Abstract

We study experimentally and theoretically light propagation and generation at the high energy range of a close-packed fcc photonic crystal of polystyrene spheres coated with a nonlinear material. We observe an enhancement of the second harmonic generation of light that may be explained on the basis of amplification effects arising from propagation at anomalous group velocities. Theoretical calculations are performed to support this assumption. The vector KKR method we use allows us to determine, from the linear response of the crystal, the behavior of the group velocity in our finite photonic structures when losses introduced by absorption or scattering by defects are taken into account assuming a nonzero imaginary part for the dielectric constant. In such structures, we predict large variations of the group velocity for wavelengths on the order or smaller than the lattice constant of the structure, where an anomalous group velocity behavior is associated with the flat bands of the photonic band structure. We find that a direct relation may be established between the group velocity reduction and the enhancement of a light generation processes such as the second harmonic generation we consider. However, frequencies for which the enhancement is found, in the finite photonic crystals we use, do not necessarily coincide with the frequencies of flat high energy bands.

© 2009 OSA

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  1. K. Sakoda, “Optical properties of photonic crystals,” Springer-Verlag, Berlin (2005).
  2. M. Scharrer, A. Yamilov, X. Wu, H. Cao, and R. P. H. Chang, “Ultraviolet lasing in high-order bands of three-dimensional ZnO photonic crystals,” Appl. Phys. Lett. 88(20), 201103 (2006).
    [CrossRef]
  3. H. Noh, M. Scharrer, M. A. Anderson, R. P. H. Chang, and H. Cao, “Photoluminescence modification by a high-order photonic band with abnormal dispersion in ZnO inverse opal,” Phys. Rev. B 77(11), 115136 (2008).
    [CrossRef]
  4. J. F. Galisteo-López and C. López, “High-energy optical response of artificial opals,” Phys. Rev. B 70(3), 035108 (2004).
    [CrossRef]
  5. H. Míguez, V. Kitaev, and G. A. Ozin, “Band spectroscopy of colloidal photonic crystal films,” Appl. Phys. Lett. 84(8), 1239 (2004).
    [CrossRef]
  6. J. F. Galisteo-López, M. Galli, A. Balestreri, M. Patrini, L. C. Andreani, and C. López, “Slow to superluminal light waves in thin 3D photonic crystals,” Opt. Express 15(23), 15342–15350 (2007).
    [CrossRef] [PubMed]
  7. N. Stefanou, V. Karathanos, and A. Modinos, “Scattering of electromagnetic waves by periodic structures,” J. Phys. Condens. Matter 4(36), 7389–7400 (1992).
    [CrossRef]
  8. N. Stefanou, V. Yannopapas, and A. Modinos, “Heterostructures of photonic crystals: Frequency bands and transmission coefficients,” Comput. Phys. Commun. 113(1), 49–77 (1998).
    [CrossRef]
  9. K. Ohtaka, “Scattering theory of low-energy photon diffraction,” J. Phys. C: Solid State 13(4), 667–680 (1980).
    [CrossRef]
  10. A. Modinos, “Scattering of electromagnetic waves by a plane of spheres-formalism,” Physica A 141(2-3), 575–588 (1987).
    [CrossRef]
  11. L. A. Dorado, R. A. Depine, and H. Míguez, “Effect of extinction on the high-energy optical response of photonic crystals,” Phys. Rev. B 75(24), 241101 (2007).
    [CrossRef]
  12. L. A. Dorado, R. A. Depine, G. Lozano, and H. Míguez, “Physical origin of the high energy optical response of three dimensional photonic crystals,” Opt. Express 15(26), 17754–17760 (2007).
    [CrossRef] [PubMed]
  13. Y. A. Vlasov, M. O’Boyle, H. F. Hamann, and S. J. McNab, “Active control of slow light on a chip with photonic crystal waveguides,” Nature 438(7064), 65–69 (2005).
    [CrossRef] [PubMed]
  14. M. D. Settle, R. J. P. Engelen, M. Salib, A. Michaeli, L. Kuipers, and T. F. Krauss, “Flatband slow light in photonic crystals featuring spatial pulse compression and terahertz bandwidth,” Opt. Express 15(1), 219–226 (2007).
    [CrossRef] [PubMed]
  15. A. Mihi, M. Ocaña, and H. Míguez, “Oriented Colloidal-Crystal Thin Films by Spin-Coating Microspheres Dispersed in Volatile Media,” Adv. Mater. 18(17), 2244–2249 (2006).
    [CrossRef]
  16. B. H. Juárez, P. D. García, D. Golmayo, A. Blanco, and C. López, “ZnO Inverse Opals by Chemical Vapor Dposition,” Adv. Mater. 17(22), 2761–2765 (2005).
    [CrossRef]
  17. A. Molinos-Gómez, M. Maymó, X. Vidal, D. Velasco, J. Martorell, and F. López-Calahorra, “Synthesis of Colloidal Photonic Crystals with High Nonlinear Optical Performance: Towards Efficient Second-Harmonic Generation with Centrosymmetric Structures,” Adv. Mater. 19(22), 3814–3818 (2007).
    [CrossRef]
  18. M. Maymó, J. Martorell, A. Molinos-Gómez, and F. López-Calahorra, “Visible second-harmonic light generated from a self-organized centrosymmetric lattice of nanospheres,” Opt. Express 14(7), 2864–2872 (2006).
    [CrossRef] [PubMed]
  19. J. Martorell, R. Vilaseca, and R. Corbalán, “Second-harmonic generation in a photonic crystal,” Appl. Phys. Lett. 70(6), 702–704 (1997).
    [CrossRef]
  20. In preparation.
  21. M. Botey, J. Martorell, J. Trull, and R. Vilaseca, “Suppression of radiation in a momentum-nonconserving nonlinear interaction,” Opt. Lett. 25(16), 1177–1179 (2000).
    [CrossRef]
  22. A. A. Fedyanin, O. Aktsipetrov, D. A. Kurdyukov, V. G. Golubev, and M. Inoue, “Nonlinear diffraction and second-harmonic generation enhancement in silicon-opal photonic crystals,” Appl. Phys. Lett. 87(15), 151111 (2005).
    [CrossRef]

