Abstract

The unusual surface plasmon modes and switching bandgap of three-dimensional (3D) photonic crystals (PCs) with pyrochlore lattices that are composed of core isotropic positive-index dielectric spheres surrounded by epsilon-negative (ENG) material shells inserted in the air are theoretically investigated in detail based on the plane wave expansion method. Numerical simulations show that the proposed double-shell structure can obtain complete photonic band gaps (PBGs) and a flatbands region. Compared to the conventional lattices, such as diamond, face-centered-cubic, body-centered-cubic, and simple-cubic lattices, a larger PBG can be achieved in the pyrochlore arrangement. It is noticed that the flatbands region is determined by the existence of surface plasmon modes. If the thickness of the ENG material shell is larger than a threshold value, the band structures of such 3D PCs will be similar to those obtained from the same structure containing pure ENG material spheres. In this case, the inserted core spheres will also not affect the band structures. It is also provided that the upper edge of the flatbands region does not depend on the topology of the lattice. Our results also demonstrate that the PBG can be manipulated by the radius of the core dielectric sphere, the dielectric constant of ENG materials, and the electronic plasma frequency, respectively. This means that the PBG can be obtained by replacing the pure ENG material spheres with such double-shell structures to save the material in the realization. Thus, such proposed 3D PCs offer a novel way to realize the potential applications.

© 2014 Optical Society of America

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    [CrossRef]
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    [CrossRef]

2013

H. F. Zhang, S. B. Liu, and X. K. Kong, “Dispersion properties of three-dimensional plasma photonic crystals in Diamond lattice arrangement,” J. Lightwave Technol. 31, 1694–1702 (2013).
[CrossRef]

H. F. Zhang, S. B. Liu, X. K. Kong, C. Chen, and B. R. Bian, “The characteristics of photonic band gaps for three-dimensional unmagnetized dielectric plasma photonic crystals with simple-cubic lattice,” Opt. Commun. 288, 82–90 (2013).
[CrossRef]

H. F. Zhang, S. B. Liu, and X. K. Kong, “Properties of anisotropic photonic band gaps in three-dimensional plasma photonic crystals containing the uniaxial material with different lattices,” Prog. Electromagn. Res. 141, 267–289 (2013).
[CrossRef]

H. F. Zhang, S. B. Liu, and X. K. Kong, “Investigation of Faraday effects in photonic band gap for tunable three-dimensional magnetized plasma photonic crystals containing the anisotropic material in diamond arrangement,” J. Electromagn. Wave Appl. 27, 1776–1791 (2013).
[CrossRef]

H. F. Zhang, S. B. Liu, and X. K. Kong, “Study of the dispersive properties of three-dimensional photonic crystals with diamond lattices containing metamaterials,” Laser Phys. 23, 105815 (2013).
[CrossRef]

H. F. Zhang, S. B. Liu, and X. K. Kong, “Investigating the dispersive properties of the three-dimensional photonic crystals with face-centered-cubic lattices containing epsilon-negative materials,” Appl. Phys. B 112, 553–563 (2013).
[CrossRef]

2012

M. Lou, Q. H. Liu, and Z. Li, “Spectral element method for band structures of three-dimensional anisotropic photonic crystals,” Phys. Rev. E 80, 56702 (2012).

H. F. Zhang, S. B. Liu, X. K. Kong, L. Zou, C. Z. Li, and W. S. Qing, “Enhancement of omnidirectional photonic band gaps in one-dimensional dielectric plasma photonic crystals with a matching layer,” Phys. Plasmas 19, 022103 (2012).
[CrossRef]

H. F. Zhang, S. B. Liu, X. K. Kong, B. R. Bian, and X. Zhao, “Properties of omnidirectional photonic band gaps in Fibonacci quasi-periodic one-dimensional superconductor photonic crystals,” Prog. Electromagn. Res. B 40, 415–431 (2012).
[CrossRef]

2011

H. F. Zhang, S. B. Liu, X. K. Kong, L. Zhou, C. Z. Li, and B. R. Bo, “Comment on “Photonic bands in two-dimensional microplasma array. I. Theoretical derivation of band structures of electromagnetic wave” [J. Appl. Phys. 101, 073304 (2007)],” J. Appl. Phys. 110, 026104 (2011).
[CrossRef]

2010

2009

2008

2007

P. Chiang, C. Yu, and H. Chang, “Analysis of two-dimensional photonic crystals using a mutildomain pseudospectral method,” Phys. Rev. E 75, 026703 (2007).
[CrossRef]

2006

A. J. Garcia-Adeva, “Band structure of photonic crystals with the symmetry of a pyrochlore lattice,” Phys. Rev. B 73, 073107 (2006).
[CrossRef]

N. Krumbholz, K. Gerlach, F. Rutz, M. Koch, R. Piesiewicz, T. Kürner, and D. Mittleman, “Ominidrectional terahertz mirror: a key element for future terahertz communication systems,” Appl. Phys. Lett. 88, 202905 (2006).
[CrossRef]

2005

K. Xu, X. Zheng, C. Li, and W. She, “Design of omnidirectional and multiple channeled filters using one-dimensional photonic crystals containing a defect layer with a negative refractive index,” Phys. Rev. E 71, 066604 (2005).
[CrossRef]

2004

L. Wang, H. Chen, and S. Zhu, “Omnidirectional gap and defect mode of one-dimensional photonic crystals with single-negative materials,” Phys. Rev. B 70, 245102 (2004).
[CrossRef]

M. Kamp, T. Happ, S. Mahnkopf, G. Duan, S. Anand, and A. Forchel, “Semiconductor photonic crystals for optoelectronics,” Phys. E 21, 802–808 (2004).
[CrossRef]

2003

N. Malkova, S. Kim, T. Dilazaro, and V. Gopalan, “Symmetrical analysis of complex two-dimensional hexagonal photonic crystals,” Phys. Rev. B 67, 125203 (2003).
[CrossRef]

S. Jun, Y. S. Cho, and S. Im, “Moving least-square method for the band-structure calculation of 2D photonic crystals,” Opt. Express 11, 541–551 (2003).
[CrossRef]

2001

Z. Wang, C. T. Chan, W. Zhang, N. Ming, and P. Sheng, “Three-dimensional self-assembly of metal nanoparticles: possible photonic crystal with a complete gap below the plasma frequency,” Phys. Rev. B 64, 113108 (2001).
[CrossRef]

2000

C. T. Chan, W. Y. Zhang, Z. L. Wang, X. Y. Lei, D. Zheng, W. Y. Tam, and P. Sheng, “Photonic band gaps from metallo-dielectric spheres,” Phys. B 279, 150–154 (2000).

