Abstract

We investigated semi-disordered photonic crystals (PCs), digital alloys, and made thorough comparisons with their counterparts, random alloys. A set of diamond lattice PC digital alloys operating in a microwave regime were prepared by alternately stacking two kinds of sub-PC systems composed of alumina and silica spheres of the same size. Measured transmission spectra as well as calculated band structures revealed that when the digital alloy period is short, band-gaps of the digital alloys are practically the same as those of the random alloys. This study indicates that the concept of digital alloys holds for photons in PCs as well.

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    [CrossRef]
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2010 (1)

2008 (2)

H. J. Kim, D.-U. Kim, Y.-G. Roh, J. Yu, H. Jeon, and Q. H. Park, “Photonic crystal alloys: a new twist in controlling photonic band structure properties,” Opt. Express 16(9), 6579–6585 (2008).
[CrossRef] [PubMed]

C. Conti and A. Fratalocchi, “Dynamic light diffusion, three-dimensional Anderson localization and lasing in inverted opals,” Nat. Phys. 4(10), 794–798 (2008).
[CrossRef]

2007 (1)

T. Schwartz, G. Bartal, S. Fishman, and M. Segev, “Transport and Anderson localization in disordered two-dimensional photonic lattices,” Nature 446(7131), 52–55 (2007).
[CrossRef] [PubMed]

2006 (3)

K. Baert, K. Song, R. A. L. Vallée, M. Van der Auweraer, and K. Clays, “Spectral narrowing of emission in self-assembled colloidal photonic superlattices,” J. Appl. Phys. 100(12), 123112 (2006).
[CrossRef]

N. C. Panoiu, R. M. Osgood, S. Zhang, and S. R. J. Brueck, “Zero-n bandgap in photonic crystal superlattices,” J. Opt. Soc. Am. B 23(3), 506–513 (2006).
[CrossRef]

E. Istrate and E. H. Sargent, “Photonic crystal heterostructures and interfaces,” Rev. Mod. Phys. 78(2), 455–481 (2006).
[CrossRef]

2005 (2)

B.-S. Song, S. Noda, T. Asano, and Y. Akahane, “Ultra-high-Q photonic double-heterostructure nanocavity,” Nat. Mater. 4(3), 207–210 (2005).
[CrossRef]

H. J. Kim, Y.-G. Roh, and H. Jeon, “Photonic bandgap engineering in mixed colloidal photonic crystals,” Jpn. J. Appl. Phys. 44(40), L1259–L1262 (2005).
[CrossRef]

2004 (1)

J. D. Song, D. C. Heo, I. K. Han, J. M. Kim, Y. T. Lee, and S.-H. Park, “Parametric study on optical properties of digital-alloy In(Ga1-zAlz)As/InP grown by molecular-beam epitaxy,” Appl. Phys. Lett. 84(6), 873–875 (2004).
[CrossRef]

2003 (1)

R. Kaspi and G. P. Donati, “Digital alloy growth in mixed As/Sb heterostructures,” J. Cryst. Growth 251(1-4), 515–520 (2003).
[CrossRef]

2001 (2)

R. Rengarajan, P. Jiang, D. C. Larrabee, V. L. Colvin, and D. M. Mittleman, “Colloidal photonic superlattices,” Phys. Rev. B 64(20), 205103 (2001).
[CrossRef]

P. Jiang, G. N. Ostojic, R. Narat, D. M. Mittleman, and V. L. Colvin, “The fabrication and bandgap engineering of photonic multilayers,” Adv. Mater. (Deerfield Beach Fla.) 13(6), 389–393 (2001).
[CrossRef]

1996 (1)

İ. İ. Tarhan and G. H. Watson, “Photonic band structure of fcc colloidal crystals,” Phys. Rev. Lett. 76(2), 315–318 (1996).
[CrossRef] [PubMed]

1994 (1)

Y.-H. Zhang and D. H. Chow, “Improved crystalline quality of AlAsxSb1-x grown on InAs by modulated molecular-beam epitaxy,” Appl. Phys. Lett. 65(25), 3239–3241 (1994).
[CrossRef]

