Abstract

The photonic band diagrams of close-packed colloidal diamond and pyrochlore structures, have been studied using Korringa-Kohn-Rostoker (KKR) and plane-wave calculations. In addition, the occurrence of a band gap has been investigated for the binary Laves structures and their constituent large- and small-sphere substructures. It was recently shown that these Laves structures give the possibility to fabricate the diamond and pyrochlore structures by self-organization. The comparison of the two calculation methods opens the possibility to study the validity and the convergence of the results, which have been an issue for diamond-related structures in the past. The KKR calculations systematically give a lower value for the gap width than the plane-wave calculations. This difference can partly be ascribed to a convergence issue in the plane-wave code when a contact point of two spheres coincides with the grid.

© 2009 Optical Society of America

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2008 (1)

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

2007 (2)

A. P. Hynninen, J. H. J. Thijssen, E. C. M. Vermolen, M. Dijkstra, and A. van Blaaderen, "Self-assembly route for photonic crystals with a bandgap in the visible region," Nat. Mater. 6, 202-205 (2007).
[CrossRef] [PubMed]

K. Busch, G. von Freymann, S. Linden, S. Mingaleev, L. Tkeshelashvili, and M. Wegener, "Periodic nanostructures for photonics," Phys. Rep. 444, 101-202 (2007).
[CrossRef]

2006 (2)

A. J. Garcia-Adeva, "Band gap atlas for photonic crystals having the symmetry of the kagome and pyrochlore lattices," New J. Phys. 8, 86 (2006).
[CrossRef]

T. T. Ngo, C. M. Liddell, M. Ghebrebrhan, and J. D. Joannopoulos, "Tetrastack: Colloidal diamond-inspired structure with omnidirectional photonic band gap for low refractive index contrast," Appl. Phys. Lett. 88, 241920 (2006).
[CrossRef]

2005 (1)

Z. L. Zhang, A. S. Keys, T. Chen, and S. C. Glotzer, "Self-assembly of patchy particles into diamond structures through molecular mimicry," Langmuir 21, 11547-11551 (2005).
[CrossRef] [PubMed]

2004 (3)

V. N. Manoharan and D. J. Pine, "Building materials by packing spheres," MRS Bull. 29, 91-95 (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," Nat. Mater. 3, 444-447 (2004).
[CrossRef] [PubMed]

P. Lodahl, A. F. van Driel, I. S. Nikolaev, A. Irman, K. Overgaag, D. L. Vanmaekelbergh, and W. L. Vos, "Controlling the dynamics of spontaneous emission from quantum dots by photonic crystals," Nature 430, 654-657 (2004).
[CrossRef] [PubMed]

2003 (1)

M. Maldovan, C. K. Ullal,W. C. Carter, and E. L. Thomas, "Exploring for 3D photonic bandgap structures in the 11 f.c.c. space groups," Nat. Mater. 2, 664-667 (2003).
[CrossRef] [PubMed]

2002 (3)

A. Moroz, "Metallo-dielectric diamond and zinc-blende photonic crystals," Phys. Rev. B 66, 115109 (2002).
[CrossRef]

A. V. Tkachenko, "Morphological diversity of DNA-colloidal self-assembly," Phys. Rev. Lett. 89, 148303 (2002).
[CrossRef] [PubMed]

F. García-Santamaría, H. T. Miyazaki, A. Urqu’?a, M. Ibisate, M. Belmonte, N. Shinya, F. Meseguer, and C. López, "Nanorobotic Manipulation of Microspheres for On-Chip Diamond Architectures," Adv. Mater. 14, 1144-1147 (2002).
[CrossRef]

2001 (1)

2000 (1)

Z. Y. Li and Z. Q. Zhang, "Fragility of photonic band gaps in inverse-opal photonic crystals," Phys. Rev. B 62, 1516-1519 (2000).
[CrossRef]

1999 (1)

A. Moroz and C. Sommers, "Photonic band gaps of three-dimensional face-centred cubic lattices," J. Phys.: Condens. Matter 11, 997-1008 (1999).
[CrossRef]

1998 (3)

R. Biswas, M. M. Sigalas, G. Subramania, and K. M. Ho, "Photonic band gaps in colloidal systems," Phys. Rev. B 57, 3701-3705 (1998).
[CrossRef]

K. Busch and S. John, "Photonic band gap formation in certain self-organizing systems," Phys. Rev. E 58, 3896-3908 (1998).
[CrossRef]

H. Míguez, F. Meseguer, C. López, A. Blanco, J. S. Moya, J. Requena, A. Mifsud, and V. Fornés, "Control of the photonic crystal properties of fcc-packed submicrometer SiO2 spheres by sintering," Adv. Mater. 10, 480-483 (1998).
[CrossRef] [PubMed]

1996 (1)

S. Simeonov, U. Bass, and A. R. McGurn, "Photonic band structure of zinc blende type periodic dielectric media," Physica B 228, 245-250 (1996).
[CrossRef]

1995 (1)

A. Moroz, "Density-of-States Calculations and Multiple-Scattering Theory for Photons," Phys. Rev. B 51, 2068-2081 (1995).
[CrossRef]

1993 (2)

