Abstract

We present results of photonic band-structure calculations for inverted photonic crystal structures. We consider a structure of air spheres in a dielectric background, arranged in an fcc lattice, with a cylindrical tunnel connecting each pair of neighboring spheres. We derive (semi)analytical expressions for the Fourier coefficients of the dielectric susceptibility, which are used as input in a standard plane-wave expansion method. We optimize the width of the photonic bandgap by applying a gradient search method and varying two geometrical parameters in the system: the ratios R/a and Rc/R, where a is the lattice constant, R is the sphere radius, and Rc is the cylinder radius. It follows from our calculations that the maximal gap width in this type of photonic-crystal structure with air spheres and cylinders in silicon is Δω/ω0=9.59%.

© 2000 Optical Society of America

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  7. E. Özbay, A. Abeyta, G. Tuttle, M. Tringides, R. Biswas, C. T. Chan, C. M. Soukoulis, and K. M. Ho, “Measurement of a three-dimensional photonic band gap in a crystal structure made of dielectric rods,” Phys. Rev. B 50, 1945–1948 (1994).
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  11. G. Subramania, K. Constant, R. Biswas, M. M. Sigalas, and K. M. Ho, “Optical photonic crystals fabricated from colloidal systems,” Appl. Phys. Lett. 74, 3933–3935 (1999).
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    [CrossRef] [PubMed]
  13. A. van Blaaderen, “Opals in a new light,” Science 282, 887–888 (1998).
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  14. B. T. Holland, C. F. Blanford, and A. Stein, “Synthesis of macroporous minerals with highly ordered three-dimensional arrays of spherical voids,” Science 281, 538–540 (1998).
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  15. A. Imhof and D. J. Pine, “Ordered macroporous materials by emulsion templating,” Nature 389, 948–951 (1997).
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    [CrossRef]
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  22. H. Míguez, F. Meseguer, C. López, Á. 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]
  23. K. Busch and S. John, “Photonic band gap formation in certain self-organizing systems,” Phys. Rev. E 58, 3896–3908 (1998).
    [CrossRef]
  24. E. N. Economou and M. M. Sigalas, “Classical wave propagation in periodic structures: Cermet versus network topology,” Phys. Rev. B 48, 13, 434–13, 438 (1993).
    [CrossRef]
  25. 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]
  26. 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]
  27. H. S. Sözüer, J. W. Haus, and R. Inguva, “Photonic bands: convergence problems with the plane wave method,” Phys. Rev. B 45, 13, 962–13, 972 (1992).
    [CrossRef]
  28. S. Datta, C. T. Chan, K. M. Ho, and C. M. Soukoulis, “Photonic band gaps in periodic dielectric structures: the scalar-wave approximation,” Phys. Rev. B 46, 10, 650–10, 656 (1992).
    [CrossRef]
  29. K. W. K. Shung and Y. C. Tsai, “Surface effects and band measurements in photonic crystals,” Phys. Rev. B 48, 11, 265–11, 269 (1993).
    [CrossRef]
  30. P. R. Villeneuve and M. Piché, “Photonic bandgaps: what is the best numerical representation of periodic structures?” J. Mod. Opt. 41, 241–256 (1994).
    [CrossRef]
  31. K. M. Leung and Y. F. Liu, “Full vector wave calculation of photonic band structures in face-centered-cubic dielectric media,” Phys. Rev. Lett. 65, 2646–2649 (1990).
    [CrossRef] [PubMed]
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    [CrossRef]
  34. C. T. Chan, S. Datta, K. M. Ho, and C. M. Soukoulis, “A7 structure: a family of photonic crystals,” Phys. Rev. B 50, 1988–1991 (1994).
    [CrossRef]
  35. W. Kohn and N. Rostoker, “Solution of the Schrödinger equation in periodic lattices with an application to metallic lithium,” Phys. Rev. 94, 1111–1120 (1954).
    [CrossRef]
  36. A. Moroz, “Inward and outward integral equations and the KKR method for photons,” J. Phys. Condens. Matter 6, 171–182 (1994).
    [CrossRef]
  37. A. Moroz and C. Sommers, “Photonic band gaps of three-dimensional face-centered cubic lattices,” J. Phys. Condens. Matter 11, 997–1008 (1999).
    [CrossRef]

1999 (5)

J. G. Fleming and S. Y. Lin, “Three-dimensional photonic crystal with a stop band from 1.35 to 1.95 μm,” Opt. Lett. 24, 49–51 (1999).
[CrossRef]

G. Subramania, K. Constant, R. Biswas, M. M. Sigalas, and K. M. Ho, “Optical photonic crystals fabricated from colloidal systems,” Appl. Phys. Lett. 74, 3933–3935 (1999).
[CrossRef]

S. G. Romanov, A. V. Fokin, and R. M. de la Rue, “Stop-band structure in complementary three-dimensional opal-based photonic crystals,” J. Phys. Condens. Matter 11, 3593–3600 (1999).
[CrossRef]

M. S. Thijssen, R. Sprik, J. E. G. J. Wijnhoven, M. Megens, T. Narayanan, A. Lagendijk, and W. L. Vos, “Inhibited light propagation and broadband reflection in photonic air-sphere crystals,” Phys. Rev. Lett. 83, 2730–2733 (1999).
[CrossRef]

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

1998 (8)

H. Míguez, F. Meseguer, C. López, Á. 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]

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

S. Y. Lin, J. G. Fleming, D. L. Hetherington, B. K. Smith, R. Biswas, K. M. Ho, M. M. Sigalas, W. Zubrzycki, S. R. Kurtz, and J. Bur, “A three-dimensional photonic crystal operating at infrared wavelengths,” Nature 394, 251–253 (1998).
[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]

A. A. Zakhidov, R. H. Baughman, Z. Iqbal, C. Cui, I. Khayrullin, S. O. Dantas, J. Marti, and V. G. Ralchenko, “Carbon structures with three-dimensional periodicity at optical wavelengths,” Science 282, 897–901 (1998).
[CrossRef] [PubMed]

