Abstract

Single layers of dielectric spheres are an interesting system to study from the fundamental and applied points of view. In this paper we present a systematic study of the influence of structural disorder on the transmission spectra of arrangements of spheres of different compactness. Glass sphere (ε=7) planes were built and their transmission spectra in the microwave range measured. Transmission behavior of this system is highly tolerant to disorder. Even in completely disordered arrangements, there is a highly rejected band with the dips of the spectrum observable. These results suggest that the collective modes of the sphere planes are formed by weakly coupled Mie modes of the individual spheres, and this coupling is governed by the average distance among the spheres. Disorder tolerance allows simpler fabrication procedures where the position of the spheres does not need to be precisely controlled.

© 2011 Optical Society of America

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    [CrossRef]
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    [CrossRef]
  35. L. L. Lima, M. A. R. C. Alencar, D. P. Caetano, D. R. Solli, and J. M. Hickmann, “The effect of disorder on two-dimensional photonic crystal waveguides,” J. Appl. Phys. 103, 123102(2008).
    [CrossRef]
  36. T. N. Langtry, A. A. Asatryan, L. C. Botten, C. M. de Sterke, R. C. McPhedran, and P. A. Robinson, “Effects of disorder in two-dimensional photonic crystal waveguides,” Phys. Rev. E 68, 026611 (2003).
    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
  44. R. Rengarajan, D. Mittleman, C. Rich, and V. Colvin, “Effect of disorder on the optical properties of colloidal crystals,” Phys. Rev. E 71, 016615 (2005).
    [CrossRef]
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    [CrossRef]
  46. A. V. Baryshev, V. A. Kosobukin, K. B. Samusev, D. E. Usvyat, and M. F. Limonov, “Light diffraction from opal-based photonic crystals with growth-induced disorder: experiment and theory,” Phys. Rev. B 73, 205118 (2006).
    [CrossRef]
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    [CrossRef]

2010

A. Andueza, R. Echeverría, P. Morales, and J. Sevilla, “Geometry influence on the transmission spectra of dielectric single layers of spheres with different compactness,” J. Appl. Phys. 107, 124902 (2010).
[CrossRef] [PubMed]

2009

B. Wang, Y. Jin, and S. He, “Effects of disorder in a photonic crystal on the extraction efficiency of a light-emitting diode,” J. Appl. Phys. 106, 014508 (2009).
[CrossRef]

L. A. Dorado and R. A. Depine, “Modeling of disorder effects and optical extinction in three-dimensional photonic crystals,” Phys. Rev. B 79, 045124 (2009).
[CrossRef]

B. Auguié and W. L. Barnes, “Diffractive coupling in gold nanoparticle arrays and the effect of disorder,” Opt. Lett. 34, 401–403 (2009).
[CrossRef] [PubMed]

C. Rockstuhl and F. Lederer, “Suppression of the local density of states in a medium made of randomly arranged dielectric spheres,” Phys. Rev. B 79, 132202 (2009).
[CrossRef]

2008

L. L. Lima, M. A. R. C. Alencar, D. P. Caetano, D. R. Solli, and J. M. Hickmann, “The effect of disorder on two-dimensional photonic crystal waveguides,” J. Appl. Phys. 103, 123102(2008).
[CrossRef]

J. Sun, Y. Li, H. Dong, P. Zhan, C. Tang, M. Zhu, and Z. Wang, “Fabrication and light-transmission properties of monolayer square symmetric colloidal crystals via controlled convective self-assembly on 1D grooves,” Adv. Mater. 20, 123–128 (2008).
[CrossRef]

A. Andueza, R. Echeverría, and J. Sevilla, “Evolution of the electromagnetic modes of a single layer of dielectric spheres with compactness,” J. Appl. Phys. 104, 043103 (2008).
[CrossRef]

Z. Y. Koide, K. Fujisawa, and M. Nakane, “Preparation of non-contact ordered array of polystyrene colloidal particles by using a metallic thin film of fused hemispheres,” Colloids Surf. A 330, 108–111 (2008).
[CrossRef]

2007

I. V. Ponomarev, M. Schwab, G. Dasbach, M. Bayer, T. L. Reinecke, J. P. Reithmaier, and A. Forchel, “Influence of geometric disorder on the band structure of a photonic crystal: Experiment and theory,” Phys. Rev. B 75, 205434(2007).
[CrossRef]

T. Prasad, V. L. Colvin, and D. M. Mittleman, “The effect of structural disorder on guided resonances in photonic crystal slabs studied with terahertz time-domain spectroscopy,” Opt. Express 15, 16954–16965 (2007).
[CrossRef] [PubMed]

A. Andueza and J. Sevilla, “Non compact single-layers of dielectric spheres electromagnetic behaviour,” Opt. Quantum Electron. 39, 311–320 (2007).
[CrossRef]

R. Meisels and F. Kuchar, “Density-of-states and wave propagation in two-dimensional photonic crystals with positional disorder,” J. Opt. A 9, S396–S402 (2007).
[CrossRef]

2006

A. V. Baryshev, V. A. Kosobukin, K. B. Samusev, D. E. Usvyat, and M. F. Limonov, “Light diffraction from opal-based photonic crystals with growth-induced disorder: experiment and theory,” Phys. Rev. B 73, 205118 (2006).
[CrossRef]

K. Vynck, K. Cassagne, and E. Centeno, “Superlattice for photonic band gap opening in monolayers of dielectric spheres,” Opt. Express 14, 6668–6674 (2006).
[CrossRef] [PubMed]

S. Matsushita and M. Shimomura, “Light-propagation patterns in freestanding two-dimensional colloidal crystals,” Colloids Surf. A 284–285, 315–319 (2006).
[CrossRef]

W. Cai and R. Piestun, “Patterning of silica microsphere monolayers with focused femtosecond laser pulses,” Appl. Phys. Lett. 88, 111112 (2006).
[CrossRef]

2005

E. Mine, M. Hirose, D. Nagao, Y. Kobayashi, and M. Konno, “Synthesis of submicrometer-sized titania spherical particles with a sol-gel method and their application to colloidal photonic crystals,” J. Colloid Interface Sci. 291, 162–168 (2005).
[CrossRef] [PubMed]

F. Jonsson, C. M. S. Torres, J. Seekamp, M. Schniedergers, A. Tiedemann, J. Ye, and R. Zentel, “Artificially inscribed defects in opal photonic crystals,” Microelectron. Eng. 78–79, 429–435 (2005).
[CrossRef]

M. Skorobogatiy, G. Bégin, and A. Talneau, “Statistical analysis of geometrical imperfections from the images of 2D photonic crystals,” Opt. Express 13, 2487–2502 (2005).
[CrossRef] [PubMed]

Y. Kurokawa, H. Miyazaki, H. T. Miyazaki, and Y. Jimba, “Effect of a semi-infinite substrate on the internal electric field intensity distribution of a monolayer of periodically arrayed dielectric spheres,” J. Phys. Soc. Jpn. 74, 924–929 (2005).
[CrossRef]