2008 (1)

H. Noh, M. Scharrer, M. A. Anderson, R. P. H. Chang, and H. Cao, “Photoluminescence modification by a high-order photonic band with abnormal dispersion in ZnO inverse opal,” Phys. Rev. B 77(11), 115136 (2008).
[CrossRef]

2007 (5)

2006 (3)

M. Maymó, J. Martorell, A. Molinos-Gómez, and F. López-Calahorra, “Visible second-harmonic light generated from a self-organized centrosymmetric lattice of nanospheres,” Opt. Express 14(7), 2864–2872 (2006).
[CrossRef] [PubMed]

A. Mihi, M. Ocaña, and H. Míguez, “Oriented Colloidal-Crystal Thin Films by Spin-Coating Microspheres Dispersed in Volatile Media,” Adv. Mater. 18(17), 2244–2249 (2006).
[CrossRef]

M. Scharrer, A. Yamilov, X. Wu, H. Cao, and R. P. H. Chang, “Ultraviolet lasing in high-order bands of three-dimensional ZnO photonic crystals,” Appl. Phys. Lett. 88(20), 201103 (2006).
[CrossRef]

2005 (3)

B. H. Juárez, P. D. García, D. Golmayo, A. Blanco, and C. López, “ZnO Inverse Opals by Chemical Vapor Dposition,” Adv. Mater. 17(22), 2761–2765 (2005).
[CrossRef]

Y. A. Vlasov, M. O’Boyle, H. F. Hamann, and S. J. McNab, “Active control of slow light on a chip with photonic crystal waveguides,” Nature 438(7064), 65–69 (2005).
[CrossRef] [PubMed]

A. A. Fedyanin, O. Aktsipetrov, D. A. Kurdyukov, V. G. Golubev, and M. Inoue, “Nonlinear diffraction and second-harmonic generation enhancement in silicon-opal photonic crystals,” Appl. Phys. Lett. 87(15), 151111 (2005).
[CrossRef]

2004 (2)

J. F. Galisteo-López and C. López, “High-energy optical response of artificial opals,” Phys. Rev. B 70(3), 035108 (2004).
[CrossRef]

H. Míguez, V. Kitaev, and G. A. Ozin, “Band spectroscopy of colloidal photonic crystal films,” Appl. Phys. Lett. 84(8), 1239 (2004).
[CrossRef]

2000 (1)

1998 (1)

N. Stefanou, V. Yannopapas, and A. Modinos, “Heterostructures of photonic crystals: Frequency bands and transmission coefficients,” Comput. Phys. Commun. 113(1), 49–77 (1998).
[CrossRef]

1997 (1)

J. Martorell, R. Vilaseca, and R. Corbalán, “Second-harmonic generation in a photonic crystal,” Appl. Phys. Lett. 70(6), 702–704 (1997).
[CrossRef]

1992 (1)

N. Stefanou, V. Karathanos, and A. Modinos, “Scattering of electromagnetic waves by periodic structures,” J. Phys. Condens. Matter 4(36), 7389–7400 (1992).
[CrossRef]

1987 (1)

A. Modinos, “Scattering of electromagnetic waves by a plane of spheres-formalism,” Physica A 141(2-3), 575–588 (1987).
[CrossRef]

1980 (1)

K. Ohtaka, “Scattering theory of low-energy photon diffraction,” J. Phys. C: Solid State 13(4), 667–680 (1980).
[CrossRef]

Aktsipetrov, O.

