusion, and localization in photonic amorphous diamond structures,” Phys. Rev. B82(11), 115116 (2010).
[CrossRef]

J. D. Forster, H. Noh, S. F. Liew, V. Saranathan, C. F. Schreck, L. Yang, J.-G. Park, R. O. Prum, S. G. J. Mochrie, C. S. O’Hern, H. Cao, and E. R. Dufresne, “Biomimetic isotropic nanostructures for structural coloration,” Adv. Mater.22(26-27), 2939–2944 (2010).
[CrossRef] [PubMed]

2009 (3)

M. Florescu, S. Torquato, and P. J. Steinhardt, “Designer disordered materials with large, complete photonic band gaps,” Proc. Natl. Acad. Sci. U.S.A.106(49), 20658–20663 (2009).
[CrossRef] [PubMed]

C. E. Zachary and S. Torquato, “Hyperuniformity in Point Patterns and Two-Phase Random Heterogeneous Media,” J. Stat. Mech.2009(12), 12015 (2009).
[CrossRef]

M. Florescu, S. Torquato, and P. J. Steinhardt, “Complete band gaps in two-dimensional photonic quasicrystals,” Phys. Rev. B80(15), 155112 (2009).
[CrossRef]

2008 (4)

R. Batten, F. H. Stillinger, and S. Torquato, “Classical disordered ground states: super ideal gases, and stealth and equi-luminous materials,” J. Appl. Phys.104(3), 033504 (2008).
[CrossRef]

Y. B. Guo, C. Divin, A. Myc, F. L. Terry, J. R. Baker, T. B. Norris, and J. Y. Ye, “Sensitive molecular binding assay using a photonic crystal structure in total internal reflection,” Opt. Express16(16), 11741–11749 (2008).
[CrossRef] [PubMed]

K. Edagawa, S. Kanoko, and M. Notomi, “Photonic amorphous diamond Structure with a 3D photonic band gap,” Phys. Rev. Lett.100(1), 013901 (2008).
[CrossRef] [PubMed]

M. C. Rechtsman, H.-C. Jeong, P. M. Chaikin, S. Torquato, and P. J. Steinhardt, “Optimized structures for photonic quasicrystals,” Phys. Rev. Lett.101(7), 073902 (2008).
[CrossRef] [PubMed]

2006 (2)

H. Altug, D. Englund, and J. Vučković, “Ultrafast photonic crystal nanocavity laser,” Nat. Phys.2(7), 484–488 (2006).
[CrossRef]

I. El-Kady, M. M. Reda Taha, and M. F. Su, “Application of photonic crystals in submicron damage detection and quantification,” Appl. Phys. Lett.88(25), 253109 (2006).
[CrossRef]

2005 (2)

W. Man, M. Megens, P. J. Steinhardt, and P. M. Chaikin, “Experimental measurement of the photonic properties of icosahedral quasicrystals,” Nature436(7053), 993–996 (2005).
[CrossRef] [PubMed]

A. Della Villa, S. Enoch, G. Tayeb, V. Pierro, V. Galdi, and F. Capolino, “Band Gap Formation and Multiple Scattering in Photonic Quasicrystals with a Penrose-Type Lattice,” Phys. Rev. Lett.94(18), 183903 (2005).
[CrossRef] [PubMed]

2003 (3)

S. Torquato and F. H. Stillinger, “Local density fluctuations, hyperuniformity, and order metrics,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.68(4), 041113 (2003).
[CrossRef] [PubMed]

A. Chutinan, S. John, and O. Toader, “Diffractionless flow of light in all-optical microchips,” Phys. Rev. Lett.90(12), 123901 (2003).
[CrossRef] [PubMed]

J. Choi, Y. Luo, R. B. Wehrspohn, R. Hillebrand, J. Schilling, and U. Gösele, “Perfect two-dimensional porous alumina photonic crystals with duplex oxide layers,” J. Appl. Phys.94(8), 4757–4762 (2003).
[CrossRef]

2002 (1)

M. A. Kaliteevski, J. M. Martinez, D. Cassagne, and J. P. Albert, “Disorder-induced modification of the transmission of light in a two-dimensional photonic crystal,” Phys. Rev. B66(11), 113101 (2002).
[CrossRef]

2001 (2)

2000 (3)

S. Noda, A. Chutinan, and M. Imada, “Trapping and emission of photons by a single defect in a photonic bandgap structure,” Nature407(6804), 608–610 (2000).
[CrossRef] [PubMed]

E. Lidorikis, M. M. Sigalas, E. N. Economou, and C. M. Soukoulis, “Gap deformation and classical wave localization in disordered two-dimensional photonic-band-gap materials,” Phys. Rev. B61(20), 13458–13464 (2000).
[CrossRef]

A. A. Asatryan, P. A. Robinson, L. C. Botten, R. C. McPhedran, N. A. Nicorovici, and C. M. de Sterke, “Effects of geometric and refractive index disorder on wave propagation in two-dimensional photonic crystals,” Phys. Rev. E. 62(44 Pt B), 5711–5720 (2000).
[CrossRef] [PubMed]

1999 (1)

H. Cao, Y. G. Zhao, S. T. Ho, E. W. Seeling, Q. H. Wang, and R. P. H. Chang, “Random laser action in semiconductor powder,” Phys. Rev. Lett.82(11), 2278–2281 (1999).
[CrossRef]

1998 (1)

Y. S. Chan, C. T. Chan, and Z. Y. Liu, “Photonic band gaps in two dimensional photonic quasicrystals,” Phys. Rev. Lett.80(5), 956–959 (1998).
[CrossRef]