X. D. Wang, T. C. Leung, B. N. Harmon, and P. Carra, "Circular Magnetic-X-Ray Dichroism in the Heavy Rare-Earth-Metals," Phys. Rev. B 47, 9087-9090 (1993).
[CrossRef]

W. H. Butler, A. Gonis, and X. G. Zhang, "Basis Functions for Arbitrary Cells in Multiple-Scattering Theory," Phys. Rev. B 48, 2118-2130 (1993).
[CrossRef]

1992 (2)

H. S. Sozuer, J. W. Haus, and R. Inguva, "Photonic Bands - Convergence Problems with the Plane-Wave Method," Phys. Rev. B 45, 13962-13972 (1992).
[CrossRef]

W. H. Butler, A. Gonis, and X. G. Zhang, "Multiple-Scattering Theory for Space-Filling Cell Potentials," Phys. Rev. B 45, 11527-11541 (1992).
[CrossRef]

1990 (1)

K. M. Ho, C. T. Chan, and C. M. Soukoulis, "Existence of a photonic gap in periodic dielectric structures," Phys. Rev. Lett. 65, 3152-3155 (1990).
[CrossRef] [PubMed]

1987 (2)

E. Yablonovitch, "Inhibited Spontaneous Emission in Solid-State Physics and Electronics," Phys. Rev. Lett. 58, 2059-2062 (1987).
[CrossRef] [PubMed]

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

1975 (1)

V. P. Bykov, "Spontaneous emission from a medium with a band spectrum," Sov. J. Quantum Electron. 4, 861-871 (1975).
[CrossRef]

1974 (1)

A. R. Williams and J. v.-W. Morgan, "Multiple scattering by non-muffin-tin potentials: general formulation," J. Phys. C 7, 37-60 (1974).
[CrossRef]

1972 (1)

V. P. Bykov, "Spontaneous emission in a periodic structure," Soviet Physics - JETP 35, 269-273 (1972).

Bass, U.

S. Simeonov, U. Bass, and A. R. McGurn, "Photonic band structure of zinc blende type periodic dielectric media," Physica B 228, 245-250 (1996).
[CrossRef]

Belmonte, M.

F. García-Santamaría, H. T. Miyazaki, A. Urqu’?a, M. Ibisate, M. Belmonte, N. Shinya, F. Meseguer, and C. López, "Nanorobotic Manipulation of Microspheres for On-Chip Diamond Architectures," Adv. Mater. 14, 1144-1147 (2002).
[CrossRef]

Biswas, R.

R. Biswas, M. M. Sigalas, G. Subramania, and K. M. Ho, "Photonic band gaps in colloidal systems," Phys. Rev. B 57, 3701-3705 (1998).
[CrossRef]

Blanco, A.

H. Míguez, F. Meseguer, C. López, A. Blanco, J. S. Moya, J. Requena, A. Mifsud, and V. Fornés, "Control of the photonic crystal properties of fcc-packed submicrometer SiO2 spheres by sintering," Adv. Mater. 10, 480-483 (1998).
[CrossRef] [PubMed]

Busch, K.

K. Busch, G. von Freymann, S. Linden, S. Mingaleev, L. Tkeshelashvili, and M. Wegener, "Periodic nanostructures for photonics," Phys. Rep. 444, 101-202 (2007).
[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," Nat. Mater. 3, 444-447 (2004).
[CrossRef] [PubMed]

K. Busch and S. John, "Photonic band gap formation in certain self-organizing systems," Phys. Rev. E 58, 3896-3908 (1998).
[CrossRef]

Butler, W. H.

W. H. Butler, A. Gonis, and X. G. Zhang, "Basis Functions for Arbitrary Cells in Multiple-Scattering Theory," Phys. Rev. B 48, 2118-2130 (1993).
[CrossRef]

W. H. Butler, A. Gonis, and X. G. Zhang, "Multiple-Scattering Theory for Space-Filling Cell Potentials," Phys. Rev. B 45, 11527-11541 (1992).
[CrossRef]

Bykov, V. P.

V. P. Bykov, "Spontaneous emission from a medium with a band spectrum," Sov. J. Quantum Electron. 4, 861-871 (1975).
[CrossRef]

V. P. Bykov, "Spontaneous emission in a periodic structure," Soviet Physics - JETP 35, 269-273 (1972).

Carra, P.

X. D. Wang, T. C. Leung, B. N. Harmon, and P. Carra, "Circular Magnetic-X-Ray Dichroism in the Heavy Rare-Earth-Metals," Phys. Rev. B 47, 9087-9090 (1993).
[CrossRef]

Carter, W. C.

M. Maldovan, C. K. Ullal,W. C. Carter, and E. L. Thomas, "Exploring for 3D photonic bandgap structures in the 11 f.c.c. space groups," Nat. Mater. 2, 664-667 (2003).
[CrossRef] [PubMed]

Chan, C. T.

K. M. Ho, C. T. Chan, and C. M. Soukoulis, "Existence of a photonic gap in periodic dielectric structures," Phys. Rev. Lett. 65, 3152-3155 (1990).
[CrossRef] [PubMed]

Chen, T.