A. van Blaaderen, “Opals in a new light,” Science 282, 887–888 (1998).
[CrossRef]

B. T. Holland, C. F. Blanford, and A. Stein, “Synthesis of macroporous minerals with highly ordered three-dimensional arrays of spherical voids,” Science 281, 538–540 (1998).
[CrossRef] [PubMed]

J. E. G. J. Wijnhoven and W. L. Vos, “Preparation of photonic crystals made of air spheres in titania,” Science 281, 802–804 (1998).
[CrossRef]

1997 (5)

J. D. Joannopoulos, P. R. Villeneuve, and S. Fan, “Photonic crystals,” Solid State Commun. 102, 165–173 (1997).
[CrossRef]

A. Imhof and D. J. Pine, “Ordered macroporous materials by emulsion templating,” Nature 389, 948–951 (1997).
[CrossRef]

O. D. Velev, T. A. Jede, R. F. Lobo, and A. M. Lenhoff, “Porous silica via colloidal crystallization,” Nature 389, 447–448 (1997).
[CrossRef]

H. Míguez, F. Meseguer, C. López, A. Mifsud, J. S. Moya, and L. Vázquez, “Evidence of fcc crystallization of SiO2 nanospheres,” Langmuir 13, 6009–6011 (1997).
[CrossRef]

V. N. Bogomolov, S. V. Gaponenko, I. N. Germanenko, A. M. Kapitonov, E. P. Petrov, N. V. Gaponenko, A. V. Prokofiev, A. N. Ponyavina, N. I. Silvanovich, and S. M. Samoilovich, “Photonic band gap phenomenon and optical properties of artificial opals,” Phys. Rev. E 55, 7619–7625 (1997).
[CrossRef]

1996 (1)

V. N. Astratov, Y. A. Vlasov, O. Z. Karimov, A. A. Kaplyanskii, Y. G. Musikhin, N. A. Bert, V. N. Bogomolov, and A. V. Prokofiev, “Photonic band gaps in 3D ordered fcc silica matrices,” Phys. Lett. A 222, 349–353 (1996).
[CrossRef]

1994 (5)

S. John and T. Quang, “Spontaneous emission near the edge of a photonic band gap,” Phys. Rev. A 50, 1764–1769 (1994).
[CrossRef] [PubMed]

E. Özbay, A. Abeyta, G. Tuttle, M. Tringides, R. Biswas, C. T. Chan, C. M. Soukoulis, and K. M. Ho, “Measurement of a three-dimensional photonic band gap in a crystal structure made of dielectric rods,” Phys. Rev. B 50, 1945–1948 (1994).
[CrossRef]

P. R. Villeneuve and M. Piché, “Photonic bandgaps: what is the best numerical representation of periodic structures?” J. Mod. Opt. 41, 241–256 (1994).
[CrossRef]

C. T. Chan, S. Datta, K. M. Ho, and C. M. Soukoulis, “A7 structure: a family of photonic crystals,” Phys. Rev. B 50, 1988–1991 (1994).
[CrossRef]

A. Moroz, “Inward and outward integral equations and the KKR method for photons,” J. Phys. Condens. Matter 6, 171–182 (1994).
[CrossRef]

1993 (2)

K. W. K. Shung and Y. C. Tsai, “Surface effects and band measurements in photonic crystals,” Phys. Rev. B 48, 11, 265–11, 269 (1993).
[CrossRef]

E. N. Economou and M. M. Sigalas, “Classical wave propagation in periodic structures: Cermet versus network topology,” Phys. Rev. B 48, 13, 434–13, 438 (1993).
[CrossRef]

1992 (2)

H. S. Sözüer, J. W. Haus, and R. Inguva, “Photonic bands: convergence problems with the plane wave method,” Phys. Rev. B 45, 13, 962–13, 972 (1992).
[CrossRef]

S. Datta, C. T. Chan, K. M. Ho, and C. M. Soukoulis, “Photonic band gaps in periodic dielectric structures: the scalar-wave approximation,” Phys. Rev. B 46, 10, 650–10, 656 (1992).
[CrossRef]

1991 (1)

E. Yablonovitch, T. J. Gmitter, and K. M. Leung, “Photonic band structure: the face-centered-cubic case employing nonspherical atoms,” Phys. Rev. Lett. 67, 2295–2298 (1991).
[CrossRef] [PubMed]

1990 (2)

K. M. Leung and Y. F. Liu, “Full vector wave calculation of photonic band structures in face-centered-cubic dielectric media,” Phys. Rev. Lett. 65, 2646–2649 (1990).
[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]

1987 (1)

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

1976 (1)

H. J. Monkhorst and J. D. Park, “Special points of Brillouin-zone integrations,” Phys. Rev. B 13, 5188–5192 (1976).
[CrossRef]

1975 (1)

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

1954 (1)

W. Kohn and N. Rostoker, “Solution of the Schrödinger equation in periodic lattices with an application to metallic lithium,” Phys. Rev. 94, 1111–1120 (1954).
[CrossRef]

Abeyta, A.

E. Özbay, A. Abeyta, G. Tuttle, M. Tringides, R. Biswas, C. T. Chan, C. M. Soukoulis, and K. M. Ho, “Measurement of a three-dimensional photonic band gap in a crystal structure made of dielectric rods,” Phys. Rev. B 50, 1945–1948 (1994).
[CrossRef]

Astratov, V. N.

V. N. Astratov, Y. A. Vlasov, O. Z. Karimov, A. A. Kaplyanskii, Y. G. Musikhin, N. A. Bert, V. N. Bogomolov, and A. V. Prokofiev, “Photonic band gaps in 3D ordered fcc silica matrices,” Phys. Lett. A 222, 349–353 (1996).
[CrossRef]

Baughman, R. H.

A. A. Zakhidov, R. H. Baughman, Z. Iqbal, C. Cui, I. Khayrullin, S. O. Dantas, J. Marti, and V. G. Ralchenko, “Carbon structures with three-dimensional periodicity at optical wavelengths,” Science 282, 897–901 (1998).
[CrossRef] [PubMed]

Bert, N. A.

