Abstract

We identified new photonic structures and phenomenon that are analogous to alloy crystals and the associated electronic bandgap engineering. From a set of diamond-lattice microwave photonic crystals of randomly mixed silica and alumina spheres but with a well defined mixing composition, we observed that both bandedges of the L-point bandgap monotonically shifted with very little bowing as the composition was varied. The observed results were in excellent agreement with the virtual crystal approximation theory originally developed for electronic properties of alloy crystals. This result signifies the similarity and correspondence between photonics and electronics.

© 2008 Optical Society of America

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  1. E. Yablonovitch, "Inhibited spontaneous emission in solid state physics and electronics," Phys. Rev. Lett. 58, 2059-2062 (1987).
    [CrossRef] [PubMed]
  2. S. John, "Strong localization of photons in certain disordered dielectric superlattices," Phys. Rev. Lett. 58, 2486-2489 (1987).
    [CrossRef] [PubMed]
  3. E. Yablonovitch and T. J. Gmitter, "Photonic band structure: the face-centered-cubic case," Phys. Rev. Lett. 63, 1950-1953 (1989).
    [CrossRef] [PubMed]
  4. E. Yablonovitch and T. J. Gmitter, "Donor and acceptor modes in photonic band structures," Phys. Rev. Lett. 67, 3380-3383 (1991).
    [CrossRef] [PubMed]
  5. B. S. Song, S. Noda, T. Asano, and Y. Akahane, "Ultra-high-Q photonic double-heterostructure nanocavity," Nat. Mater. 4, 207-210 (2005).
    [CrossRef]
  6. T. Schwartz, G. Bartal, S. Fishman, M. Segev, "Transport and Anderson localization in disordered two-dimensional photonic lattices," Nature 446, 52-55 (2007).
    [CrossRef] [PubMed]
  7. http://nobelprize.org/nobel_prizes/physics/laureates/2000/
  8. H. J. Kim, Y.-G. Roh, and H. Jeon, "Photonic bandgap engineering in mixed colloidal photonic crystals," Jpn. J. Appl. Phys. 44, L1259-L1262 (2005).
    [CrossRef]
  9. J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals: Molding the Flow of Light (Princeton University Press, New Jersey, 1995).
  10. S.-Y. Lin, E. Chow, V. Hietala, P. R. Villeneuve, and J. D. Joannopoulos, "Experimental demonstration of guiding and bending of electromagnetic waves in a photonic crystal," Science 282, 274-276 (1998).
    [CrossRef] [PubMed]
  11. M. Bayindir and E. Ozbay, "Dropping of electromagnetic waves through localized modes in three-dimensional photonic band gap structures," Appl. Phys. Lett. 81, 4514-4516 (2002).
    [CrossRef]
  12. Y.-G. Roh, S. Yoon, H. Jeon, S. -H. Han, and Q. -H. Park, "Experimental verification of cross talk reduction in photonic crystal waveguide crossings," Appl. Phys. Lett. 85, 3351-3353 (2004).
    [CrossRef]
  13. C. M. Soukoulis, M. Kafesaki, and E. N. Economou, "Negative index materials: new frontiers in optics," Adv. Mater. 18, 1941-1952 (2006).
    [CrossRef]
  14. D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, D. R. Smith, "Metamaterial electromagnetic cloak at microwave frequencies," Science 314, 977-980 (2006).
    [CrossRef] [PubMed]
  15. L. Nordheim, "The electron theory of metals," Ann. Phys., Lpz. 9, 607-641 (1931).
    [CrossRef]
  16. K. M. Ho, C. T. Chan, and C. M. Soukoulis, "Existence of a photonic gap in periodic dielectric structures," Phys. Rev. Lett. 65, 3152-3155 (1990).
    [CrossRef] [PubMed]
  17. D. Richardson, "The composition dependence of energy bands in mixed semi- conductor systems with zincblende structures," J. Phys. C: Solid State Phys. 4, L289-L292 (1971).
    [CrossRef]
  18. L. Vegard, "Die Konstitution der Mischkristalle und die Raumfüllung der Atome," Z. Phys. 5, 17-26 (1921)
    [CrossRef]

2007 (1)

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

2006 (2)

C. M. Soukoulis, M. Kafesaki, and E. N. Economou, "Negative index materials: new frontiers in optics," Adv. Mater. 18, 1941-1952 (2006).
[CrossRef]

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, D. R. Smith, "Metamaterial electromagnetic cloak at microwave frequencies," Science 314, 977-980 (2006).
[CrossRef] [PubMed]

2005 (2)

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

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

2004 (1)