R. Rengarajan, D. Mittleman, C. Rich, and V. Colvin, “Effect of disorder on the optical properties of colloidal crystals,” Phys. Rev. E 71, 016615 (2005).
[CrossRef]

D. M. Beggs, M. A. Kaliteevski, S. Brand, R. A. Abram, D. Cassagne, and J. P. Albert, “Disorder induced modification of reflection and transmission spectra of a two-dimensional photonic crystal with an incomplete band-gap,” J. Phys. Condens. Matter 17, 4049–4055 (2005).
[CrossRef]

2004

T. Kondo, S. Yamaguti, M. Hangyo, K. Yamamoto, Y. Segawa, and K. Ohtaka, “Refractive index dependence of the transmission properties for a photonic crystal array of dielectric spheres,” Phys. Rev. B 70, 235113 (2004).
[CrossRef]

Y. Kurokawa, Y. Jimba, and H. Miyazaki, “Internal electric-field distribution of a monolayer of periodically arrayed dielectric spheres,” Phys. Rev. B 70, 155107 (2004).
[CrossRef]

Y. Kurokawa, H. Miyazaki, and Y. Jimba, “Optical band structure and near-field intensity of a periodically arrayed monolayer of dielectric spheres on dielectric substrate of finite thickness,” Phys. Rev. B 69, 155117 (2004).
[CrossRef]

W. R. Frei and H. T. Johnson, “Finite-element analysis of disorder effects in photonic crystals,” Phys. Rev. B 70, 165116(2004).
[CrossRef]

2003

T. N. Langtry, A. A. Asatryan, L. C. Botten, C. M. de Sterke, R. C. McPhedran, and P. A. Robinson, “Effects of disorder in two-dimensional photonic crystal waveguides,” Phys. Rev. E 68, 026611 (2003).
[CrossRef]

M. A. Kaliteevski, J. M. Martinez, D. Cassagne, and J. P. Albert, “Disorder-induced modification of the attenuation of light in a two-dimensional photonic crystal with complete band gap,” Phys. Status Solidi A 195, 612–617 (2003).
[CrossRef]

2002

Y. Kurokawa, H. Miyazaki, and Y. Jimba, “Light scattering from a monolayer of periodically arrayed dielectric spheres on dielectric substrates,” Phys. Rev. B 65, 2011021 (2002).
[CrossRef]

R. Sainidou, N. Stefanou, I. E. Psarobas, and A. Modinos, “Scattering of elastic waves by a periodic monolayer of spheres,” Phys. Rev. B 66, 024303 (2002).
[CrossRef]

T. Kondo, M. Hangyo, S. Yamaguchi, S. Yano, Y. Segawa, and K. Ohtaka, “Transmission characteristics of a two-dimensional photonic crystal array of dielectric spheres using subterahertz time domain spectroscopy,” Phys. Rev. B 66, 331111 (2002).
[CrossRef]

2000

H. T. Miyazaki, H. Miyazaki, K. Ohtaka, and T. Sato, “Photonic band in two-dimensional lattices of micrometer-sized spheres mechanically arranged under a scanning electron microscope,” J. Appl. Phys. 87, 7152–7158 (2000).
[CrossRef]

K. Ohtaka, Y. Suda, S. Nagano, T. Ueta, A. Imada, T. Koda, J. S. Bae, K. Mizuno, S. Yano, and Y. Segawa, “Photonic band effects in a two-dimensional array of dielectric spheres in the millimeter-wave region,” Phys. Rev. B 61, 5267–5279(2000).
[CrossRef]

1999

H. Y. Ryu, J. K. Hwang, and Y. H. Lee, “Effect of size nonuniformities on the band gap of two-dimensional photonic crystals,” Phys. Rev. B 59, 5463–5469 (1999).
[CrossRef]

A. A. Asatryan, P. A. Robinson, L. C. Botten, R. C. McPhedran, N. A. Nicorovici, and C. M. de Sterke, “Effects of disorder on wave propagation in two-dimensional photonic crystals,” Phys. Rev. E 60, 6118–6127 (1999).
[CrossRef]

M. M. Sigalas, C. M. Soukoulis, C. T. Chan, R. Biswas, and K. M. Ho, “Effect of disorder on photonic band gaps,” Phys. Rev. B 59, 12767–12770 (1999).
[CrossRef]

1996

K. Ohtaka and Y. Tanabe, “Photonic band using vector spherical waves. I. Various properties of Bloch electric fields and heavy photons,” J. Phys. Soc. Jpn. 65, 2265–2275 (1996).
[CrossRef]

K. Ohtaka and Y. Tanabe, “Photonic bands using vector spherical waves. II. Reflectivity, coherence and local field,” J. Phys. Soc. Jpn. 65, 2276–2284 (1996).
[CrossRef]

K. Ohtaka and Y. Tanabe, “Photonic bands using vector spherical waves. III. Group-theoretical treatment,” J. Phys. Soc. Jpn. 65, 2670–2684 (1996).
[CrossRef]

1995

S. H. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “Theoretical investigation of fabrication-related disorder on the properties of photonic crystals,” J. Appl. Phys. 78, 1415–1418 (1995).
[CrossRef]

1987

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

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

1982

K. Ohtaka and M. Inoue, “Light scattering from macroscopic spherical bodies. I. Integrated density of states of transverse electromagnetic fields,” Phys. Rev. B 25, 677–688 (1982).
[CrossRef]

1980

K. Ohtaka, “Scattering theory of low-energy photon diffraction,” J. Phys. C 13, 667–680 (1980).
[CrossRef]

1979

K. Ohtaka, “Energy band of photons and low-energy photon diffraction,” Phys. Rev. B 19, 5057–5067 (1979).
[CrossRef]

Abram, R. A.

D. M. Beggs, M. A. Kaliteevski, S. Brand, R. A. Abram, D. Cassagne, and J. P. Albert, “Disorder induced modification of reflection and transmission spectra of a two-dimensional photonic crystal with an incomplete band-gap,” J. Phys. Condens. Matter 17, 4049–4055 (2005).
[CrossRef]

Albert, J. P.

D. M. Beggs, M. A. Kaliteevski, S. Brand, R. A. Abram, D. Cassagne, and J. P. Albert, “Disorder induced modification of reflection and transmission spectra of a two-dimensional photonic crystal with an incomplete band-gap,” J. Phys. Condens. Matter 17, 4049–4055 (2005).
[CrossRef]

M. A. Kaliteevski, J. M. Martinez, D. Cassagne, and J. P. Albert, “Disorder-induced modification of the attenuation of light in a two-dimensional photonic crystal with complete band gap,” Phys. Status Solidi A 195, 612–617 (2003).
[CrossRef]

Alencar, M. A. R. C.

L. L. Lima, M. A. R. C. Alencar, D. P. Caetano, D. R. Solli, and J. M. Hickmann, “The effect of disorder on two-dimensional photonic crystal waveguides,” J. Appl. Phys. 103, 123102(2008).
[CrossRef]

Andueza, A.