1993 (1)

M. A. Khan, J. N. Kuznia, D. T. Olson, T. George, and W. T. Pike, “GaN/AlN digital alloy short-period superlattices by switched atomic layer metalorganic chemical vapor deposition,” Appl. Phys. Lett. 63(25), 3470–3472 (1993).
[CrossRef]

1990 (1)

K. M. Ho, C. T. Chan, and C. M. Soukoulis, “Existence of a photonic gap in periodic dielectric structures,” Phys. Rev. Lett. 65(25), 3152–3155 (1990).
[CrossRef] [PubMed]

1987 (3)

E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett. 58(20), 2059–2062 (1987).
[CrossRef] [PubMed]

S. John, “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett. 58(23), 2486–2489 (1987).
[CrossRef] [PubMed]

F. Capasso, “Band-gap engineering: from physics and materials to new semiconductor devices,” Science 235(4785), 172–176 (1987).
[CrossRef] [PubMed]

1971 (1)

Z. I. Alferov, V. M. Andreev, D. Z. Garbuzov, Y. V. Zhilyaev, E. P. Morozov, E. L. Portnoi, and V. G. Trofim, “Investigation of the influence of the AlAs–GaAs heterostructure parameters on the laser threshold current and the realization of continuous emission at room temperature,” Sov. Phys. Semicond. 4, 1573–1575 (1971).

1970 (2)

I. Hayashi, M. B. Panish, P. W. Foy, and S. Sumski, “Junction lasers which operate continuously at room temperature,” Appl. Phys. Lett. 17(3), 109–111 (1970).
[CrossRef]

L. Esaki and R. Tsu, “Superlattice and negative differential conductivity in semiconductors,” IBM J. Res. Develop. 14(1), 61–65 (1970).
[CrossRef]

1958 (1)

P. W. Anderson, “Absence of diffusion in certain random lattices,” Phys. Rev. 109(5), 1492–1505 (1958).
[CrossRef]

1931 (1)

L. Nordheim, “The electron theory of metals,” Ann. Phys Lpz. 9(5), 607–640 (1931).
[CrossRef]

1921 (1)

L. Vegard, “Die Konstitution der Mischkristalle und die Raumfüllung der Atome,” Z. Phys. 5(1), 17–26 (1921).
[CrossRef]

Akahane, Y.

B.-S. Song, S. Noda, T. Asano, and Y. Akahane, “Ultra-high-Q photonic double-heterostructure nanocavity,” Nat. Mater. 4(3), 207–210 (2005).
[CrossRef]

Alferov, Z. I.

Z. I. Alferov, V. M. Andreev, D. Z. Garbuzov, Y. V. Zhilyaev, E. P. Morozov, E. L. Portnoi, and V. G. Trofim, “Investigation of the influence of the AlAs–GaAs heterostructure parameters on the laser threshold current and the realization of continuous emission at room temperature,” Sov. Phys. Semicond. 4, 1573–1575 (1971).

Anderson, P. W.

P. W. Anderson, “Absence of diffusion in certain random lattices,” Phys. Rev. 109(5), 1492–1505 (1958).
[CrossRef]

Andreev, V. M.

Z. I. Alferov, V. M. Andreev, D. Z. Garbuzov, Y. V. Zhilyaev, E. P. Morozov, E. L. Portnoi, and V. G. Trofim, “Investigation of the influence of the AlAs–GaAs heterostructure parameters on the laser threshold current and the realization of continuous emission at room temperature,” Sov. Phys. Semicond. 4, 1573–1575 (1971).

Asano, T.

B.-S. Song, S. Noda, T. Asano, and Y. Akahane, “Ultra-high-Q photonic double-heterostructure nanocavity,” Nat. Mater. 4(3), 207–210 (2005).
[CrossRef]

Baert, K.

K. Baert, K. Song, R. A. L. Vallée, M. Van der Auweraer, and K. Clays, “Spectral narrowing of emission in self-assembled colloidal photonic superlattices,” J. Appl. Phys. 100(12), 123112 (2006).
[CrossRef]

Bartal, G.