Y.-G. Roh, S. Yoon, H. Jeon, S. -H. Han, and Q. -H. Park, "Experimental verification of cross talk reduction in photonic crystal waveguide crossings," Appl. Phys. Lett. 85, 3351-3353 (2004).
[CrossRef]

2002 (1)

M. Bayindir and E. Ozbay, "Dropping of electromagnetic waves through localized modes in three-dimensional photonic band gap structures," Appl. Phys. Lett. 81, 4514-4516 (2002).
[CrossRef]

1998 (1)

S.-Y. Lin, E. Chow, V. Hietala, P. R. Villeneuve, and J. D. Joannopoulos, "Experimental demonstration of guiding and bending of electromagnetic waves in a photonic crystal," Science 282, 274-276 (1998).
[CrossRef] [PubMed]

1991 (1)

E. Yablonovitch and T. J. Gmitter, "Donor and acceptor modes in photonic band structures," Phys. Rev. Lett. 67, 3380-3383 (1991).
[CrossRef] [PubMed]

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, 3152-3155 (1990).
[CrossRef] [PubMed]

1989 (1)

E. Yablonovitch and T. J. Gmitter, "Photonic band structure: the face-centered-cubic case," Phys. Rev. Lett. 63, 1950-1953 (1989).
[CrossRef] [PubMed]

1987 (2)

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]

1971 (1)

D. Richardson, "The composition dependence of energy bands in mixed semi- conductor systems with zincblende structures," J. Phys. C: Solid State Phys. 4, L289-L292 (1971).
[CrossRef]

1931 (1)

L. Nordheim, "The electron theory of metals," Ann. Phys., Lpz. 9, 607-641 (1931).
[CrossRef]

1921 (1)

L. Vegard, "Die Konstitution der Mischkristalle und die Raumfüllung der Atome," Z. Phys. 5, 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, 207-210 (2005).
[CrossRef]

Asano, T.

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

Bartal, G.

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

Bayindir, M.

M. Bayindir and E. Ozbay, "Dropping of electromagnetic waves through localized modes in three-dimensional photonic band gap structures," Appl. Phys. Lett. 81, 4514-4516 (2002).
[CrossRef]

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, 3152-3155 (1990).
[CrossRef] [PubMed]

Chow, E.

S.-Y. Lin, E. Chow, V. Hietala, P. R. Villeneuve, and J. D. Joannopoulos, "Experimental demonstration of guiding and bending of electromagnetic waves in a photonic crystal," Science 282, 274-276 (1998).
[CrossRef] [PubMed]

Cummer, S. A.

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, D. R. Smith, "Metamaterial electromagnetic cloak at microwave frequencies," Science 314, 977-980 (2006).
[CrossRef] [PubMed]

Economou, E. N.

C. M. Soukoulis, M. Kafesaki, and E. N. Economou, "Negative index materials: new frontiers in optics," Adv. Mater. 18, 1941-1952 (2006).
[CrossRef]

Fishman, S.

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

Gmitter, T. J.

E. Yablonovitch and T. J. Gmitter, "Donor and acceptor modes in photonic band structures," Phys. Rev. Lett. 67, 3380-3383 (1991).
[CrossRef] [PubMed]

E. Yablonovitch and T. J. Gmitter, "Photonic band structure: the face-centered-cubic case," Phys. Rev. Lett. 63, 1950-1953 (1989).
[CrossRef] [PubMed]

Han, S. -H.

Y.-G. Roh, S. Yoon, H. Jeon, S. -H. Han, and Q. -H. Park, "Experimental verification of cross talk reduction in photonic crystal waveguide crossings," Appl. Phys. Lett. 85, 3351-3353 (2004).
[CrossRef]

Hietala, V.

S.-Y. Lin, E. Chow, V. Hietala, P. R. Villeneuve, and J. D. Joannopoulos, "Experimental demonstration of guiding and bending of electromagnetic waves in a photonic crystal," Science 282, 274-276 (1998).
[CrossRef] [PubMed]

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, 3152-3155 (1990).
[CrossRef] [PubMed]

Jeon, H.

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

Y.-G. Roh, S. Yoon, H. Jeon, S. -H. Han, and Q. -H. Park, "Experimental verification of cross talk reduction in photonic crystal waveguide crossings," Appl. Phys. Lett. 85, 3351-3353 (2004).
[CrossRef]

Joannopoulos, J. D.

S.-Y. Lin, E. Chow, V. Hietala, P. R. Villeneuve, and J. D. Joannopoulos, "Experimental demonstration of guiding and bending of electromagnetic waves in a photonic crystal," Science 282, 274-276 (1998).
[CrossRef] [PubMed]

John, S.