A. A. Fedyanin, O. Aktsipetrov, D. A. Kurdyukov, V. G. Golubev, and M. Inoue, “Nonlinear diffraction and second-harmonic generation enhancement in silicon-opal photonic crystals,” Appl. Phys. Lett. 87(15), 151111 (2005).
[CrossRef]

Anderson, M. A.

H. Noh, M. Scharrer, M. A. Anderson, R. P. H. Chang, and H. Cao, “Photoluminescence modification by a high-order photonic band with abnormal dispersion in ZnO inverse opal,” Phys. Rev. B 77(11), 115136 (2008).
[CrossRef]

Andreani, L. C.

Balestreri, A.

Blanco, A.

B. H. Juárez, P. D. García, D. Golmayo, A. Blanco, and C. López, “ZnO Inverse Opals by Chemical Vapor Dposition,” Adv. Mater. 17(22), 2761–2765 (2005).
[CrossRef]

Botey, M.

Cao, H.

H. Noh, M. Scharrer, M. A. Anderson, R. P. H. Chang, and H. Cao, “Photoluminescence modification by a high-order photonic band with abnormal dispersion in ZnO inverse opal,” Phys. Rev. B 77(11), 115136 (2008).
[CrossRef]

M. Scharrer, A. Yamilov, X. Wu, H. Cao, and R. P. H. Chang, “Ultraviolet lasing in high-order bands of three-dimensional ZnO photonic crystals,” Appl. Phys. Lett. 88(20), 201103 (2006).
[CrossRef]

Chang, R. P. H.

H. Noh, M. Scharrer, M. A. Anderson, R. P. H. Chang, and H. Cao, “Photoluminescence modification by a high-order photonic band with abnormal dispersion in ZnO inverse opal,” Phys. Rev. B 77(11), 115136 (2008).
[CrossRef]

M. Scharrer, A. Yamilov, X. Wu, H. Cao, and R. P. H. Chang, “Ultraviolet lasing in high-order bands of three-dimensional ZnO photonic crystals,” Appl. Phys. Lett. 88(20), 201103 (2006).
[CrossRef]

Corbalán, R.

J. Martorell, R. Vilaseca, and R. Corbalán, “Second-harmonic generation in a photonic crystal,” Appl. Phys. Lett. 70(6), 702–704 (1997).
[CrossRef]

Depine, R. A.

L. A. Dorado, R. A. Depine, and H. Míguez, “Effect of extinction on the high-energy optical response of photonic crystals,” Phys. Rev. B 75(24), 241101 (2007).
[CrossRef]

L. A. Dorado, R. A. Depine, G. Lozano, and H. Míguez, “Physical origin of the high energy optical response of three dimensional photonic crystals,” Opt. Express 15(26), 17754–17760 (2007).
[CrossRef] [PubMed]

Dorado, L. A.

L. A. Dorado, R. A. Depine, G. Lozano, and H. Míguez, “Physical origin of the high energy optical response of three dimensional photonic crystals,” Opt. Express 15(26), 17754–17760 (2007).
[CrossRef] [PubMed]

L. A. Dorado, R. A. Depine, and H. Míguez, “Effect of extinction on the high-energy optical response of photonic crystals,” Phys. Rev. B 75(24), 241101 (2007).
[CrossRef]

Engelen, R. J. P.

Fedyanin, A. A.

A. A. Fedyanin, O. Aktsipetrov, D. A. Kurdyukov, V. G. Golubev, and M. Inoue, “Nonlinear diffraction and second-harmonic generation enhancement in silicon-opal photonic crystals,” Appl. Phys. Lett. 87(15), 151111 (2005).
[CrossRef]

Galisteo-López, J. F.

Galli, M.

García, P. D.

B. H. Juárez, P. D. García, D. Golmayo, A. Blanco, and C. López, “ZnO Inverse Opals by Chemical Vapor Dposition,” Adv. Mater. 17(22), 2761–2765 (2005).
[CrossRef]

Golmayo, D.