A. Andueza, R. Echeverría, P. Morales, and J. Sevilla, “Geometry influence on the transmission spectra of dielectric single layers of spheres with different compactness,” J. Appl. Phys. 107, 124902 (2010).
[CrossRef] [PubMed]

A. Andueza, R. Echeverría, and J. Sevilla, “Evolution of the electromagnetic modes of a single layer of dielectric spheres with compactness,” J. Appl. Phys. 104, 043103 (2008).
[CrossRef]

A. Andueza and J. Sevilla, “Non compact single-layers of dielectric spheres electromagnetic behaviour,” Opt. Quantum Electron. 39, 311–320 (2007).
[CrossRef]

Asatryan, A. A.

T. N. Langtry, A. A. Asatryan, L. C. Botten, C. M. de Sterke, R. C. McPhedran, and P. A. Robinson, “Effects of disorder in two-dimensional photonic crystal waveguides,” Phys. Rev. E 68, 026611 (2003).
[CrossRef]

A. A. Asatryan, P. A. Robinson, L. C. Botten, R. C. McPhedran, N. A. Nicorovici, and C. M. de Sterke, “Effects of disorder on wave propagation in two-dimensional photonic crystals,” Phys. Rev. E 60, 6118–6127 (1999).
[CrossRef]

Auguié, B.

Bae, J. S.

K. Ohtaka, Y. Suda, S. Nagano, T. Ueta, A. Imada, T. Koda, J. S. Bae, K. Mizuno, S. Yano, and Y. Segawa, “Photonic band effects in a two-dimensional array of dielectric spheres in the millimeter-wave region,” Phys. Rev. B 61, 5267–5279(2000).
[CrossRef]

Barnes, W. L.

Baryshev, A. V.

A. V. Baryshev, V. A. Kosobukin, K. B. Samusev, D. E. Usvyat, and M. F. Limonov, “Light diffraction from opal-based photonic crystals with growth-induced disorder: experiment and theory,” Phys. Rev. B 73, 205118 (2006).
[CrossRef]

Bayer, M.

I. V. Ponomarev, M. Schwab, G. Dasbach, M. Bayer, T. L. Reinecke, J. P. Reithmaier, and A. Forchel, “Influence of geometric disorder on the band structure of a photonic crystal: Experiment and theory,” Phys. Rev. B 75, 205434(2007).
[CrossRef]

Beggs, D. M.

D. M. Beggs, M. A. Kaliteevski, S. Brand, R. A. Abram, D. Cassagne, and J. P. Albert, “Disorder induced modification of reflection and transmission spectra of a two-dimensional photonic crystal with an incomplete band-gap,” J. Phys. Condens. Matter 17, 4049–4055 (2005).
[CrossRef]

Bégin, G.

Biswas, R.

M. M. Sigalas, C. M. Soukoulis, C. T. Chan, R. Biswas, and K. M. Ho, “Effect of disorder on photonic band gaps,” Phys. Rev. B 59, 12767–12770 (1999).
[CrossRef]

Botten, L. C.

T. N. Langtry, A. A. Asatryan, L. C. Botten, C. M. de Sterke, R. C. McPhedran, and P. A. Robinson, “Effects of disorder in two-dimensional photonic crystal waveguides,” Phys. Rev. E 68, 026611 (2003).
[CrossRef]

A. A. Asatryan, P. A. Robinson, L. C. Botten, R. C. McPhedran, N. A. Nicorovici, and C. M. de Sterke, “Effects of disorder on wave propagation in two-dimensional photonic crystals,” Phys. Rev. E 60, 6118–6127 (1999).
[CrossRef]

Brand, S.

D. M. Beggs, M. A. Kaliteevski, S. Brand, R. A. Abram, D. Cassagne, and J. P. Albert, “Disorder induced modification of reflection and transmission spectra of a two-dimensional photonic crystal with an incomplete band-gap,” J. Phys. Condens. Matter 17, 4049–4055 (2005).
[CrossRef]

Caetano, D. P.

L. L. Lima, M. A. R. C. Alencar, D. P. Caetano, D. R. Solli, and J. M. Hickmann, “The effect of disorder on two-dimensional photonic crystal waveguides,” J. Appl. Phys. 103, 123102(2008).
[CrossRef]

Cai, W.

W. Cai and R. Piestun, “Patterning of silica microsphere monolayers with focused femtosecond laser pulses,” Appl. Phys. Lett. 88, 111112 (2006).
[CrossRef]

Cassagne, D.

D. M. Beggs, M. A. Kaliteevski, S. Brand, R. A. Abram, D. Cassagne, and J. P. Albert, “Disorder induced modification of reflection and transmission spectra of a two-dimensional photonic crystal with an incomplete band-gap,” J. Phys. Condens. Matter 17, 4049–4055 (2005).
[CrossRef]

M. A. Kaliteevski, J. M. Martinez, D. Cassagne, and J. P. Albert, “Disorder-induced modification of the attenuation of light in a two-dimensional photonic crystal with complete band gap,” Phys. Status Solidi A 195, 612–617 (2003).
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I. V. Ponomarev, M. Schwab, G. Dasbach, M. Bayer, T. L. Reinecke, J. P. Reithmaier, and A. Forchel, “Influence of geometric disorder on the band structure of a photonic crystal: Experiment and theory,” Phys. Rev. B 75, 205434(2007).
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T. N. Langtry, A. A. Asatryan, L. C. Botten, C. M. de Sterke, R. C. McPhedran, and P. A. Robinson, “Effects of disorder in two-dimensional photonic crystal waveguides,” Phys. Rev. E 68, 026611 (2003).
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A. A. Asatryan, P. A. Robinson, L. C. Botten, R. C. McPhedran, N. A. Nicorovici, and C. M. de Sterke, “Effects of disorder on wave propagation in two-dimensional photonic crystals,” Phys. Rev. E 60, 6118–6127 (1999).
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L. A. Dorado and R. A. Depine, “Modeling of disorder effects and optical extinction in three-dimensional photonic crystals,” Phys. Rev. B 79, 045124 (2009).
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A. Andueza, R. Echeverría, P. Morales, and J. Sevilla, “Geometry influence on the transmission spectra of dielectric single layers of spheres with different compactness,” J. Appl. Phys. 107, 124902 (2010).
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I. V. Ponomarev, M. Schwab, G. Dasbach, M. Bayer, T. L. Reinecke, J. P. Reithmaier, and A. Forchel, “Influence of geometric disorder on the band structure of a photonic crystal: Experiment and theory,” Phys. Rev. B 75, 205434(2007).
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Z. Y. Koide, K. Fujisawa, and M. Nakane, “Preparation of non-contact ordered array of polystyrene colloidal particles by using a metallic thin film of fused hemispheres,” Colloids Surf. A 330, 108–111 (2008).
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Hangyo, M.

