Abstract

Hybrid 2D-3D heterostructures are a very promising way for waveguiding light in 3D photonic structures. Single-mode waveguiding of light has been demonstrated in heterostructures where a 2D photonic crystal consisting of a triangular lattice of silicon rods in air was intercalated between two silicon inverse opals. In this paper, we show that by using a graphite lattice of rods instead of a triangular one, it is possible to enlarge the maximal single-mode waveguiding bandwidth by more than 70 %, i.e. up to 129 nm centered on 1.55 μm. The sensibility to the 2D layer structure parameters is lower, offering enhanced experimental flexibility in the design of the structure.

© 2007 Optical Society of America

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  1. J. D. Joannopoulos, R. Meade, and J. Winn, Photonic crystals: Molding the flow of light (Princeton University Press, Princeton, N.J., 1995).
  2. S. Noda, K. Tomoda, N. Yamamoto, and A. Chutinan, "Full three-dimensional photonic bandgap crystals at near-infrared wavelengths," Science 289, 604-606 (2000).
    [CrossRef] [PubMed]
  3. A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, "High transmission through sharp bends in photonic crystal waveguides," Phys. Rev. Lett. 77, 3787-3790 (1996).
    [CrossRef] [PubMed]
  4. S. Johnson, P. R. Villeneuve, S. Fan, and J. D. Joannopoulos, "Linear waveguides in photonic-crystal slabs," Phys. Rev. B 62, 8212-8222 (2000).
    [CrossRef]
  5. V. Lousse, J. Shin, and S. Fan, "Conditions for designing single-mode air-core waveguides in three-dimensional photonic crystals," Appl. Phys. Lett. 89, 161103 (2006).
    [CrossRef]
  6. P. Braun, S. Rinne, and F. García-Santamaría, "Introducing defects in 3D photonic crystals: State of the art," Adv. Mater. 18, 2665-2678 (2006).
    [CrossRef]
  7. A. Chutinan, S. John, and O. Toader, "Diffractionless flow of light in all-optical microchips," Phys. Rev. Lett. 90, 123901 (2003).
    [CrossRef] [PubMed]
  8. Photonic Band Gap Materials, edited by C. M. Soukoulis (Kluwer Academic Publishers, Dordrecht, 1996).
  9. A. Blanco, E. Chomski, S. Grabtchak, M. Ibisate, S. John, S. W. Leonard, C. Lopez, F. Mezeguer, H. Miguez, J. P. Mondia, G. A. Ozin, O. Toader, and H. M. van Driel, "Large-scale synthesis of a silicon photonic crystal with a complete three-dimensional bandgap near 1.5 micrometres," Nature 405, 437-440 (2000).
    [CrossRef] [PubMed]
  10. Y. A. Vlasov, X.-Z. Bo, J. C. Sturm, and D. J. Norris, "On-chip natural assembly of silicon photonic bandgap crystals," Nature 414, 289-293 (2001).
    [CrossRef] [PubMed]
  11. V. Lousse, and S. Fan, "Waveguides in inverted opal photonic crystals," Opt. Express 14, 866-878 (2005).
    [CrossRef]
  12. A. Chutinan, and S. John, "Diffractionless flow of light in two- and three-dimensional photonic band gap heterostructures: Theory, design rules and simulations," Phys. Rev. E 71, 026605 (2005).
    [CrossRef]
  13. D. Cassagne, C. Jouanin, and D. Bertho, "Hexagonal photonic band gaps," Phys. Rev. B 53, 7134-7142 (1996).
    [CrossRef]
  14. S. Johnson, and J. D. Joannopoulos, "Block-iterative frequency-domain methods for Maxwell’s equations in a planewave basis," Opt. Express 8, 173-190 (2001).
    [CrossRef] [PubMed]

2006

V. Lousse, J. Shin, and S. Fan, "Conditions for designing single-mode air-core waveguides in three-dimensional photonic crystals," Appl. Phys. Lett. 89, 161103 (2006).
[CrossRef]