B. H. Juárez, P. D. García, D. Golmayo, A. Blanco, and C. López, “ZnO Inverse Opals by Chemical Vapor Dposition,” Adv. Mater. 17(22), 2761–2765 (2005).
[CrossRef]

Golubev, V. G.

A. A. Fedyanin, O. Aktsipetrov, D. A. Kurdyukov, V. G. Golubev, and M. Inoue, “Nonlinear diffraction and second-harmonic generation enhancement in silicon-opal photonic crystals,” Appl. Phys. Lett. 87(15), 151111 (2005).
[CrossRef]

Hamann, H. F.

Y. A. Vlasov, M. O’Boyle, H. F. Hamann, and S. J. McNab, “Active control of slow light on a chip with photonic crystal waveguides,” Nature 438(7064), 65–69 (2005).
[CrossRef] [PubMed]

Inoue, M.

A. A. Fedyanin, O. Aktsipetrov, D. A. Kurdyukov, V. G. Golubev, and M. Inoue, “Nonlinear diffraction and second-harmonic generation enhancement in silicon-opal photonic crystals,” Appl. Phys. Lett. 87(15), 151111 (2005).
[CrossRef]

Juárez, B. H.

B. H. Juárez, P. D. García, D. Golmayo, A. Blanco, and C. López, “ZnO Inverse Opals by Chemical Vapor Dposition,” Adv. Mater. 17(22), 2761–2765 (2005).
[CrossRef]

Karathanos, V.

N. Stefanou, V. Karathanos, and A. Modinos, “Scattering of electromagnetic waves by periodic structures,” J. Phys. Condens. Matter 4(36), 7389–7400 (1992).
[CrossRef]

Kitaev, V.

H. Míguez, V. Kitaev, and G. A. Ozin, “Band spectroscopy of colloidal photonic crystal films,” Appl. Phys. Lett. 84(8), 1239 (2004).
[CrossRef]

Krauss, T. F.

Kuipers, L.

Kurdyukov, D. A.

A. A. Fedyanin, O. Aktsipetrov, D. A. Kurdyukov, V. G. Golubev, and M. Inoue, “Nonlinear diffraction and second-harmonic generation enhancement in silicon-opal photonic crystals,” Appl. Phys. Lett. 87(15), 151111 (2005).
[CrossRef]

López, C.

J. F. Galisteo-López, M. Galli, A. Balestreri, M. Patrini, L. C. Andreani, and C. López, “Slow to superluminal light waves in thin 3D photonic crystals,” Opt. Express 15(23), 15342–15350 (2007).
[CrossRef] [PubMed]

B. H. Juárez, P. D. García, D. Golmayo, A. Blanco, and C. López, “ZnO Inverse Opals by Chemical Vapor Dposition,” Adv. Mater. 17(22), 2761–2765 (2005).
[CrossRef]

J. F. Galisteo-López and C. López, “High-energy optical response of artificial opals,” Phys. Rev. B 70(3), 035108 (2004).
[CrossRef]

López-Calahorra, F.

A. Molinos-Gómez, M. Maymó, X. Vidal, D. Velasco, J. Martorell, and F. López-Calahorra, “Synthesis of Colloidal Photonic Crystals with High Nonlinear Optical Performance: Towards Efficient Second-Harmonic Generation with Centrosymmetric Structures,” Adv. Mater. 19(22), 3814–3818 (2007).
[CrossRef]

M. Maymó, J. Martorell, A. Molinos-Gómez, and F. López-Calahorra, “Visible second-harmonic light generated from a self-organized centrosymmetric lattice of nanospheres,” Opt. Express 14(7), 2864–2872 (2006).
[CrossRef] [PubMed]

Lozano, G.

Martorell, J.

A. Molinos-Gómez, M. Maymó, X. Vidal, D. Velasco, J. Martorell, and F. López-Calahorra, “Synthesis of Colloidal Photonic Crystals with High Nonlinear Optical Performance: Towards Efficient Second-Harmonic Generation with Centrosymmetric Structures,” Adv. Mater. 19(22), 3814–3818 (2007).
[CrossRef]

M. Maymó, J. Martorell, A. Molinos-Gómez, and F. López-Calahorra, “Visible second-harmonic light generated from a self-organized centrosymmetric lattice of nanospheres,” Opt. Express 14(7), 2864–2872 (2006).
[CrossRef] [PubMed]

M. Botey, J. Martorell, J. Trull, and R. Vilaseca, “Suppression of radiation in a momentum-nonconserving nonlinear interaction,” Opt. Lett. 25(16), 1177–1179 (2000).
[CrossRef]

J. Martorell, R. Vilaseca, and R. Corbalán, “Second-harmonic generation in a photonic crystal,” Appl. Phys. Lett. 70(6), 702–704 (1997).
[CrossRef]

Maymó, M.