Z. L. Zhang, A. S. Keys, T. Chen, and S. C. Glotzer, "Self-assembly of patchy particles into diamond structures through molecular mimicry," Langmuir 21, 11547-11551 (2005).
[CrossRef] [PubMed]

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," Nat. Mater. 3, 444-447 (2004).
[CrossRef] [PubMed]

Dijkstra, M.

A. P. Hynninen, J. H. J. Thijssen, E. C. M. Vermolen, M. Dijkstra, and A. van Blaaderen, "Self-assembly route for photonic crystals with a bandgap in the visible region," Nat. Mater. 6, 202-205 (2007).
[CrossRef] [PubMed]

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] [PubMed]

Fornés, V.

H. Míguez, F. Meseguer, C. López, A. Blanco, J. S. Moya, J. Requena, A. Mifsud, and V. Fornés, "Control of the photonic crystal properties of fcc-packed submicrometer SiO2 spheres by sintering," Adv. Mater. 10, 480-483 (1998).
[CrossRef] [PubMed]

Garcia-Adeva, A. J.

A. J. Garcia-Adeva, "Band gap atlas for photonic crystals having the symmetry of the kagome and pyrochlore lattices," New J. Phys. 8, 86 (2006).
[CrossRef]

García-Santamaría, F.

F. García-Santamaría, H. T. Miyazaki, A. Urqu’?a, M. Ibisate, M. Belmonte, N. Shinya, F. Meseguer, and C. López, "Nanorobotic Manipulation of Microspheres for On-Chip Diamond Architectures," Adv. Mater. 14, 1144-1147 (2002).
[CrossRef]

Ghebrebrhan, M.

T. T. Ngo, C. M. Liddell, M. Ghebrebrhan, and J. D. Joannopoulos, "Tetrastack: Colloidal diamond-inspired structure with omnidirectional photonic band gap for low refractive index contrast," Appl. Phys. Lett. 88, 241920 (2006).
[CrossRef]

Glotzer, S. C.

Z. L. Zhang, A. S. Keys, T. Chen, and S. C. Glotzer, "Self-assembly of patchy particles into diamond structures through molecular mimicry," Langmuir 21, 11547-11551 (2005).
[CrossRef] [PubMed]

Gonis, A.

W. H. Butler, A. Gonis, and X. G. Zhang, "Basis Functions for Arbitrary Cells in Multiple-Scattering Theory," Phys. Rev. B 48, 2118-2130 (1993).
[CrossRef]

W. H. Butler, A. Gonis, and X. G. Zhang, "Multiple-Scattering Theory for Space-Filling Cell Potentials," Phys. Rev. B 45, 11527-11541 (1992).
[CrossRef]

Harmon, B. N.

X. D. Wang, T. C. Leung, B. N. Harmon, and P. Carra, "Circular Magnetic-X-Ray Dichroism in the Heavy Rare-Earth-Metals," Phys. Rev. B 47, 9087-9090 (1993).
[CrossRef]

Haus, J. W.

H. S. Sozuer, J. W. Haus, and R. Inguva, "Photonic Bands - Convergence Problems with the Plane-Wave Method," Phys. Rev. B 45, 13962-13972 (1992).
[CrossRef]

Ho, K. M.

R. Biswas, M. M. Sigalas, G. Subramania, and K. M. Ho, "Photonic band gaps in colloidal systems," Phys. Rev. B 57, 3701-3705 (1998).
[CrossRef]

K. M. Ho, C. T. Chan, and C. M. Soukoulis, "Existence of a photonic gap in periodic dielectric structures," Phys. Rev. Lett. 65, 3152-3155 (1990).
[CrossRef] [PubMed]

Hynninen, A. P.

A. P. Hynninen, J. H. J. Thijssen, E. C. M. Vermolen, M. Dijkstra, and A. van Blaaderen, "Self-assembly route for photonic crystals with a bandgap in the visible region," Nat. Mater. 6, 202-205 (2007).
[CrossRef] [PubMed]

Ibisate, M.

F. García-Santamaría, H. T. Miyazaki, A. Urqu’?a, M. Ibisate, M. Belmonte, N. Shinya, F. Meseguer, and C. López, "Nanorobotic Manipulation of Microspheres for On-Chip Diamond Architectures," Adv. Mater. 14, 1144-1147 (2002).
[CrossRef]

Inguva, R.

H. S. Sozuer, J. W. Haus, and R. Inguva, "Photonic Bands - Convergence Problems with the Plane-Wave Method," Phys. Rev. B 45, 13962-13972 (1992).
[CrossRef]

Irman, A.

P. Lodahl, A. F. van Driel, I. S. Nikolaev, A. Irman, K. Overgaag, D. L. Vanmaekelbergh, and W. L. Vos, "Controlling the dynamics of spontaneous emission from quantum dots by photonic crystals," Nature 430, 654-657 (2004).
[CrossRef] [PubMed]

Joannopoulos, J. D.

T. T. Ngo, C. M. Liddell, M. Ghebrebrhan, and J. D. Joannopoulos, "Tetrastack: Colloidal diamond-inspired structure with omnidirectional photonic band gap for low refractive index contrast," Appl. Phys. Lett. 88, 241920 (2006).
[CrossRef]

S. G. Johnson and J. D. Joannopoulos, "Block-iterative frequency-domain methods for Maxwell’s equations in a planewave basis," Opt. Express 8, 173-190 (2001).
[CrossRef] [PubMed]

John, S.