P. Braun, S. Rinne, and F. García-Santamaría, "Introducing defects in 3D photonic crystals: State of the art," Adv. Mater. 18, 2665-2678 (2006).
[CrossRef]

2005

A. Chutinan, and S. John, "Diffractionless flow of light in two- and three-dimensional photonic band gap heterostructures: Theory, design rules and simulations," Phys. Rev. E 71, 026605 (2005).
[CrossRef]

V. Lousse, and S. Fan, "Waveguides in inverted opal photonic crystals," Opt. Express 14, 866-878 (2005).
[CrossRef]

2003

A. Chutinan, S. John, and O. Toader, "Diffractionless flow of light in all-optical microchips," Phys. Rev. Lett. 90, 123901 (2003).
[CrossRef] [PubMed]

2001

Y. A. Vlasov, X.-Z. Bo, J. C. Sturm, and D. J. Norris, "On-chip natural assembly of silicon photonic bandgap crystals," Nature 414, 289-293 (2001).
[CrossRef] [PubMed]

S. Johnson, and J. D. Joannopoulos, "Block-iterative frequency-domain methods for Maxwell’s equations in a planewave basis," Opt. Express 8, 173-190 (2001).
[CrossRef] [PubMed]

2000

S. Johnson, P. R. Villeneuve, S. Fan, and J. D. Joannopoulos, "Linear waveguides in photonic-crystal slabs," Phys. Rev. B 62, 8212-8222 (2000).
[CrossRef]

S. Noda, K. Tomoda, N. Yamamoto, and A. Chutinan, "Full three-dimensional photonic bandgap crystals at near-infrared wavelengths," Science 289, 604-606 (2000).
[CrossRef] [PubMed]

A. Blanco, E. Chomski, S. Grabtchak, M. Ibisate, S. John, S. W. Leonard, C. Lopez, F. Mezeguer, H. Miguez, J. P. Mondia, G. A. Ozin, O. Toader, and H. M. van Driel, "Large-scale synthesis of a silicon photonic crystal with a complete three-dimensional bandgap near 1.5 micrometres," Nature 405, 437-440 (2000).
[CrossRef] [PubMed]

1996

A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, "High transmission through sharp bends in photonic crystal waveguides," Phys. Rev. Lett. 77, 3787-3790 (1996).
[CrossRef] [PubMed]

D. Cassagne, C. Jouanin, and D. Bertho, "Hexagonal photonic band gaps," Phys. Rev. B 53, 7134-7142 (1996).
[CrossRef]

Bertho, D.

D. Cassagne, C. Jouanin, and D. Bertho, "Hexagonal photonic band gaps," Phys. Rev. B 53, 7134-7142 (1996).
[CrossRef]

Blanco, A.

A. Blanco, E. Chomski, S. Grabtchak, M. Ibisate, S. John, S. W. Leonard, C. Lopez, F. Mezeguer, H. Miguez, J. P. Mondia, G. A. Ozin, O. Toader, and H. M. van Driel, "Large-scale synthesis of a silicon photonic crystal with a complete three-dimensional bandgap near 1.5 micrometres," Nature 405, 437-440 (2000).
[CrossRef] [PubMed]

Bo, X.-Z.

Y. A. Vlasov, X.-Z. Bo, J. C. Sturm, and D. J. Norris, "On-chip natural assembly of silicon photonic bandgap crystals," Nature 414, 289-293 (2001).
[CrossRef] [PubMed]

Braun, P.

P. Braun, S. Rinne, and F. García-Santamaría, "Introducing defects in 3D photonic crystals: State of the art," Adv. Mater. 18, 2665-2678 (2006).
[CrossRef]

Cassagne, D.

D. Cassagne, C. Jouanin, and D. Bertho, "Hexagonal photonic band gaps," Phys. Rev. B 53, 7134-7142 (1996).
[CrossRef]

Chen, J. C.

A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, "High transmission through sharp bends in photonic crystal waveguides," Phys. Rev. Lett. 77, 3787-3790 (1996).
[CrossRef] [PubMed]

Chomski, E.