V. N. Astratov, Y. A. Vlasov, O. Z. Karimov, A. A. Kaplyanskii, Y. G. Musikhin, N. A. Bert, V. N. Bogomolov, and A. V. Prokofiev, “Photonic band gaps in 3D ordered fcc silica matrices,” Phys. Lett. A 222, 349–353 (1996).
[CrossRef]

Biswas, R.

G. Subramania, K. Constant, R. Biswas, M. M. Sigalas, and K. M. Ho, “Optical photonic crystals fabricated from colloidal systems,” Appl. Phys. Lett. 74, 3933–3935 (1999).
[CrossRef]

S. Y. Lin, J. G. Fleming, D. L. Hetherington, B. K. Smith, R. Biswas, K. M. Ho, M. M. Sigalas, W. Zubrzycki, S. R. Kurtz, and J. Bur, “A three-dimensional photonic crystal operating at infrared wavelengths,” Nature 394, 251–253 (1998).
[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]

E. Özbay, A. Abeyta, G. Tuttle, M. Tringides, R. Biswas, C. T. Chan, C. M. Soukoulis, and K. M. Ho, “Measurement of a three-dimensional photonic band gap in a crystal structure made of dielectric rods,” Phys. Rev. B 50, 1945–1948 (1994).
[CrossRef]

Blanco, Á.

H. Míguez, F. Meseguer, C. López, Á. 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]

Blanford, C. F.

B. T. Holland, C. F. Blanford, and A. Stein, “Synthesis of macroporous minerals with highly ordered three-dimensional arrays of spherical voids,” Science 281, 538–540 (1998).
[CrossRef] [PubMed]

Bogomolov, V. N.

V. N. Bogomolov, S. V. Gaponenko, I. N. Germanenko, A. M. Kapitonov, E. P. Petrov, N. V. Gaponenko, A. V. Prokofiev, A. N. Ponyavina, N. I. Silvanovich, and S. M. Samoilovich, “Photonic band gap phenomenon and optical properties of artificial opals,” Phys. Rev. E 55, 7619–7625 (1997).
[CrossRef]

V. N. Astratov, Y. A. Vlasov, O. Z. Karimov, A. A. Kaplyanskii, Y. G. Musikhin, N. A. Bert, V. N. Bogomolov, and A. V. Prokofiev, “Photonic band gaps in 3D ordered fcc silica matrices,” Phys. Lett. A 222, 349–353 (1996).
[CrossRef]

Bur, J.

S. Y. Lin, J. G. Fleming, D. L. Hetherington, B. K. Smith, R. Biswas, K. M. Ho, M. M. Sigalas, W. Zubrzycki, S. R. Kurtz, and J. Bur, “A three-dimensional photonic crystal operating at infrared wavelengths,” Nature 394, 251–253 (1998).
[CrossRef]

Busch, K.

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

Chan, C. T.

E. Özbay, A. Abeyta, G. Tuttle, M. Tringides, R. Biswas, C. T. Chan, C. M. Soukoulis, and K. M. Ho, “Measurement of a three-dimensional photonic band gap in a crystal structure made of dielectric rods,” Phys. Rev. B 50, 1945–1948 (1994).
[CrossRef]

C. T. Chan, S. Datta, K. M. Ho, and C. M. Soukoulis, “A7 structure: a family of photonic crystals,” Phys. Rev. B 50, 1988–1991 (1994).
[CrossRef]

S. Datta, C. T. Chan, K. M. Ho, and C. M. Soukoulis, “Photonic band gaps in periodic dielectric structures: the scalar-wave approximation,” Phys. Rev. B 46, 10, 650–10, 656 (1992).
[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]

Constant, K.

G. Subramania, K. Constant, R. Biswas, M. M. Sigalas, and K. M. Ho, “Optical photonic crystals fabricated from colloidal systems,” Appl. Phys. Lett. 74, 3933–3935 (1999).
[CrossRef]

Cui, C.

A. A. Zakhidov, R. H. Baughman, Z. Iqbal, C. Cui, I. Khayrullin, S. O. Dantas, J. Marti, and V. G. Ralchenko, “Carbon structures with three-dimensional periodicity at optical wavelengths,” Science 282, 897–901 (1998).
[CrossRef] [PubMed]

Dantas, S. O.

A. A. Zakhidov, R. H. Baughman, Z. Iqbal, C. Cui, I. Khayrullin, S. O. Dantas, J. Marti, and V. G. Ralchenko, “Carbon structures with three-dimensional periodicity at optical wavelengths,” Science 282, 897–901 (1998).
[CrossRef] [PubMed]

Datta, S.

C. T. Chan, S. Datta, K. M. Ho, and C. M. Soukoulis, “A7 structure: a family of photonic crystals,” Phys. Rev. B 50, 1988–1991 (1994).
[CrossRef]

S. Datta, C. T. Chan, K. M. Ho, and C. M. Soukoulis, “Photonic band gaps in periodic dielectric structures: the scalar-wave approximation,” Phys. Rev. B 46, 10, 650–10, 656 (1992).
[CrossRef]

de la Rue, R. M.

S. G. Romanov, A. V. Fokin, and R. M. de la Rue, “Stop-band structure in complementary three-dimensional opal-based photonic crystals,” J. Phys. Condens. Matter 11, 3593–3600 (1999).
[CrossRef]

Economou, E. N.

E. N. Economou and M. M. Sigalas, “Classical wave propagation in periodic structures: Cermet versus network topology,” Phys. Rev. B 48, 13, 434–13, 438 (1993).
[CrossRef]

Fan, S.

J. D. Joannopoulos, P. R. Villeneuve, and S. Fan, “Photonic crystals,” Solid State Commun. 102, 165–173 (1997).
[CrossRef]

Fleming, J. G.

J. G. Fleming and S. Y. Lin, “Three-dimensional photonic crystal with a stop band from 1.35 to 1.95 μm,” Opt. Lett. 24, 49–51 (1999).
[CrossRef]

S. Y. Lin, J. G. Fleming, D. L. Hetherington, B. K. Smith, R. Biswas, K. M. Ho, M. M. Sigalas, W. Zubrzycki, S. R. Kurtz, and J. Bur, “A three-dimensional photonic crystal operating at infrared wavelengths,” Nature 394, 251–253 (1998).
[CrossRef]

Fokin, A. V.

