Abstract

We study the low frequency photonic band structures in square Mediterranean and hexagonal snowflake metallic structures, both constructed upon two sets of adjustable tiles. The band formation and evolution are comparatively investigated with respect to local resonances and their variations following the modulations of the tile sizes and shapes. We show that the lowest frequency bands are formed by s-like resonance modes sustained by the structure tiles, of which the contributions vary following local structure modulations, and, under certain conditions, the second bands (above the first photonic bandgaps) are formed by p-like modes sustained by the same tiles. The s and p bands can both be described in the framework of a tight-binding model, allowing band structure analyses in terms of relations between local resonance modes and their mutual correlations. In this schema, the plasma gaps and the first photonic bandgaps arise naturally from local structure patterns, which determine both the local resonance conditions and their correlation relations.

© 2014 Optical Society of America

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2013 (1)

2012 (3)

V. Yannopapas, “Non-reciprocal photonic bands in a two-dimensional holey metal filled with a magnetoelectric material,” J. Opt. 14, 085105 (2012).
[CrossRef]

K. Wang, “Light wave states in quasi-periodic metallic structures,” Phys. Rev. B 86, 235110 (2012).
[CrossRef]

S. Belousov, M. Bogdanova, A. Deinega, S. Eyderman, I. Valuev, Y. Lozovik, I. Polischuk, B. Potapkin, B. Ramamurthi, T. Deng, and V. Midha, “Using metallic photonic crystals as visible light sources,” Phys. Rev. B 86, 174201 (2012).
[CrossRef]

2011 (1)

C. Bauer, G. Kobiela, and H. Giessen, “Optical properties of two-dimensional quasi-crystalline plasmonic arrays,” Phys. Rev. B 84, 193104 (2011).
[CrossRef]

2010 (2)

2009 (2)

C. Forestiere, G. Miano, G. Rubinacci, and L. Dal Negro, “Role of aperiodic order in the spectral, localization, and scaling properties of plasmon modes for the design of nanoparticle arrays,” Phys. Rev. B 79, 085404 (2009).
[CrossRef]

W. Withayachumnankul and D. Abbott, “Metamaterials in the terahertz regime,” IEEE Photon. J. 1, 99–118 (2009).
[CrossRef]

2008 (2)

L. Dal Negro, N. Feng, and A. Gopinath, “Electromagnetic coupling and plasmon localization in deterministic aperiodic arrays,” J. Opt. A 10, 064013 (2008).
[CrossRef]

Y. Wang, “Fabrication and characterization of metallic quasi-periodic structures,” Opt. Express 16, 1090–1095 (2008).
[CrossRef]

2007 (1)

S. E. Han, A. Stein, and D. J. Norris, “Tailoring self-assembled metallic photonic crystals for modified thermal emission,” Phys. Rev. Lett. 99, 053906 (2007).
[CrossRef]

2006 (3)

2003 (1)

2002 (1)

J. G. Fleming, S. Y. Lin, I. El-Kady, R. Biswas, and K. M. Ho, “All-metallic three-dimensional photonic crystals with a large infrared bandgap,” Nature 417, 52–55 (2002).
[CrossRef]

2001 (1)

M. M. Bayindir, E. Cubukcu, I. Bulu, and E. Ozbay, “Photonic bandgaps and localization in two-dimensional metallic quasi-crystals,” Europhys. Lett. 56, 41–46 (2001).
[CrossRef]

2000 (1)

M. Bayindir, B. Temelkuran, and E. Ozbay, “Tight-binding description of the coupled defect modes in three-dimensional photonic crystal,” Phys. Rev. Lett. 84, 2140–2143 (2000).
[CrossRef]

1999 (2)

A. Yariv, Y. Xu, R. K. Lee, and A. Scherer, “Coupled-resonator optical waveguide: a proposal and analysis,” Opt. Lett. 24, 711–713 (1999).
[CrossRef]

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

1998 (7)

G. Guida, D. Maystre, G. Tayeb, and P. Vincent, “Mean-field theory of two-dimensional metallic photonic crystals,” J. Opt. Soc. Am. B 15, 2308–2315 (1998).
[CrossRef]

G. Guida, “Numerical study of bandgaps generated by randomly perturbed bidimensional metallic cubic photonic crystals,” Opt. Commun. 156, 294–296 (1998).
[CrossRef]

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391, 667–669 (1998).
[CrossRef]