A. Blanco, E. Chomski, S. Grabtchak, M. Ibisate, S. John, S. W. Leonard, C. Lopez, F. Mezeguer, H. Miguez, J. P. Mondia, G. A. Ozin, O. Toader, and H. M. van Driel, "Large-scale synthesis of a silicon photonic crystal with a complete three-dimensional bandgap near 1.5 micrometres," Nature 405, 437-440 (2000).
[CrossRef] [PubMed]

Chutinan, A.

A. Chutinan, and S. John, "Diffractionless flow of light in two- and three-dimensional photonic band gap heterostructures: Theory, design rules and simulations," Phys. Rev. E 71, 026605 (2005).
[CrossRef]

A. Chutinan, S. John, and O. Toader, "Diffractionless flow of light in all-optical microchips," Phys. Rev. Lett. 90, 123901 (2003).
[CrossRef] [PubMed]

S. Noda, K. Tomoda, N. Yamamoto, and A. Chutinan, "Full three-dimensional photonic bandgap crystals at near-infrared wavelengths," Science 289, 604-606 (2000).
[CrossRef] [PubMed]

Fan, S.

V. Lousse, J. Shin, and S. Fan, "Conditions for designing single-mode air-core waveguides in three-dimensional photonic crystals," Appl. Phys. Lett. 89, 161103 (2006).
[CrossRef]

V. Lousse, and S. Fan, "Waveguides in inverted opal photonic crystals," Opt. Express 14, 866-878 (2005).
[CrossRef]

S. Johnson, P. R. Villeneuve, S. Fan, and J. D. Joannopoulos, "Linear waveguides in photonic-crystal slabs," Phys. Rev. B 62, 8212-8222 (2000).
[CrossRef]

A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, "High transmission through sharp bends in photonic crystal waveguides," Phys. Rev. Lett. 77, 3787-3790 (1996).
[CrossRef] [PubMed]

García-Santamaría, F.

P. Braun, S. Rinne, and F. García-Santamaría, "Introducing defects in 3D photonic crystals: State of the art," Adv. Mater. 18, 2665-2678 (2006).
[CrossRef]

Grabtchak, S.

A. Blanco, E. Chomski, S. Grabtchak, M. Ibisate, S. John, S. W. Leonard, C. Lopez, F. Mezeguer, H. Miguez, J. P. Mondia, G. A. Ozin, O. Toader, and H. M. van Driel, "Large-scale synthesis of a silicon photonic crystal with a complete three-dimensional bandgap near 1.5 micrometres," Nature 405, 437-440 (2000).
[CrossRef] [PubMed]

Ibisate, M.

A. Blanco, E. Chomski, S. Grabtchak, M. Ibisate, S. John, S. W. Leonard, C. Lopez, F. Mezeguer, H. Miguez, J. P. Mondia, G. A. Ozin, O. Toader, and H. M. van Driel, "Large-scale synthesis of a silicon photonic crystal with a complete three-dimensional bandgap near 1.5 micrometres," Nature 405, 437-440 (2000).
[CrossRef] [PubMed]

Joannopoulos, J. D.

S. Johnson, and J. D. Joannopoulos, "Block-iterative frequency-domain methods for Maxwell’s equations in a planewave basis," Opt. Express 8, 173-190 (2001).
[CrossRef] [PubMed]

S. Johnson, P. R. Villeneuve, S. Fan, and J. D. Joannopoulos, "Linear waveguides in photonic-crystal slabs," Phys. Rev. B 62, 8212-8222 (2000).
[CrossRef]

A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, "High transmission through sharp bends in photonic crystal waveguides," Phys. Rev. Lett. 77, 3787-3790 (1996).
[CrossRef] [PubMed]

John, S.

A. Chutinan, and S. John, "Diffractionless flow of light in two- and three-dimensional photonic band gap heterostructures: Theory, design rules and simulations," Phys. Rev. E 71, 026605 (2005).
[CrossRef]

A. Chutinan, S. John, and O. Toader, "Diffractionless flow of light in all-optical microchips," Phys. Rev. Lett. 90, 123901 (2003).
[CrossRef] [PubMed]

A. Blanco, E. Chomski, S. Grabtchak, M. Ibisate, S. John, S. W. Leonard, C. Lopez, F. Mezeguer, H. Miguez, J. P. Mondia, G. A. Ozin, O. Toader, and H. M. van Driel, "Large-scale synthesis of a silicon photonic crystal with a complete three-dimensional bandgap near 1.5 micrometres," Nature 405, 437-440 (2000).
[CrossRef] [PubMed]

Johnson, S.