1994 (1)

K. M. Ho, C. T. Chan, C. M. Soukoulis, R. Biswas, and M. Sigalas, “Photonic band gaps in three dimensions: New layer-by-layer periodic structures,” Solid State Commun.89(5), 413–416 (1994).
[CrossRef]

1993 (1)

I. Schnitzer, E. Yablonovitch, C. Caneau, T. J. Gmitter, and A. Scherer, “30% external quantum efficiency from surface textured, thin film light emitting diodes,” Appl. Phys. Lett.63(16), 2174–2176 (1993).
[CrossRef]

1988 (1)

X. C. Zeng, D. J. Bergman, P. M. Hui, and D. Stroud, “Effective-medium theory for weakly nonlinear composites,” Phys. Rev. B Condens. Matter38(15), 10970–10973 (1988).
[CrossRef] [PubMed]

1987 (2)

S. John, “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett.58(23), 2486–2489 (1987).
[CrossRef] [PubMed]

E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett.58(20), 2059–2062 (1987).
[CrossRef] [PubMed]

Albert, J. P.

M. A. Kaliteevski, J. M. Martinez, D. Cassagne, and J. P. Albert, “Disorder-induced modification of the transmission of light in a two-dimensional photonic crystal,” Phys. Rev. B66(11), 113101 (2002).
[CrossRef]

Altug, H.

H. Altug, D. Englund, and J. Vučković, “Ultrafast photonic crystal nanocavity laser,” Nat. Phys.2(7), 484–488 (2006).
[CrossRef]

Asatryan, A. A.

A. A. Asatryan, P. A. Robinson, L. C. Botten, R. C. McPhedran, N. A. Nicorovici, and C. M. de Sterke, “Effects of geometric and refractive index disorder on wave propagation in two-dimensional photonic crystals,” Phys. Rev. E. 62(44 Pt B), 5711–5720 (2000).
[CrossRef] [PubMed]

Baker, J. R.

Batten, R.

R. Batten, F. H. Stillinger, and S. Torquato, “Classical disordered ground states: super ideal gases, and stealth and equi-luminous materials,” J. Appl. Phys.104(3), 033504 (2008).
[CrossRef]

Bergman, D. J.

X. C. Zeng, D. J. Bergman, P. M. Hui, and D. Stroud, “Effective-medium theory for weakly nonlinear composites,” Phys. Rev. B Condens. Matter38(15), 10970–10973 (1988).
[CrossRef] [PubMed]

Biswas, R.

K. M. Ho, C. T. Chan, C. M. Soukoulis, R. Biswas, and M. Sigalas, “Photonic band gaps in three dimensions: New layer-by-layer periodic structures,” Solid State Commun.89(5), 413–416 (1994).
[CrossRef]

Bossa, B.

J. Duplat, B. Bossa, and E. Villermaux, “On two-dimensional foam ageing,” J. Fluid Mech.673, 147–179 (2011).
[CrossRef]

Botten, L. C.

A. A. Asatryan, P. A. Robinson, L. C. Botten, R. C. McPhedran, N. A. Nicorovici, and C. M. de Sterke, “Effects of geometric and refractive index disorder on wave propagation in two-dimensional photonic crystals,” Phys. Rev. E. 62(44 Pt B), 5711–5720 (2000).
[CrossRef] [PubMed]

Burresi, M.

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]

Caneau, C.

I. Schnitzer, E. Yablonovitch, C. Caneau, T. J. Gmitter, and A. Scherer, “30% external quantum efficiency from surface textured, thin film light emitting diodes,” Appl. Phys. Lett.63(16), 2174–2176 (1993).
[CrossRef]

Cao, H.

J. D. Forster, H. Noh, S. F. Liew, V. Saranathan, C. F. Schreck, L. Yang, J.-G. Park, R. O. Prum, S. G. J. Mochrie, C. S. O’Hern, H. Cao, and E. R. Dufresne, “Biomimetic isotropic nanostructures for structural coloration,” Adv. Mater.22(26-27), 2939–2944 (2010).
[CrossRef] [PubMed]

H. Cao, Y. G. Zhao, S. T. Ho, E. W. Seeling, Q. H. Wang, and R. P. H. Chang, “Random laser action in semiconductor powder,” Phys. Rev. Lett.82(11), 2278–2281 (1999).
[CrossRef]

Capolino, F.

A. Della Villa, S. Enoch, G. Tayeb, V. Pierro, V. Galdi, and F. Capolino, “Band Gap Formation and Multiple Scattering in Photonic Quasicrystals with a Penrose-Type Lattice,” Phys. Rev. Lett.94(18), 183903 (2005).
[CrossRef] [PubMed]

Cassagne, D.

M. A. Kaliteevski, J. M. Martinez, D. Cassagne, and J. P. Albert, “Disorder-induced modification of the transmission of light in a two-dimensional photonic crystal,” Phys. Rev. B66(11), 113101 (2002).
[CrossRef]

Chabanov, A. A.

A. A. Chabanov and A. Z. Genack, “Photon Localization in Resonant Media,” Phys. Rev. Lett.87(15), 153901 (2001).
[CrossRef] [PubMed]

Chaikin, P. M.