T. Schwartz, G. Bartal, S. Fishman, and M. Segev, “Transport and Anderson localization in disordered two-dimensional photonic lattices,” Nature 446(7131), 52–55 (2007).
[CrossRef] [PubMed]

Brueck, S. R. J.

Capasso, F.

F. Capasso, “Band-gap engineering: from physics and materials to new semiconductor devices,” Science 235(4785), 172–176 (1987).
[CrossRef] [PubMed]

Chan, C. T.

K. M. Ho, C. T. Chan, and C. M. Soukoulis, “Existence of a photonic gap in periodic dielectric structures,” Phys. Rev. Lett. 65(25), 3152–3155 (1990).
[CrossRef] [PubMed]

Chow, D. H.

Y.-H. Zhang and D. H. Chow, “Improved crystalline quality of AlAsxSb1-x grown on InAs by modulated molecular-beam epitaxy,” Appl. Phys. Lett. 65(25), 3239–3241 (1994).
[CrossRef]

Clays, K.

K. Baert, K. Song, R. A. L. Vallée, M. Van der Auweraer, and K. Clays, “Spectral narrowing of emission in self-assembled colloidal photonic superlattices,” J. Appl. Phys. 100(12), 123112 (2006).
[CrossRef]

Colvin, V. L.

R. Rengarajan, P. Jiang, D. C. Larrabee, V. L. Colvin, and D. M. Mittleman, “Colloidal photonic superlattices,” Phys. Rev. B 64(20), 205103 (2001).
[CrossRef]

P. Jiang, G. N. Ostojic, R. Narat, D. M. Mittleman, and V. L. Colvin, “The fabrication and bandgap engineering of photonic multilayers,” Adv. Mater. (Deerfield Beach Fla.) 13(6), 389–393 (2001).
[CrossRef]

Conti, C.

C. Conti and A. Fratalocchi, “Dynamic light diffusion, three-dimensional Anderson localization and lasing in inverted opals,” Nat. Phys. 4(10), 794–798 (2008).
[CrossRef]

Donati, G. P.

R. Kaspi and G. P. Donati, “Digital alloy growth in mixed As/Sb heterostructures,” J. Cryst. Growth 251(1-4), 515–520 (2003).
[CrossRef]

Esaki, L.

L. Esaki and R. Tsu, “Superlattice and negative differential conductivity in semiconductors,” IBM J. Res. Develop. 14(1), 61–65 (1970).
[CrossRef]

Fishman, S.

T. Schwartz, G. Bartal, S. Fishman, and M. Segev, “Transport and Anderson localization in disordered two-dimensional photonic lattices,” Nature 446(7131), 52–55 (2007).
[CrossRef] [PubMed]

Foy, P. W.

I. Hayashi, M. B. Panish, P. W. Foy, and S. Sumski, “Junction lasers which operate continuously at room temperature,” Appl. Phys. Lett. 17(3), 109–111 (1970).
[CrossRef]

Fratalocchi, A.

C. Conti and A. Fratalocchi, “Dynamic light diffusion, three-dimensional Anderson localization and lasing in inverted opals,” Nat. Phys. 4(10), 794–798 (2008).
[CrossRef]

Garbuzov, D. Z.

Z. I. Alferov, V. M. Andreev, D. Z. Garbuzov, Y. V. Zhilyaev, E. P. Morozov, E. L. Portnoi, and V. G. Trofim, “Investigation of the influence of the AlAs–GaAs heterostructure parameters on the laser threshold current and the realization of continuous emission at room temperature,” Sov. Phys. Semicond. 4, 1573–1575 (1971).

George, T.

M. A. Khan, J. N. Kuznia, D. T. Olson, T. George, and W. T. Pike, “GaN/AlN digital alloy short-period superlattices by switched atomic layer metalorganic chemical vapor deposition,” Appl. Phys. Lett. 63(25), 3470–3472 (1993).
[CrossRef]

Han, I. K.