S. Johnson, and J. D. Joannopoulos, "Block-iterative frequency-domain methods for Maxwell’s equations in a planewave basis," Opt. Express 8, 173-190 (2001).
[CrossRef] [PubMed]

S. Johnson, P. R. Villeneuve, S. Fan, and J. D. Joannopoulos, "Linear waveguides in photonic-crystal slabs," Phys. Rev. B 62, 8212-8222 (2000).
[CrossRef]

Jouanin, C.

D. Cassagne, C. Jouanin, and D. Bertho, "Hexagonal photonic band gaps," Phys. Rev. B 53, 7134-7142 (1996).
[CrossRef]

Kurland, I.

A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, "High transmission through sharp bends in photonic crystal waveguides," Phys. Rev. Lett. 77, 3787-3790 (1996).
[CrossRef] [PubMed]

Leonard, S. W.

A. Blanco, E. Chomski, S. Grabtchak, M. Ibisate, S. John, S. W. Leonard, C. Lopez, F. Mezeguer, H. Miguez, J. P. Mondia, G. A. Ozin, O. Toader, and H. M. van Driel, "Large-scale synthesis of a silicon photonic crystal with a complete three-dimensional bandgap near 1.5 micrometres," Nature 405, 437-440 (2000).
[CrossRef] [PubMed]

Lopez, C.

A. Blanco, E. Chomski, S. Grabtchak, M. Ibisate, S. John, S. W. Leonard, C. Lopez, F. Mezeguer, H. Miguez, J. P. Mondia, G. A. Ozin, O. Toader, and H. M. van Driel, "Large-scale synthesis of a silicon photonic crystal with a complete three-dimensional bandgap near 1.5 micrometres," Nature 405, 437-440 (2000).
[CrossRef] [PubMed]

Lousse, V.

V. Lousse, J. Shin, and S. Fan, "Conditions for designing single-mode air-core waveguides in three-dimensional photonic crystals," Appl. Phys. Lett. 89, 161103 (2006).
[CrossRef]

V. Lousse, and S. Fan, "Waveguides in inverted opal photonic crystals," Opt. Express 14, 866-878 (2005).
[CrossRef]

Mekis, A.

A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, "High transmission through sharp bends in photonic crystal waveguides," Phys. Rev. Lett. 77, 3787-3790 (1996).
[CrossRef] [PubMed]

Mezeguer, F.

A. Blanco, E. Chomski, S. Grabtchak, M. Ibisate, S. John, S. W. Leonard, C. Lopez, F. Mezeguer, H. Miguez, J. P. Mondia, G. A. Ozin, O. Toader, and H. M. van Driel, "Large-scale synthesis of a silicon photonic crystal with a complete three-dimensional bandgap near 1.5 micrometres," Nature 405, 437-440 (2000).
[CrossRef] [PubMed]

Miguez, H.

A. Blanco, E. Chomski, S. Grabtchak, M. Ibisate, S. John, S. W. Leonard, C. Lopez, F. Mezeguer, H. Miguez, J. P. Mondia, G. A. Ozin, O. Toader, and H. M. van Driel, "Large-scale synthesis of a silicon photonic crystal with a complete three-dimensional bandgap near 1.5 micrometres," Nature 405, 437-440 (2000).
[CrossRef] [PubMed]

Mondia, J. P.

A. Blanco, E. Chomski, S. Grabtchak, M. Ibisate, S. John, S. W. Leonard, C. Lopez, F. Mezeguer, H. Miguez, J. P. Mondia, G. A. Ozin, O. Toader, and H. M. van Driel, "Large-scale synthesis of a silicon photonic crystal with a complete three-dimensional bandgap near 1.5 micrometres," Nature 405, 437-440 (2000).
[CrossRef] [PubMed]

Noda, S.