S. G. Romanov, A. V. Fokin, and R. M. de la Rue, “Stop-band structure in complementary three-dimensional opal-based photonic crystals,” J. Phys. Condens. Matter 11, 3593–3600 (1999).
[CrossRef]

Fornés, V.

H. Míguez, F. Meseguer, C. López, Á. 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]

Gaponenko, N. V.

V. N. Bogomolov, S. V. Gaponenko, I. N. Germanenko, A. M. Kapitonov, E. P. Petrov, N. V. Gaponenko, A. V. Prokofiev, A. N. Ponyavina, N. I. Silvanovich, and S. M. Samoilovich, “Photonic band gap phenomenon and optical properties of artificial opals,” Phys. Rev. E 55, 7619–7625 (1997).
[CrossRef]

Gaponenko, S. V.

V. N. Bogomolov, S. V. Gaponenko, I. N. Germanenko, A. M. Kapitonov, E. P. Petrov, N. V. Gaponenko, A. V. Prokofiev, A. N. Ponyavina, N. I. Silvanovich, and S. M. Samoilovich, “Photonic band gap phenomenon and optical properties of artificial opals,” Phys. Rev. E 55, 7619–7625 (1997).
[CrossRef]

Germanenko, I. N.

V. N. Bogomolov, S. V. Gaponenko, I. N. Germanenko, A. M. Kapitonov, E. P. Petrov, N. V. Gaponenko, A. V. Prokofiev, A. N. Ponyavina, N. I. Silvanovich, and S. M. Samoilovich, “Photonic band gap phenomenon and optical properties of artificial opals,” Phys. Rev. E 55, 7619–7625 (1997).
[CrossRef]

Gmitter, T. J.

E. Yablonovitch, T. J. Gmitter, and K. M. Leung, “Photonic band structure: the face-centered-cubic case employing nonspherical atoms,” Phys. Rev. Lett. 67, 2295–2298 (1991).
[CrossRef] [PubMed]

Haus, J. W.

H. S. Sözüer, J. W. Haus, and R. Inguva, “Photonic bands: convergence problems with the plane wave method,” Phys. Rev. B 45, 13, 962–13, 972 (1992).
[CrossRef]

Hetherington, D. L.

S. Y. Lin, J. G. Fleming, D. L. Hetherington, B. K. Smith, R. Biswas, K. M. Ho, M. M. Sigalas, W. Zubrzycki, S. R. Kurtz, and J. Bur, “A three-dimensional photonic crystal operating at infrared wavelengths,” Nature 394, 251–253 (1998).
[CrossRef]

Ho, K. M.

G. Subramania, K. Constant, R. Biswas, M. M. Sigalas, and K. M. Ho, “Optical photonic crystals fabricated from colloidal systems,” Appl. Phys. Lett. 74, 3933–3935 (1999).
[CrossRef]

S. Y. Lin, J. G. Fleming, D. L. Hetherington, B. K. Smith, R. Biswas, K. M. Ho, M. M. Sigalas, W. Zubrzycki, S. R. Kurtz, and J. Bur, “A three-dimensional photonic crystal operating at infrared wavelengths,” Nature 394, 251–253 (1998).
[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]

C. T. Chan, S. Datta, K. M. Ho, and C. M. Soukoulis, “A7 structure: a family of photonic crystals,” Phys. Rev. B 50, 1988–1991 (1994).
[CrossRef]

E. Özbay, A. Abeyta, G. Tuttle, M. Tringides, R. Biswas, C. T. Chan, C. M. Soukoulis, and K. M. Ho, “Measurement of a three-dimensional photonic band gap in a crystal structure made of dielectric rods,” Phys. Rev. B 50, 1945–1948 (1994).
[CrossRef]

S. Datta, C. T. Chan, K. M. Ho, and C. M. Soukoulis, “Photonic band gaps in periodic dielectric structures: the scalar-wave approximation,” Phys. Rev. B 46, 10, 650–10, 656 (1992).
[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]

Holland, B. T.

B. T. Holland, C. F. Blanford, and A. Stein, “Synthesis of macroporous minerals with highly ordered three-dimensional arrays of spherical voids,” Science 281, 538–540 (1998).
[CrossRef] [PubMed]

Imhof, A.

A. Imhof and D. J. Pine, “Ordered macroporous materials by emulsion templating,” Nature 389, 948–951 (1997).
[CrossRef]

Inguva, R.

H. S. Sözüer, J. W. Haus, and R. Inguva, “Photonic bands: convergence problems with the plane wave method,” Phys. Rev. B 45, 13, 962–13, 972 (1992).
[CrossRef]

Iqbal, Z.

A. A. Zakhidov, R. H. Baughman, Z. Iqbal, C. Cui, I. Khayrullin, S. O. Dantas, J. Marti, and V. G. Ralchenko, “Carbon structures with three-dimensional periodicity at optical wavelengths,” Science 282, 897–901 (1998).
[CrossRef] [PubMed]

Jede, T. A.

O. D. Velev, T. A. Jede, R. F. Lobo, and A. M. Lenhoff, “Porous silica via colloidal crystallization,” Nature 389, 447–448 (1997).
[CrossRef]

Joannopoulos, J. D.

J. D. Joannopoulos, P. R. Villeneuve, and S. Fan, “Photonic crystals,” Solid State Commun. 102, 165–173 (1997).
[CrossRef]

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 and T. Quang, “Spontaneous emission near the edge of a photonic band gap,” Phys. Rev. A 50, 1764–1769 (1994).
[CrossRef] [PubMed]

Kapitonov, A. M.

V. N. Bogomolov, S. V. Gaponenko, I. N. Germanenko, A. M. Kapitonov, E. P. Petrov, N. V. Gaponenko, A. V. Prokofiev, A. N. Ponyavina, N. I. Silvanovich, and S. M. Samoilovich, “Photonic band gap phenomenon and optical properties of artificial opals,” Phys. Rev. E 55, 7619–7625 (1997).
[CrossRef]

Kaplyanskii, A. A.