T. Kondo, S. Yamaguti, M. Hangyo, K. Yamamoto, Y. Segawa, and K. Ohtaka, “Refractive index dependence of the transmission properties for a photonic crystal array of dielectric spheres,” Phys. Rev. B 70, 235113 (2004).
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T. Kondo, M. Hangyo, S. Yamaguchi, S. Yano, Y. Segawa, and K. Ohtaka, “Transmission characteristics of a two-dimensional photonic crystal array of dielectric spheres using subterahertz time domain spectroscopy,” Phys. Rev. B 66, 331111 (2002).
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L. L. Lima, M. A. R. C. Alencar, D. P. Caetano, D. R. Solli, and J. M. Hickmann, “The effect of disorder on two-dimensional photonic crystal waveguides,” J. Appl. Phys. 103, 123102(2008).
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E. Mine, M. Hirose, D. Nagao, Y. Kobayashi, and M. Konno, “Synthesis of submicrometer-sized titania spherical particles with a sol-gel method and their application to colloidal photonic crystals,” J. Colloid Interface Sci. 291, 162–168 (2005).
[CrossRef] [PubMed]

Ho, K. M.

M. M. Sigalas, C. M. Soukoulis, C. T. Chan, R. Biswas, and K. M. Ho, “Effect of disorder on photonic band gaps,” Phys. Rev. B 59, 12767–12770 (1999).
[CrossRef]

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H. Y. Ryu, J. K. Hwang, and Y. H. Lee, “Effect of size nonuniformities on the band gap of two-dimensional photonic crystals,” Phys. Rev. B 59, 5463–5469 (1999).
[CrossRef]

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K. Ohtaka, Y. Suda, S. Nagano, T. Ueta, A. Imada, T. Koda, J. S. Bae, K. Mizuno, S. Yano, and Y. Segawa, “Photonic band effects in a two-dimensional array of dielectric spheres in the millimeter-wave region,” Phys. Rev. B 61, 5267–5279(2000).
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K. Ohtaka and M. Inoue, “Light scattering from macroscopic spherical bodies. I. Integrated density of states of transverse electromagnetic fields,” Phys. Rev. B 25, 677–688 (1982).
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Y. Kurokawa, H. Miyazaki, H. T. Miyazaki, and Y. Jimba, “Effect of a semi-infinite substrate on the internal electric field intensity distribution of a monolayer of periodically arrayed dielectric spheres,” J. Phys. Soc. Jpn. 74, 924–929 (2005).
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Y. Kurokawa, H. Miyazaki, and Y. Jimba, “Optical band structure and near-field intensity of a periodically arrayed monolayer of dielectric spheres on dielectric substrate of finite thickness,” Phys. Rev. B 69, 155117 (2004).
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Y. Kurokawa, Y. Jimba, and H. Miyazaki, “Internal electric-field distribution of a monolayer of periodically arrayed dielectric spheres,” Phys. Rev. B 70, 155107 (2004).
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Y. Kurokawa, H. Miyazaki, and Y. Jimba, “Light scattering from a monolayer of periodically arrayed dielectric spheres on dielectric substrates,” Phys. Rev. B 65, 2011021 (2002).
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B. Wang, Y. Jin, and S. He, “Effects of disorder in a photonic crystal on the extraction efficiency of a light-emitting diode,” J. Appl. Phys. 106, 014508 (2009).
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S. H. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “Theoretical investigation of fabrication-related disorder on the properties of photonic crystals,” J. Appl. Phys. 78, 1415–1418 (1995).
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F. Jonsson, C. M. S. Torres, J. Seekamp, M. Schniedergers, A. Tiedemann, J. Ye, and R. Zentel, “Artificially inscribed defects in opal photonic crystals,” Microelectron. Eng. 78–79, 429–435 (2005).
[CrossRef]

Kaliteevski, M. A.

D. M. Beggs, M. A. Kaliteevski, S. Brand, R. A. Abram, D. Cassagne, and J. P. Albert, “Disorder induced modification of reflection and transmission spectra of a two-dimensional photonic crystal with an incomplete band-gap,” J. Phys. Condens. Matter 17, 4049–4055 (2005).
[CrossRef]

M. A. Kaliteevski, J. M. Martinez, D. Cassagne, and J. P. Albert, “Disorder-induced modification of the attenuation of light in a two-dimensional photonic crystal with complete band gap,” Phys. Status Solidi A 195, 612–617 (2003).
[CrossRef]

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E. Mine, M. Hirose, D. Nagao, Y. Kobayashi, and M. Konno, “Synthesis of submicrometer-sized titania spherical particles with a sol-gel method and their application to colloidal photonic crystals,” J. Colloid Interface Sci. 291, 162–168 (2005).
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Z. Y. Koide, K. Fujisawa, and M. Nakane, “Preparation of non-contact ordered array of polystyrene colloidal particles by using a metallic thin film of fused hemispheres,” Colloids Surf. A 330, 108–111 (2008).
[CrossRef]

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T. Kondo, S. Yamaguti, M. Hangyo, K. Yamamoto, Y. Segawa, and K. Ohtaka, “Refractive index dependence of the transmission properties for a photonic crystal array of dielectric spheres,” Phys. Rev. B 70, 235113 (2004).
[CrossRef]

T. Kondo, M. Hangyo, S. Yamaguchi, S. Yano, Y. Segawa, and K. Ohtaka, “Transmission characteristics of a two-dimensional photonic crystal array of dielectric spheres using subterahertz time domain spectroscopy,” Phys. Rev. B 66, 331111 (2002).
[CrossRef]

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E. Mine, M. Hirose, D. Nagao, Y. Kobayashi, and M. Konno, “Synthesis of submicrometer-sized titania spherical particles with a sol-gel method and their application to colloidal photonic crystals,” J. Colloid Interface Sci. 291, 162–168 (2005).
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A. V. Baryshev, V. A. Kosobukin, K. B. Samusev, D. E. Usvyat, and M. F. Limonov, “Light diffraction from opal-based photonic crystals with growth-induced disorder: experiment and theory,” Phys. Rev. B 73, 205118 (2006).
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R. Meisels and F. Kuchar, “Density-of-states and wave propagation in two-dimensional photonic crystals with positional disorder,” J. Opt. A 9, S396–S402 (2007).
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Y. Kurokawa, H. Miyazaki, H. T. Miyazaki, and Y. Jimba, “Effect of a semi-infinite substrate on the internal electric field intensity distribution of a monolayer of periodically arrayed dielectric spheres,” J. Phys. Soc. Jpn. 74, 924–929 (2005).
[CrossRef]

Y. Kurokawa, H. Miyazaki, and Y. Jimba, “Optical band structure and near-field intensity of a periodically arrayed monolayer of dielectric spheres on dielectric substrate of finite thickness,” Phys. Rev. B 69, 155117 (2004).
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Y. Kurokawa, Y. Jimba, and H. Miyazaki, “Internal electric-field distribution of a monolayer of periodically arrayed dielectric spheres,” Phys. Rev. B 70, 155107 (2004).
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Y. Kurokawa, H. Miyazaki, and Y. Jimba, “Light scattering from a monolayer of periodically arrayed dielectric spheres on dielectric substrates,” Phys. Rev. B 65, 2011021 (2002).
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T. N. Langtry, A. A. Asatryan, L. C. Botten, C. M. de Sterke, R. C. McPhedran, and P. A. Robinson, “Effects of disorder in two-dimensional photonic crystal waveguides,” Phys. Rev. E 68, 026611 (2003).
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C. Rockstuhl and F. Lederer, “Suppression of the local density of states in a medium made of randomly arranged dielectric spheres,” Phys. Rev. B 79, 132202 (2009).
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H. Y. Ryu, J. K. Hwang, and Y. H. Lee, “Effect of size nonuniformities on the band gap of two-dimensional photonic crystals,” Phys. Rev. B 59, 5463–5469 (1999).
[CrossRef]

Li, Y.