J. D. Song, D. C. Heo, I. K. Han, J. M. Kim, Y. T. Lee, and S.-H. Park, “Parametric study on optical properties of digital-alloy In(Ga1-zAlz)As/InP grown by molecular-beam epitaxy,” Appl. Phys. Lett. 84(6), 873–875 (2004).
[CrossRef]

Hayashi, I.

I. Hayashi, M. B. Panish, P. W. Foy, and S. Sumski, “Junction lasers which operate continuously at room temperature,” Appl. Phys. Lett. 17(3), 109–111 (1970).
[CrossRef]

Heo, D. C.

J. D. Song, D. C. Heo, I. K. Han, J. M. Kim, Y. T. Lee, and S.-H. Park, “Parametric study on optical properties of digital-alloy In(Ga1-zAlz)As/InP grown by molecular-beam epitaxy,” Appl. Phys. Lett. 84(6), 873–875 (2004).
[CrossRef]

Ho, K. M.

K. M. Ho, C. T. Chan, and C. M. Soukoulis, “Existence of a photonic gap in periodic dielectric structures,” Phys. Rev. Lett. 65(25), 3152–3155 (1990).
[CrossRef] [PubMed]

Istrate, E.

E. Istrate and E. H. Sargent, “Photonic crystal heterostructures and interfaces,” Rev. Mod. Phys. 78(2), 455–481 (2006).
[CrossRef]

Jeon, H.

Jiang, P.

P. Jiang, G. N. Ostojic, R. Narat, D. M. Mittleman, and V. L. Colvin, “The fabrication and bandgap engineering of photonic multilayers,” Adv. Mater. (Deerfield Beach Fla.) 13(6), 389–393 (2001).
[CrossRef]

R. Rengarajan, P. Jiang, D. C. Larrabee, V. L. Colvin, and D. M. Mittleman, “Colloidal photonic superlattices,” Phys. Rev. B 64(20), 205103 (2001).
[CrossRef]

John, S.

S. John, “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett. 58(23), 2486–2489 (1987).
[CrossRef] [PubMed]

Kaspi, R.

R. Kaspi and G. P. Donati, “Digital alloy growth in mixed As/Sb heterostructures,” J. Cryst. Growth 251(1-4), 515–520 (2003).
[CrossRef]

Khan, M. A.

M. A. Khan, J. N. Kuznia, D. T. Olson, T. George, and W. T. Pike, “GaN/AlN digital alloy short-period superlattices by switched atomic layer metalorganic chemical vapor deposition,” Appl. Phys. Lett. 63(25), 3470–3472 (1993).
[CrossRef]

Kim, D.-U.

Kim, H. J.

H. J. Kim, D.-U. Kim, Y.-G. Roh, J. Yu, H. Jeon, and Q. H. Park, “Photonic crystal alloys: a new twist in controlling photonic band structure properties,” Opt. Express 16(9), 6579–6585 (2008).
[CrossRef] [PubMed]

H. J. Kim, Y.-G. Roh, and H. Jeon, “Photonic bandgap engineering in mixed colloidal photonic crystals,” Jpn. J. Appl. Phys. 44(40), L1259–L1262 (2005).
[CrossRef]

Kim, J. M.

J. D. Song, D. C. Heo, I. K. Han, J. M. Kim, Y. T. Lee, and S.-H. Park, “Parametric study on optical properties of digital-alloy In(Ga1-zAlz)As/InP grown by molecular-beam epitaxy,” Appl. Phys. Lett. 84(6), 873–875 (2004).
[CrossRef]

Kim, S.

Kuznia, J. N.

M. A. Khan, J. N. Kuznia, D. T. Olson, T. George, and W. T. Pike, “GaN/AlN digital alloy short-period superlattices by switched atomic layer metalorganic chemical vapor deposition,” Appl. Phys. Lett. 63(25), 3470–3472 (1993).
[CrossRef]

Larrabee, D. C.