V. N. Astratov, Y. A. Vlasov, O. Z. Karimov, A. A. Kaplyanskii, Y. G. Musikhin, N. A. Bert, V. N. Bogomolov, and A. V. Prokofiev, “Photonic band gaps in 3D ordered fcc silica matrices,” Phys. Lett. A 222, 349–353 (1996).
[CrossRef]

Karimov, O. Z.

V. N. Astratov, Y. A. Vlasov, O. Z. Karimov, A. A. Kaplyanskii, Y. G. Musikhin, N. A. Bert, V. N. Bogomolov, and A. V. Prokofiev, “Photonic band gaps in 3D ordered fcc silica matrices,” Phys. Lett. A 222, 349–353 (1996).
[CrossRef]

Khayrullin, I.

A. A. Zakhidov, R. H. Baughman, Z. Iqbal, C. Cui, I. Khayrullin, S. O. Dantas, J. Marti, and V. G. Ralchenko, “Carbon structures with three-dimensional periodicity at optical wavelengths,” Science 282, 897–901 (1998).
[CrossRef] [PubMed]

Kohn, W.

W. Kohn and N. Rostoker, “Solution of the Schrödinger equation in periodic lattices with an application to metallic lithium,” Phys. Rev. 94, 1111–1120 (1954).
[CrossRef]

Kurtz, S. R.

S. Y. Lin, J. G. Fleming, D. L. Hetherington, B. K. Smith, R. Biswas, K. M. Ho, M. M. Sigalas, W. Zubrzycki, S. R. Kurtz, and J. Bur, “A three-dimensional photonic crystal operating at infrared wavelengths,” Nature 394, 251–253 (1998).
[CrossRef]

Lagendijk, A.

M. S. Thijssen, R. Sprik, J. E. G. J. Wijnhoven, M. Megens, T. Narayanan, A. Lagendijk, and W. L. Vos, “Inhibited light propagation and broadband reflection in photonic air-sphere crystals,” Phys. Rev. Lett. 83, 2730–2733 (1999).
[CrossRef]

Lenhoff, A. M.

O. D. Velev, T. A. Jede, R. F. Lobo, and A. M. Lenhoff, “Porous silica via colloidal crystallization,” Nature 389, 447–448 (1997).
[CrossRef]

Leung, K. M.

E. Yablonovitch, T. J. Gmitter, and K. M. Leung, “Photonic band structure: the face-centered-cubic case employing nonspherical atoms,” Phys. Rev. Lett. 67, 2295–2298 (1991).
[CrossRef] [PubMed]

K. M. Leung and Y. F. Liu, “Full vector wave calculation of photonic band structures in face-centered-cubic dielectric media,” Phys. Rev. Lett. 65, 2646–2649 (1990).
[CrossRef] [PubMed]

Lin, S. Y.

J. G. Fleming and S. Y. Lin, “Three-dimensional photonic crystal with a stop band from 1.35 to 1.95 μm,” Opt. Lett. 24, 49–51 (1999).
[CrossRef]

S. Y. Lin, J. G. Fleming, D. L. Hetherington, B. K. Smith, R. Biswas, K. M. Ho, M. M. Sigalas, W. Zubrzycki, S. R. Kurtz, and J. Bur, “A three-dimensional photonic crystal operating at infrared wavelengths,” Nature 394, 251–253 (1998).
[CrossRef]

Liu, Y. F.

K. M. Leung and Y. F. Liu, “Full vector wave calculation of photonic band structures in face-centered-cubic dielectric media,” Phys. Rev. Lett. 65, 2646–2649 (1990).
[CrossRef] [PubMed]

Lobo, R. F.

O. D. Velev, T. A. Jede, R. F. Lobo, and A. M. Lenhoff, “Porous silica via colloidal crystallization,” Nature 389, 447–448 (1997).
[CrossRef]

López, C.

H. Míguez, F. Meseguer, C. López, Á. 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]

H. Míguez, F. Meseguer, C. López, A. Mifsud, J. S. Moya, and L. Vázquez, “Evidence of fcc crystallization of SiO2 nanospheres,” Langmuir 13, 6009–6011 (1997).
[CrossRef]

Marti, J.

A. A. Zakhidov, R. H. Baughman, Z. Iqbal, C. Cui, I. Khayrullin, S. O. Dantas, J. Marti, and V. G. Ralchenko, “Carbon structures with three-dimensional periodicity at optical wavelengths,” Science 282, 897–901 (1998).
[CrossRef] [PubMed]

Megens, M.

M. S. Thijssen, R. Sprik, J. E. G. J. Wijnhoven, M. Megens, T. Narayanan, A. Lagendijk, and W. L. Vos, “Inhibited light propagation and broadband reflection in photonic air-sphere crystals,” Phys. Rev. Lett. 83, 2730–2733 (1999).
[CrossRef]

Meseguer, F.

H. Míguez, F. Meseguer, C. López, Á. 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]

H. Míguez, F. Meseguer, C. López, A. Mifsud, J. S. Moya, and L. Vázquez, “Evidence of fcc crystallization of SiO2 nanospheres,” Langmuir 13, 6009–6011 (1997).
[CrossRef]

Mifsud, A.

H. Míguez, F. Meseguer, C. López, Á. 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]

H. Míguez, F. Meseguer, C. López, A. Mifsud, J. S. Moya, and L. Vázquez, “Evidence of fcc crystallization of SiO2 nanospheres,” Langmuir 13, 6009–6011 (1997).
[CrossRef]

Míguez, H.

H. Míguez, F. Meseguer, C. López, Á. 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]

H. Míguez, F. Meseguer, C. López, A. Mifsud, J. S. Moya, and L. Vázquez, “Evidence of fcc crystallization of SiO2 nanospheres,” Langmuir 13, 6009–6011 (1997).
[CrossRef]

Monkhorst, H. J.

H. J. Monkhorst and J. D. Park, “Special points of Brillouin-zone integrations,” Phys. Rev. B 13, 5188–5192 (1976).
[CrossRef]

Moroz, A.

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

A. Moroz, “Inward and outward integral equations and the KKR method for photons,” J. Phys. Condens. Matter 6, 171–182 (1994).
[CrossRef]

Moya, J. S.