J. Sun, Y. Li, H. Dong, P. Zhan, C. Tang, M. Zhu, and Z. Wang, “Fabrication and light-transmission properties of monolayer square symmetric colloidal crystals via controlled convective self-assembly on 1D grooves,” Adv. Mater. 20, 123–128 (2008).
[CrossRef]

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L. L. Lima, M. A. R. C. Alencar, D. P. Caetano, D. R. Solli, and J. M. Hickmann, “The effect of disorder on two-dimensional photonic crystal waveguides,” J. Appl. Phys. 103, 123102(2008).
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A. V. Baryshev, V. A. Kosobukin, K. B. Samusev, D. E. Usvyat, and M. F. Limonov, “Light diffraction from opal-based photonic crystals with growth-induced disorder: experiment and theory,” Phys. Rev. B 73, 205118 (2006).
[CrossRef]

Martinez, J. M.

M. A. Kaliteevski, J. M. Martinez, D. Cassagne, and J. P. Albert, “Disorder-induced modification of the attenuation of light in a two-dimensional photonic crystal with complete band gap,” Phys. Status Solidi A 195, 612–617 (2003).
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T. N. Langtry, A. A. Asatryan, L. C. Botten, C. M. de Sterke, R. C. McPhedran, and P. A. Robinson, “Effects of disorder in two-dimensional photonic crystal waveguides,” Phys. Rev. E 68, 026611 (2003).
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A. A. Asatryan, P. A. Robinson, L. C. Botten, R. C. McPhedran, N. A. Nicorovici, and C. M. de Sterke, “Effects of disorder on wave propagation in two-dimensional photonic crystals,” Phys. Rev. E 60, 6118–6127 (1999).
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J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals: Molding the Flow of Light (Princeton University Press, 1995).

Meisels, R.

R. Meisels and F. Kuchar, “Density-of-states and wave propagation in two-dimensional photonic crystals with positional disorder,” J. Opt. A 9, S396–S402 (2007).
[CrossRef]

Mine, E.

E. Mine, M. Hirose, D. Nagao, Y. Kobayashi, and M. Konno, “Synthesis of submicrometer-sized titania spherical particles with a sol-gel method and their application to colloidal photonic crystals,” J. Colloid Interface Sci. 291, 162–168 (2005).
[CrossRef] [PubMed]

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R. Rengarajan, D. Mittleman, C. Rich, and V. Colvin, “Effect of disorder on the optical properties of colloidal crystals,” Phys. Rev. E 71, 016615 (2005).
[CrossRef]

Mittleman, D. M.

Miyazaki, H.

Y. Kurokawa, H. Miyazaki, H. T. Miyazaki, and Y. Jimba, “Effect of a semi-infinite substrate on the internal electric field intensity distribution of a monolayer of periodically arrayed dielectric spheres,” J. Phys. Soc. Jpn. 74, 924–929 (2005).
[CrossRef]

Y. Kurokawa, H. Miyazaki, and Y. Jimba, “Optical band structure and near-field intensity of a periodically arrayed monolayer of dielectric spheres on dielectric substrate of finite thickness,” Phys. Rev. B 69, 155117 (2004).
[CrossRef]

Y. Kurokawa, Y. Jimba, and H. Miyazaki, “Internal electric-field distribution of a monolayer of periodically arrayed dielectric spheres,” Phys. Rev. B 70, 155107 (2004).
[CrossRef]

Y. Kurokawa, H. Miyazaki, and Y. Jimba, “Light scattering from a monolayer of periodically arrayed dielectric spheres on dielectric substrates,” Phys. Rev. B 65, 2011021 (2002).
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H. T. Miyazaki, H. Miyazaki, K. Ohtaka, and T. Sato, “Photonic band in two-dimensional lattices of micrometer-sized spheres mechanically arranged under a scanning electron microscope,” J. Appl. Phys. 87, 7152–7158 (2000).
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Miyazaki, H. T.

Y. Kurokawa, H. Miyazaki, H. T. Miyazaki, and Y. Jimba, “Effect of a semi-infinite substrate on the internal electric field intensity distribution of a monolayer of periodically arrayed dielectric spheres,” J. Phys. Soc. Jpn. 74, 924–929 (2005).
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H. T. Miyazaki, H. Miyazaki, K. Ohtaka, and T. Sato, “Photonic band in two-dimensional lattices of micrometer-sized spheres mechanically arranged under a scanning electron microscope,” J. Appl. Phys. 87, 7152–7158 (2000).
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K. Ohtaka, Y. Suda, S. Nagano, T. Ueta, A. Imada, T. Koda, J. S. Bae, K. Mizuno, S. Yano, and Y. Segawa, “Photonic band effects in a two-dimensional array of dielectric spheres in the millimeter-wave region,” Phys. Rev. B 61, 5267–5279(2000).
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R. Sainidou, N. Stefanou, I. E. Psarobas, and A. Modinos, “Scattering of elastic waves by a periodic monolayer of spheres,” Phys. Rev. B 66, 024303 (2002).
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A. Andueza, R. Echeverría, P. Morales, and J. Sevilla, “Geometry influence on the transmission spectra of dielectric single layers of spheres with different compactness,” J. Appl. Phys. 107, 124902 (2010).
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K. Ohtaka, Y. Suda, S. Nagano, T. Ueta, A. Imada, T. Koda, J. S. Bae, K. Mizuno, S. Yano, and Y. Segawa, “Photonic band effects in a two-dimensional array of dielectric spheres in the millimeter-wave region,” Phys. Rev. B 61, 5267–5279(2000).
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E. Mine, M. Hirose, D. Nagao, Y. Kobayashi, and M. Konno, “Synthesis of submicrometer-sized titania spherical particles with a sol-gel method and their application to colloidal photonic crystals,” J. Colloid Interface Sci. 291, 162–168 (2005).
[CrossRef] [PubMed]

Nakane, M.