K. Busch and S. John, "Photonic band gap formation in certain self-organizing systems," Phys. Rev. E 58, 3896-3908 (1998).
[CrossRef]

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

Johnson, S. G.

Kanoko, S.

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

Keys, A. S.

Z. L. Zhang, A. S. Keys, T. Chen, and S. C. Glotzer, "Self-assembly of patchy particles into diamond structures through molecular mimicry," Langmuir 21, 11547-11551 (2005).
[CrossRef] [PubMed]

Leung, T. C.

X. D. Wang, T. C. Leung, B. N. Harmon, and P. Carra, "Circular Magnetic-X-Ray Dichroism in the Heavy Rare-Earth-Metals," Phys. Rev. B 47, 9087-9090 (1993).
[CrossRef]

Li, Z. Y.

Z. Y. Li and Z. Q. Zhang, "Fragility of photonic band gaps in inverse-opal photonic crystals," Phys. Rev. B 62, 1516-1519 (2000).
[CrossRef]

Liddell, C. M.

T. T. Ngo, C. M. Liddell, M. Ghebrebrhan, and J. D. Joannopoulos, "Tetrastack: Colloidal diamond-inspired structure with omnidirectional photonic band gap for low refractive index contrast," Appl. Phys. Lett. 88, 241920 (2006).
[CrossRef]

Linden, S.

K. Busch, G. von Freymann, S. Linden, S. Mingaleev, L. Tkeshelashvili, and M. Wegener, "Periodic nanostructures for photonics," Phys. Rep. 444, 101-202 (2007).
[CrossRef]

Lodahl, P.

P. Lodahl, A. F. van Driel, I. S. Nikolaev, A. Irman, K. Overgaag, D. L. Vanmaekelbergh, and W. L. Vos, "Controlling the dynamics of spontaneous emission from quantum dots by photonic crystals," Nature 430, 654-657 (2004).
[CrossRef] [PubMed]

López, C.

F. García-Santamaría, H. T. Miyazaki, A. Urqu’?a, M. Ibisate, M. Belmonte, N. Shinya, F. Meseguer, and C. López, "Nanorobotic Manipulation of Microspheres for On-Chip Diamond Architectures," Adv. Mater. 14, 1144-1147 (2002).
[CrossRef]

H. Míguez, F. Meseguer, C. López, A. Blanco, J. S. Moya, J. Requena, A. Mifsud, and V. Fornés, "Control of the photonic crystal properties of fcc-packed submicrometer SiO2 spheres by sintering," Adv. Mater. 10, 480-483 (1998).
[CrossRef] [PubMed]

Maldovan, M.

M. Maldovan, C. K. Ullal,W. C. Carter, and E. L. Thomas, "Exploring for 3D photonic bandgap structures in the 11 f.c.c. space groups," Nat. Mater. 2, 664-667 (2003).
[CrossRef] [PubMed]

Manoharan, V. N.

V. N. Manoharan and D. J. Pine, "Building materials by packing spheres," MRS Bull. 29, 91-95 (2004).
[CrossRef]

McGurn, A. R.

S. Simeonov, U. Bass, and A. R. McGurn, "Photonic band structure of zinc blende type periodic dielectric media," Physica B 228, 245-250 (1996).
[CrossRef]

Meseguer, F.

F. García-Santamaría, H. T. Miyazaki, A. Urqu’?a, M. Ibisate, M. Belmonte, N. Shinya, F. Meseguer, and C. López, "Nanorobotic Manipulation of Microspheres for On-Chip Diamond Architectures," Adv. Mater. 14, 1144-1147 (2002).
[CrossRef]

H. Míguez, F. Meseguer, C. López, A. Blanco, J. S. Moya, J. Requena, A. Mifsud, and V. Fornés, "Control of the photonic crystal properties of fcc-packed submicrometer SiO2 spheres by sintering," Adv. Mater. 10, 480-483 (1998).
[CrossRef] [PubMed]

Mifsud, A.

H. Míguez, F. Meseguer, C. López, A. Blanco, J. S. Moya, J. Requena, A. Mifsud, and V. Fornés, "Control of the photonic crystal properties of fcc-packed submicrometer SiO2 spheres by sintering," Adv. Mater. 10, 480-483 (1998).
[CrossRef] [PubMed]

Míguez, H.

H. Míguez, F. Meseguer, C. López, A. Blanco, J. S. Moya, J. Requena, A. Mifsud, and V. Fornés, "Control of the photonic crystal properties of fcc-packed submicrometer SiO2 spheres by sintering," Adv. Mater. 10, 480-483 (1998).
[CrossRef] [PubMed]

Mingaleev, S.

K. Busch, G. von Freymann, S. Linden, S. Mingaleev, L. Tkeshelashvili, and M. Wegener, "Periodic nanostructures for photonics," Phys. Rep. 444, 101-202 (2007).
[CrossRef]

Miyazaki, H. T.