H. Míguez, F. Meseguer, C. López, Á. 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]

H. Míguez, F. Meseguer, C. López, A. Mifsud, J. S. Moya, and L. Vázquez, “Evidence of fcc crystallization of SiO2 nanospheres,” Langmuir 13, 6009–6011 (1997).
[CrossRef]

Musikhin, Y. G.

V. N. Astratov, Y. A. Vlasov, O. Z. Karimov, A. A. Kaplyanskii, Y. G. Musikhin, N. A. Bert, V. N. Bogomolov, and A. V. Prokofiev, “Photonic band gaps in 3D ordered fcc silica matrices,” Phys. Lett. A 222, 349–353 (1996).
[CrossRef]

Narayanan, T.

M. S. Thijssen, R. Sprik, J. E. G. J. Wijnhoven, M. Megens, T. Narayanan, A. Lagendijk, and W. L. Vos, “Inhibited light propagation and broadband reflection in photonic air-sphere crystals,” Phys. Rev. Lett. 83, 2730–2733 (1999).
[CrossRef]

Özbay, E.

E. Özbay, A. Abeyta, G. Tuttle, M. Tringides, R. Biswas, C. T. Chan, C. M. Soukoulis, and K. M. Ho, “Measurement of a three-dimensional photonic band gap in a crystal structure made of dielectric rods,” Phys. Rev. B 50, 1945–1948 (1994).
[CrossRef]

Park, J. D.

H. J. Monkhorst and J. D. Park, “Special points of Brillouin-zone integrations,” Phys. Rev. B 13, 5188–5192 (1976).
[CrossRef]

Petrov, E. P.

V. N. Bogomolov, S. V. Gaponenko, I. N. Germanenko, A. M. Kapitonov, E. P. Petrov, N. V. Gaponenko, A. V. Prokofiev, A. N. Ponyavina, N. I. Silvanovich, and S. M. Samoilovich, “Photonic band gap phenomenon and optical properties of artificial opals,” Phys. Rev. E 55, 7619–7625 (1997).
[CrossRef]

Piché, M.

P. R. Villeneuve and M. Piché, “Photonic bandgaps: what is the best numerical representation of periodic structures?” J. Mod. Opt. 41, 241–256 (1994).
[CrossRef]

Pine, D. J.

A. Imhof and D. J. Pine, “Ordered macroporous materials by emulsion templating,” Nature 389, 948–951 (1997).
[CrossRef]

Ponyavina, A. N.

V. N. Bogomolov, S. V. Gaponenko, I. N. Germanenko, A. M. Kapitonov, E. P. Petrov, N. V. Gaponenko, A. V. Prokofiev, A. N. Ponyavina, N. I. Silvanovich, and S. M. Samoilovich, “Photonic band gap phenomenon and optical properties of artificial opals,” Phys. Rev. E 55, 7619–7625 (1997).
[CrossRef]

Prokofiev, A. V.

V. N. Bogomolov, S. V. Gaponenko, I. N. Germanenko, A. M. Kapitonov, E. P. Petrov, N. V. Gaponenko, A. V. Prokofiev, A. N. Ponyavina, N. I. Silvanovich, and S. M. Samoilovich, “Photonic band gap phenomenon and optical properties of artificial opals,” Phys. Rev. E 55, 7619–7625 (1997).
[CrossRef]

V. N. Astratov, Y. A. Vlasov, O. Z. Karimov, A. A. Kaplyanskii, Y. G. Musikhin, N. A. Bert, V. N. Bogomolov, and A. V. Prokofiev, “Photonic band gaps in 3D ordered fcc silica matrices,” Phys. Lett. A 222, 349–353 (1996).
[CrossRef]

Quang, T.

S. John and T. Quang, “Spontaneous emission near the edge of a photonic band gap,” Phys. Rev. A 50, 1764–1769 (1994).
[CrossRef] [PubMed]

Ralchenko, V. G.

A. A. Zakhidov, R. H. Baughman, Z. Iqbal, C. Cui, I. Khayrullin, S. O. Dantas, J. Marti, and V. G. Ralchenko, “Carbon structures with three-dimensional periodicity at optical wavelengths,” Science 282, 897–901 (1998).
[CrossRef] [PubMed]

Requena, J.

H. Míguez, F. Meseguer, C. López, Á. 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]

Romanov, S. G.

S. G. Romanov, A. V. Fokin, and R. M. de la Rue, “Stop-band structure in complementary three-dimensional opal-based photonic crystals,” J. Phys. Condens. Matter 11, 3593–3600 (1999).
[CrossRef]

Rostoker, N.

W. Kohn and N. Rostoker, “Solution of the Schrödinger equation in periodic lattices with an application to metallic lithium,” Phys. Rev. 94, 1111–1120 (1954).
[CrossRef]

Samoilovich, S. M.

V. N. Bogomolov, S. V. Gaponenko, I. N. Germanenko, A. M. Kapitonov, E. P. Petrov, N. V. Gaponenko, A. V. Prokofiev, A. N. Ponyavina, N. I. Silvanovich, and S. M. Samoilovich, “Photonic band gap phenomenon and optical properties of artificial opals,” Phys. Rev. E 55, 7619–7625 (1997).
[CrossRef]

Shung, K. W. K.

K. W. K. Shung and Y. C. Tsai, “Surface effects and band measurements in photonic crystals,” Phys. Rev. B 48, 11, 265–11, 269 (1993).
[CrossRef]

Sigalas, M. M.

G. Subramania, K. Constant, R. Biswas, M. M. Sigalas, and K. M. Ho, “Optical photonic crystals fabricated from colloidal systems,” Appl. Phys. Lett. 74, 3933–3935 (1999).
[CrossRef]

S. Y. Lin, J. G. Fleming, D. L. Hetherington, B. K. Smith, R. Biswas, K. M. Ho, M. M. Sigalas, W. Zubrzycki, S. R. Kurtz, and J. Bur, “A three-dimensional photonic crystal operating at infrared wavelengths,” Nature 394, 251–253 (1998).
[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]

E. N. Economou and M. M. Sigalas, “Classical wave propagation in periodic structures: Cermet versus network topology,” Phys. Rev. B 48, 13, 434–13, 438 (1993).
[CrossRef]

Silvanovich, N. I.