Z. Y. Koide, K. Fujisawa, and M. Nakane, “Preparation of non-contact ordered array of polystyrene colloidal particles by using a metallic thin film of fused hemispheres,” Colloids Surf. A 330, 108–111 (2008).
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A. A. Asatryan, P. A. Robinson, L. C. Botten, R. C. McPhedran, N. A. Nicorovici, and C. M. de Sterke, “Effects of disorder on wave propagation in two-dimensional photonic crystals,” Phys. Rev. E 60, 6118–6127 (1999).
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T. Kondo, S. Yamaguti, M. Hangyo, K. Yamamoto, Y. Segawa, and K. Ohtaka, “Refractive index dependence of the transmission properties for a photonic crystal array of dielectric spheres,” Phys. Rev. B 70, 235113 (2004).
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T. Kondo, M. Hangyo, S. Yamaguchi, S. Yano, Y. Segawa, and K. Ohtaka, “Transmission characteristics of a two-dimensional photonic crystal array of dielectric spheres using subterahertz time domain spectroscopy,” Phys. Rev. B 66, 331111 (2002).
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H. T. Miyazaki, H. Miyazaki, K. Ohtaka, and T. Sato, “Photonic band in two-dimensional lattices of micrometer-sized spheres mechanically arranged under a scanning electron microscope,” J. Appl. Phys. 87, 7152–7158 (2000).
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K. Ohtaka, Y. Suda, S. Nagano, T. Ueta, A. Imada, T. Koda, J. S. Bae, K. Mizuno, S. Yano, and Y. Segawa, “Photonic band effects in a two-dimensional array of dielectric spheres in the millimeter-wave region,” Phys. Rev. B 61, 5267–5279(2000).
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I. V. Ponomarev, M. Schwab, G. Dasbach, M. Bayer, T. L. Reinecke, J. P. Reithmaier, and A. Forchel, “Influence of geometric disorder on the band structure of a photonic crystal: Experiment and theory,” Phys. Rev. B 75, 205434(2007).
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Psarobas, I. E.

R. Sainidou, N. Stefanou, I. E. Psarobas, and A. Modinos, “Scattering of elastic waves by a periodic monolayer of spheres,” Phys. Rev. B 66, 024303 (2002).
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I. V. Ponomarev, M. Schwab, G. Dasbach, M. Bayer, T. L. Reinecke, J. P. Reithmaier, and A. Forchel, “Influence of geometric disorder on the band structure of a photonic crystal: Experiment and theory,” Phys. Rev. B 75, 205434(2007).
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I. V. Ponomarev, M. Schwab, G. Dasbach, M. Bayer, T. L. Reinecke, J. P. Reithmaier, and A. Forchel, “Influence of geometric disorder on the band structure of a photonic crystal: Experiment and theory,” Phys. Rev. B 75, 205434(2007).
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R. Rengarajan, D. Mittleman, C. Rich, and V. Colvin, “Effect of disorder on the optical properties of colloidal crystals,” Phys. Rev. E 71, 016615 (2005).
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R. Rengarajan, D. Mittleman, C. Rich, and V. Colvin, “Effect of disorder on the optical properties of colloidal crystals,” Phys. Rev. E 71, 016615 (2005).
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T. N. Langtry, A. A. Asatryan, L. C. Botten, C. M. de Sterke, R. C. McPhedran, and P. A. Robinson, “Effects of disorder in two-dimensional photonic crystal waveguides,” Phys. Rev. E 68, 026611 (2003).
[CrossRef]

A. A. Asatryan, P. A. Robinson, L. C. Botten, R. C. McPhedran, N. A. Nicorovici, and C. M. de Sterke, “Effects of disorder on wave propagation in two-dimensional photonic crystals,” Phys. Rev. E 60, 6118–6127 (1999).
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C. Rockstuhl and F. Lederer, “Suppression of the local density of states in a medium made of randomly arranged dielectric spheres,” Phys. Rev. B 79, 132202 (2009).
[CrossRef]

Ryu, H. Y.

H. Y. Ryu, J. K. Hwang, and Y. H. Lee, “Effect of size nonuniformities on the band gap of two-dimensional photonic crystals,” Phys. Rev. B 59, 5463–5469 (1999).
[CrossRef]

Sainidou, R.

R. Sainidou, N. Stefanou, I. E. Psarobas, and A. Modinos, “Scattering of elastic waves by a periodic monolayer of spheres,” Phys. Rev. B 66, 024303 (2002).
[CrossRef]

Samusev, K. B.

A. V. Baryshev, V. A. Kosobukin, K. B. Samusev, D. E. Usvyat, and M. F. Limonov, “Light diffraction from opal-based photonic crystals with growth-induced disorder: experiment and theory,” Phys. Rev. B 73, 205118 (2006).
[CrossRef]

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H. T. Miyazaki, H. Miyazaki, K. Ohtaka, and T. Sato, “Photonic band in two-dimensional lattices of micrometer-sized spheres mechanically arranged under a scanning electron microscope,” J. Appl. Phys. 87, 7152–7158 (2000).
[CrossRef]

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F. Jonsson, C. M. S. Torres, J. Seekamp, M. Schniedergers, A. Tiedemann, J. Ye, and R. Zentel, “Artificially inscribed defects in opal photonic crystals,” Microelectron. Eng. 78–79, 429–435 (2005).
[CrossRef]

Schwab, M.

I. V. Ponomarev, M. Schwab, G. Dasbach, M. Bayer, T. L. Reinecke, J. P. Reithmaier, and A. Forchel, “Influence of geometric disorder on the band structure of a photonic crystal: Experiment and theory,” Phys. Rev. B 75, 205434(2007).
[CrossRef]

Seekamp, J.

F. Jonsson, C. M. S. Torres, J. Seekamp, M. Schniedergers, A. Tiedemann, J. Ye, and R. Zentel, “Artificially inscribed defects in opal photonic crystals,” Microelectron. Eng. 78–79, 429–435 (2005).
[CrossRef]

Segawa, Y.

T. Kondo, S. Yamaguti, M. Hangyo, K. Yamamoto, Y. Segawa, and K. Ohtaka, “Refractive index dependence of the transmission properties for a photonic crystal array of dielectric spheres,” Phys. Rev. B 70, 235113 (2004).
[CrossRef]

T. Kondo, M. Hangyo, S. Yamaguchi, S. Yano, Y. Segawa, and K. Ohtaka, “Transmission characteristics of a two-dimensional photonic crystal array of dielectric spheres using subterahertz time domain spectroscopy,” Phys. Rev. B 66, 331111 (2002).
[CrossRef]

K. Ohtaka, Y. Suda, S. Nagano, T. Ueta, A. Imada, T. Koda, J. S. Bae, K. Mizuno, S. Yano, and Y. Segawa, “Photonic band effects in a two-dimensional array of dielectric spheres in the millimeter-wave region,” Phys. Rev. B 61, 5267–5279(2000).
[CrossRef]

Sevilla, J.