F. García-Santamaría, H. T. Miyazaki, A. Urqu’?a, M. Ibisate, M. Belmonte, N. Shinya, F. Meseguer, and C. López, "Nanorobotic Manipulation of Microspheres for On-Chip Diamond Architectures," Adv. Mater. 14, 1144-1147 (2002).
[CrossRef]

Morgan, J. v.-W.

A. R. Williams and J. v.-W. Morgan, "Multiple scattering by non-muffin-tin potentials: general formulation," J. Phys. C 7, 37-60 (1974).
[CrossRef]

Moroz, A.

A. Moroz, "Metallo-dielectric diamond and zinc-blende photonic crystals," Phys. Rev. B 66, 115109 (2002).
[CrossRef]

A. Moroz and C. Sommers, "Photonic band gaps of three-dimensional face-centred cubic lattices," J. Phys.: Condens. Matter 11, 997-1008 (1999).
[CrossRef]

A. Moroz, "Density-of-States Calculations and Multiple-Scattering Theory for Photons," Phys. Rev. B 51, 2068-2081 (1995).
[CrossRef]

Moya, J. S.

H. Míguez, F. Meseguer, C. López, A. Blanco, J. S. Moya, J. Requena, A. Mifsud, and V. Fornés, "Control of the photonic crystal properties of fcc-packed submicrometer SiO2 spheres by sintering," Adv. Mater. 10, 480-483 (1998).
[CrossRef] [PubMed]

Ngo, T. T.

T. T. Ngo, C. M. Liddell, M. Ghebrebrhan, and J. D. Joannopoulos, "Tetrastack: Colloidal diamond-inspired structure with omnidirectional photonic band gap for low refractive index contrast," Appl. Phys. Lett. 88, 241920 (2006).
[CrossRef]

Nikolaev, I. S.

P. Lodahl, A. F. van Driel, I. S. Nikolaev, A. Irman, K. Overgaag, D. L. Vanmaekelbergh, and W. L. Vos, "Controlling the dynamics of spontaneous emission from quantum dots by photonic crystals," Nature 430, 654-657 (2004).
[CrossRef] [PubMed]

Notomi, M.

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

Overgaag, K.

P. Lodahl, A. F. van Driel, I. S. Nikolaev, A. Irman, K. Overgaag, D. L. Vanmaekelbergh, and W. L. Vos, "Controlling the dynamics of spontaneous emission from quantum dots by photonic crystals," Nature 430, 654-657 (2004).
[CrossRef] [PubMed]

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," Nat. Mater. 3, 444-447 (2004).
[CrossRef] [PubMed]

Pine, D. J.

V. N. Manoharan and D. J. Pine, "Building materials by packing spheres," MRS Bull. 29, 91-95 (2004).
[CrossRef]

Requena, J.

H. Míguez, F. Meseguer, C. López, A. Blanco, J. S. Moya, J. Requena, A. Mifsud, and V. Fornés, "Control of the photonic crystal properties of fcc-packed submicrometer SiO2 spheres by sintering," Adv. Mater. 10, 480-483 (1998).
[CrossRef] [PubMed]

S¨oz¨uer, H. S.

H. S. Sozuer, J. W. Haus, and R. Inguva, "Photonic Bands - Convergence Problems with the Plane-Wave Method," Phys. Rev. B 45, 13962-13972 (1992).
[CrossRef]

Shinya, N.

F. García-Santamaría, H. T. Miyazaki, A. Urqu’?a, M. Ibisate, M. Belmonte, N. Shinya, F. Meseguer, and C. López, "Nanorobotic Manipulation of Microspheres for On-Chip Diamond Architectures," Adv. Mater. 14, 1144-1147 (2002).
[CrossRef]

Sigalas, M. M.

R. Biswas, M. M. Sigalas, G. Subramania, and K. M. Ho, "Photonic band gaps in colloidal systems," Phys. Rev. B 57, 3701-3705 (1998).
[CrossRef]

Simeonov, S.

S. Simeonov, U. Bass, and A. R. McGurn, "Photonic band structure of zinc blende type periodic dielectric media," Physica B 228, 245-250 (1996).
[CrossRef]

Sommers, C.

A. Moroz and C. Sommers, "Photonic band gaps of three-dimensional face-centred cubic lattices," J. Phys.: Condens. Matter 11, 997-1008 (1999).
[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," Nat. Mater. 3, 444-447 (2004).
[CrossRef] [PubMed]

K. M. Ho, C. T. Chan, and C. M. Soukoulis, "Existence of a photonic gap in periodic dielectric structures," Phys. Rev. Lett. 65, 3152-3155 (1990).
[CrossRef] [PubMed]

Subramania, G.

R. Biswas, M. M. Sigalas, G. Subramania, and K. M. Ho, "Photonic band gaps in colloidal systems," Phys. Rev. B 57, 3701-3705 (1998).
[CrossRef]

Thijssen, J. H. J.

A. P. Hynninen, J. H. J. Thijssen, E. C. M. Vermolen, M. Dijkstra, and A. van Blaaderen, "Self-assembly route for photonic crystals with a bandgap in the visible region," Nat. Mater. 6, 202-205 (2007).
[CrossRef] [PubMed]

Thomas, E. L.