W. Y. Zhang, X. Y. Lei, Z. L. Wang, D. G. Zheng, W. Y. Tam, C. T. Chan, and P. Sheng,. “Roubust photonic band gap from tunable scatterers,” Phys. Rev. Lett. 84, 2853–2856 (2000).
[CrossRef]

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett. 84, 4184–4187 (2000).
[CrossRef]

J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85, 3966–3969 (2000).
[CrossRef]

1999

A. Moroz, “Three-dimensional complete photonic-band-gap structure in the visible,” Phys. Rev. Lett. 83, 5274–5277 (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

V. Kuzmiak and A. A. Maradudin, “Distribution of electromagnetic field and group velocities in two-dimensional periodic systems with dissipative metallic components,” Phy. Rev. B 58, 7230–7251 (1998).
[CrossRef]

Z. Y. Li, J. Wang, and B. Y. Gu, “Creation of partial band gaps in anisotropic photonic-band-gap structures,” Phys. Rev. B 58, 3721–3729 (1998).
[CrossRef]

1993

1992

H. S. Sözüer, J. W. Haus, and R. Inguva, “Photonic bands: convergence problems with the plane-wave method,” Phys. Rev. B 5, 13962 (1992).
[CrossRef]

1987

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

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

1968

V. G. Veselago, “The electrodynamics of substance with simultaneously negative values of ε and μ,” Sov. Phys. Uspekhi 10, 509–514 (1968).

Anand, S.

M. Kamp, T. Happ, S. Mahnkopf, G. Duan, S. Anand, and A. Forchel, “Semiconductor photonic crystals for optoelectronics,” Phys. E 21, 802–808 (2004).
[CrossRef]

Aryal, D. P.

D. P. Aryal, K. L. Tsakmakidis, and O. Hess, “Complete bandgap switching in photonic crystals,” J. New Phys. 11, 073011 (2009).
[CrossRef]

Aydin, K.

Bian, B. R.

H. F. Zhang, S. B. Liu, X. K. Kong, C. Chen, and B. R. Bian, “The characteristics of photonic band gaps for three-dimensional unmagnetized dielectric plasma photonic crystals with simple-cubic lattice,” Opt. Commun. 288, 82–90 (2013).
[CrossRef]

H. F. Zhang, S. B. Liu, X. K. Kong, B. R. Bian, and X. Zhao, “Properties of omnidirectional photonic band gaps in Fibonacci quasi-periodic one-dimensional superconductor photonic crystals,” Prog. Electromagn. Res. B 40, 415–431 (2012).
[CrossRef]

Bo, B. R.

H. F. Zhang, S. B. Liu, X. K. Kong, L. Zhou, C. Z. Li, and B. R. Bo, “Comment on “Photonic bands in two-dimensional microplasma array. I. Theoretical derivation of band structures of electromagnetic wave” [J. Appl. Phys. 101, 073304 (2007)],” J. Appl. Phys. 110, 026104 (2011).
[CrossRef]

Chan, C. T.

Z. Wang, C. T. Chan, W. Zhang, N. Ming, and P. Sheng, “Three-dimensional self-assembly of metal nanoparticles: possible photonic crystal with a complete gap below the plasma frequency,” Phys. Rev. B 64, 113108 (2001).
[CrossRef]

W. Y. Zhang, X. Y. Lei, Z. L. Wang, D. G. Zheng, W. Y. Tam, C. T. Chan, and P. Sheng,. “Roubust photonic band gap from tunable scatterers,” Phys. Rev. Lett. 84, 2853–2856 (2000).
[CrossRef]

C. T. Chan, W. Y. Zhang, Z. L. Wang, X. Y. Lei, D. Zheng, W. Y. Tam, and P. Sheng, “Photonic band gaps from metallo-dielectric spheres,” Phys. B 279, 150–154 (2000).

Chang, H.

P. Chiang, C. Yu, and H. Chang, “Analysis of two-dimensional photonic crystals using a mutildomain pseudospectral method,” Phys. Rev. E 75, 026703 (2007).
[CrossRef]

Chen, C.

H. F. Zhang, S. B. Liu, X. K. Kong, C. Chen, and B. R. Bian, “The characteristics of photonic band gaps for three-dimensional unmagnetized dielectric plasma photonic crystals with simple-cubic lattice,” Opt. Commun. 288, 82–90 (2013).
[CrossRef]

Chen, H.

L. Wang, H. Chen, and S. Zhu, “Omnidirectional gap and defect mode of one-dimensional photonic crystals with single-negative materials,” Phys. Rev. B 70, 245102 (2004).
[CrossRef]

Chen, Y.

Chiang, P.

P. Chiang, C. Yu, and H. Chang, “Analysis of two-dimensional photonic crystals using a mutildomain pseudospectral method,” Phys. Rev. E 75, 026703 (2007).
[CrossRef]

Cho, Y. S.

Deng, X. H.

X. H. Deng, N. H. Liu, J. T. Liu, Q. H. Liao, and T. B. Yu, “Enlargement of polarization-independent omnidirectional band gaps in the photonic heterostrucutures containing single-negative materials,” J. Opt. Soc. Am. B 27, 1174–1178 (2010).
[CrossRef]

X. H. Deng, J. T. Liu, J. H. Huang, L. Zou, and N. H. Liu, “Omnidirectional band gap in Fibonacci quasicrystal containing single-negative materials,” J. Phys. Condens. Matter 22, 055403 (2010).
[CrossRef]

Dilazaro, T.

N. Malkova, S. Kim, T. Dilazaro, and V. Gopalan, “Symmetrical analysis of complex two-dimensional hexagonal photonic crystals,” Phys. Rev. B 67, 125203 (2003).
[CrossRef]

Duan, G.

M. Kamp, T. Happ, S. Mahnkopf, G. Duan, S. Anand, and A. Forchel, “Semiconductor photonic crystals for optoelectronics,” Phys. E 21, 802–808 (2004).
[CrossRef]

Economou, E. N.

Forchel, A.

M. Kamp, T. Happ, S. Mahnkopf, G. Duan, S. Anand, and A. Forchel, “Semiconductor photonic crystals for optoelectronics,” Phys. E 21, 802–808 (2004).
[CrossRef]

Garcia-Adeva, A. J.

A. J. Garcia-Adeva, “Band structure of photonic crystals with the symmetry of a pyrochlore lattice,” Phys. Rev. B 73, 073107 (2006).
[CrossRef]

Gerlach, K.