M. C. Rechtsman, H.-C. Jeong, P. M. Chaikin, S. Torquato, and P. J. Steinhardt, “Optimized structures for photonic quasicrystals,” Phys. Rev. Lett.101(7), 073902 (2008).
[CrossRef] [PubMed]

W. Man, M. Megens, P. J. Steinhardt, and P. M. Chaikin, “Experimental measurement of the photonic properties of icosahedral quasicrystals,” Nature436(7053), 993–996 (2005).
[CrossRef] [PubMed]

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, ” (unpublished. under review with Proc. Natl. Acad. Sci.).

Chan, C. T.

Y. S. Chan, C. T. Chan, and Z. Y. Liu, “Photonic band gaps in two dimensional photonic quasicrystals,” Phys. Rev. Lett.80(5), 956–959 (1998).
[CrossRef]

K. M. Ho, C. T. Chan, C. M. Soukoulis, R. Biswas, and M. Sigalas, “Photonic band gaps in three dimensions: New layer-by-layer periodic structures,” Solid State Commun.89(5), 413–416 (1994).
[CrossRef]

Chan, Y. S.

Y. S. Chan, C. T. Chan, and Z. Y. Liu, “Photonic band gaps in two dimensional photonic quasicrystals,” Phys. Rev. Lett.80(5), 956–959 (1998).
[CrossRef]

Chang, R. P. H.

H. Cao, Y. G. Zhao, S. T. Ho, E. W. Seeling, Q. H. Wang, and R. P. H. Chang, “Random laser action in semiconductor powder,” Phys. Rev. Lett.82(11), 2278–2281 (1999).
[CrossRef]

Choi, J.

J. Choi, Y. Luo, R. B. Wehrspohn, R. Hillebrand, J. Schilling, and U. Gösele, “Perfect two-dimensional porous alumina photonic crystals with duplex oxide layers,” J. Appl. Phys.94(8), 4757–4762 (2003).
[CrossRef]

Chutinan, A.

A. Chutinan, S. John, and O. Toader, “Diffractionless flow of light in all-optical microchips,” Phys. Rev. Lett.90(12), 123901 (2003).
[CrossRef] [PubMed]

S. Noda, A. Chutinan, and M. Imada, “Trapping and emission of photons by a single defect in a photonic bandgap structure,” Nature407(6804), 608–610 (2000).
[CrossRef] [PubMed]

de Sterke, C. M.

A. A. Asatryan, P. A. Robinson, L. C. Botten, R. C. McPhedran, N. A. Nicorovici, and C. M. de Sterke, “Effects of geometric and refractive index disorder on wave propagation in two-dimensional photonic crystals,” Phys. Rev. E. 62(44 Pt B), 5711–5720 (2000).
[CrossRef] [PubMed]

Della Villa, A.

A. Della Villa, S. Enoch, G. Tayeb, V. Pierro, V. Galdi, and F. Capolino, “Band Gap Formation and Multiple Scattering in Photonic Quasicrystals with a Penrose-Type Lattice,” Phys. Rev. Lett.94(18), 183903 (2005).
[CrossRef] [PubMed]

Divin, C.

Dufresne, E. R.

J. D. Forster, H. Noh, S. F. Liew, V. Saranathan, C. F. Schreck, L. Yang, J.-G. Park, R. O. Prum, S. G. J. Mochrie, C. S. O’Hern, H. Cao, and E. R. Dufresne, “Biomimetic isotropic nanostructures for structural coloration,” Adv. Mater.22(26-27), 2939–2944 (2010).
[CrossRef] [PubMed]

Duplat, J.

J. Duplat, B. Bossa, and E. Villermaux, “On two-dimensional foam ageing,” J. Fluid Mech.673, 147–179 (2011).
[CrossRef]

Economou, E. N.

E. Lidorikis, M. M. Sigalas, E. N. Economou, and C. M. Soukoulis, “Gap deformation and classical wave localization in disordered two-dimensional photonic-band-gap materials,” Phys. Rev. B61(20), 13458–13464 (2000).
[CrossRef]

Edagawa, K.

S. Imagawa, K. Edagawa, K. Morita, T. Niino, Y. Kagawa, and M. Notomi, “Photonic band-gap formation, light diffusion, and localization in photonic amorphous diamond structures,” Phys. Rev. B82(11), 115116 (2010).
[CrossRef]

K. Edagawa, S. Kanoko, and M. Notomi, “Photonic amorphous diamond Structure with a 3D photonic band gap,” Phys. Rev. Lett.100(1), 013901 (2008).
[CrossRef] [PubMed]

El-Kady, I.

I. El-Kady, M. M. Reda Taha, and M. F. Su, “Application of photonic crystals in submicron damage detection and quantification,” Appl. Phys. Lett.88(25), 253109 (2006).
[CrossRef]

Englund, D.

H. Altug, D. Englund, and J. Vučković, “Ultrafast photonic crystal nanocavity laser,” Nat. Phys.2(7), 484–488 (2006).
[CrossRef]

Enoch, S.

A. Della Villa, S. Enoch, G. Tayeb, V. Pierro, V. Galdi, and F. Capolino, “Band Gap Formation and Multiple Scattering in Photonic Quasicrystals with a Penrose-Type Lattice,” Phys. Rev. Lett.94(18), 183903 (2005).
[CrossRef] [PubMed]

Fei, G. T.

Ferré-Borrull, J.

M. M. Rahman, J. Ferré-Borrull, J. Pallarès, and L. F. Marsal, “Photonic stop bands of two-dimensional quasi-random structures based on macroporous silicon,” Phys. Status Solidi. C8(3), 1066–1070 (2011).
[CrossRef]

Florescu, M.