M. Maldovan, C. K. Ullal,W. C. Carter, and E. L. Thomas, "Exploring for 3D photonic bandgap structures in the 11 f.c.c. space groups," Nat. Mater. 2, 664-667 (2003).
[CrossRef] [PubMed]

Tkachenko, A. V.

A. V. Tkachenko, "Morphological diversity of DNA-colloidal self-assembly," Phys. Rev. Lett. 89, 148303 (2002).
[CrossRef] [PubMed]

Tkeshelashvili, L.

K. Busch, G. von Freymann, S. Linden, S. Mingaleev, L. Tkeshelashvili, and M. Wegener, "Periodic nanostructures for photonics," Phys. Rep. 444, 101-202 (2007).
[CrossRef]

Ullal, C. K.

M. Maldovan, C. K. Ullal,W. C. Carter, and E. L. Thomas, "Exploring for 3D photonic bandgap structures in the 11 f.c.c. space groups," Nat. Mater. 2, 664-667 (2003).
[CrossRef] [PubMed]

Urqu’ia, A.

F. García-Santamaría, H. T. Miyazaki, A. Urqu’?a, M. Ibisate, M. Belmonte, N. Shinya, F. Meseguer, and C. López, "Nanorobotic Manipulation of Microspheres for On-Chip Diamond Architectures," Adv. Mater. 14, 1144-1147 (2002).
[CrossRef]

van Blaaderen, A.

A. P. Hynninen, J. H. J. Thijssen, E. C. M. Vermolen, M. Dijkstra, and A. van Blaaderen, "Self-assembly route for photonic crystals with a bandgap in the visible region," Nat. Mater. 6, 202-205 (2007).
[CrossRef] [PubMed]

van Driel, A. F.

P. Lodahl, A. F. van Driel, I. S. Nikolaev, A. Irman, K. Overgaag, D. L. Vanmaekelbergh, and W. L. Vos, "Controlling the dynamics of spontaneous emission from quantum dots by photonic crystals," Nature 430, 654-657 (2004).
[CrossRef] [PubMed]

Vanmaekelbergh, D. L.

P. Lodahl, A. F. van Driel, I. S. Nikolaev, A. Irman, K. Overgaag, D. L. Vanmaekelbergh, and W. L. Vos, "Controlling the dynamics of spontaneous emission from quantum dots by photonic crystals," Nature 430, 654-657 (2004).
[CrossRef] [PubMed]

Vermolen, E. C. M.

A. P. Hynninen, J. H. J. Thijssen, E. C. M. Vermolen, M. Dijkstra, and A. van Blaaderen, "Self-assembly route for photonic crystals with a bandgap in the visible region," Nat. Mater. 6, 202-205 (2007).
[CrossRef] [PubMed]

von Freymann, G.

K. Busch, G. von Freymann, S. Linden, S. Mingaleev, L. Tkeshelashvili, and M. Wegener, "Periodic nanostructures for photonics," Phys. Rep. 444, 101-202 (2007).
[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," Nat. Mater. 3, 444-447 (2004).
[CrossRef] [PubMed]

Vos, W. L.

P. Lodahl, A. F. van Driel, I. S. Nikolaev, A. Irman, K. Overgaag, D. L. Vanmaekelbergh, and W. L. Vos, "Controlling the dynamics of spontaneous emission from quantum dots by photonic crystals," Nature 430, 654-657 (2004).
[CrossRef] [PubMed]

Wang, X. D.

X. D. Wang, T. C. Leung, B. N. Harmon, and P. Carra, "Circular Magnetic-X-Ray Dichroism in the Heavy Rare-Earth-Metals," Phys. Rev. B 47, 9087-9090 (1993).
[CrossRef]

Wegener, M.

K. Busch, G. von Freymann, S. Linden, S. Mingaleev, L. Tkeshelashvili, and M. Wegener, "Periodic nanostructures for photonics," Phys. Rep. 444, 101-202 (2007).
[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," Nat. Mater. 3, 444-447 (2004).
[CrossRef] [PubMed]

Williams, A. R.

A. R. Williams and J. v.-W. Morgan, "Multiple scattering by non-muffin-tin potentials: general formulation," J. Phys. C 7, 37-60 (1974).
[CrossRef]

Yablonovitch, E.

E. Yablonovitch, "Inhibited Spontaneous Emission in Solid-State Physics and Electronics," Phys. Rev. Lett. 58, 2059-2062 (1987).
[CrossRef] [PubMed]

Zhang, X. G.

W. H. Butler, A. Gonis, and X. G. Zhang, "Basis Functions for Arbitrary Cells in Multiple-Scattering Theory," Phys. Rev. B 48, 2118-2130 (1993).
[CrossRef]

W. H. Butler, A. Gonis, and X. G. Zhang, "Multiple-Scattering Theory for Space-Filling Cell Potentials," Phys. Rev. B 45, 11527-11541 (1992).
[CrossRef]

Zhang, Z. L.

Z. L. Zhang, A. S. Keys, T. Chen, and S. C. Glotzer, "Self-assembly of patchy particles into diamond structures through molecular mimicry," Langmuir 21, 11547-11551 (2005).
[CrossRef] [PubMed]

Zhang, Z. Q.