N. Krumbholz, K. Gerlach, F. Rutz, M. Koch, R. Piesiewicz, T. Kürner, and D. Mittleman, “Ominidrectional terahertz mirror: a key element for future terahertz communication systems,” Appl. Phys. Lett. 88, 202905 (2006).
[CrossRef]

Gopalan, V.

N. Malkova, S. Kim, T. Dilazaro, and V. Gopalan, “Symmetrical analysis of complex two-dimensional hexagonal photonic crystals,” Phys. Rev. B 67, 125203 (2003).
[CrossRef]

Gu, B. Y.

Z. Y. Li, J. Wang, and B. Y. Gu, “Creation of partial band gaps in anisotropic photonic-band-gap structures,” Phys. Rev. B 58, 3721–3729 (1998).
[CrossRef]

Haggans, C. W.

Happ, T.

M. Kamp, T. Happ, S. Mahnkopf, G. Duan, S. Anand, and A. Forchel, “Semiconductor photonic crystals for optoelectronics,” Phys. E 21, 802–808 (2004).
[CrossRef]

Haus, J. W.

H. S. Sözüer, J. W. Haus, and R. Inguva, “Photonic bands: convergence problems with the plane-wave method,” Phys. Rev. B 5, 13962 (1992).
[CrossRef]

Hess, O.

D. P. Aryal, K. L. Tsakmakidis, and O. Hess, “Complete bandgap switching in photonic crystals,” J. New Phys. 11, 073011 (2009).
[CrossRef]

Huang, J. H.

X. H. Deng, J. T. Liu, J. H. Huang, L. Zou, and N. H. Liu, “Omnidirectional band gap in Fibonacci quasicrystal containing single-negative materials,” J. Phys. Condens. Matter 22, 055403 (2010).
[CrossRef]

Im, S.

Inguva, R.

H. S. Sözüer, J. W. Haus, and R. Inguva, “Photonic bands: convergence problems with the plane-wave method,” Phys. Rev. B 5, 13962 (1992).
[CrossRef]

Joannopoulos, J. J.

J. J. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals: Molding the Flow of Light (Princeton University, 1995).

John, S.

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

Jun, S.

Kafesaki, M.

Kamp, M.

M. Kamp, T. Happ, S. Mahnkopf, G. Duan, S. Anand, and A. Forchel, “Semiconductor photonic crystals for optoelectronics,” Phys. E 21, 802–808 (2004).
[CrossRef]

Kim, S.

N. Malkova, S. Kim, T. Dilazaro, and V. Gopalan, “Symmetrical analysis of complex two-dimensional hexagonal photonic crystals,” Phys. Rev. B 67, 125203 (2003).
[CrossRef]

Koch, M.

N. Krumbholz, K. Gerlach, F. Rutz, M. Koch, R. Piesiewicz, T. Kürner, and D. Mittleman, “Ominidrectional terahertz mirror: a key element for future terahertz communication systems,” Appl. Phys. Lett. 88, 202905 (2006).
[CrossRef]

Kockaert, P.

Kong, X. K.

H. F. Zhang, S. B. Liu, and X. K. Kong, “Dispersion properties of three-dimensional plasma photonic crystals in Diamond lattice arrangement,” J. Lightwave Technol. 31, 1694–1702 (2013).
[CrossRef]

H. F. Zhang, S. B. Liu, and X. K. Kong, “Study of the dispersive properties of three-dimensional photonic crystals with diamond lattices containing metamaterials,” Laser Phys. 23, 105815 (2013).
[CrossRef]

H. F. Zhang, S. B. Liu, and X. K. Kong, “Investigating the dispersive properties of the three-dimensional photonic crystals with face-centered-cubic lattices containing epsilon-negative materials,” Appl. Phys. B 112, 553–563 (2013).
[CrossRef]

H. F. Zhang, S. B. Liu, and X. K. Kong, “Investigation of Faraday effects in photonic band gap for tunable three-dimensional magnetized plasma photonic crystals containing the anisotropic material in diamond arrangement,” J. Electromagn. Wave Appl. 27, 1776–1791 (2013).
[CrossRef]

H. F. Zhang, S. B. Liu, X. K. Kong, C. Chen, and B. R. Bian, “The characteristics of photonic band gaps for three-dimensional unmagnetized dielectric plasma photonic crystals with simple-cubic lattice,” Opt. Commun. 288, 82–90 (2013).
[CrossRef]

H. F. Zhang, S. B. Liu, and X. K. Kong, “Properties of anisotropic photonic band gaps in three-dimensional plasma photonic crystals containing the uniaxial material with different lattices,” Prog. Electromagn. Res. 141, 267–289 (2013).
[CrossRef]

H. F. Zhang, S. B. Liu, X. K. Kong, B. R. Bian, and X. Zhao, “Properties of omnidirectional photonic band gaps in Fibonacci quasi-periodic one-dimensional superconductor photonic crystals,” Prog. Electromagn. Res. B 40, 415–431 (2012).
[CrossRef]

H. F. Zhang, S. B. Liu, X. K. Kong, L. Zou, C. Z. Li, and W. S. Qing, “Enhancement of omnidirectional photonic band gaps in one-dimensional dielectric plasma photonic crystals with a matching layer,” Phys. Plasmas 19, 022103 (2012).
[CrossRef]

H. F. Zhang, S. B. Liu, X. K. Kong, L. Zhou, C. Z. Li, and B. R. Bo, “Comment on “Photonic bands in two-dimensional microplasma array. I. Theoretical derivation of band structures of electromagnetic wave” [J. Appl. Phys. 101, 073304 (2007)],” J. Appl. Phys. 110, 026104 (2011).
[CrossRef]

Koschny, T.

Krumbholz, N.

N. Krumbholz, K. Gerlach, F. Rutz, M. Koch, R. Piesiewicz, T. Kürner, and D. Mittleman, “Ominidrectional terahertz mirror: a key element for future terahertz communication systems,” Appl. Phys. Lett. 88, 202905 (2006).
[CrossRef]

Kürner, T.

N. Krumbholz, K. Gerlach, F. Rutz, M. Koch, R. Piesiewicz, T. Kürner, and D. Mittleman, “Ominidrectional terahertz mirror: a key element for future terahertz communication systems,” Appl. Phys. Lett. 88, 202905 (2006).
[CrossRef]

Kuzmiak, V.

V. Kuzmiak and A. A. Maradudin, “Distribution of electromagnetic field and group velocities in two-dimensional periodic systems with dissipative metallic components,” Phy. Rev. B 58, 7230–7251 (1998).
[CrossRef]

Lei, X. Y.