M. Florescu, P. J. Steinhardt, and S. Torquato, “Optical cavities and waveguides in hyperuniform disordered photonic solids,” Phys. Rev. B87(16), 165116 (2013).
[CrossRef]

M. Florescu, S. Torquato, and P. J. Steinhardt, “Complete band gaps in two-dimensional photonic quasicrystals,” Phys. Rev. B80(15), 155112 (2009).
[CrossRef]

M. Florescu, S. Torquato, and P. J. Steinhardt, “Designer disordered materials with large, complete photonic band gaps,” Proc. Natl. Acad. Sci. U.S.A.106(49), 20658–20663 (2009).
[CrossRef] [PubMed]

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, ” (unpublished. under review with Proc. Natl. Acad. Sci.).

Forster, J. D.

J. D. Forster, H. Noh, S. F. Liew, V. Saranathan, C. F. Schreck, L. Yang, J.-G. Park, R. O. Prum, S. G. J. Mochrie, C. S. O’Hern, H. Cao, and E. R. Dufresne, “Biomimetic isotropic nanostructures for structural coloration,” Adv. Mater.22(26-27), 2939–2944 (2010).
[CrossRef] [PubMed]

Galdi, V.

A. Della Villa, S. Enoch, G. Tayeb, V. Pierro, V. Galdi, and F. Capolino, “Band Gap Formation and Multiple Scattering in Photonic Quasicrystals with a Penrose-Type Lattice,” Phys. Rev. Lett.94(18), 183903 (2005).
[CrossRef] [PubMed]

Genack, A. Z.

A. A. Chabanov and A. Z. Genack, “Photon Localization in Resonant Media,” Phys. Rev. Lett.87(15), 153901 (2001).
[CrossRef] [PubMed]

Gmitter, T. J.

I. Schnitzer, E. Yablonovitch, C. Caneau, T. J. Gmitter, and A. Scherer, “30% external quantum efficiency from surface textured, thin film light emitting diodes,” Appl. Phys. Lett.63(16), 2174–2176 (1993).
[CrossRef]

Gondaira, K.

K. Ishizaki, M. Koumura, K. Suzuki, K. Gondaira, and S. Noda, “Realization of three-dimensional guiding of photons in photonic crystals,” Nat. Photonics7(2), 133–137 (2013).
[CrossRef]

Gösele, U.

J. Choi, Y. Luo, R. B. Wehrspohn, R. Hillebrand, J. Schilling, and U. Gösele, “Perfect two-dimensional porous alumina photonic crystals with duplex oxide layers,” J. Appl. Phys.94(8), 4757–4762 (2003).
[CrossRef]

Guo, Y. B.

Hashemizad, S. R.

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, ” (unpublished. under review with Proc. Natl. Acad. Sci.).

He, Y.

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, ” (unpublished. under review with Proc. Natl. Acad. Sci.).

Hillebrand, R.

J. Choi, Y. Luo, R. B. Wehrspohn, R. Hillebrand, J. Schilling, and U. Gösele, “Perfect two-dimensional porous alumina photonic crystals with duplex oxide layers,” J. Appl. Phys.94(8), 4757–4762 (2003).
[CrossRef]

Ho, K. M.

K. M. Ho, C. T. Chan, C. M. Soukoulis, R. Biswas, and M. Sigalas, “Photonic band gaps in three dimensions: New layer-by-layer periodic structures,” Solid State Commun.89(5), 413–416 (1994).
[CrossRef]

Ho, S. T.

H. Cao, Y. G. Zhao, S. T. Ho, E. W. Seeling, Q. H. Wang, and R. P. H. Chang, “Random laser action in semiconductor powder,” Phys. Rev. Lett.82(11), 2278–2281 (1999).
[CrossRef]

Hui, P. M.

X. C. Zeng, D. J. Bergman, P. M. Hui, and D. Stroud, “Effective-medium theory for weakly nonlinear composites,” Phys. Rev. B Condens. Matter38(15), 10970–10973 (1988).
[CrossRef] [PubMed]

Imada, M.

S. Noda, A. Chutinan, and M. Imada, “Trapping and emission of photons by a single defect in a photonic bandgap structure,” Nature407(6804), 608–610 (2000).
[CrossRef] [PubMed]

Imagawa, S.

S. Imagawa, K. Edagawa, K. Morita, T. Niino, Y. Kagawa, and M. Notomi, “Photonic band-gap formation, light diffusion, and localization in photonic amorphous diamond structures,” Phys. Rev. B82(11), 115116 (2010).
[CrossRef]

Ishizaki, K.

K. Ishizaki, M. Koumura, K. Suzuki, K. Gondaira, and S. Noda, “Realization of three-dimensional guiding of photons in photonic crystals,” Nat. Photonics7(2), 133–137 (2013).
[CrossRef]

Jeong, H.-C.

M. C. Rechtsman, H.-C. Jeong, P. M. Chaikin, S. Torquato, and P. J. Steinhardt, “Optimized structures for photonic quasicrystals,” Phys. Rev. Lett.101(7), 073902 (2008).
[CrossRef] [PubMed]

Joannopoulos, J.

John, S.

A. Chutinan, S. John, and O. Toader, “Diffractionless flow of light in all-optical microchips,” Phys. Rev. Lett.90(12), 123901 (2003).
[CrossRef] [PubMed]

S. John, “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett.58(23), 2486–2489 (1987).
[CrossRef] [PubMed]

Johnson, S.

Kagawa, Y.