Z. Y. Li and Z. Q. Zhang, "Fragility of photonic band gaps in inverse-opal photonic crystals," Phys. Rev. B 62, 1516-1519 (2000).
[CrossRef]

Adv. Mater. (2)

F. García-Santamaría, H. T. Miyazaki, A. Urqu’?a, M. Ibisate, M. Belmonte, N. Shinya, F. Meseguer, and C. López, "Nanorobotic Manipulation of Microspheres for On-Chip Diamond Architectures," Adv. Mater. 14, 1144-1147 (2002).
[CrossRef]

H. Míguez, F. Meseguer, C. López, A. Blanco, J. S. Moya, J. Requena, A. Mifsud, and V. Fornés, "Control of the photonic crystal properties of fcc-packed submicrometer SiO2 spheres by sintering," Adv. Mater. 10, 480-483 (1998).
[CrossRef] [PubMed]

Appl. Phys. Lett. (1)

T. T. Ngo, C. M. Liddell, M. Ghebrebrhan, and J. D. Joannopoulos, "Tetrastack: Colloidal diamond-inspired structure with omnidirectional photonic band gap for low refractive index contrast," Appl. Phys. Lett. 88, 241920 (2006).
[CrossRef]

J. Phys. C (1)

A. R. Williams and J. v.-W. Morgan, "Multiple scattering by non-muffin-tin potentials: general formulation," J. Phys. C 7, 37-60 (1974).
[CrossRef]

J. Phys.: Condens. Matter (1)

A. Moroz and C. Sommers, "Photonic band gaps of three-dimensional face-centred cubic lattices," J. Phys.: Condens. Matter 11, 997-1008 (1999).
[CrossRef]

Langmuir (1)

Z. L. Zhang, A. S. Keys, T. Chen, and S. C. Glotzer, "Self-assembly of patchy particles into diamond structures through molecular mimicry," Langmuir 21, 11547-11551 (2005).
[CrossRef] [PubMed]

MRS Bull. (1)

V. N. Manoharan and D. J. Pine, "Building materials by packing spheres," MRS Bull. 29, 91-95 (2004).
[CrossRef]

Nat. Mater. (3)

A. P. Hynninen, J. H. J. Thijssen, E. C. M. Vermolen, M. Dijkstra, and A. van Blaaderen, "Self-assembly route for photonic crystals with a bandgap in the visible region," Nat. Mater. 6, 202-205 (2007).
[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," Nat. Mater. 3, 444-447 (2004).
[CrossRef] [PubMed]

M. Maldovan, C. K. Ullal,W. C. Carter, and E. L. Thomas, "Exploring for 3D photonic bandgap structures in the 11 f.c.c. space groups," Nat. Mater. 2, 664-667 (2003).
[CrossRef] [PubMed]

Nature (1)

P. Lodahl, A. F. van Driel, I. S. Nikolaev, A. Irman, K. Overgaag, D. L. Vanmaekelbergh, and W. L. Vos, "Controlling the dynamics of spontaneous emission from quantum dots by photonic crystals," Nature 430, 654-657 (2004).
[CrossRef] [PubMed]

New J. Phys. (1)

A. J. Garcia-Adeva, "Band gap atlas for photonic crystals having the symmetry of the kagome and pyrochlore lattices," New J. Phys. 8, 86 (2006).
[CrossRef]

Opt. Express (1)

Phys. Rep. (1)

K. Busch, G. von Freymann, S. Linden, S. Mingaleev, L. Tkeshelashvili, and M. Wegener, "Periodic nanostructures for photonics," Phys. Rep. 444, 101-202 (2007).
[CrossRef]

Phys. Rev. B (8)

A. Moroz, "Metallo-dielectric diamond and zinc-blende photonic crystals," Phys. Rev. B 66, 115109 (2002).
[CrossRef]

W. H. Butler, A. Gonis, and X. G. Zhang, "Multiple-Scattering Theory for Space-Filling Cell Potentials," Phys. Rev. B 45, 11527-11541 (1992).
[CrossRef]

W. H. Butler, A. Gonis, and X. G. Zhang, "Basis Functions for Arbitrary Cells in Multiple-Scattering Theory," Phys. Rev. B 48, 2118-2130 (1993).
[CrossRef]

Z. Y. Li and Z. Q. Zhang, "Fragility of photonic band gaps in inverse-opal photonic crystals," Phys. Rev. B 62, 1516-1519 (2000).
[CrossRef]

H. S. Sozuer, J. W. Haus, and R. Inguva, "Photonic Bands - Convergence Problems with the Plane-Wave Method," Phys. Rev. B 45, 13962-13972 (1992).
[CrossRef]

R. Biswas, M. M. Sigalas, G. Subramania, and K. M. Ho, "Photonic band gaps in colloidal systems," Phys. Rev. B 57, 3701-3705 (1998).
[CrossRef]

X. D. Wang, T. C. Leung, B. N. Harmon, and P. Carra, "Circular Magnetic-X-Ray Dichroism in the Heavy Rare-Earth-Metals," Phys. Rev. B 47, 9087-9090 (1993).
[CrossRef]

A. Moroz, "Density-of-States Calculations and Multiple-Scattering Theory for Photons," Phys. Rev. B 51, 2068-2081 (1995).
[CrossRef]