C. T. Chan, W. Y. Zhang, Z. L. Wang, X. Y. Lei, D. Zheng, W. Y. Tam, and P. Sheng, “Photonic band gaps from metallo-dielectric spheres,” Phys. B 279, 150–154 (2000).

W. Y. Zhang, X. Y. Lei, Z. L. Wang, D. G. Zheng, W. Y. Tam, C. T. Chan, and P. Sheng,. “Roubust photonic band gap from tunable scatterers,” Phys. Rev. Lett. 84, 2853–2856 (2000).
[CrossRef]

Li, C.

K. Xu, X. Zheng, C. Li, and W. She, “Design of omnidirectional and multiple channeled filters using one-dimensional photonic crystals containing a defect layer with a negative refractive index,” Phys. Rev. E 71, 066604 (2005).
[CrossRef]

Li, C. Z.

H. F. Zhang, S. B. Liu, X. K. Kong, L. Zou, C. Z. Li, and W. S. Qing, “Enhancement of omnidirectional photonic band gaps in one-dimensional dielectric plasma photonic crystals with a matching layer,” Phys. Plasmas 19, 022103 (2012).
[CrossRef]

H. F. Zhang, S. B. Liu, X. K. Kong, L. Zhou, C. Z. Li, and B. R. Bo, “Comment on “Photonic bands in two-dimensional microplasma array. I. Theoretical derivation of band structures of electromagnetic wave” [J. Appl. Phys. 101, 073304 (2007)],” J. Appl. Phys. 110, 026104 (2011).
[CrossRef]

Li, L.

Li, Z.

M. Lou, Q. H. Liu, and Z. Li, “Spectral element method for band structures of three-dimensional anisotropic photonic crystals,” Phys. Rev. E 80, 56702 (2012).

Li, Z. Y.

Z. Y. Li, J. Wang, and B. Y. Gu, “Creation of partial band gaps in anisotropic photonic-band-gap structures,” Phys. Rev. B 58, 3721–3729 (1998).
[CrossRef]

Liao, Q. H.

Liu, J. T.

X. H. Deng, N. H. Liu, J. T. Liu, Q. H. Liao, and T. B. Yu, “Enlargement of polarization-independent omnidirectional band gaps in the photonic heterostrucutures containing single-negative materials,” J. Opt. Soc. Am. B 27, 1174–1178 (2010).
[CrossRef]

X. H. Deng, J. T. Liu, J. H. Huang, L. Zou, and N. H. Liu, “Omnidirectional band gap in Fibonacci quasicrystal containing single-negative materials,” J. Phys. Condens. Matter 22, 055403 (2010).
[CrossRef]

Liu, N. H.

X. H. Deng, J. T. Liu, J. H. Huang, L. Zou, and N. H. Liu, “Omnidirectional band gap in Fibonacci quasicrystal containing single-negative materials,” J. Phys. Condens. Matter 22, 055403 (2010).
[CrossRef]

X. H. Deng, N. H. Liu, J. T. Liu, Q. H. Liao, and T. B. Yu, “Enlargement of polarization-independent omnidirectional band gaps in the photonic heterostrucutures containing single-negative materials,” J. Opt. Soc. Am. B 27, 1174–1178 (2010).
[CrossRef]

Liu, Q. H.

M. Lou, Q. H. Liu, and Z. Li, “Spectral element method for band structures of three-dimensional anisotropic photonic crystals,” Phys. Rev. E 80, 56702 (2012).

Liu, S. B.

H. F. Zhang, S. B. Liu, and X. K. Kong, “Study of the dispersive properties of three-dimensional photonic crystals with diamond lattices containing metamaterials,” Laser Phys. 23, 105815 (2013).
[CrossRef]

H. F. Zhang, S. B. Liu, and X. K. Kong, “Investigating the dispersive properties of the three-dimensional photonic crystals with face-centered-cubic lattices containing epsilon-negative materials,” Appl. Phys. B 112, 553–563 (2013).
[CrossRef]

H. F. Zhang, S. B. Liu, and X. K. Kong, “Dispersion properties of three-dimensional plasma photonic crystals in Diamond lattice arrangement,” J. Lightwave Technol. 31, 1694–1702 (2013).
[CrossRef]

H. F. Zhang, S. B. Liu, X. K. Kong, C. Chen, and B. R. Bian, “The characteristics of photonic band gaps for three-dimensional unmagnetized dielectric plasma photonic crystals with simple-cubic lattice,” Opt. Commun. 288, 82–90 (2013).
[CrossRef]

H. F. Zhang, S. B. Liu, and X. K. Kong, “Investigation of Faraday effects in photonic band gap for tunable three-dimensional magnetized plasma photonic crystals containing the anisotropic material in diamond arrangement,” J. Electromagn. Wave Appl. 27, 1776–1791 (2013).
[CrossRef]

H. F. Zhang, S. B. Liu, and X. K. Kong, “Properties of anisotropic photonic band gaps in three-dimensional plasma photonic crystals containing the uniaxial material with different lattices,” Prog. Electromagn. Res. 141, 267–289 (2013).
[CrossRef]

H. F. Zhang, S. B. Liu, X. K. Kong, B. R. Bian, and X. Zhao, “Properties of omnidirectional photonic band gaps in Fibonacci quasi-periodic one-dimensional superconductor photonic crystals,” Prog. Electromagn. Res. B 40, 415–431 (2012).
[CrossRef]

H. F. Zhang, S. B. Liu, X. K. Kong, L. Zou, C. Z. Li, and W. S. Qing, “Enhancement of omnidirectional photonic band gaps in one-dimensional dielectric plasma photonic crystals with a matching layer,” Phys. Plasmas 19, 022103 (2012).
[CrossRef]

H. F. Zhang, S. B. Liu, X. K. Kong, L. Zhou, C. Z. Li, and B. R. Bo, “Comment on “Photonic bands in two-dimensional microplasma array. I. Theoretical derivation of band structures of electromagnetic wave” [J. Appl. Phys. 101, 073304 (2007)],” J. Appl. Phys. 110, 026104 (2011).
[CrossRef]

Lou, M.

M. Lou, Q. H. Liu, and Z. Li, “Spectral element method for band structures of three-dimensional anisotropic photonic crystals,” Phys. Rev. E 80, 56702 (2012).

Mahnkopf, S.

M. Kamp, T. Happ, S. Mahnkopf, G. Duan, S. Anand, and A. Forchel, “Semiconductor photonic crystals for optoelectronics,” Phys. E 21, 802–808 (2004).
[CrossRef]

Malkova, N.

N. Malkova, S. Kim, T. Dilazaro, and V. Gopalan, “Symmetrical analysis of complex two-dimensional hexagonal photonic crystals,” Phys. Rev. B 67, 125203 (2003).
[CrossRef]

Maradudin, A. A.