V. N. Bogomolov, S. V. Gaponenko, I. N. Germanenko, A. M. Kapitonov, E. P. Petrov, N. V. Gaponenko, A. V. Prokofiev, A. N. Ponyavina, N. I. Silvanovich, and S. M. Samoilovich, “Photonic band gap phenomenon and optical properties of artificial opals,” Phys. Rev. E 55, 7619–7625 (1997).
[CrossRef]

Smith, B. K.

S. Y. Lin, J. G. Fleming, D. L. Hetherington, B. K. Smith, R. Biswas, K. M. Ho, M. M. Sigalas, W. Zubrzycki, S. R. Kurtz, and J. Bur, “A three-dimensional photonic crystal operating at infrared wavelengths,” Nature 394, 251–253 (1998).
[CrossRef]

Sommers, C.

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

Soukoulis, C. M.

C. T. Chan, S. Datta, K. M. Ho, and C. M. Soukoulis, “A7 structure: a family of photonic crystals,” Phys. Rev. B 50, 1988–1991 (1994).
[CrossRef]

E. Özbay, A. Abeyta, G. Tuttle, M. Tringides, R. Biswas, C. T. Chan, C. M. Soukoulis, and K. M. Ho, “Measurement of a three-dimensional photonic band gap in a crystal structure made of dielectric rods,” Phys. Rev. B 50, 1945–1948 (1994).
[CrossRef]

S. Datta, C. T. Chan, K. M. Ho, and C. M. Soukoulis, “Photonic band gaps in periodic dielectric structures: the scalar-wave approximation,” Phys. Rev. B 46, 10, 650–10, 656 (1992).
[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]

Sözüer, H. S.

H. S. Sözüer, J. W. Haus, and R. Inguva, “Photonic bands: convergence problems with the plane wave method,” Phys. Rev. B 45, 13, 962–13, 972 (1992).
[CrossRef]

Sprik, R.

M. S. Thijssen, R. Sprik, J. E. G. J. Wijnhoven, M. Megens, T. Narayanan, A. Lagendijk, and W. L. Vos, “Inhibited light propagation and broadband reflection in photonic air-sphere crystals,” Phys. Rev. Lett. 83, 2730–2733 (1999).
[CrossRef]

Stein, A.

B. T. Holland, C. F. Blanford, and A. Stein, “Synthesis of macroporous minerals with highly ordered three-dimensional arrays of spherical voids,” Science 281, 538–540 (1998).
[CrossRef] [PubMed]

Subramania, G.

G. Subramania, K. Constant, R. Biswas, M. M. Sigalas, and K. M. Ho, “Optical photonic crystals fabricated from colloidal systems,” Appl. Phys. Lett. 74, 3933–3935 (1999).
[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]

Thijssen, M. S.

M. S. Thijssen, R. Sprik, J. E. G. J. Wijnhoven, M. Megens, T. Narayanan, A. Lagendijk, and W. L. Vos, “Inhibited light propagation and broadband reflection in photonic air-sphere crystals,” Phys. Rev. Lett. 83, 2730–2733 (1999).
[CrossRef]

Tringides, M.

E. Özbay, A. Abeyta, G. Tuttle, M. Tringides, R. Biswas, C. T. Chan, C. M. Soukoulis, and K. M. Ho, “Measurement of a three-dimensional photonic band gap in a crystal structure made of dielectric rods,” Phys. Rev. B 50, 1945–1948 (1994).
[CrossRef]

Tsai, Y. C.

K. W. K. Shung and Y. C. Tsai, “Surface effects and band measurements in photonic crystals,” Phys. Rev. B 48, 11, 265–11, 269 (1993).
[CrossRef]

Tuttle, G.

E. Özbay, A. Abeyta, G. Tuttle, M. Tringides, R. Biswas, C. T. Chan, C. M. Soukoulis, and K. M. Ho, “Measurement of a three-dimensional photonic band gap in a crystal structure made of dielectric rods,” Phys. Rev. B 50, 1945–1948 (1994).
[CrossRef]

van Blaaderen, A.

A. van Blaaderen, “Opals in a new light,” Science 282, 887–888 (1998).
[CrossRef]

Vázquez, L.

H. Míguez, F. Meseguer, C. López, A. Mifsud, J. S. Moya, and L. Vázquez, “Evidence of fcc crystallization of SiO2 nanospheres,” Langmuir 13, 6009–6011 (1997).
[CrossRef]

Velev, O. D.

O. D. Velev, T. A. Jede, R. F. Lobo, and A. M. Lenhoff, “Porous silica via colloidal crystallization,” Nature 389, 447–448 (1997).
[CrossRef]

Villeneuve, P. R.

J. D. Joannopoulos, P. R. Villeneuve, and S. Fan, “Photonic crystals,” Solid State Commun. 102, 165–173 (1997).
[CrossRef]

P. R. Villeneuve and M. Piché, “Photonic bandgaps: what is the best numerical representation of periodic structures?” J. Mod. Opt. 41, 241–256 (1994).
[CrossRef]

Vlasov, Y. A.

V. N. Astratov, Y. A. Vlasov, O. Z. Karimov, A. A. Kaplyanskii, Y. G. Musikhin, N. A. Bert, V. N. Bogomolov, and A. V. Prokofiev, “Photonic band gaps in 3D ordered fcc silica matrices,” Phys. Lett. A 222, 349–353 (1996).
[CrossRef]

Vos, W. L.

M. S. Thijssen, R. Sprik, J. E. G. J. Wijnhoven, M. Megens, T. Narayanan, A. Lagendijk, and W. L. Vos, “Inhibited light propagation and broadband reflection in photonic air-sphere crystals,” Phys. Rev. Lett. 83, 2730–2733 (1999).
[CrossRef]

J. E. G. J. Wijnhoven and W. L. Vos, “Preparation of photonic crystals made of air spheres in titania,” Science 281, 802–804 (1998).
[CrossRef]

Wijnhoven, J. E. G. J.