A. Andueza, R. Echeverría, P. Morales, and J. Sevilla, “Geometry influence on the transmission spectra of dielectric single layers of spheres with different compactness,” J. Appl. Phys. 107, 124902 (2010).
[CrossRef] [PubMed]

A. Andueza, R. Echeverría, and J. Sevilla, “Evolution of the electromagnetic modes of a single layer of dielectric spheres with compactness,” J. Appl. Phys. 104, 043103 (2008).
[CrossRef]

A. Andueza and J. Sevilla, “Non compact single-layers of dielectric spheres electromagnetic behaviour,” Opt. Quantum Electron. 39, 311–320 (2007).
[CrossRef]

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S. Matsushita and M. Shimomura, “Light-propagation patterns in freestanding two-dimensional colloidal crystals,” Colloids Surf. A 284–285, 315–319 (2006).
[CrossRef]

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M. M. Sigalas, C. M. Soukoulis, C. T. Chan, R. Biswas, and K. M. Ho, “Effect of disorder on photonic band gaps,” Phys. Rev. B 59, 12767–12770 (1999).
[CrossRef]

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L. L. Lima, M. A. R. C. Alencar, D. P. Caetano, D. R. Solli, and J. M. Hickmann, “The effect of disorder on two-dimensional photonic crystal waveguides,” J. Appl. Phys. 103, 123102(2008).
[CrossRef]

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J. Sun, Y. Li, H. Dong, P. Zhan, C. Tang, M. Zhu, and Z. Wang, “Fabrication and light-transmission properties of monolayer square symmetric colloidal crystals via controlled convective self-assembly on 1D grooves,” Adv. Mater. 20, 123–128 (2008).
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[CrossRef]

Tang, C.

J. Sun, Y. Li, H. Dong, P. Zhan, C. Tang, M. Zhu, and Z. Wang, “Fabrication and light-transmission properties of monolayer square symmetric colloidal crystals via controlled convective self-assembly on 1D grooves,” Adv. Mater. 20, 123–128 (2008).
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F. Jonsson, C. M. S. Torres, J. Seekamp, M. Schniedergers, A. Tiedemann, J. Ye, and R. Zentel, “Artificially inscribed defects in opal photonic crystals,” Microelectron. Eng. 78–79, 429–435 (2005).
[CrossRef]

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F. Jonsson, C. M. S. Torres, J. Seekamp, M. Schniedergers, A. Tiedemann, J. Ye, and R. Zentel, “Artificially inscribed defects in opal photonic crystals,” Microelectron. Eng. 78–79, 429–435 (2005).
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K. Ohtaka, Y. Suda, S. Nagano, T. Ueta, A. Imada, T. Koda, J. S. Bae, K. Mizuno, S. Yano, and Y. Segawa, “Photonic band effects in a two-dimensional array of dielectric spheres in the millimeter-wave region,” Phys. Rev. B 61, 5267–5279(2000).
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A. V. Baryshev, V. A. Kosobukin, K. B. Samusev, D. E. Usvyat, and M. F. Limonov, “Light diffraction from opal-based photonic crystals with growth-induced disorder: experiment and theory,” Phys. Rev. B 73, 205118 (2006).
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B. Wang, Y. Jin, and S. He, “Effects of disorder in a photonic crystal on the extraction efficiency of a light-emitting diode,” J. Appl. Phys. 106, 014508 (2009).
[CrossRef]

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J. Sun, Y. Li, H. Dong, P. Zhan, C. Tang, M. Zhu, and Z. Wang, “Fabrication and light-transmission properties of monolayer square symmetric colloidal crystals via controlled convective self-assembly on 1D grooves,” Adv. Mater. 20, 123–128 (2008).
[CrossRef]

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

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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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T. Kondo, M. Hangyo, S. Yamaguchi, S. Yano, Y. Segawa, and K. Ohtaka, “Transmission characteristics of a two-dimensional photonic crystal array of dielectric spheres using subterahertz time domain spectroscopy,” Phys. Rev. B 66, 331111 (2002).
[CrossRef]

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T. Kondo, S. Yamaguti, M. Hangyo, K. Yamamoto, Y. Segawa, and K. Ohtaka, “Refractive index dependence of the transmission properties for a photonic crystal array of dielectric spheres,” Phys. Rev. B 70, 235113 (2004).
[CrossRef]

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T. Kondo, S. Yamaguti, M. Hangyo, K. Yamamoto, Y. Segawa, and K. Ohtaka, “Refractive index dependence of the transmission properties for a photonic crystal array of dielectric spheres,” Phys. Rev. B 70, 235113 (2004).
[CrossRef]

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T. Kondo, M. Hangyo, S. Yamaguchi, S. Yano, Y. Segawa, and K. Ohtaka, “Transmission characteristics of a two-dimensional photonic crystal array of dielectric spheres using subterahertz time domain spectroscopy,” Phys. Rev. B 66, 331111 (2002).
[CrossRef]

K. Ohtaka, Y. Suda, S. Nagano, T. Ueta, A. Imada, T. Koda, J. S. Bae, K. Mizuno, S. Yano, and Y. Segawa, “Photonic band effects in a two-dimensional array of dielectric spheres in the millimeter-wave region,” Phys. Rev. B 61, 5267–5279(2000).
[CrossRef]

Ye, J.

F. Jonsson, C. M. S. Torres, J. Seekamp, M. Schniedergers, A. Tiedemann, J. Ye, and R. Zentel, “Artificially inscribed defects in opal photonic crystals,” Microelectron. Eng. 78–79, 429–435 (2005).
[CrossRef]

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F. Jonsson, C. M. S. Torres, J. Seekamp, M. Schniedergers, A. Tiedemann, J. Ye, and R. Zentel, “Artificially inscribed defects in opal photonic crystals,” Microelectron. Eng. 78–79, 429–435 (2005).
[CrossRef]

Zhan, P.

J. Sun, Y. Li, H. Dong, P. Zhan, C. Tang, M. Zhu, and Z. Wang, “Fabrication and light-transmission properties of monolayer square symmetric colloidal crystals via controlled convective self-assembly on 1D grooves,” Adv. Mater. 20, 123–128 (2008).
[CrossRef]

Zhu, M.

J. Sun, Y. Li, H. Dong, P. Zhan, C. Tang, M. Zhu, and Z. Wang, “Fabrication and light-transmission properties of monolayer square symmetric colloidal crystals via controlled convective self-assembly on 1D grooves,” Adv. Mater. 20, 123–128 (2008).
[CrossRef]

Adv. Mater.

J. Sun, Y. Li, H. Dong, P. Zhan, C. Tang, M. Zhu, and Z. Wang, “Fabrication and light-transmission properties of monolayer square symmetric colloidal crystals via controlled convective self-assembly on 1D grooves,” Adv. Mater. 20, 123–128 (2008).
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Appl. Phys. Lett.