V. Kuzmiak and A. A. Maradudin, “Distribution of electromagnetic field and group velocities in two-dimensional periodic systems with dissipative metallic components,” Phy. Rev. B 58, 7230–7251 (1998).
[CrossRef]

Meade, R. D.

J. J. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals: Molding the Flow of Light (Princeton University, 1995).

Ming, N.

Z. Wang, C. T. Chan, W. Zhang, N. Ming, and P. Sheng, “Three-dimensional self-assembly of metal nanoparticles: possible photonic crystal with a complete gap below the plasma frequency,” Phys. Rev. B 64, 113108 (2001).
[CrossRef]

Mittleman, D.

N. Krumbholz, K. Gerlach, F. Rutz, M. Koch, R. Piesiewicz, T. Kürner, and D. Mittleman, “Ominidrectional terahertz mirror: a key element for future terahertz communication systems,” Appl. Phys. Lett. 88, 202905 (2006).
[CrossRef]

Moroz, A.

A. Moroz, “Three-dimensional complete photonic-band-gap structure in the visible,” Phys. Rev. Lett. 83, 5274–5277 (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]

Nemat-Nasser, S. C.

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett. 84, 4184–4187 (2000).
[CrossRef]

Ozbay, E.

Padilla, W. J.

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett. 84, 4184–4187 (2000).
[CrossRef]

Penciu, R. S.

Pendry, J. B.

J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85, 3966–3969 (2000).
[CrossRef]

Piesiewicz, R.

N. Krumbholz, K. Gerlach, F. Rutz, M. Koch, R. Piesiewicz, T. Kürner, and D. Mittleman, “Ominidrectional terahertz mirror: a key element for future terahertz communication systems,” Appl. Phys. Lett. 88, 202905 (2006).
[CrossRef]

Qing, W. S.

H. F. Zhang, S. B. Liu, X. K. Kong, L. Zou, C. Z. Li, and W. S. Qing, “Enhancement of omnidirectional photonic band gaps in one-dimensional dielectric plasma photonic crystals with a matching layer,” Phys. Plasmas 19, 022103 (2012).
[CrossRef]

Rutz, F.

N. Krumbholz, K. Gerlach, F. Rutz, M. Koch, R. Piesiewicz, T. Kürner, and D. Mittleman, “Ominidrectional terahertz mirror: a key element for future terahertz communication systems,” Appl. Phys. Lett. 88, 202905 (2006).
[CrossRef]

Sande, G. V. d.

Schultz, S.

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett. 84, 4184–4187 (2000).
[CrossRef]

She, W.

K. Xu, X. Zheng, C. Li, and W. She, “Design of omnidirectional and multiple channeled filters using one-dimensional photonic crystals containing a defect layer with a negative refractive index,” Phys. Rev. E 71, 066604 (2005).
[CrossRef]

Sheng, P.

Z. Wang, C. T. Chan, W. Zhang, N. Ming, and P. Sheng, “Three-dimensional self-assembly of metal nanoparticles: possible photonic crystal with a complete gap below the plasma frequency,” Phys. Rev. B 64, 113108 (2001).
[CrossRef]

W. Y. Zhang, X. Y. Lei, Z. L. Wang, D. G. Zheng, W. Y. Tam, C. T. Chan, and P. Sheng,. “Roubust photonic band gap from tunable scatterers,” Phys. Rev. Lett. 84, 2853–2856 (2000).
[CrossRef]

C. T. Chan, W. Y. Zhang, Z. L. Wang, X. Y. Lei, D. Zheng, W. Y. Tam, and P. Sheng, “Photonic band gaps from metallo-dielectric spheres,” Phys. B 279, 150–154 (2000).

Smith, D. R.

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett. 84, 4184–4187 (2000).
[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.

Sözüer, H. S.

H. S. Sözüer, J. W. Haus, and R. Inguva, “Photonic bands: convergence problems with the plane-wave method,” Phys. Rev. B 5, 13962 (1992).
[CrossRef]

Tam, W. Y.

W. Y. Zhang, X. Y. Lei, Z. L. Wang, D. G. Zheng, W. Y. Tam, C. T. Chan, and P. Sheng,. “Roubust photonic band gap from tunable scatterers,” Phys. Rev. Lett. 84, 2853–2856 (2000).
[CrossRef]

C. T. Chan, W. Y. Zhang, Z. L. Wang, X. Y. Lei, D. Zheng, W. Y. Tam, and P. Sheng, “Photonic band gaps from metallo-dielectric spheres,” Phys. B 279, 150–154 (2000).

Tassin, P.

Tlidi, M.

Tsakmakidis, K. L.

D. P. Aryal, K. L. Tsakmakidis, and O. Hess, “Complete bandgap switching in photonic crystals,” J. New Phys. 11, 073011 (2009).
[CrossRef]

Veretennicoff, I.

Veselago, V. G.

V. G. Veselago, “The electrodynamics of substance with simultaneously negative values of ε and μ,” Sov. Phys. Uspekhi 10, 509–514 (1968).

Vier, D. C.

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett. 84, 4184–4187 (2000).
[CrossRef]

Wang, J.

Z. Y. Li, J. Wang, and B. Y. Gu, “Creation of partial band gaps in anisotropic photonic-band-gap structures,” Phys. Rev. B 58, 3721–3729 (1998).
[CrossRef]

Wang, L.

L. Wang, H. Chen, and S. Zhu, “Omnidirectional gap and defect mode of one-dimensional photonic crystals with single-negative materials,” Phys. Rev. B 70, 245102 (2004).
[CrossRef]

Wang, Z.

Z. Wang, C. T. Chan, W. Zhang, N. Ming, and P. Sheng, “Three-dimensional self-assembly of metal nanoparticles: possible photonic crystal with a complete gap below the plasma frequency,” Phys. Rev. B 64, 113108 (2001).
[CrossRef]

Wang, Z. L.

W. Y. Zhang, X. Y. Lei, Z. L. Wang, D. G. Zheng, W. Y. Tam, C. T. Chan, and P. Sheng,. “Roubust photonic band gap from tunable scatterers,” Phys. Rev. Lett. 84, 2853–2856 (2000).
[CrossRef]

C. T. Chan, W. Y. Zhang, Z. L. Wang, X. Y. Lei, D. Zheng, W. Y. Tam, and P. Sheng, “Photonic band gaps from metallo-dielectric spheres,” Phys. B 279, 150–154 (2000).

Winn, J. N.