S. Imagawa, K. Edagawa, K. Morita, T. Niino, Y. Kagawa, and M. Notomi, “Photonic band-gap formation, light diffusion, and localization in photonic amorphous diamond structures,” Phys. Rev. B82(11), 115116 (2010).
[CrossRef]

Kaliteevski, M. A.

M. A. Kaliteevski, J. M. Martinez, D. Cassagne, and J. P. Albert, “Disorder-induced modification of the transmission of light in a two-dimensional photonic crystal,” Phys. Rev. B66(11), 113101 (2002).
[CrossRef]

Kanoko, S.

K. Edagawa, S. Kanoko, and M. Notomi, “Photonic amorphous diamond Structure with a 3D photonic band gap,” Phys. Rev. Lett.100(1), 013901 (2008).
[CrossRef] [PubMed]

Koumura, M.

K. Ishizaki, M. Koumura, K. Suzuki, K. Gondaira, and S. Noda, “Realization of three-dimensional guiding of photons in photonic crystals,” Nat. Photonics7(2), 133–137 (2013).
[CrossRef]

Leung, B. Y.C.

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, ” (unpublished. under review with Proc. Natl. Acad. Sci.).

Li, H.

Lidorikis, E.

E. Lidorikis, M. M. Sigalas, E. N. Economou, and C. M. Soukoulis, “Gap deformation and classical wave localization in disordered two-dimensional photonic-band-gap materials,” Phys. Rev. B61(20), 13458–13464 (2000).
[CrossRef]

Liew, S. F.

J. D. Forster, H. Noh, S. F. Liew, V. Saranathan, C. F. Schreck, L. Yang, J.-G. Park, R. O. Prum, S. G. J. Mochrie, C. S. O’Hern, H. Cao, and E. R. Dufresne, “Biomimetic isotropic nanostructures for structural coloration,” Adv. Mater.22(26-27), 2939–2944 (2010).
[CrossRef] [PubMed]

Liner, D. R.

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, ” (unpublished. under review with Proc. Natl. Acad. Sci.).

Liu, Z. Y.

Y. S. Chan, C. T. Chan, and Z. Y. Liu, “Photonic band gaps in two dimensional photonic quasicrystals,” Phys. Rev. Lett.80(5), 956–959 (1998).
[CrossRef]

Luo, Y.

J. Choi, Y. Luo, R. B. Wehrspohn, R. Hillebrand, J. Schilling, and U. Gösele, “Perfect two-dimensional porous alumina photonic crystals with duplex oxide layers,” J. Appl. Phys.94(8), 4757–4762 (2003).
[CrossRef]

Man, W.

W. Man, M. Megens, P. J. Steinhardt, and P. M. Chaikin, “Experimental measurement of the photonic properties of icosahedral quasicrystals,” Nature436(7053), 993–996 (2005).
[CrossRef] [PubMed]

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, ” (unpublished. under review with Proc. Natl. Acad. Sci.).

Marsal, L. F.

M. M. Rahman, J. Ferré-Borrull, J. Pallarès, and L. F. Marsal, “Photonic stop bands of two-dimensional quasi-random structures based on macroporous silicon,” Phys. Status Solidi. C8(3), 1066–1070 (2011).
[CrossRef]

Martinez, J. M.

M. A. Kaliteevski, J. M. Martinez, D. Cassagne, and J. P. Albert, “Disorder-induced modification of the transmission of light in a two-dimensional photonic crystal,” Phys. Rev. B66(11), 113101 (2002).
[CrossRef]

McPhedran, R. C.

A. A. Asatryan, P. A. Robinson, L. C. Botten, R. C. McPhedran, N. A. Nicorovici, and C. M. de Sterke, “Effects of geometric and refractive index disorder on wave propagation in two-dimensional photonic crystals,” Phys. Rev. E. 62(44 Pt B), 5711–5720 (2000).
[CrossRef] [PubMed]

Megens, M.

W. Man, M. Megens, P. J. Steinhardt, and P. M. Chaikin, “Experimental measurement of the photonic properties of icosahedral quasicrystals,” Nature436(7053), 993–996 (2005).
[CrossRef] [PubMed]

Mochrie, S. G. J.

J. D. Forster, H. Noh, S. F. Liew, V. Saranathan, C. F. Schreck, L. Yang, J.-G. Park, R. O. Prum, S. G. J. Mochrie, C. S. O’Hern, H. Cao, and E. R. Dufresne, “Biomimetic isotropic nanostructures for structural coloration,” Adv. Mater.22(26-27), 2939–2944 (2010).
[CrossRef] [PubMed]

Morita, K.

S. Imagawa, K. Edagawa, K. Morita, T. Niino, Y. Kagawa, and M. Notomi, “Photonic band-gap formation, light diffusion, and localization in photonic amorphous diamond structures,” Phys. Rev. B82(11), 115116 (2010).
[CrossRef]

Myc, A.

Nicorovici, N. A.

A. A. Asatryan, P. A. Robinson, L. C. Botten, R. C. McPhedran, N. A. Nicorovici, and C. M. de Sterke, “Effects of geometric and refractive index disorder on wave propagation in two-dimensional photonic crystals,” Phys. Rev. E. 62(44 Pt B), 5711–5720 (2000).
[CrossRef] [PubMed]

Niino, T.

S. Imagawa, K. Edagawa, K. Morita, T. Niino, Y. Kagawa, and M. Notomi, “Photonic band-gap formation, light diffusion, and localization in photonic amorphous diamond structures,” Phys. Rev. B82(11), 115116 (2010).
[CrossRef]

Noda, S.