R. Rengarajan, P. Jiang, D. C. Larrabee, V. L. Colvin, and D. M. Mittleman, “Colloidal photonic superlattices,” Phys. Rev. B 64(20), 205103 (2001).
[CrossRef]

Lee, J.

Lee, Y. T.

J. D. Song, D. C. Heo, I. K. Han, J. M. Kim, Y. T. Lee, and S.-H. Park, “Parametric study on optical properties of digital-alloy In(Ga1-zAlz)As/InP grown by molecular-beam epitaxy,” Appl. Phys. Lett. 84(6), 873–875 (2004).
[CrossRef]

Mittleman, D. M.

R. Rengarajan, P. Jiang, D. C. Larrabee, V. L. Colvin, and D. M. Mittleman, “Colloidal photonic superlattices,” Phys. Rev. B 64(20), 205103 (2001).
[CrossRef]

P. Jiang, G. N. Ostojic, R. Narat, D. M. Mittleman, and V. L. Colvin, “The fabrication and bandgap engineering of photonic multilayers,” Adv. Mater. (Deerfield Beach Fla.) 13(6), 389–393 (2001).
[CrossRef]

Morozov, E. P.

Z. I. Alferov, V. M. Andreev, D. Z. Garbuzov, Y. V. Zhilyaev, E. P. Morozov, E. L. Portnoi, and V. G. Trofim, “Investigation of the influence of the AlAs–GaAs heterostructure parameters on the laser threshold current and the realization of continuous emission at room temperature,” Sov. Phys. Semicond. 4, 1573–1575 (1971).

Narat, R.

P. Jiang, G. N. Ostojic, R. Narat, D. M. Mittleman, and V. L. Colvin, “The fabrication and bandgap engineering of photonic multilayers,” Adv. Mater. (Deerfield Beach Fla.) 13(6), 389–393 (2001).
[CrossRef]

Noda, S.

B.-S. Song, S. Noda, T. Asano, and Y. Akahane, “Ultra-high-Q photonic double-heterostructure nanocavity,” Nat. Mater. 4(3), 207–210 (2005).
[CrossRef]

Nordheim, L.

L. Nordheim, “The electron theory of metals,” Ann. Phys Lpz. 9(5), 607–640 (1931).
[CrossRef]

Olson, D. T.

M. A. Khan, J. N. Kuznia, D. T. Olson, T. George, and W. T. Pike, “GaN/AlN digital alloy short-period superlattices by switched atomic layer metalorganic chemical vapor deposition,” Appl. Phys. Lett. 63(25), 3470–3472 (1993).
[CrossRef]

Osgood, R. M.

Ostojic, G. N.

P. Jiang, G. N. Ostojic, R. Narat, D. M. Mittleman, and V. L. Colvin, “The fabrication and bandgap engineering of photonic multilayers,” Adv. Mater. (Deerfield Beach Fla.) 13(6), 389–393 (2001).
[CrossRef]

Panish, M. B.

I. Hayashi, M. B. Panish, P. W. Foy, and S. Sumski, “Junction lasers which operate continuously at room temperature,” Appl. Phys. Lett. 17(3), 109–111 (1970).
[CrossRef]

Panoiu, N. C.

Park, Q. H.

Park, S.-H.

J. D. Song, D. C. Heo, I. K. Han, J. M. Kim, Y. T. Lee, and S.-H. Park, “Parametric study on optical properties of digital-alloy In(Ga1-zAlz)As/InP grown by molecular-beam epitaxy,” Appl. Phys. Lett. 84(6), 873–875 (2004).
[CrossRef]

Pike, W. T.

M. A. Khan, J. N. Kuznia, D. T. Olson, T. George, and W. T. Pike, “GaN/AlN digital alloy short-period superlattices by switched atomic layer metalorganic chemical vapor deposition,” Appl. Phys. Lett. 63(25), 3470–3472 (1993).
[CrossRef]

Portnoi, E. L.