B. Temelkuran, E. Ozbay, M. Sigalas, G. Tuttle, C. M. Soukoulis, and K. M. Ho, “Reflection properties of metallic photonic crystals,” Appl. Phys. A 66, 363–365 (1998).
[CrossRef]

N. Stefanou and A. Modinos, “Impurity bands in photonic insulators,” Phys. Rev. B 57, 12127–12133 (1998).
[CrossRef]

E. Lidorikis, M. M. Sigalas, E. N. Economou, and C. M. Soukoulis, “Tight-binding parameterization for photonic bandgap materials,” Phys. Rev. Lett. 81, 1405–1408 (1998).
[CrossRef]

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Low frequency plasmons in thin-wire structures,” J. Phys. 10, 4785–4809 (1998).
[CrossRef]

1996 (2)

J. B. Pendry, A. J. Holden, W. J. Stewart, and I. Youngs, “Extremely low frequency plasmons in metallic mesostructures,” Phys. Rev. Lett. 76, 4773–4776 (1996).
[CrossRef]

D. F. Sievenpiper, M. E. Sickmiller, and E. Yablonovitch, “3D wire mesh photonic crystals,” Phys. Rev. Lett. 76, 2480–2483 (1996).
[CrossRef]

1994 (1)

J. B. Pendry, “Photonic band structures,” J. Mod. Opt. 41, 209–229 (1994).
[CrossRef]

1987 (1)

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

1956 (1)

R. S. Mulliken, “Erratum: report on notation for the spectra of polyatomic molecules,” J. Chem. Phys. 24, 1118 (1956).

1955 (1)

R. S. Mulliken, “Report on notation for the spectra of polyatomic molecules,” J. Chem. Phys. 23, 1997–2011 (1955).

Abbott, D.

W. Withayachumnankul and D. Abbott, “Metamaterials in the terahertz regime,” IEEE Photon. J. 1, 99–118 (2009).
[CrossRef]

Ashcroft, N. W.

N. W. Ashcroft and N. D. Mermin, Solid State Physics (Saunders College, 1976), Chap. 10, pp. 175–190.

Bauer, C.

C. Bauer, G. Kobiela, and H. Giessen, “Optical properties of two-dimensional quasi-crystalline plasmonic arrays,” Phys. Rev. B 84, 193104 (2011).
[CrossRef]

Bayindir, M.

M. Bayindir, B. Temelkuran, and E. Ozbay, “Tight-binding description of the coupled defect modes in three-dimensional photonic crystal,” Phys. Rev. Lett. 84, 2140–2143 (2000).
[CrossRef]

Bayindir, M. M.

M. M. Bayindir, E. Cubukcu, I. Bulu, and E. Ozbay, “Photonic bandgaps and localization in two-dimensional metallic quasi-crystals,” Europhys. Lett. 56, 41–46 (2001).
[CrossRef]

Belousov, S.

S. Belousov, M. Bogdanova, A. Deinega, S. Eyderman, I. Valuev, Y. Lozovik, I. Polischuk, B. Potapkin, B. Ramamurthi, T. Deng, and V. Midha, “Using metallic photonic crystals as visible light sources,” Phys. Rev. B 86, 174201 (2012).
[CrossRef]

Biswas, R.

S. Y. Lin, J. G. Fleming, Z. Y. Li, I. El-Kady, R. Biswas, and K. M. Ho, “Origin of absorption enhancement in a tungsten, three-dimensional photonic crystal,” J. Opt. Soc. Am. B 20, 1538–1541 (2003).
[CrossRef]

J. G. Fleming, S. Y. Lin, I. El-Kady, R. Biswas, and K. M. Ho, “All-metallic three-dimensional photonic crystals with a large infrared bandgap,” Nature 417, 52–55 (2002).
[CrossRef]

Bogdanova, M.

S. Belousov, M. Bogdanova, A. Deinega, S. Eyderman, I. Valuev, Y. Lozovik, I. Polischuk, B. Potapkin, B. Ramamurthi, T. Deng, and V. Midha, “Using metallic photonic crystals as visible light sources,” Phys. Rev. B 86, 174201 (2012).
[CrossRef]

Bulu, I.

M. M. Bayindir, E. Cubukcu, I. Bulu, and E. Ozbay, “Photonic bandgaps and localization in two-dimensional metallic quasi-crystals,” Europhys. Lett. 56, 41–46 (2001).
[CrossRef]

Chan, C. T.