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

Justice, B. J.

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, D. R. Smith, "Metamaterial electromagnetic cloak at microwave frequencies," Science 314, 977-980 (2006).
[CrossRef] [PubMed]

Kafesaki, M.

C. M. Soukoulis, M. Kafesaki, and E. N. Economou, "Negative index materials: new frontiers in optics," Adv. Mater. 18, 1941-1952 (2006).
[CrossRef]

Kim, H. J.

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

Lin, S.-Y.

S.-Y. Lin, E. Chow, V. Hietala, P. R. Villeneuve, and J. D. Joannopoulos, "Experimental demonstration of guiding and bending of electromagnetic waves in a photonic crystal," Science 282, 274-276 (1998).
[CrossRef] [PubMed]

Mock, J. J.

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, D. R. Smith, "Metamaterial electromagnetic cloak at microwave frequencies," Science 314, 977-980 (2006).
[CrossRef] [PubMed]

Noda, S.

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

Nordheim, L.

L. Nordheim, "The electron theory of metals," Ann. Phys., Lpz. 9, 607-641 (1931).
[CrossRef]

Ozbay, E.

M. Bayindir and E. Ozbay, "Dropping of electromagnetic waves through localized modes in three-dimensional photonic band gap structures," Appl. Phys. Lett. 81, 4514-4516 (2002).
[CrossRef]

Park, Q. -H.

Y.-G. Roh, S. Yoon, H. Jeon, S. -H. Han, and Q. -H. Park, "Experimental verification of cross talk reduction in photonic crystal waveguide crossings," Appl. Phys. Lett. 85, 3351-3353 (2004).
[CrossRef]

Pendry, J. B.

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, D. R. Smith, "Metamaterial electromagnetic cloak at microwave frequencies," Science 314, 977-980 (2006).
[CrossRef] [PubMed]

Richardson, D.

D. Richardson, "The composition dependence of energy bands in mixed semi- conductor systems with zincblende structures," J. Phys. C: Solid State Phys. 4, L289-L292 (1971).
[CrossRef]

Roh, Y.-G.

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

Y.-G. Roh, S. Yoon, H. Jeon, S. -H. Han, and Q. -H. Park, "Experimental verification of cross talk reduction in photonic crystal waveguide crossings," Appl. Phys. Lett. 85, 3351-3353 (2004).
[CrossRef]

Schurig, D.

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, D. R. Smith, "Metamaterial electromagnetic cloak at microwave frequencies," Science 314, 977-980 (2006).
[CrossRef] [PubMed]

Schwartz, T.

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

Segev, M.

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

Smith, D. R.

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, D. R. Smith, "Metamaterial electromagnetic cloak at microwave frequencies," Science 314, 977-980 (2006).
[CrossRef] [PubMed]

Song, B. S.

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

Soukoulis, C. M.

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

Soukoulis, C. M.

C. M. Soukoulis, M. Kafesaki, and E. N. Economou, "Negative index materials: new frontiers in optics," Adv. Mater. 18, 1941-1952 (2006).
[CrossRef]

Starr, A. F.

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, D. R. Smith, "Metamaterial electromagnetic cloak at microwave frequencies," Science 314, 977-980 (2006).
[CrossRef] [PubMed]

Vegard, L.

L. Vegard, "Die Konstitution der Mischkristalle und die Raumfüllung der Atome," Z. Phys. 5, 17-26 (1921)
[CrossRef]

Villeneuve, P. R.

S.-Y. Lin, E. Chow, V. Hietala, P. R. Villeneuve, and J. D. Joannopoulos, "Experimental demonstration of guiding and bending of electromagnetic waves in a photonic crystal," Science 282, 274-276 (1998).
[CrossRef] [PubMed]

Yablonovitch, E.

E. Yablonovitch and T. J. Gmitter, "Donor and acceptor modes in photonic band structures," Phys. Rev. Lett. 67, 3380-3383 (1991).
[CrossRef] [PubMed]

E. Yablonovitch and T. J. Gmitter, "Photonic band structure: the face-centered-cubic case," Phys. Rev. Lett. 63, 1950-1953 (1989).
[CrossRef] [PubMed]

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

Yoon, S.