J. J. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals: Molding the Flow of Light (Princeton University, 1995).

Xu, K.

K. Xu, X. Zheng, C. Li, and W. She, “Design of omnidirectional and multiple channeled filters using one-dimensional photonic crystals containing a defect layer with a negative refractive index,” Phys. Rev. E 71, 066604 (2005).
[CrossRef]

Yablonovitch, E.

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

Yu, C.

P. Chiang, C. Yu, and H. Chang, “Analysis of two-dimensional photonic crystals using a mutildomain pseudospectral method,” Phys. Rev. E 75, 026703 (2007).
[CrossRef]

Yu, T. B.

Zhang, H. F.

H. F. Zhang, S. B. Liu, X. K. Kong, C. Chen, and B. R. Bian, “The characteristics of photonic band gaps for three-dimensional unmagnetized dielectric plasma photonic crystals with simple-cubic lattice,” Opt. Commun. 288, 82–90 (2013).
[CrossRef]

H. F. Zhang, S. B. Liu, and X. K. Kong, “Investigation of Faraday effects in photonic band gap for tunable three-dimensional magnetized plasma photonic crystals containing the anisotropic material in diamond arrangement,” J. Electromagn. Wave Appl. 27, 1776–1791 (2013).
[CrossRef]

H. F. Zhang, S. B. Liu, and X. K. Kong, “Properties of anisotropic photonic band gaps in three-dimensional plasma photonic crystals containing the uniaxial material with different lattices,” Prog. Electromagn. Res. 141, 267–289 (2013).
[CrossRef]

H. F. Zhang, S. B. Liu, and X. K. Kong, “Dispersion properties of three-dimensional plasma photonic crystals in Diamond lattice arrangement,” J. Lightwave Technol. 31, 1694–1702 (2013).
[CrossRef]

H. F. Zhang, S. B. Liu, and X. K. Kong, “Study of the dispersive properties of three-dimensional photonic crystals with diamond lattices containing metamaterials,” Laser Phys. 23, 105815 (2013).
[CrossRef]

H. F. Zhang, S. B. Liu, and X. K. Kong, “Investigating the dispersive properties of the three-dimensional photonic crystals with face-centered-cubic lattices containing epsilon-negative materials,” Appl. Phys. B 112, 553–563 (2013).
[CrossRef]

H. F. Zhang, S. B. Liu, X. K. Kong, L. Zou, C. Z. Li, and W. S. Qing, “Enhancement of omnidirectional photonic band gaps in one-dimensional dielectric plasma photonic crystals with a matching layer,” Phys. Plasmas 19, 022103 (2012).
[CrossRef]

H. F. Zhang, S. B. Liu, X. K. Kong, B. R. Bian, and X. Zhao, “Properties of omnidirectional photonic band gaps in Fibonacci quasi-periodic one-dimensional superconductor photonic crystals,” Prog. Electromagn. Res. B 40, 415–431 (2012).
[CrossRef]

H. F. Zhang, S. B. Liu, X. K. Kong, L. Zhou, C. Z. Li, and B. R. Bo, “Comment on “Photonic bands in two-dimensional microplasma array. I. Theoretical derivation of band structures of electromagnetic wave” [J. Appl. Phys. 101, 073304 (2007)],” J. Appl. Phys. 110, 026104 (2011).
[CrossRef]

Zhang, W.

Z. Wang, C. T. Chan, W. Zhang, N. Ming, and P. Sheng, “Three-dimensional self-assembly of metal nanoparticles: possible photonic crystal with a complete gap below the plasma frequency,” Phys. Rev. B 64, 113108 (2001).
[CrossRef]

Zhang, W. Y.

W. Y. Zhang, X. Y. Lei, Z. L. Wang, D. G. Zheng, W. Y. Tam, C. T. Chan, and P. Sheng,. “Roubust photonic band gap from tunable scatterers,” Phys. Rev. Lett. 84, 2853–2856 (2000).
[CrossRef]

C. T. Chan, W. Y. Zhang, Z. L. Wang, X. Y. Lei, D. Zheng, W. Y. Tam, and P. Sheng, “Photonic band gaps from metallo-dielectric spheres,” Phys. B 279, 150–154 (2000).

Zhao, X.

H. F. Zhang, S. B. Liu, X. K. Kong, B. R. Bian, and X. Zhao, “Properties of omnidirectional photonic band gaps in Fibonacci quasi-periodic one-dimensional superconductor photonic crystals,” Prog. Electromagn. Res. B 40, 415–431 (2012).
[CrossRef]

Zheng, D.

C. T. Chan, W. Y. Zhang, Z. L. Wang, X. Y. Lei, D. Zheng, W. Y. Tam, and P. Sheng, “Photonic band gaps from metallo-dielectric spheres,” Phys. B 279, 150–154 (2000).

Zheng, D. G.

W. Y. Zhang, X. Y. Lei, Z. L. Wang, D. G. Zheng, W. Y. Tam, C. T. Chan, and P. Sheng,. “Roubust photonic band gap from tunable scatterers,” Phys. Rev. Lett. 84, 2853–2856 (2000).
[CrossRef]

Zheng, X.

K. Xu, X. Zheng, C. Li, and W. She, “Design of omnidirectional and multiple channeled filters using one-dimensional photonic crystals containing a defect layer with a negative refractive index,” Phys. Rev. E 71, 066604 (2005).
[CrossRef]

Zhou, L.

H. F. Zhang, S. B. Liu, X. K. Kong, L. Zhou, C. Z. Li, and B. R. Bo, “Comment on “Photonic bands in two-dimensional microplasma array. I. Theoretical derivation of band structures of electromagnetic wave” [J. Appl. Phys. 101, 073304 (2007)],” J. Appl. Phys. 110, 026104 (2011).
[CrossRef]

Zhu, S.

L. Wang, H. Chen, and S. Zhu, “Omnidirectional gap and defect mode of one-dimensional photonic crystals with single-negative materials,” Phys. Rev. B 70, 245102 (2004).
[CrossRef]

Zou, L.

H. F. Zhang, S. B. Liu, X. K. Kong, L. Zou, C. Z. Li, and W. S. Qing, “Enhancement of omnidirectional photonic band gaps in one-dimensional dielectric plasma photonic crystals with a matching layer,” Phys. Plasmas 19, 022103 (2012).
[CrossRef]

X. H. Deng, J. T. Liu, J. H. Huang, L. Zou, and N. H. Liu, “Omnidirectional band gap in Fibonacci quasicrystal containing single-negative materials,” J. Phys. Condens. Matter 22, 055403 (2010).
[CrossRef]

Appl. Phys. B

H. F. Zhang, S. B. Liu, and X. K. Kong, “Investigating the dispersive properties of the three-dimensional photonic crystals with face-centered-cubic lattices containing epsilon-negative materials,” Appl. Phys. B 112, 553–563 (2013).
[CrossRef]

Appl. Phys. Lett.