J. T. K. Wan and C. T. Chan, “Thermal emission by metallic photonic crystal slabs,” Appl. Phys. Lett. 89, 041915 (2006).
[CrossRef]

Chan, D. L. C.

Chen, G.

Chen, Y. H.

Cubukcu, E.

M. M. Bayindir, E. Cubukcu, I. Bulu, and E. Ozbay, “Photonic bandgaps and localization in two-dimensional metallic quasi-crystals,” Europhys. Lett. 56, 41–46 (2001).
[CrossRef]

Dal Negro, L.

C. Forestiere, G. Miano, G. Rubinacci, and L. Dal Negro, “Role of aperiodic order in the spectral, localization, and scaling properties of plasmon modes for the design of nanoparticle arrays,” Phys. Rev. B 79, 085404 (2009).
[CrossRef]

L. Dal Negro, N. Feng, and A. Gopinath, “Electromagnetic coupling and plasmon localization in deterministic aperiodic arrays,” J. Opt. A 10, 064013 (2008).
[CrossRef]

Deinega, A.

S. Belousov, M. Bogdanova, A. Deinega, S. Eyderman, I. Valuev, Y. Lozovik, I. Polischuk, B. Potapkin, B. Ramamurthi, T. Deng, and V. Midha, “Using metallic photonic crystals as visible light sources,” Phys. Rev. B 86, 174201 (2012).
[CrossRef]

Deng, T.

S. Belousov, M. Bogdanova, A. Deinega, S. Eyderman, I. Valuev, Y. Lozovik, I. Polischuk, B. Potapkin, B. Ramamurthi, T. Deng, and V. Midha, “Using metallic photonic crystals as visible light sources,” Phys. Rev. B 86, 174201 (2012).
[CrossRef]

Dong, J. W.

Ebbesen, T. W.

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391, 667–669 (1998).
[CrossRef]

Economou, E. N.

E. Lidorikis, M. M. Sigalas, E. N. Economou, and C. M. Soukoulis, “Tight-binding parameterization for photonic bandgap materials,” Phys. Rev. Lett. 81, 1405–1408 (1998).
[CrossRef]

El-Kady, I.

S. Y. Lin, J. G. Fleming, Z. Y. Li, I. El-Kady, R. Biswas, and K. M. Ho, “Origin of absorption enhancement in a tungsten, three-dimensional photonic crystal,” J. Opt. Soc. Am. B 20, 1538–1541 (2003).
[CrossRef]

J. G. Fleming, S. Y. Lin, I. El-Kady, R. Biswas, and K. M. Ho, “All-metallic three-dimensional photonic crystals with a large infrared bandgap,” Nature 417, 52–55 (2002).
[CrossRef]

Eyderman, S.

S. Belousov, M. Bogdanova, A. Deinega, S. Eyderman, I. Valuev, Y. Lozovik, I. Polischuk, B. Potapkin, B. Ramamurthi, T. Deng, and V. Midha, “Using metallic photonic crystals as visible light sources,” Phys. Rev. B 86, 174201 (2012).
[CrossRef]

Feng, N.

L. Dal Negro, N. Feng, and A. Gopinath, “Electromagnetic coupling and plasmon localization in deterministic aperiodic arrays,” J. Opt. A 10, 064013 (2008).
[CrossRef]

Fleming, J. G.

S. Y. Lin, J. G. Fleming, Z. Y. Li, I. El-Kady, R. Biswas, and K. M. Ho, “Origin of absorption enhancement in a tungsten, three-dimensional photonic crystal,” J. Opt. Soc. Am. B 20, 1538–1541 (2003).
[CrossRef]

J. G. Fleming, S. Y. Lin, I. El-Kady, R. Biswas, and K. M. Ho, “All-metallic three-dimensional photonic crystals with a large infrared bandgap,” Nature 417, 52–55 (2002).
[CrossRef]

Forestiere, C.

C. Forestiere, G. Miano, G. Rubinacci, and L. Dal Negro, “Role of aperiodic order in the spectral, localization, and scaling properties of plasmon modes for the design of nanoparticle arrays,” Phys. Rev. B 79, 085404 (2009).
[CrossRef]

Ghaemi, H. F.

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391, 667–669 (1998).
[CrossRef]

Giessen, H.