Y.-G. Roh, S. Yoon, H. Jeon, S. -H. Han, and Q. -H. Park, "Experimental verification of cross talk reduction in photonic crystal waveguide crossings," Appl. Phys. Lett. 85, 3351-3353 (2004).
[CrossRef]

Adv. Mater. (1)

C. M. Soukoulis, M. Kafesaki, and E. N. Economou, "Negative index materials: new frontiers in optics," Adv. Mater. 18, 1941-1952 (2006).
[CrossRef]

Appl. Phys. Lett. (2)

M. Bayindir and E. Ozbay, "Dropping of electromagnetic waves through localized modes in three-dimensional photonic band gap structures," Appl. Phys. Lett. 81, 4514-4516 (2002).
[CrossRef]

Y.-G. Roh, S. Yoon, H. Jeon, S. -H. Han, and Q. -H. Park, "Experimental verification of cross talk reduction in photonic crystal waveguide crossings," Appl. Phys. Lett. 85, 3351-3353 (2004).
[CrossRef]

J. Phys. C: Solid State Phys. (1)

D. Richardson, "The composition dependence of energy bands in mixed semi- conductor systems with zincblende structures," J. Phys. C: Solid State Phys. 4, L289-L292 (1971).
[CrossRef]

Jpn. J. Appl. Phys. (1)

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

Lpz. (1)

L. Nordheim, "The electron theory of metals," Ann. Phys., Lpz. 9, 607-641 (1931).
[CrossRef]

Nat. Mater. (1)

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

Nature (1)

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

Phys. Rev. Lett. (5)

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]

E. Yablonovitch and T. J. Gmitter, "Photonic band structure: the face-centered-cubic case," Phys. Rev. Lett. 63, 1950-1953 (1989).
[CrossRef] [PubMed]

E. Yablonovitch and T. J. Gmitter, "Donor and acceptor modes in photonic band structures," Phys. Rev. Lett. 67, 3380-3383 (1991).
[CrossRef] [PubMed]

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

Science (2)

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, D. R. Smith, "Metamaterial electromagnetic cloak at microwave frequencies," Science 314, 977-980 (2006).
[CrossRef] [PubMed]

S.-Y. Lin, E. Chow, V. Hietala, P. R. Villeneuve, and J. D. Joannopoulos, "Experimental demonstration of guiding and bending of electromagnetic waves in a photonic crystal," Science 282, 274-276 (1998).
[CrossRef] [PubMed]

Z. Phys. (1)

L. Vegard, "Die Konstitution der Mischkristalle und die Raumfüllung der Atome," Z. Phys. 5, 17-26 (1921)
[CrossRef]

Other (2)

http://nobelprize.org/nobel_prizes/physics/laureates/2000/

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

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Figures (4)

Fig. 1.
Fig. 1.

Atomic configuration of the diamond structure in the conventional cubic cell (a), and in an extended scheme after reoriented such that the [111] crystal direction points upward (b). In a-b, two groups of atoms, (0,0,0) and (¼,¼,¼) in their relative coordinates, are distinguished by color contrast. (c) Diamond lattice photonic crystal composed of hard spheres of equal size, with the nearest neighbor spheres in contact with each other. Different crystal planes of the diamond lattice photonic crystal: (111) (d) and (-110) (e). In (c)-(e), colors are used to distinguish among different unit layers that are stacked vertically in the actual samples.

Fig. 2.
Fig. 2.

Photographic images of the completed diamond lattice photonic crystal alloys with alumina sphere compositions of x=0 (a), x=0.5 (B), and x=1 (C). Each plate in the stack contains 504 holes that are filled with pairs of either silica or alumina spheres. Insets are the amplified images showing the detailed sphere arrangements for the corresponding photonic crystals. (d) Anatomy of the x=0.5 mixed photonic crystal, which explicitly shows that individual unit plates have different sphere configurations.

Fig. 3.
Fig. 3.

(a). Evolution of transmission spectrum of the alumina photonic crystal (x=1). As the number of the unit plates increases, the transmission stopband becomes distinct. Well-defined bandedges, which are indicated by two arrows, develop themselves on both sides of the transmission stopband. (b) Comparison between the measured transmission stopband and the calculated L-point bandgap for the alumina photonic crystal (x=1; top two panels) and for the silica photonic crystal (x=0; bottom two panels)

Fig. 4.
Fig. 4.

(a). Transmission spectra of the mixed photonic crystals for the full range of alumina sphere mixing composition: From the top, x=1, 0.9, 0.7, 0.5, 0.3, 0.1, and 0. (b) Photonic bandedge positions as a function of alumina sphere composition x. Squares are experimental results deduced from (a), whereas the lines are calculated using the virtual crystal approximation theory. The theoretical lines, especially the dielectric bandedge line, show slight bowing effect. (c) Transmission spectra for an ensemble of the x=0.5 mixed photonic crystals. Multiple transmission spectra are intentionally drawn on top of each other to make directly visible the intrinsic fluctuation associated with the ensemble (of the same composition but different mixing configurations).

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