W. Cai and R. Piestun, “Patterning of silica microsphere monolayers with focused femtosecond laser pulses,” Appl. Phys. Lett. 88, 111112 (2006).
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S. Matsushita and M. Shimomura, “Light-propagation patterns in freestanding two-dimensional colloidal crystals,” Colloids Surf. A 284–285, 315–319 (2006).
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A. Andueza, R. Echeverría, P. Morales, and J. Sevilla, “Geometry influence on the transmission spectra of dielectric single layers of spheres with different compactness,” J. Appl. Phys. 107, 124902 (2010).
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L. L. Lima, M. A. R. C. Alencar, D. P. Caetano, D. R. Solli, and J. M. Hickmann, “The effect of disorder on two-dimensional photonic crystal waveguides,” J. Appl. Phys. 103, 123102(2008).
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[CrossRef]

A. Andueza, R. Echeverría, and J. Sevilla, “Evolution of the electromagnetic modes of a single layer of dielectric spheres with compactness,” J. Appl. Phys. 104, 043103 (2008).
[CrossRef]

B. Wang, Y. Jin, and S. He, “Effects of disorder in a photonic crystal on the extraction efficiency of a light-emitting diode,” J. Appl. Phys. 106, 014508 (2009).
[CrossRef]

S. H. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “Theoretical investigation of fabrication-related disorder on the properties of photonic crystals,” J. Appl. Phys. 78, 1415–1418 (1995).
[CrossRef]

J. Colloid Interface Sci.

E. Mine, M. Hirose, D. Nagao, Y. Kobayashi, and M. Konno, “Synthesis of submicrometer-sized titania spherical particles with a sol-gel method and their application to colloidal photonic crystals,” J. Colloid Interface Sci. 291, 162–168 (2005).
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R. Meisels and F. Kuchar, “Density-of-states and wave propagation in two-dimensional photonic crystals with positional disorder,” J. Opt. A 9, S396–S402 (2007).
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[CrossRef]

J. Phys. Soc. Jpn.

K. Ohtaka and Y. Tanabe, “Photonic band using vector spherical waves. I. Various properties of Bloch electric fields and heavy photons,” J. Phys. Soc. Jpn. 65, 2265–2275 (1996).
[CrossRef]

K. Ohtaka and Y. Tanabe, “Photonic bands using vector spherical waves. II. Reflectivity, coherence and local field,” J. Phys. Soc. Jpn. 65, 2276–2284 (1996).
[CrossRef]

K. Ohtaka and Y. Tanabe, “Photonic bands using vector spherical waves. III. Group-theoretical treatment,” J. Phys. Soc. Jpn. 65, 2670–2684 (1996).
[CrossRef]

Y. Kurokawa, H. Miyazaki, H. T. Miyazaki, and Y. Jimba, “Effect of a semi-infinite substrate on the internal electric field intensity distribution of a monolayer of periodically arrayed dielectric spheres,” J. Phys. Soc. Jpn. 74, 924–929 (2005).
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Microelectron. Eng.

F. Jonsson, C. M. S. Torres, J. Seekamp, M. Schniedergers, A. Tiedemann, J. Ye, and R. Zentel, “Artificially inscribed defects in opal photonic crystals,” Microelectron. Eng. 78–79, 429–435 (2005).
[CrossRef]

Opt. Express

Opt. Lett.

Opt. Quantum Electron.

A. Andueza and J. Sevilla, “Non compact single-layers of dielectric spheres electromagnetic behaviour,” Opt. Quantum Electron. 39, 311–320 (2007).
[CrossRef]

Phys. Rev. B

R. Sainidou, N. Stefanou, I. E. Psarobas, and A. Modinos, “Scattering of elastic waves by a periodic monolayer of spheres,” Phys. Rev. B 66, 024303 (2002).
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[CrossRef]

T. Kondo, S. Yamaguti, M. Hangyo, K. Yamamoto, Y. Segawa, and K. Ohtaka, “Refractive index dependence of the transmission properties for a photonic crystal array of dielectric spheres,” Phys. Rev. B 70, 235113 (2004).
[CrossRef]

T. Kondo, M. Hangyo, S. Yamaguchi, S. Yano, Y. Segawa, and K. Ohtaka, “Transmission characteristics of a two-dimensional photonic crystal array of dielectric spheres using subterahertz time domain spectroscopy,” Phys. Rev. B 66, 331111 (2002).
[CrossRef]

Y. Kurokawa, Y. Jimba, and H. Miyazaki, “Internal electric-field distribution of a monolayer of periodically arrayed dielectric spheres,” Phys. Rev. B 70, 155107 (2004).
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L. A. Dorado and R. A. Depine, “Modeling of disorder effects and optical extinction in three-dimensional photonic crystals,” Phys. Rev. B 79, 045124 (2009).
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[CrossRef]

M. M. Sigalas, C. M. Soukoulis, C. T. Chan, R. Biswas, and K. M. Ho, “Effect of disorder on photonic band gaps,” Phys. Rev. B 59, 12767–12770 (1999).
[CrossRef]

A. V. Baryshev, V. A. Kosobukin, K. B. Samusev, D. E. Usvyat, and M. F. Limonov, “Light diffraction from opal-based photonic crystals with growth-induced disorder: experiment and theory,” Phys. Rev. B 73, 205118 (2006).
[CrossRef]

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Phys. Rev. E

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A. A. Asatryan, P. A. Robinson, L. C. Botten, R. C. McPhedran, N. A. Nicorovici, and C. M. de Sterke, “Effects of disorder on wave propagation in two-dimensional photonic crystals,” Phys. Rev. E 60, 6118–6127 (1999).
[CrossRef]

T. N. Langtry, A. A. Asatryan, L. C. Botten, C. M. de Sterke, R. C. McPhedran, and P. A. Robinson, “Effects of disorder in two-dimensional photonic crystal waveguides,” Phys. Rev. E 68, 026611 (2003).
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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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Phys. Status Solidi A

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[CrossRef]

Other

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

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Figures (4)

Fig. 1
Fig. 1

Photography of single layers of glass spheres of f f = 0.24 with different degrees of disorder included: (a)  σ = 4 % , (b)  σ = 8 % , (c)  σ = 12 % , and (d) completely random sample.

Fig. 2
Fig. 2

Procedure of disordering of the regular lattice. Each sphere is displaced from its original position according to the randomly generated values of θ and ρ.

Fig. 3
Fig. 3

PCF calculated for samples of f f = 0.16 and with different degrees of disorder, measured by σ. The inset shows, magnified, the PFC for the first value of r.

Fig. 4
Fig. 4

Transmission spectra of two-dimensional dielectric arrays with Φ = 8 mm for (a)  Λ = 11.35 mm ( f f = 0.3 ), (b)  Λ = 13 mm ( f f = 0.24 ), and (c)  Λ = 15.5 mm ( f f = 0.16 ). Perfect sample with no disorder in the lattice parameter is represented with different samples with slight and large disorder in the lattice parameter.

Equations (2)

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x = x 0 + ρ cos θ ,
y = y 0 + ρ sin θ .

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