K. Ishizaki, M. Koumura, K. Suzuki, K. Gondaira, and S. Noda, “Realization of three-dimensional guiding of photons in photonic crystals,” Nat. Photonics7(2), 133–137 (2013).
[CrossRef]

S. Noda, A. Chutinan, and M. Imada, “Trapping and emission of photons by a single defect in a photonic bandgap structure,” Nature407(6804), 608–610 (2000).
[CrossRef] [PubMed]

Noh, H.

J. D. Forster, H. Noh, S. F. Liew, V. Saranathan, C. F. Schreck, L. Yang, J.-G. Park, R. O. Prum, S. G. J. Mochrie, C. S. O’Hern, H. Cao, and E. R. Dufresne, “Biomimetic isotropic nanostructures for structural coloration,” Adv. Mater.22(26-27), 2939–2944 (2010).
[CrossRef] [PubMed]

Norris, T. B.

Notomi, M.

S. Imagawa, K. Edagawa, K. Morita, T. Niino, Y. Kagawa, and M. Notomi, “Photonic band-gap formation, light diffusion, and localization in photonic amorphous diamond structures,” Phys. Rev. B82(11), 115116 (2010).
[CrossRef]

K. Edagawa, S. Kanoko, and M. Notomi, “Photonic amorphous diamond Structure with a 3D photonic band gap,” Phys. Rev. Lett.100(1), 013901 (2008).
[CrossRef] [PubMed]

O’Hern, C. S.

J. D. Forster, H. Noh, S. F. Liew, V. Saranathan, C. F. Schreck, L. Yang, J.-G. Park, R. O. Prum, S. G. J. Mochrie, C. S. O’Hern, H. Cao, and E. R. Dufresne, “Biomimetic isotropic nanostructures for structural coloration,” Adv. Mater.22(26-27), 2939–2944 (2010).
[CrossRef] [PubMed]

Pallarès, J.

M. M. Rahman, J. Ferré-Borrull, J. Pallarès, and L. F. Marsal, “Photonic stop bands of two-dimensional quasi-random structures based on macroporous silicon,” Phys. Status Solidi. C8(3), 1066–1070 (2011).
[CrossRef]

Park, J.-G.

J. D. Forster, H. Noh, S. F. Liew, V. Saranathan, C. F. Schreck, L. Yang, J.-G. Park, R. O. Prum, S. G. J. Mochrie, C. S. O’Hern, H. Cao, and E. R. Dufresne, “Biomimetic isotropic nanostructures for structural coloration,” Adv. Mater.22(26-27), 2939–2944 (2010).
[CrossRef] [PubMed]

Pierro, V.

A. Della Villa, S. Enoch, G. Tayeb, V. Pierro, V. Galdi, and F. Capolino, “Band Gap Formation and Multiple Scattering in Photonic Quasicrystals with a Penrose-Type Lattice,” Phys. Rev. Lett.94(18), 183903 (2005).
[CrossRef] [PubMed]

Prum, R. O.

J. D. Forster, H. Noh, S. F. Liew, V. Saranathan, C. F. Schreck, L. Yang, J.-G. Park, R. O. Prum, S. G. J. Mochrie, C. S. O’Hern, H. Cao, and E. R. Dufresne, “Biomimetic isotropic nanostructures for structural coloration,” Adv. Mater.22(26-27), 2939–2944 (2010).
[CrossRef] [PubMed]

Rahman, M. M.

M. M. Rahman, J. Ferré-Borrull, J. Pallarès, and L. F. Marsal, “Photonic stop bands of two-dimensional quasi-random structures based on macroporous silicon,” Phys. Status Solidi. C8(3), 1066–1070 (2011).
[CrossRef]

Rechtsman, M. C.

M. C. Rechtsman, H.-C. Jeong, P. M. Chaikin, S. Torquato, and P. J. Steinhardt, “Optimized structures for photonic quasicrystals,” Phys. Rev. Lett.101(7), 073902 (2008).
[CrossRef] [PubMed]

Reda Taha, M. M.

I. El-Kady, M. M. Reda Taha, and M. F. Su, “Application of photonic crystals in submicron damage detection and quantification,” Appl. Phys. Lett.88(25), 253109 (2006).
[CrossRef]

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]

Robinson, P. A.

A. A. Asatryan, P. A. Robinson, L. C. Botten, R. C. McPhedran, N. A. Nicorovici, and C. M. de Sterke, “Effects of geometric and refractive index disorder on wave propagation in two-dimensional photonic crystals,” Phys. Rev. E. 62(44 Pt B), 5711–5720 (2000).
[CrossRef] [PubMed]

Saranathan, V.

J. D. Forster, H. Noh, S. F. Liew, V. Saranathan, C. F. Schreck, L. Yang, J.-G. Park, R. O. Prum, S. G. J. Mochrie, C. S. O’Hern, H. Cao, and E. R. Dufresne, “Biomimetic isotropic nanostructures for structural coloration,” Adv. Mater.22(26-27), 2939–2944 (2010).
[CrossRef] [PubMed]

Scherer, A.

I. Schnitzer, E. Yablonovitch, C. Caneau, T. J. Gmitter, and A. Scherer, “30% external quantum efficiency from surface textured, thin film light emitting diodes,” Appl. Phys. Lett.63(16), 2174–2176 (1993).
[CrossRef]

Schilling, J.