S. Noda, K. Tomoda, N. Yamamoto, and A. Chutinan, "Full three-dimensional photonic bandgap crystals at near-infrared wavelengths," Science 289, 604-606 (2000).
[CrossRef] [PubMed]

Norris, D. J.

Y. A. Vlasov, X.-Z. Bo, J. C. Sturm, and D. J. Norris, "On-chip natural assembly of silicon photonic bandgap crystals," Nature 414, 289-293 (2001).
[CrossRef] [PubMed]

Ozin, G. A.

A. Blanco, E. Chomski, S. Grabtchak, M. Ibisate, S. John, S. W. Leonard, C. Lopez, F. Mezeguer, H. Miguez, J. P. Mondia, G. A. Ozin, O. Toader, and H. M. van Driel, "Large-scale synthesis of a silicon photonic crystal with a complete three-dimensional bandgap near 1.5 micrometres," Nature 405, 437-440 (2000).
[CrossRef] [PubMed]

Rinne, S.

P. Braun, S. Rinne, and F. García-Santamaría, "Introducing defects in 3D photonic crystals: State of the art," Adv. Mater. 18, 2665-2678 (2006).
[CrossRef]

Shin, J.

V. Lousse, J. Shin, and S. Fan, "Conditions for designing single-mode air-core waveguides in three-dimensional photonic crystals," Appl. Phys. Lett. 89, 161103 (2006).
[CrossRef]

Sturm, J. C.

Y. A. Vlasov, X.-Z. Bo, J. C. Sturm, and D. J. Norris, "On-chip natural assembly of silicon photonic bandgap crystals," Nature 414, 289-293 (2001).
[CrossRef] [PubMed]

Toader, O.

A. Chutinan, S. John, and O. Toader, "Diffractionless flow of light in all-optical microchips," Phys. Rev. Lett. 90, 123901 (2003).
[CrossRef] [PubMed]

A. Blanco, E. Chomski, S. Grabtchak, M. Ibisate, S. John, S. W. Leonard, C. Lopez, F. Mezeguer, H. Miguez, J. P. Mondia, G. A. Ozin, O. Toader, and H. M. van Driel, "Large-scale synthesis of a silicon photonic crystal with a complete three-dimensional bandgap near 1.5 micrometres," Nature 405, 437-440 (2000).
[CrossRef] [PubMed]

Tomoda, K.

S. Noda, K. Tomoda, N. Yamamoto, and A. Chutinan, "Full three-dimensional photonic bandgap crystals at near-infrared wavelengths," Science 289, 604-606 (2000).
[CrossRef] [PubMed]

van Driel, H. M.

A. Blanco, E. Chomski, S. Grabtchak, M. Ibisate, S. John, S. W. Leonard, C. Lopez, F. Mezeguer, H. Miguez, J. P. Mondia, G. A. Ozin, O. Toader, and H. M. van Driel, "Large-scale synthesis of a silicon photonic crystal with a complete three-dimensional bandgap near 1.5 micrometres," Nature 405, 437-440 (2000).
[CrossRef] [PubMed]

Villeneuve, P. R.

S. Johnson, P. R. Villeneuve, S. Fan, and J. D. Joannopoulos, "Linear waveguides in photonic-crystal slabs," Phys. Rev. B 62, 8212-8222 (2000).
[CrossRef]

A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, "High transmission through sharp bends in photonic crystal waveguides," Phys. Rev. Lett. 77, 3787-3790 (1996).
[CrossRef] [PubMed]

Vlasov, Y. A.

Y. A. Vlasov, X.-Z. Bo, J. C. Sturm, and D. J. Norris, "On-chip natural assembly of silicon photonic bandgap crystals," Nature 414, 289-293 (2001).
[CrossRef] [PubMed]

Yamamoto, N.

S. Noda, K. Tomoda, N. Yamamoto, and A. Chutinan, "Full three-dimensional photonic bandgap crystals at near-infrared wavelengths," Science 289, 604-606 (2000).
[CrossRef] [PubMed]

Adv. Mater.