Z. I. Alferov, V. M. Andreev, D. Z. Garbuzov, Y. V. Zhilyaev, E. P. Morozov, E. L. Portnoi, and V. G. Trofim, “Investigation of the influence of the AlAs–GaAs heterostructure parameters on the laser threshold current and the realization of continuous emission at room temperature,” Sov. Phys. Semicond. 4, 1573–1575 (1971).

Rengarajan, R.

R. Rengarajan, P. Jiang, D. C. Larrabee, V. L. Colvin, and D. M. Mittleman, “Colloidal photonic superlattices,” Phys. Rev. B 64(20), 205103 (2001).
[CrossRef]

Roh, Y.-G.

H. J. Kim, D.-U. Kim, Y.-G. Roh, J. Yu, H. Jeon, and Q. H. Park, “Photonic crystal alloys: a new twist in controlling photonic band structure properties,” Opt. Express 16(9), 6579–6585 (2008).
[CrossRef] [PubMed]

H. J. Kim, Y.-G. Roh, and H. Jeon, “Photonic bandgap engineering in mixed colloidal photonic crystals,” Jpn. J. Appl. Phys. 44(40), L1259–L1262 (2005).
[CrossRef]

Sargent, E. H.

E. Istrate and E. H. Sargent, “Photonic crystal heterostructures and interfaces,” Rev. Mod. Phys. 78(2), 455–481 (2006).
[CrossRef]

Schwartz, T.

T. Schwartz, G. Bartal, S. Fishman, and M. Segev, “Transport and Anderson localization in disordered two-dimensional photonic lattices,” Nature 446(7131), 52–55 (2007).
[CrossRef] [PubMed]

Segev, M.

T. Schwartz, G. Bartal, S. Fishman, and M. Segev, “Transport and Anderson localization in disordered two-dimensional photonic lattices,” Nature 446(7131), 52–55 (2007).
[CrossRef] [PubMed]

Seok, H.

Song, B.-S.

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[CrossRef]

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[CrossRef]

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[CrossRef]

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[CrossRef] [PubMed]

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[CrossRef]

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[CrossRef]

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K. Baert, K. Song, R. A. L. Vallée, M. Van der Auweraer, and K. Clays, “Spectral narrowing of emission in self-assembled colloidal photonic superlattices,” J. Appl. Phys. 100(12), 123112 (2006).
[CrossRef]

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[CrossRef]

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İ. İ. Tarhan and G. H. Watson, “Photonic band structure of fcc colloidal crystals,” Phys. Rev. Lett. 76(2), 315–318 (1996).
[CrossRef] [PubMed]

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E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett. 58(20), 2059–2062 (1987).
[CrossRef] [PubMed]

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[CrossRef]

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Z. I. Alferov, V. M. Andreev, D. Z. Garbuzov, Y. V. Zhilyaev, E. P. Morozov, E. L. Portnoi, and V. G. Trofim, “Investigation of the influence of the AlAs–GaAs heterostructure parameters on the laser threshold current and the realization of continuous emission at room temperature,” Sov. Phys. Semicond. 4, 1573–1575 (1971).

Adv. Mater. (Deerfield Beach Fla.) (1)

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[CrossRef]

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[CrossRef]

I. Hayashi, M. B. Panish, P. W. Foy, and S. Sumski, “Junction lasers which operate continuously at room temperature,” Appl. Phys. Lett. 17(3), 109–111 (1970).
[CrossRef]

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[CrossRef]

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[CrossRef]

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L. Esaki and R. Tsu, “Superlattice and negative differential conductivity in semiconductors,” IBM J. Res. Develop. 14(1), 61–65 (1970).
[CrossRef]

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K. Baert, K. Song, R. A. L. Vallée, M. Van der Auweraer, and K. Clays, “Spectral narrowing of emission in self-assembled colloidal photonic superlattices,” J. Appl. Phys. 100(12), 123112 (2006).
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R. Kaspi and G. P. Donati, “Digital alloy growth in mixed As/Sb heterostructures,” J. Cryst. Growth 251(1-4), 515–520 (2003).
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C. Conti and A. Fratalocchi, “Dynamic light diffusion, three-dimensional Anderson localization and lasing in inverted opals,” Nat. Phys. 4(10), 794–798 (2008).
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[CrossRef]