J. Choi, Y. Luo, R. B. Wehrspohn, R. Hillebrand, J. Schilling, and U. Gösele, “Perfect two-dimensional porous alumina photonic crystals with duplex oxide layers,” J. Appl. Phys.94(8), 4757–4762 (2003).
[CrossRef]

Schnitzer, I.

I. Schnitzer, E. Yablonovitch, C. Caneau, T. J. Gmitter, and A. Scherer, “30% external quantum efficiency from surface textured, thin film light emitting diodes,” Appl. Phys. Lett.63(16), 2174–2176 (1993).
[CrossRef]

Schreck, C. F.

J. D. Forster, H. Noh, S. F. Liew, V. Saranathan, C. F. Schreck, L. Yang, J.-G. Park, R. O. Prum, S. G. J. Mochrie, C. S. O’Hern, H. Cao, and E. R. Dufresne, “Biomimetic isotropic nanostructures for structural coloration,” Adv. Mater.22(26-27), 2939–2944 (2010).
[CrossRef] [PubMed]

Seeling, E. W.

H. Cao, Y. G. Zhao, S. T. Ho, E. W. Seeling, Q. H. Wang, and R. P. H. Chang, “Random laser action in semiconductor powder,” Phys. Rev. Lett.82(11), 2278–2281 (1999).
[CrossRef]

Shang, G. L.

Sigalas, M.

K. M. Ho, C. T. Chan, C. M. Soukoulis, R. Biswas, and M. Sigalas, “Photonic band gaps in three dimensions: New layer-by-layer periodic structures,” Solid State Commun.89(5), 413–416 (1994).
[CrossRef]

Sigalas, M. M.

E. Lidorikis, M. M. Sigalas, E. N. Economou, and C. M. Soukoulis, “Gap deformation and classical wave localization in disordered two-dimensional photonic-band-gap materials,” Phys. Rev. B61(20), 13458–13464 (2000).
[CrossRef]

Soukoulis, C. M.

E. Lidorikis, M. M. Sigalas, E. N. Economou, and C. M. Soukoulis, “Gap deformation and classical wave localization in disordered two-dimensional photonic-band-gap materials,” Phys. Rev. B61(20), 13458–13464 (2000).
[CrossRef]

K. M. Ho, C. T. Chan, C. M. Soukoulis, R. Biswas, and M. Sigalas, “Photonic band gaps in three dimensions: New layer-by-layer periodic structures,” Solid State Commun.89(5), 413–416 (1994).
[CrossRef]

Steinhardt, P. J.

M. Florescu, P. J. Steinhardt, and S. Torquato, “Optical cavities and waveguides in hyperuniform disordered photonic solids,” Phys. Rev. B87(16), 165116 (2013).
[CrossRef]

M. Florescu, S. Torquato, and P. J. Steinhardt, “Complete band gaps in two-dimensional photonic quasicrystals,” Phys. Rev. B80(15), 155112 (2009).
[CrossRef]

M. Florescu, S. Torquato, and P. J. Steinhardt, “Designer disordered materials with large, complete photonic band gaps,” Proc. Natl. Acad. Sci. U.S.A.106(49), 20658–20663 (2009).
[CrossRef] [PubMed]

M. C. Rechtsman, H.-C. Jeong, P. M. Chaikin, S. Torquato, and P. J. Steinhardt, “Optimized structures for photonic quasicrystals,” Phys. Rev. Lett.101(7), 073902 (2008).
[CrossRef] [PubMed]

W. Man, M. Megens, P. J. Steinhardt, and P. M. Chaikin, “Experimental measurement of the photonic properties of icosahedral quasicrystals,” Nature436(7053), 993–996 (2005).
[CrossRef] [PubMed]

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, ” (unpublished. under review with Proc. Natl. Acad. Sci.).

Stillinger, F. H.

R. Batten, F. H. Stillinger, and S. Torquato, “Classical disordered ground states: super ideal gases, and stealth and equi-luminous materials,” J. Appl. Phys.104(3), 033504 (2008).
[CrossRef]

S. Torquato and F. H. Stillinger, “Local density fluctuations, hyperuniformity, and order metrics,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.68(4), 041113 (2003).
[CrossRef] [PubMed]

Stroud, D.

X. C. Zeng, D. J. Bergman, P. M. Hui, and D. Stroud, “Effective-medium theory for weakly nonlinear composites,” Phys. Rev. B Condens. Matter38(15), 10970–10973 (1988).
[CrossRef] [PubMed]

Su, M. F.

I. El-Kady, M. M. Reda Taha, and M. F. Su, “Application of photonic crystals in submicron damage detection and quantification,” Appl. Phys. Lett.88(25), 253109 (2006).
[CrossRef]

Su, Y.

Suzuki, K.

K. Ishizaki, M. Koumura, K. Suzuki, K. Gondaira, and S. Noda, “Realization of three-dimensional guiding of photons in photonic crystals,” Nat. Photonics7(2), 133–137 (2013).
[CrossRef]

Tayeb, G.

A. Della Villa, S. Enoch, G. Tayeb, V. Pierro, V. Galdi, and F. Capolino, “Band Gap Formation and Multiple Scattering in Photonic Quasicrystals with a Penrose-Type Lattice,” Phys. Rev. Lett.94(18), 183903 (2005).
[CrossRef] [PubMed]

Terry, F. L.

Toader, O.

A. Chutinan, S. John, and O. Toader, “Diffractionless flow of light in all-optical microchips,” Phys. Rev. Lett.90(12), 123901 (2003).
[CrossRef] [PubMed]

Torquato, S.