C. Bauer, G. Kobiela, and H. Giessen, “Optical properties of two-dimensional quasi-crystalline plasmonic arrays,” Phys. Rev. B 84, 193104 (2011).
[CrossRef]

Gopinath, A.

L. Dal Negro, N. Feng, and A. Gopinath, “Electromagnetic coupling and plasmon localization in deterministic aperiodic arrays,” J. Opt. A 10, 064013 (2008).
[CrossRef]

Grünbaum, B.

B. Grünbaum and G. S. Shephard, Tilings and Patterns (Freeman, 1987), pp. 57–65.

Gu, M.

Guida, G.

G. Guida, “Numerical study of bandgaps generated by randomly perturbed bidimensional metallic cubic photonic crystals,” Opt. Commun. 156, 294–296 (1998).
[CrossRef]

G. Guida, D. Maystre, G. Tayeb, and P. Vincent, “Mean-field theory of two-dimensional metallic photonic crystals,” J. Opt. Soc. Am. B 15, 2308–2315 (1998).
[CrossRef]

Han, S. E.

S. E. Han, A. Stein, and D. J. Norris, “Tailoring self-assembled metallic photonic crystals for modified thermal emission,” Phys. Rev. Lett. 99, 053906 (2007).
[CrossRef]

Ho, K. M.

S. Y. Lin, J. G. Fleming, Z. Y. Li, I. El-Kady, R. Biswas, and K. M. Ho, “Origin of absorption enhancement in a tungsten, three-dimensional photonic crystal,” J. Opt. Soc. Am. B 20, 1538–1541 (2003).
[CrossRef]

J. G. Fleming, S. Y. Lin, I. El-Kady, R. Biswas, and K. M. Ho, “All-metallic three-dimensional photonic crystals with a large infrared bandgap,” Nature 417, 52–55 (2002).
[CrossRef]

B. Temelkuran, E. Ozbay, M. Sigalas, G. Tuttle, C. M. Soukoulis, and K. M. Ho, “Reflection properties of metallic photonic crystals,” Appl. Phys. A 66, 363–365 (1998).
[CrossRef]

Holden, A. J.

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Low frequency plasmons in thin-wire structures,” J. Phys. 10, 4785–4809 (1998).
[CrossRef]

J. B. Pendry, A. J. Holden, W. J. Stewart, and I. Youngs, “Extremely low frequency plasmons in metallic mesostructures,” Phys. Rev. Lett. 76, 4773–4776 (1996).
[CrossRef]

Hossain, M. M.

Jia, B.

Joannopoulos, J. D.

Kim, K.

Kobiela, G.

C. Bauer, G. Kobiela, and H. Giessen, “Optical properties of two-dimensional quasi-crystalline plasmonic arrays,” Phys. Rev. B 84, 193104 (2011).
[CrossRef]

Lee, R. K.

Lezec, H. J.

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391, 667–669 (1998).
[CrossRef]

Li, Z. Y.

Liang, G. Q.

Lidorikis, E.

E. Lidorikis, M. M. Sigalas, E. N. Economou, and C. M. Soukoulis, “Tight-binding parameterization for photonic bandgap materials,” Phys. Rev. Lett. 81, 1405–1408 (1998).
[CrossRef]

Lin, S. Y.

S. Y. Lin, J. G. Fleming, Z. Y. Li, I. El-Kady, R. Biswas, and K. M. Ho, “Origin of absorption enhancement in a tungsten, three-dimensional photonic crystal,” J. Opt. Soc. Am. B 20, 1538–1541 (2003).
[CrossRef]

J. G. Fleming, S. Y. Lin, I. El-Kady, R. Biswas, and K. M. Ho, “All-metallic three-dimensional photonic crystals with a large infrared bandgap,” Nature 417, 52–55 (2002).
[CrossRef]

Lozovik, Y.

S. Belousov, M. Bogdanova, A. Deinega, S. Eyderman, I. Valuev, Y. Lozovik, I. Polischuk, B. Potapkin, B. Ramamurthi, T. Deng, and V. Midha, “Using metallic photonic crystals as visible light sources,” Phys. Rev. B 86, 174201 (2012).
[CrossRef]

Maystre, D.

Mermin, N. D.

N. W. Ashcroft and N. D. Mermin, Solid State Physics (Saunders College, 1976), Chap. 10, pp. 175–190.

Miano, G.