P. Braun, S. Rinne, and F. García-Santamaría, "Introducing defects in 3D photonic crystals: State of the art," Adv. Mater. 18, 2665-2678 (2006).
[CrossRef]

Appl. Phys. Lett.

V. Lousse, J. Shin, and S. Fan, "Conditions for designing single-mode air-core waveguides in three-dimensional photonic crystals," Appl. Phys. Lett. 89, 161103 (2006).
[CrossRef]

Nature

A. Blanco, E. Chomski, S. Grabtchak, M. Ibisate, S. John, S. W. Leonard, C. Lopez, F. Mezeguer, H. Miguez, J. P. Mondia, G. A. Ozin, O. Toader, and H. M. van Driel, "Large-scale synthesis of a silicon photonic crystal with a complete three-dimensional bandgap near 1.5 micrometres," Nature 405, 437-440 (2000).
[CrossRef] [PubMed]

Y. A. Vlasov, X.-Z. Bo, J. C. Sturm, and D. J. Norris, "On-chip natural assembly of silicon photonic bandgap crystals," Nature 414, 289-293 (2001).
[CrossRef] [PubMed]

Opt. Express

Phys. Rev. B

D. Cassagne, C. Jouanin, and D. Bertho, "Hexagonal photonic band gaps," Phys. Rev. B 53, 7134-7142 (1996).
[CrossRef]

S. Johnson, P. R. Villeneuve, S. Fan, and J. D. Joannopoulos, "Linear waveguides in photonic-crystal slabs," Phys. Rev. B 62, 8212-8222 (2000).
[CrossRef]

Phys. Rev. E

A. Chutinan, and S. John, "Diffractionless flow of light in two- and three-dimensional photonic band gap heterostructures: Theory, design rules and simulations," Phys. Rev. E 71, 026605 (2005).
[CrossRef]

Phys. Rev. Lett.

A. Chutinan, S. John, and O. Toader, "Diffractionless flow of light in all-optical microchips," Phys. Rev. Lett. 90, 123901 (2003).
[CrossRef] [PubMed]

A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, "High transmission through sharp bends in photonic crystal waveguides," Phys. Rev. Lett. 77, 3787-3790 (1996).
[CrossRef] [PubMed]

Science

S. Noda, K. Tomoda, N. Yamamoto, and A. Chutinan, "Full three-dimensional photonic bandgap crystals at near-infrared wavelengths," Science 289, 604-606 (2000).
[CrossRef] [PubMed]

Other

J. D. Joannopoulos, R. Meade, and J. Winn, Photonic crystals: Molding the flow of light (Princeton University Press, Princeton, N.J., 1995).

Photonic Band Gap Materials, edited by C. M. Soukoulis (Kluwer Academic Publishers, Dordrecht, 1996).

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Figures (4)

Fig. 1.
Fig. 1.

Schematic of an inverse opal structure stacked along the <111> direction of its FCC lattice. (a) is a side view of the inverse opal. (b) and (c) are cross-sections of an optimized inverse opal structure halfway between two layers of spheres and in the middle of one, respectively. In (b) and (c), the black and white areas correspond to silicon and air regions, respectively.

Fig. 2.
Fig. 2.

Schematic of an inverse opal-based 2D-3D heterostructure with a 2D PhC layer, consisting of a graphite arrangement of dielectric rods in air. The 2D layer parameters correspond to the structure yielding maximal waveguiding bandwidth (rod radius r=0.10a and layer thickness t=0.20a).

Fig. 3.
Fig. 3.

Dispersion relation of the optimal single-mode waveguide along the ΓK direction of the graphite lattice. The inset shows the time-averaged magnetic-field energy density of the single-mode at the wavevector ka/2π=0.2.

Fig. 4.
Fig. 4.

Single-mode waveguiding bandwidth as a function of the layer thickness and rod radius. The white lines drawn on the bandwidth surface are isosurface curves delimiting bandwidths from 40 nm to 120 nm in steps of 10 nm.

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