N. Krumbholz, K. Gerlach, F. Rutz, M. Koch, R. Piesiewicz, T. Kürner, and D. Mittleman, “Ominidrectional terahertz mirror: a key element for future terahertz communication systems,” Appl. Phys. Lett. 88, 202905 (2006).
[CrossRef]

J. Appl. Phys.

H. F. Zhang, S. B. Liu, X. K. Kong, L. Zhou, C. Z. Li, and B. R. Bo, “Comment on “Photonic bands in two-dimensional microplasma array. I. Theoretical derivation of band structures of electromagnetic wave” [J. Appl. Phys. 101, 073304 (2007)],” J. Appl. Phys. 110, 026104 (2011).
[CrossRef]

J. Electromagn. Wave Appl.

H. F. Zhang, S. B. Liu, and X. K. Kong, “Investigation of Faraday effects in photonic band gap for tunable three-dimensional magnetized plasma photonic crystals containing the anisotropic material in diamond arrangement,” J. Electromagn. Wave Appl. 27, 1776–1791 (2013).
[CrossRef]

J. Lightwave Technol.

J. New Phys.

D. P. Aryal, K. L. Tsakmakidis, and O. Hess, “Complete bandgap switching in photonic crystals,” J. New Phys. 11, 073011 (2009).
[CrossRef]

J. Opt. Soc. Am. A

J. Opt. Soc. Am. B

J. Phys. Condens. Matter

X. H. Deng, J. T. Liu, J. H. Huang, L. Zou, and N. H. Liu, “Omnidirectional band gap in Fibonacci quasicrystal containing single-negative materials,” J. Phys. Condens. Matter 22, 055403 (2010).
[CrossRef]

J. Phys.: Condens. Matter

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

Laser Phys.

H. F. Zhang, S. B. Liu, and X. K. Kong, “Study of the dispersive properties of three-dimensional photonic crystals with diamond lattices containing metamaterials,” Laser Phys. 23, 105815 (2013).
[CrossRef]

Opt. Commun.

H. F. Zhang, S. B. Liu, X. K. Kong, C. Chen, and B. R. Bian, “The characteristics of photonic band gaps for three-dimensional unmagnetized dielectric plasma photonic crystals with simple-cubic lattice,” Opt. Commun. 288, 82–90 (2013).
[CrossRef]

Opt. Express

Phy. Rev. B

V. Kuzmiak and A. A. Maradudin, “Distribution of electromagnetic field and group velocities in two-dimensional periodic systems with dissipative metallic components,” Phy. Rev. B 58, 7230–7251 (1998).
[CrossRef]

Phys. B

C. T. Chan, W. Y. Zhang, Z. L. Wang, X. Y. Lei, D. Zheng, W. Y. Tam, and P. Sheng, “Photonic band gaps from metallo-dielectric spheres,” Phys. B 279, 150–154 (2000).

Phys. E

M. Kamp, T. Happ, S. Mahnkopf, G. Duan, S. Anand, and A. Forchel, “Semiconductor photonic crystals for optoelectronics,” Phys. E 21, 802–808 (2004).
[CrossRef]

Phys. Plasmas

H. F. Zhang, S. B. Liu, X. K. Kong, L. Zou, C. Z. Li, and W. S. Qing, “Enhancement of omnidirectional photonic band gaps in one-dimensional dielectric plasma photonic crystals with a matching layer,” Phys. Plasmas 19, 022103 (2012).
[CrossRef]

Phys. Rev. B

Z. Wang, C. T. Chan, W. Zhang, N. Ming, and P. Sheng, “Three-dimensional self-assembly of metal nanoparticles: possible photonic crystal with a complete gap below the plasma frequency,” Phys. Rev. B 64, 113108 (2001).
[CrossRef]

H. S. Sözüer, J. W. Haus, and R. Inguva, “Photonic bands: convergence problems with the plane-wave method,” Phys. Rev. B 5, 13962 (1992).
[CrossRef]

L. Wang, H. Chen, and S. Zhu, “Omnidirectional gap and defect mode of one-dimensional photonic crystals with single-negative materials,” Phys. Rev. B 70, 245102 (2004).
[CrossRef]

Z. Y. Li, J. Wang, and B. Y. Gu, “Creation of partial band gaps in anisotropic photonic-band-gap structures,” Phys. Rev. B 58, 3721–3729 (1998).
[CrossRef]

N. Malkova, S. Kim, T. Dilazaro, and V. Gopalan, “Symmetrical analysis of complex two-dimensional hexagonal photonic crystals,” Phys. Rev. B 67, 125203 (2003).
[CrossRef]

A. J. Garcia-Adeva, “Band structure of photonic crystals with the symmetry of a pyrochlore lattice,” Phys. Rev. B 73, 073107 (2006).
[CrossRef]

Phys. Rev. E

P. Chiang, C. Yu, and H. Chang, “Analysis of two-dimensional photonic crystals using a mutildomain pseudospectral method,” Phys. Rev. E 75, 026703 (2007).
[CrossRef]

M. Lou, Q. H. Liu, and Z. Li, “Spectral element method for band structures of three-dimensional anisotropic photonic crystals,” Phys. Rev. E 80, 56702 (2012).

K. Xu, X. Zheng, C. Li, and W. She, “Design of omnidirectional and multiple channeled filters using one-dimensional photonic crystals containing a defect layer with a negative refractive index,” Phys. Rev. E 71, 066604 (2005).
[CrossRef]

Phys. Rev. Lett.

W. Y. Zhang, X. Y. Lei, Z. L. Wang, D. G. Zheng, W. Y. Tam, C. T. Chan, and P. Sheng,. “Roubust photonic band gap from tunable scatterers,” Phys. Rev. Lett. 84, 2853–2856 (2000).
[CrossRef]

A. Moroz, “Three-dimensional complete photonic-band-gap structure in the visible,” Phys. Rev. Lett. 83, 5274–5277 (1999).
[CrossRef]

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

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

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett. 84, 4184–4187 (2000).
[CrossRef]

J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85, 3966–3969 (2000).
[CrossRef]

Prog. Electromagn. Res.