C. Forestiere, G. Miano, G. Rubinacci, and L. Dal Negro, “Role of aperiodic order in the spectral, localization, and scaling properties of plasmon modes for the design of nanoparticle arrays,” Phys. Rev. B 79, 085404 (2009).
[CrossRef]

Midha, V.

S. Belousov, M. Bogdanova, A. Deinega, S. Eyderman, I. Valuev, Y. Lozovik, I. Polischuk, B. Potapkin, B. Ramamurthi, T. Deng, and V. Midha, “Using metallic photonic crystals as visible light sources,” Phys. Rev. B 86, 174201 (2012).
[CrossRef]

Modinos, A.

N. Stefanou and A. Modinos, “Impurity bands in photonic insulators,” Phys. Rev. B 57, 12127–12133 (1998).
[CrossRef]

Moroz, A.

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

Mulliken, R. S.

R. S. Mulliken, “Erratum: report on notation for the spectra of polyatomic molecules,” J. Chem. Phys. 24, 1118 (1956).

R. S. Mulliken, “Report on notation for the spectra of polyatomic molecules,” J. Chem. Phys. 23, 1997–2011 (1955).

Norris, D. J.

S. E. Han, A. Stein, and D. J. Norris, “Tailoring self-assembled metallic photonic crystals for modified thermal emission,” Phys. Rev. Lett. 99, 053906 (2007).
[CrossRef]

Ozbay, E.

M. M. Bayindir, E. Cubukcu, I. Bulu, and E. Ozbay, “Photonic bandgaps and localization in two-dimensional metallic quasi-crystals,” Europhys. Lett. 56, 41–46 (2001).
[CrossRef]

M. Bayindir, B. Temelkuran, and E. Ozbay, “Tight-binding description of the coupled defect modes in three-dimensional photonic crystal,” Phys. Rev. Lett. 84, 2140–2143 (2000).
[CrossRef]

B. Temelkuran, E. Ozbay, M. Sigalas, G. Tuttle, C. M. Soukoulis, and K. M. Ho, “Reflection properties of metallic photonic crystals,” Appl. Phys. A 66, 363–365 (1998).
[CrossRef]

Pendry, J. B.

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Low frequency plasmons in thin-wire structures,” J. Phys. 10, 4785–4809 (1998).
[CrossRef]

J. B. Pendry, A. J. Holden, W. J. Stewart, and I. Youngs, “Extremely low frequency plasmons in metallic mesostructures,” Phys. Rev. Lett. 76, 4773–4776 (1996).
[CrossRef]

J. B. Pendry, “Photonic band structures,” J. Mod. Opt. 41, 209–229 (1994).
[CrossRef]

Polischuk, I.

S. Belousov, M. Bogdanova, A. Deinega, S. Eyderman, I. Valuev, Y. Lozovik, I. Polischuk, B. Potapkin, B. Ramamurthi, T. Deng, and V. Midha, “Using metallic photonic crystals as visible light sources,” Phys. Rev. B 86, 174201 (2012).
[CrossRef]

Potapkin, B.

S. Belousov, M. Bogdanova, A. Deinega, S. Eyderman, I. Valuev, Y. Lozovik, I. Polischuk, B. Potapkin, B. Ramamurthi, T. Deng, and V. Midha, “Using metallic photonic crystals as visible light sources,” Phys. Rev. B 86, 174201 (2012).
[CrossRef]

Ramamurthi, B.

S. Belousov, M. Bogdanova, A. Deinega, S. Eyderman, I. Valuev, Y. Lozovik, I. Polischuk, B. Potapkin, B. Ramamurthi, T. Deng, and V. Midha, “Using metallic photonic crystals as visible light sources,” Phys. Rev. B 86, 174201 (2012).
[CrossRef]

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J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Low frequency plasmons in thin-wire structures,” J. Phys. 10, 4785–4809 (1998).
[CrossRef]

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C. Forestiere, G. Miano, G. Rubinacci, and L. Dal Negro, “Role of aperiodic order in the spectral, localization, and scaling properties of plasmon modes for the design of nanoparticle arrays,” Phys. Rev. B 79, 085404 (2009).
[CrossRef]

Scherer, A.

Shephard, G. S.