Phys. Rev. Lett. (4)

K. M. Ho, C. T. Chan, and C. M. Soukoulis, “Existence of a photonic gap in periodic dielectric structures,” Phys. Rev. Lett. 65(25), 3152–3155 (1990).
[CrossRef] [PubMed]

İ. İ. Tarhan and G. H. Watson, “Photonic band structure of fcc colloidal crystals,” Phys. Rev. Lett. 76(2), 315–318 (1996).
[CrossRef] [PubMed]

E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett. 58(20), 2059–2062 (1987).
[CrossRef] [PubMed]

S. John, “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett. 58(23), 2486–2489 (1987).
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Z. I. Alferov, V. M. Andreev, D. Z. Garbuzov, Y. V. Zhilyaev, E. P. Morozov, E. L. Portnoi, and V. G. Trofim, “Investigation of the influence of the AlAs–GaAs heterostructure parameters on the laser threshold current and the realization of continuous emission at room temperature,” Sov. Phys. Semicond. 4, 1573–1575 (1971).

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L. Vegard, “Die Konstitution der Mischkristalle und die Raumfüllung der Atome,” Z. Phys. 5(1), 17–26 (1921).
[CrossRef]

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Figures (6)

Fig. 1
Fig. 1

(a) Schematic of the photonic crystal digital alloy structure constructed in the diamond lattice. The superlattice period of the example structure corresponds to 3 unit plates, composed of 2 alumina (yellow) plates and 1 silica (red) plate, which results in the alumina composition ratio of x = 2/3. (b) Actual photo images of the individual unit plates and the final digital alloy structure, the schematic of which is illustrated in (a). The stacking direction of the unit plates corresponds to [111] in the conventional cubic cell. The inset illustrates a schematically drawn side-view of the unit plate.

Fig. 2
Fig. 2

(a) Unit cell of the diamond structure used in the 3D PWE calculations. a 1 and a 2 are the primitive vectors of the 2D hexagonal lattice structure on the unit plate, whereas a 3 is along the stacking direction of the unit plates. (b) The 1st Brillouin zone of the structure illustrated in (a). (A) is the wavevector at the zone boundary in the [111] direction.

Fig. 3
Fig. 3

Measured transmission spectra of the PC digital alloys (DA; thick solid line) and random alloys (RA; thin solid line) with composition ratios of x = 0, 1/3, 1/2, 2/3, and 1. For the given composition ratios, the digital alloy period is chosen to be the shortest. The regions shaded in red represent the PBGs of random alloys calculated using the 3D PWE method with effective refractive indices.

Fig. 4
Fig. 4

Calculated band structures for the PC digital alloy structures of an identical composition of x = 2/3 but with different superlattice periods: (a) [(Al2O3)2(SiO2)1], (b) [(Al2O3)4(SiO2)2], and (c) [(Al2O3)6(SiO2)3]. The corresponding unit cells used for the calculations are shown next to the band structures.

Fig. 5
Fig. 5

Transmission spectra for PC digital alloys with different composition ratios: (a) x = 1/3, (b) x = 1/2, and (c) x = 2/3. Panels in each column represent different superlattice periods for the given composition. The PBGs calculated for the given digital alloy structures using the 3D PWE method are shaded in red.

Fig. 6
Fig. 6

Transmission spectra measured for the PC digital alloys with a fixed composition ratio of x = l/(l + m) = 1/2, but of different superlattice periods: (a) l = m = 1, (b) l = m = 3, (c) l = m = 4, (d) l = m = 6, and (e) l = m = 12. Transmission spectra for the pure PCs (x = 0 and 1) are also presented in (f) for comparison. Eye-guides for the PBGs of x = 0 (red), x = 1 (blue), and x = 1/2 (purple) are shaded.

Equations (1)

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ε e f f ( x ) = x ε a l u m i n a + ( 1 x ) ε s i l i c a

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