H. F. Zhang, S. B. Liu, and X. K. Kong, “Properties of anisotropic photonic band gaps in three-dimensional plasma photonic crystals containing the uniaxial material with different lattices,” Prog. Electromagn. Res. 141, 267–289 (2013).
[CrossRef]

Prog. Electromagn. Res. B

H. F. Zhang, S. B. Liu, X. K. Kong, B. R. Bian, and X. Zhao, “Properties of omnidirectional photonic band gaps in Fibonacci quasi-periodic one-dimensional superconductor photonic crystals,” Prog. Electromagn. Res. B 40, 415–431 (2012).
[CrossRef]

Sov. Phys. Uspekhi

V. G. Veselago, “The electrodynamics of substance with simultaneously negative values of ε and μ,” Sov. Phys. Uspekhi 10, 509–514 (1968).

Other

J. J. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals: Molding the Flow of Light (Princeton University, 1995).

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Figures (12)

Fig. 1.
Fig. 1.

Schematic structure of such 3D PCs with pyrochlore lattices. (a) 3D PCs structure and illustration of a unit cell, (b) rhombohedral axes with respect to the cubic unit cell, and (c) first irreducible Brillouin zone showing symmetry point used for computing the anisotropic PBGs.

Fig. 2.
Fig. 2.

Calculated band structures for 3D PCs with εa=12, ωp=0.05ωp0, γ=0.02ωpl, and r=0.19a, respectively. The red shaded region indicates PBG.

Fig. 3.
Fig. 3.

Calculated band structures for 3D PCs with similar case to Fig. 2 except that the lattices are different. (a) sc lattices, (b) fcc lattices, (c) diamond lattices, and (d) bcc lattices.

Fig. 4.
Fig. 4.

Band structures for such 3D PCs with na=6.2, εb=1, εc=1, R1=0.1a, and R2=0.1756a but with different ωp and γ. (a) ωp=0, γ=0; (b) ωp=0.15ωp0, γ=0.02ωpl.

Fig. 5.
Fig. 5.

Schematic structure of such 3D PCs with similar case to Fig. 4 except that the lattices are different. (a) Diamond lattices, (b) fcc lattices, (c) bcc lattices, and (d) sc lattices.

Fig. 6.
Fig. 6.

Both edges of the flatbands regions as a function of R1 with na=6.2, εb=1, εc=1, R2=0.1756a, ωp=0.15ωp0, and γ=0.02ωpl as such PCs with the diamond, fcc, bcc, sc, and pyrochlore lattices.

Fig. 7.
Fig. 7.

Band structures for such 3D PCs with na=6.2, εb=1, εc=1, R2=0.1756a, ωp=0.15ωp0, and γ=0.02ωpl but with different R1. (a) R1=0, (b) R1=0.01a, (c) R1=0.02a, and (d) R1=0.04a.

Fig. 8.
Fig. 8.

Band structures for such 3D PCs with R1=0.03a, εb=1, εc=1, R2=0.1756a, ωp=0.15ωp0, and γ=0.02ωpl but with different inserted core sphere. (a) εa=12.4, (b) na=6.2, (c) Te (no=4.8, ne=6.2), and (d) Tl3AsSe3 (no=3.35, ne=3.16).

Fig. 9.
Fig. 9.

Band structures for such 3D PCs with R1=0.03a, εb=38.44, εc=1, R2=0.1756a, ωp=0.15ωp0, and γ=0.02ωpl but with different inserted core sphere. (a) εa=12.4, (b) εa=4, (c) Te (no=4.8, ne=6.2), and (d) Tl3AsSe3 (no=3.35, ne=3.16).

Fig. 10.
Fig. 10.

Effects of R1 on the first PBG and its relative bandwidth for such 3D PCs with na=6.2, εc=1, εb=1, ωp=0.15ωp0, γ=0.02ωpl, and R2=0.1756a, respectively. The shaded region indicates the PBG. (a) First PBG and (b) relative bandwidth.

Fig. 11.
Fig. 11.

Effects of ωp on the first PBG and its relative bandwidth for such 3D PCs with na=6.2, εc=1, εb=1, R1=0.03a, ωp=0.15ωp0, γ=0.02ωpl, and R2=0.1756a, respectively. The shaded region indicates the PBG. (a) First PBG and (b) relative bandwidth.

Fig. 12.
Fig. 12.

Effects of εc on the first PBG and its relative bandwidth for such 3D PCs with na=6.2, R1=0.1a, εb=1, ωp=0.15ωp0, γ=0.02ωpl, and R2=0.1756a, respectively. The shaded region indicates the PBG. (a) First PBG and (b) relative bandwidth.

Equations (9)

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εp(ω)=εcωp2ω(ω+jγ),
κG={(ω2+jγωεcω2+jεcγωωp21εb)4f2+(1εaω2+jγωεcω2+jεcγωωp2)4f1+1εb,G=0(ω2+jγωεcω2+jεcγωωp21εb)·i=14e(G·vi)·3f2(sin(|G|R2)(|G|R2)cos(|G|R2)(|G|R2)3)+(1εaω2+jγωεcω2+jεcγωωp2)·i=14e(G·vi)·3f1(sin(|G|R1)(|G|R1)cos(|G|R1)(|G|R1)3),G0,
μ4Iμ3Tμ2UμVW=0,
T(G|G)=jγcδG·G,
U(G|G)={ωp2εcc2+[1εb+(1εc1εb)4f2+(1εa1εc)4f1]·M}δG·G+{(1εc1εb)i=14e(G·vi)·3f2(sin(|GG|R2)(|GG|R2)cos(|GG|R2)(|GG|R2)3)+(1εa1εc)i=14e(G·vi)·3f1(sin(|GG|R1)(|GG|R1)cos(|GG|R1)(|GG|R1)3)}·M,
V(G|G)={jγc[1εb+(1εc1εb)4f2+(1εa1εc)4f1]·M}δG·G+jγc{(1εc1εb)i=14e(G·vi)·3f2(sin(|GG|R2)(|GG|R2)cos(|GG|R2)(|GG|R2)3)+(1εa1εc)i=14e(G·vi)·3f1(sin(|GG|R1)(|GG|R1)cos(|GG|R1)(|GG|R1)3)}·M,
W(G|G)={(ωp2εcεbc2ωp2εcεac24f1+ωp2εcεac24f2)·M}δG·Gωp2εcεac2i=14e(G·vi)·3f1(sin(|GG|R1)(|GG|R1)cos(|GG|R1)(|GG|R1)3)·M+ωp2εcεac2i=14e(G·vi)·3f2(sin(|GG|R2)(|GG|R2)cos(|GG|R2)(|GG|R2)3)·M,
Qz=μzQ=[0I0000I0000IWVUT].
εeff=εb(1+2f1αc)1f1αc,

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