B. Grünbaum and G. S. Shephard, Tilings and Patterns (Freeman, 1987), pp. 57–65.

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D. F. Sievenpiper, M. E. Sickmiller, and E. Yablonovitch, “3D wire mesh photonic crystals,” Phys. Rev. Lett. 76, 2480–2483 (1996).
[CrossRef]

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D. F. Sievenpiper, M. E. Sickmiller, and E. Yablonovitch, “3D wire mesh photonic crystals,” Phys. Rev. Lett. 76, 2480–2483 (1996).
[CrossRef]

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B. Temelkuran, E. Ozbay, M. Sigalas, G. Tuttle, C. M. Soukoulis, and K. M. Ho, “Reflection properties of metallic photonic crystals,” Appl. Phys. A 66, 363–365 (1998).
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E. Lidorikis, M. M. Sigalas, E. N. Economou, and C. M. Soukoulis, “Tight-binding parameterization for photonic bandgap materials,” Phys. Rev. Lett. 81, 1405–1408 (1998).
[CrossRef]

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Soukoulis, C. M.

B. Temelkuran, E. Ozbay, M. Sigalas, G. Tuttle, C. M. Soukoulis, and K. M. Ho, “Reflection properties of metallic photonic crystals,” Appl. Phys. A 66, 363–365 (1998).
[CrossRef]

E. Lidorikis, M. M. Sigalas, E. N. Economou, and C. M. Soukoulis, “Tight-binding parameterization for photonic bandgap materials,” Phys. Rev. Lett. 81, 1405–1408 (1998).
[CrossRef]

Stefanou, N.

N. Stefanou and A. Modinos, “Impurity bands in photonic insulators,” Phys. Rev. B 57, 12127–12133 (1998).
[CrossRef]

Stein, A.

S. E. Han, A. Stein, and D. J. Norris, “Tailoring self-assembled metallic photonic crystals for modified thermal emission,” Phys. Rev. Lett. 99, 053906 (2007).
[CrossRef]

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J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Low frequency plasmons in thin-wire structures,” J. Phys. 10, 4785–4809 (1998).
[CrossRef]

J. B. Pendry, A. J. Holden, W. J. Stewart, and I. Youngs, “Extremely low frequency plasmons in metallic mesostructures,” Phys. Rev. Lett. 76, 4773–4776 (1996).
[CrossRef]

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Tayeb, G.

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M. Bayindir, B. Temelkuran, and E. Ozbay, “Tight-binding description of the coupled defect modes in three-dimensional photonic crystal,” Phys. Rev. Lett. 84, 2140–2143 (2000).
[CrossRef]

B. Temelkuran, E. Ozbay, M. Sigalas, G. Tuttle, C. M. Soukoulis, and K. M. Ho, “Reflection properties of metallic photonic crystals,” Appl. Phys. A 66, 363–365 (1998).
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B. Temelkuran, E. Ozbay, M. Sigalas, G. Tuttle, C. M. Soukoulis, and K. M. Ho, “Reflection properties of metallic photonic crystals,” Appl. Phys. A 66, 363–365 (1998).
[CrossRef]

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S. Belousov, M. Bogdanova, A. Deinega, S. Eyderman, I. Valuev, Y. Lozovik, I. Polischuk, B. Potapkin, B. Ramamurthi, T. Deng, and V. Midha, “Using metallic photonic crystals as visible light sources,” Phys. Rev. B 86, 174201 (2012).
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K. Wang, “Light wave states in quasi-periodic metallic structures,” Phys. Rev. B 86, 235110 (2012).
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D. F. Sievenpiper, M. E. Sickmiller, and E. Yablonovitch, “3D wire mesh photonic crystals,” Phys. Rev. Lett. 76, 2480–2483 (1996).
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E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett. 58, 2059–2062 (1987).
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J. B. Pendry, A. J. Holden, W. J. Stewart, and I. Youngs, “Extremely low frequency plasmons in metallic mesostructures,” Phys. Rev. Lett. 76, 4773–4776 (1996).
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B. Temelkuran, E. Ozbay, M. Sigalas, G. Tuttle, C. M. Soukoulis, and K. M. Ho, “Reflection properties of metallic photonic crystals,” Appl. Phys. A 66, 363–365 (1998).
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L. Dal Negro, N. Feng, and A. Gopinath, “Electromagnetic coupling and plasmon localization in deterministic aperiodic arrays,” J. Opt. A 10, 064013 (2008).
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J. Phys. (1)

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Low frequency plasmons in thin-wire structures,” J. Phys. 10, 4785–4809 (1998).
[CrossRef]

Nature (2)