Phys. Rev. E (1)

K. Busch and S. John, "Photonic band gap formation in certain self-organizing systems," Phys. Rev. E 58, 3896-3908 (1998).
[CrossRef]

Phys. Rev. Lett. (5)

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

A. V. Tkachenko, "Morphological diversity of DNA-colloidal self-assembly," Phys. Rev. Lett. 89, 148303 (2002).
[CrossRef] [PubMed]

K. M. Ho, C. T. Chan, and C. M. Soukoulis, "Existence of a photonic gap in periodic dielectric structures," Phys. Rev. Lett. 65, 3152-3155 (1990).
[CrossRef] [PubMed]

E. Yablonovitch, "Inhibited Spontaneous Emission in Solid-State Physics and Electronics," Phys. Rev. Lett. 58, 2059-2062 (1987).
[CrossRef] [PubMed]

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

Physica B (1)

S. Simeonov, U. Bass, and A. R. McGurn, "Photonic band structure of zinc blende type periodic dielectric media," Physica B 228, 245-250 (1996).
[CrossRef]

Sov. J. Quantum Electron. (1)

V. P. Bykov, "Spontaneous emission from a medium with a band spectrum," Sov. J. Quantum Electron. 4, 861-871 (1975).
[CrossRef]

Soviet Physics - JETP (1)

V. P. Bykov, "Spontaneous emission in a periodic structure," Soviet Physics - JETP 35, 269-273 (1972).

Other (3)

Photonic Crystals and Light Localization in the 21st Century, NATO Science Series (C): Mathematical and Physical Sciences (Kluwer Academic, Dordrecht, 2001).

K. Busch, S. Lolkes, R. B. Wehrspohn, and H. Foll (ed.), Photonic Crystals: Advances in Design, Fabrication, and Characterization (Wiley-VCH, Berlin, 2004).
[CrossRef]

"http://ab-initio.mit.edu/wiki/index.php/Main Page,".

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Figures (5)

Fig. 1.
Fig. 1.

(a) Convergence of the maximum frequency of band 2 and the minimum frequency of band 3 of the KKR band structure of the direct pyrochlore crystal of close-packed silicon spheres in air (dielectric contrast 12) with increasing values of lmax . (b) Relative gap width of various MgCu2 structures. The large spheres are close-packed, the small sphere radius is varied. A size ratio of rS /rL = 0 corresponds to diamond, rS /rL ≈ 0.82 corresponds to close-packed MgCu2. All spheres consist of silicon (ε= 12), the surrounding medium is air (ε= 1). For negative relative gap widths, the maximum of the lower band is higher than the minimum of the higher band, therefore, the structure has no band gap. The line is a guide to the eye. (c-d) Band structure diagrams calculated by the plane-wave method (solid lines) and the KKR method (symbols) of (c) a direct diamond crystal and (d) a direct pyrochlore crystal, both of silicon spheres in air (dielectric contrast 12). Resolution 32 was used for the direct pyrochlore structure. Resolution 28 was used for the direct diamond structure, because we found that the lower branch in Fig. 3(a) converges faster, see Section 4.

Fig. 2.
Fig. 2.

The relative gap width of the photonic band gap between bands 2 and 3, as a function of the dielectric contrast, for the direct diamond and pyrochlore structures and their inverse structures at the maximum sphere packing fraction (of 34% and 37%, respectively), calculated by using both the KKR-method (lmax = 9) and MPB software (resolution 32 for the inverse structures and the direct pyrochlore structure and resolution 28 for the direct diamond structure, see Section 4). Note the difference in scale on the vertical axes. The solid lines are a guide to the eye.

Fig. 3.
Fig. 3.

Relative gap width between bands 2 and 3 of a close packed diamond structure of silicon spheres in air as a function of the chosen resolution in the MPB software with (a) the origin of coordinates on one of the spheres or (b) with the origin halfway between the center of the sphere and the contact point with the other sphere. The solid lines are a guide to the eye. The insets are 2D representations of the positions of the spheres and their contact point (white circle) with respect to the grid of the unit cell for resolution 4 (solid grid) and resolution 8 (solid+dashed grid).

Fig. 4.
Fig. 4.

Comparison of the maximum frequency for band 2 and the minimum frequency for band 3 for different resolutions. (a) Graph showing the calculated maximum frequency of band 2 and the calculated minimum frequency of band 3 as a function of the plane wave resolution for a configuration with one sphere in the origin. The straight dashed lines show the calculated values using the KKR method. The maximum frequency of band 2 (b) and the minimum frequency of band 3 (c) as a function of the dielectric contrast for the KKR method (open triangles) and for the plane wave method with resolution 32 (closed triangles).

Fig. 5.
Fig. 5.

Illustration of the deviation of the results the different calculation methods and resolutions as a function of the relative radius near close packing for a configuration with one sphere in the origin. (a) The relative gap width as a function of the radius (expressed in r cp ). (b) Difference between the results of plane wave calculations at a resolution of 32 and the results of plane wave calculations at a resolution of 28 (solid squares) and between the results of plane wave calculations at a resolution of 32 and the results of the KKR method (open circles).

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