M. S. Thijssen, R. Sprik, J. E. G. J. Wijnhoven, M. Megens, T. Narayanan, A. Lagendijk, and W. L. Vos, “Inhibited light propagation and broadband reflection in photonic air-sphere crystals,” Phys. Rev. Lett. 83, 2730–2733 (1999).
[CrossRef]

J. E. G. J. Wijnhoven and W. L. Vos, “Preparation of photonic crystals made of air spheres in titania,” Science 281, 802–804 (1998).
[CrossRef]

Yablonovitch, E.

E. Yablonovitch, T. J. Gmitter, and K. M. Leung, “Photonic band structure: the face-centered-cubic case employing nonspherical atoms,” Phys. Rev. Lett. 67, 2295–2298 (1991).
[CrossRef] [PubMed]

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

Zakhidov, A. A.

A. A. Zakhidov, R. H. Baughman, Z. Iqbal, C. Cui, I. Khayrullin, S. O. Dantas, J. Marti, and V. G. Ralchenko, “Carbon structures with three-dimensional periodicity at optical wavelengths,” Science 282, 897–901 (1998).
[CrossRef] [PubMed]

Zubrzycki, W.

S. Y. Lin, J. G. Fleming, D. L. Hetherington, B. K. Smith, R. Biswas, K. M. Ho, M. M. Sigalas, W. Zubrzycki, S. R. Kurtz, and J. Bur, “A three-dimensional photonic crystal operating at infrared wavelengths,” Nature 394, 251–253 (1998).
[CrossRef]

Adv. Mater. (1)

H. Míguez, F. Meseguer, C. López, Á. 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]

Appl. Phys. Lett. (1)

G. Subramania, K. Constant, R. Biswas, M. M. Sigalas, and K. M. Ho, “Optical photonic crystals fabricated from colloidal systems,” Appl. Phys. Lett. 74, 3933–3935 (1999).
[CrossRef]

J. Mod. Opt. (1)

P. R. Villeneuve and M. Piché, “Photonic bandgaps: what is the best numerical representation of periodic structures?” J. Mod. Opt. 41, 241–256 (1994).
[CrossRef]

J. Phys. Condens. Matter (3)

A. Moroz, “Inward and outward integral equations and the KKR method for photons,” J. Phys. Condens. Matter 6, 171–182 (1994).
[CrossRef]

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Figures (6)

Fig. 1
Fig. 1

(a) Three-dimensional visualization of an fcc air-sphere crystal with nonoverlapping air spheres, each of them connected to all of its 12 nearest neighbors by cylindrical air tunnels. The particular structure shown here has geometrical parameters, which for a silicon background (gray) optimize the bandgap (see Section 3). (b) Schematic cross section of the structure in (a) with definitions of the lengths a, R, and Rc indicated.

Fig. 2
Fig. 2

First Brillouin zone for the fcc lattice (body-centered cubic in reciprocal space). The important symmetry points are denoted by the conventional symbols.

Fig. 3
Fig. 3

Photonic band structure of a closely packed fcc crystal of air spheres in silicon, calculated with N=339 plane waves. This particular example has no cylinders connecting neighboring spheres.

Fig. 4
Fig. 4

Relative width of the full photonic bandgap between bands eight and nine in the fcc inverted opals as a function of Rc/a. The background material is silicon (Si;n=3.415). The number of plane waves used is N=339. The four curves have been calculated for (a) R/a=0.3437, (b) R/a=0.3486, (c) R/a=0.3504, and (d) R/a=0.3536. For Rc=0 these values correspond to ϕ=68%, ϕ=71%, ϕ=72%, and ϕ=74%, respectively.

Fig. 5
Fig. 5

Photonic band structure of an fcc inverted opal with silicon (n=3.415) as the dielectric medium and with geometrical parameters R/a=0.3201 and Rc/R=0.398. These parameters optimize the relative width of the full gap between the eighth and ninth bands to Δω/ω0=9.59% at ω0/2π=0.746c/a. The volume-filling fraction of air spheres and cylinders in this structure is ϕ=66.3%. The number of plane waves used is N=1037.

Fig. 6
Fig. 6

Density of states (DOS) corresponding to the photonic band structure depicted in Fig. 5.

Equations (23)

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η(r)=1(r)=m ηm exp(-igm·r),
ηm=1ΩΩη(r)exp(igm·r)dr,
×[η(r)×H]=-1c22Ht2,
H(r,t)=exp(iωt)mkλ=13 hmλ(k)uˆmλ exp(-ikm·r),
l klkmηm-luˆm2·uˆl2-uˆm2·uˆl1-uˆm1·uˆl2uˆm1·uˆl1hl1(k)hl2(k)
=ωc2hm1(k)hm2(k).
Mml=klkmηm-luˆm2·uˆl2-uˆm2·uˆl1-uˆm1·uˆl2uˆm1·uˆl1.
χm=1ΩΩ χ(r)exp(igm·r)dr,
m=δm,0+χm.
m,mm-m.
ηm,mηm-m=m,m-1.
E=SB=1+χS1+χB1+XE
XE=χS-χB1+χB.
ϕ=-803π(R/a)3+12π2(Rc/a)2+32πR2-Rc2a3.
Qmρ=[gmz2+½(gmx±gmy)2]1/2,
Qmz=½ 2(gmxgmy);
χm=XE16πR3a3S(gmR)+QmI(Qm)
S(x)sin x-x cos xx3.
I(Qm)=8 φ=02π ρ=0Rc/a z=[(R/a)2-ρ2]1/21/42×ρ exp(iρQmρ cos φ)×cos(Qmzz)dρdzdφ,
I(Qm)=16π 0Rc/a ρJ0(ρQmρ)×{1/42-[(R/a)2-ρ2]1/2}dρ
I(Qm)=16πQmz0Rc/a ρJ0(ρQmρ)sinQmz42-sin{Qmz[(R/a)2-ρ2]1/2}dρ
Δωω0=2 ω+-ω-ω++ω-.
f[df/d(R/a),df/d(Rc/R)]

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