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391, 667–669 (1998).
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J. G. Fleming, S. Y. Lin, I. El-Kady, R. Biswas, and K. M. Ho, “All-metallic three-dimensional photonic crystals with a large infrared bandgap,” Nature 417, 52–55 (2002).
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Opt. Commun. (1)

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Opt. Express (5)

Opt. Lett. (1)

Phys. Rev. B (6)

N. Stefanou and A. Modinos, “Impurity bands in photonic insulators,” Phys. Rev. B 57, 12127–12133 (1998).
[CrossRef]

K. Wang, “Light localization in photonic bandgaps of quasi-periodic dielectric structures,” Phys. Rev. B 82, 045119 (2010).
[CrossRef]

K. Wang, “Light wave states in quasi-periodic metallic structures,” Phys. Rev. B 86, 235110 (2012).
[CrossRef]

C. Forestiere, G. Miano, G. Rubinacci, and L. Dal Negro, “Role of aperiodic order in the spectral, localization, and scaling properties of plasmon modes for the design of nanoparticle arrays,” Phys. Rev. B 79, 085404 (2009).
[CrossRef]

C. Bauer, G. Kobiela, and H. Giessen, “Optical properties of two-dimensional quasi-crystalline plasmonic arrays,” Phys. Rev. B 84, 193104 (2011).
[CrossRef]

S. Belousov, M. Bogdanova, A. Deinega, S. Eyderman, I. Valuev, Y. Lozovik, I. Polischuk, B. Potapkin, B. Ramamurthi, T. Deng, and V. Midha, “Using metallic photonic crystals as visible light sources,” Phys. Rev. B 86, 174201 (2012).
[CrossRef]

Phys. Rev. Lett. (7)

S. E. Han, A. Stein, and D. J. Norris, “Tailoring self-assembled metallic photonic crystals for modified thermal emission,” Phys. Rev. Lett. 99, 053906 (2007).
[CrossRef]

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

D. F. Sievenpiper, M. E. Sickmiller, and E. Yablonovitch, “3D wire mesh photonic crystals,” Phys. Rev. Lett. 76, 2480–2483 (1996).
[CrossRef]

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

J. B. Pendry, A. J. Holden, W. J. Stewart, and I. Youngs, “Extremely low frequency plasmons in metallic mesostructures,” Phys. Rev. Lett. 76, 4773–4776 (1996).
[CrossRef]

E. Lidorikis, M. M. Sigalas, E. N. Economou, and C. M. Soukoulis, “Tight-binding parameterization for photonic bandgap materials,” Phys. Rev. Lett. 81, 1405–1408 (1998).
[CrossRef]

M. Bayindir, B. Temelkuran, and E. Ozbay, “Tight-binding description of the coupled defect modes in three-dimensional photonic crystal,” Phys. Rev. Lett. 84, 2140–2143 (2000).
[CrossRef]

Other (3)

N. W. Ashcroft and N. D. Mermin, Solid State Physics (Saunders College, 1976), Chap. 10, pp. 175–190.

http://en.wikipedia.org/wiki/Truncated_square_tiling .

B. Grünbaum and G. S. Shephard, Tilings and Patterns (Freeman, 1987), pp. 57–65.

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Figures (7)

Fig. 1.
Fig. 1.

Mediterranean (a) and snowflake (b) tilings, constructed by tiles A and B (or B1 and B2). The unit cells, with parameter a, are delimited by dashed lines. The relative sizes of these tiles, as well as the shapes of the B (or B1 and B2) tiles, can be modulated by varying l without changing a.

Fig. 2.
Fig. 2.

Low frequency s-like resonance modes inside the A (a) and B (b) tiles of the Mediterranean tiling for, respectively, l=0 and 0.6a, and inside the A (c) and B2 (d) tiles of the snowflake tiling for, respectively, l=0.2 and 0.6a.

Fig. 3.
Fig. 3.

s bands for different l values for the Mediterranean tiling obtained by the FDTD method (various symbols). Curves obtained from the tight-binding model using the parameters in Table 1 are depicted by solid lines. For each l value, the bands at Γ point display, in order of increasing frequency levels, 1A1g and 2A1g symmetries (only the first bands for l=(21)a and 0.60a are shown).