M. Florescu, P. J. Steinhardt, and S. Torquato, “Optical cavities and waveguides in hyperuniform disordered photonic solids,” Phys. Rev. B87(16), 165116 (2013).
[CrossRef]

M. Florescu, S. Torquato, and P. J. Steinhardt, “Complete band gaps in two-dimensional photonic quasicrystals,” Phys. Rev. B80(15), 155112 (2009).
[CrossRef]

C. E. Zachary and S. Torquato, “Hyperuniformity in Point Patterns and Two-Phase Random Heterogeneous Media,” J. Stat. Mech.2009(12), 12015 (2009).
[CrossRef]

M. Florescu, S. Torquato, and P. J. Steinhardt, “Designer disordered materials with large, complete photonic band gaps,” Proc. Natl. Acad. Sci. U.S.A.106(49), 20658–20663 (2009).
[CrossRef] [PubMed]

M. C. Rechtsman, H.-C. Jeong, P. M. Chaikin, S. Torquato, and P. J. Steinhardt, “Optimized structures for photonic quasicrystals,” Phys. Rev. Lett.101(7), 073902 (2008).
[CrossRef] [PubMed]

R. Batten, F. H. Stillinger, and S. Torquato, “Classical disordered ground states: super ideal gases, and stealth and equi-luminous materials,” J. Appl. Phys.104(3), 033504 (2008).
[CrossRef]

S. Torquato and F. H. Stillinger, “Local density fluctuations, hyperuniformity, and order metrics,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.68(4), 041113 (2003).
[CrossRef] [PubMed]

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, ” (unpublished. under review with Proc. Natl. Acad. Sci.).

Villermaux, E.

J. Duplat, B. Bossa, and E. Villermaux, “On two-dimensional foam ageing,” J. Fluid Mech.673, 147–179 (2011).
[CrossRef]

Vuckovic, J.

H. Altug, D. Englund, and J. Vučković, “Ultrafast photonic crystal nanocavity laser,” Nat. Phys.2(7), 484–488 (2006).
[CrossRef]

Vynck, K.

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]

Wang, Q. H.

H. Cao, Y. G. Zhao, S. T. Ho, E. W. Seeling, Q. H. Wang, and R. P. H. Chang, “Random laser action in semiconductor powder,” Phys. Rev. Lett.82(11), 2278–2281 (1999).
[CrossRef]

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Figures (6)

Fig. 1
Fig. 1

Photos of the samples used in this study. All structures are 100 mm high. a) The square lattice crystal (lattice spacing = 6.60 mm). b) The triangular lattice crystal with (lattice spacing = 6.60 mm). c) The five-fold symmetric quasicrystal (lattice spacing = 6.58 mm). d) The hyperuniform disordered structure (average inter-vertex spacing a = 5.72 mm). The volume-filling fraction is 40.5% for all the samples.

Fig. 2
Fig. 2

Contour plots of the measured transmission as a function of frequency and incident angle. a) Square-lattice crystal. b) Triangular-lattice crystal. c) The five-fold quasicrystal. d) The hyperuniform disordered structure. For crystals or quasicrystals, stop bands (blocking regions) occur due to Bragg scattering, and their center frequency and width vary rapidly with the incident angle. In the five-fold quasicrystal, the angular difference between the most different symmetry directions is small enough to allow the blocking frequencies to overlap in all directions to form PBGs. In the hyperuniform disordered sample, a truly isotropic PBG is observed around 23.5 GHz despite the low index-contrast of 1.6:1 and the lack of Bragg scattering.

Fig. 3
Fig. 3

Measured transmission and calculated structure factors for the four samples tested. Contour plots (top) in polar coordinates of the measured transmission as a function of frequency, which is the distance to the pole in the radial direction (f = r, 15 to 35 GHz), and incident angle which is the angular coordinates (θ, 0 to 360 degree) and calculated structure factors (bottom). a) The square crystalline lattice. b) The triangular crystalline lattice. c) The five-fold quasicrystal. d) The hyperuniform disordered structure. For the crystals and the quasicrystal, stop bands, due to Bragg scattering, are seen to occur along their Brillouin zone boundaries, directly related to the corresponding structure factors. Large angular variations prevent PBG formation at low index-contrast. The structure factor for the hyperuniform disordered structure is isotropic and continuous. It has been engineered to be equal to zero for small wavenumbers, and exhibits a broad ring of maximum values around a characteristic wavelength range. Correspondingly, a truly isotropic PBG is observed.

Fig. 4
Fig. 4

Simulated band structures (blue). a) Square-lattice crystal. b) Triangular-lattice crystal. c) The five-fold quasicrystal. d) The hyperuniform disordered structure. The frequency axis covers our measurement range of 15-35 GHz. The inserts in c) and d) show a portion of the supercell used for the corresponding simulations. The calculated PBG for the hyperuniform disordered sample is from 23.1GHz to 24.1 GHz, in good agreement with the measured gap.

Fig. 5
Fig. 5

Simulation results of magnetic-field distribution of states near the bandgap. a) A state below the PBG. b) A state above the PBG. Zoom-in inserts show the relation of the field distribution to the cell walls. The positive (negative) values of the field are represented by the red (blue) shade and the dielectric wall boundaries are shown in black.

Fig. 6
Fig. 6

Calculated field concentration factor as a function of frequency. The two vertical dashed lines represent the calculated bandgap boundaries.

Equations (1)

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C F high-index region d 2 rε(r) | E(r) | 2 supercell d 2 rε(r) | E(r) | 2 .

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