Fig. 4.
Fig. 4.

s bands for different l values for the snowflake tiling obtained by the FDTD method (various symbols). Curves obtained from the tight-binding model using the parameters in Table 2 are depicted by solid lines. The frequency scale in (b) is the same as in (a), whereas that in (c) is ten times that in (a). The bands at Γ point display, in order of increasing frequency levels, 1A1g, 2A1g and B1u symmetries for l<a/3, and 1A1g, B1u and 2A1g symmetries for l>a/3, respectively (only the first band for l=0.20a and the first and second bands for l=0.60a are shown).

Fig. 5.
Fig. 5.

Electric field distributions at Γ points corresponding to the low (a) and high frequency (b) bands for l=0.20a for the Mediterranean tiling (see Fig. 3), and the low (c) and high frequency [(d) and (e)] bands for l=0.33a for the snowflake tiling (see Fig. 4). The unit cells are delimited by dashed lines. The ± signs indicate the field polarities.

Fig. 6.
Fig. 6.

s and p bands for the Mediterranean (a) and snowflake (b) tilings for, respectively, l=(21)a and a/3, obtained by the FDTD method (circles). The curves calculated from the tight-binding model using the parameters in Tables 5 and 6 (for the p bands) and in Tables 1 and 2 (for the s bands), are depicted by solid lines.

Fig. 7.
Fig. 7.

px and py modes inside the B tile of the Mediterranean tiling [(a) and (b)] and the hexagonal tile of the snowflake tiling [(e) and (f)], as well as the electric field distributions corresponding to the two p bands at Γ points in Fig. 6 [(c), (d) and (g), (h)]. The unit cells are delimited by dashed lines. The ± signs indicate the field polarities.

Tables (6)

Tables Icon

Table 1. Mediterranean Tiling Energy Levels, Overlaps, and Shifts for Various l Valuesa

Tables Icon

Table 2. Snowflake Tiling Energy Levels, Overlaps, and Shifts for Various l Valuesa

Tables Icon

Table 3. Mediterranean Tiling Equation (1) Coefficients at Γ Point for Various l Values from Tight-Binding and FDTD Methods

Tables Icon

Table 4. Snowflake Tiling Equation (1) Coefficients at Γ Point for Various l Values from Tight-Binding and FDTD Methods

Tables Icon

Table 5. Mediterranean Tiling Energy Levels, Integrals, and Shifts for l=(21)a

Tables Icon

Table 6. Snowflake Tiling Energy Levels, Integrals, and Shifts for l=a/3a

Equations (10)

Equations on this page are rendered with MathJax. Learn more.

|Ψk(r)=meikRmNqbq(k)eikdp|ϕq(rRmdq),
H=H0+ΔU(r),
αpq=ϕp|ϕqβp=ΔU(r)ϕp|ϕpγpq=ϕp|ΔU(r)|ϕq.
det[(ωsA2ωk2)(1+ζαssσAA)βsAζγssσAAη[γssσABαssσAB(ωsB2ωk2)]η[γssσABαssσAB(ωsA2ωk2)](ωsB2ωk2)(1+ζαssσBB)βsBζγssσBB]=0
ζ=2[cos(kxa)+cos(kya)]η=4cos(kxa/2)cos(kya/2),
det[ωsA2βsAχγssσAAωk2ξ[γssσAB1αssσAB1(ωsB12ωk2)]ξ*[γssσAB2αssσAB2(ωsB22ωk2)]ξ*[γssσAB1αssσAB1(ωsA2ωk2)]ωsB12βsB1χγssσB1B1ωk2ξ[γssσB1B2αssσB1B2(ωsB22ωk2)]ξ[γssσAB2αssσAB2(ωsA2ωk2)]ξ*[γssσB1B2αssσB1B2(ωsB12ωk2)]ωsB22βsB2χγssσB2B2ωk2]=0
ξ=eikya/3+2eikya/23cos(kxa/2)χ=2[coskxa+cos(kxa/2+3kya/2)+cos(kxa/23kya/2)]
det[ωpxB2βpxB2γppπBcos(kya)2γppσBcos(kxa)ωk200ωpyB2βpyB2γppπBcos(kxa)2γppσBcos(kya)ωk2]=0,
det[ωpx2βpx2γppσcos(kxb)μ(3γppπ+γppσ)ωk23ν(γppπγppσ)3ν(γppπγppσ)ωpy2βpy2γppπcos(kxb)μ(γppπ+3γppσ)ωk2]=0
μ=cos(kxb/2)cos(ky3b/2)ν=sin(kxb/2)sin(ky3b/2)

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