A. Molinos-Gómez, M. Maymó, X. Vidal, D. Velasco, J. Martorell, and F. López-Calahorra, “Synthesis of Colloidal Photonic Crystals with High Nonlinear Optical Performance: Towards Efficient Second-Harmonic Generation with Centrosymmetric Structures,” Adv. Mater. 19(22), 3814–3818 (2007).
[CrossRef]

M. Maymó, J. Martorell, A. Molinos-Gómez, and F. López-Calahorra, “Visible second-harmonic light generated from a self-organized centrosymmetric lattice of nanospheres,” Opt. Express 14(7), 2864–2872 (2006).
[CrossRef] [PubMed]

McNab, S. J.

Y. A. Vlasov, M. O’Boyle, H. F. Hamann, and S. J. McNab, “Active control of slow light on a chip with photonic crystal waveguides,” Nature 438(7064), 65–69 (2005).
[CrossRef] [PubMed]

Michaeli, A.

Míguez, H.

L. A. Dorado, R. A. Depine, and H. Míguez, “Effect of extinction on the high-energy optical response of photonic crystals,” Phys. Rev. B 75(24), 241101 (2007).
[CrossRef]

L. A. Dorado, R. A. Depine, G. Lozano, and H. Míguez, “Physical origin of the high energy optical response of three dimensional photonic crystals,” Opt. Express 15(26), 17754–17760 (2007).
[CrossRef] [PubMed]

A. Mihi, M. Ocaña, and H. Míguez, “Oriented Colloidal-Crystal Thin Films by Spin-Coating Microspheres Dispersed in Volatile Media,” Adv. Mater. 18(17), 2244–2249 (2006).
[CrossRef]

H. Míguez, V. Kitaev, and G. A. Ozin, “Band spectroscopy of colloidal photonic crystal films,” Appl. Phys. Lett. 84(8), 1239 (2004).
[CrossRef]

Mihi, A.

A. Mihi, M. Ocaña, and H. Míguez, “Oriented Colloidal-Crystal Thin Films by Spin-Coating Microspheres Dispersed in Volatile Media,” Adv. Mater. 18(17), 2244–2249 (2006).
[CrossRef]

Modinos, A.

N. Stefanou, V. Yannopapas, and A. Modinos, “Heterostructures of photonic crystals: Frequency bands and transmission coefficients,” Comput. Phys. Commun. 113(1), 49–77 (1998).
[CrossRef]

N. Stefanou, V. Karathanos, and A. Modinos, “Scattering of electromagnetic waves by periodic structures,” J. Phys. Condens. Matter 4(36), 7389–7400 (1992).
[CrossRef]

A. Modinos, “Scattering of electromagnetic waves by a plane of spheres-formalism,” Physica A 141(2-3), 575–588 (1987).
[CrossRef]

Molinos-Gómez, A.

A. Molinos-Gómez, M. Maymó, X. Vidal, D. Velasco, J. Martorell, and F. López-Calahorra, “Synthesis of Colloidal Photonic Crystals with High Nonlinear Optical Performance: Towards Efficient Second-Harmonic Generation with Centrosymmetric Structures,” Adv. Mater. 19(22), 3814–3818 (2007).
[CrossRef]

M. Maymó, J. Martorell, A. Molinos-Gómez, and F. López-Calahorra, “Visible second-harmonic light generated from a self-organized centrosymmetric lattice of nanospheres,” Opt. Express 14(7), 2864–2872 (2006).
[CrossRef] [PubMed]

Noh, H.

H. Noh, M. Scharrer, M. A. Anderson, R. P. H. Chang, and H. Cao, “Photoluminescence modification by a high-order photonic band with abnormal dispersion in ZnO inverse opal,” Phys. Rev. B 77(11), 115136 (2008).
[CrossRef]

O’Boyle, M.

Y. A. Vlasov, M. O’Boyle, H. F. Hamann, and S. J. McNab, “Active control of slow light on a chip with photonic crystal waveguides,” Nature 438(7064), 65–69 (2005).
[CrossRef] [PubMed]

Ocaña, M.

A. Mihi, M. Ocaña, and H. Míguez, “Oriented Colloidal-Crystal Thin Films by Spin-Coating Microspheres Dispersed in Volatile Media,” Adv. Mater. 18(17), 2244–2249 (2006).
[CrossRef]

Ohtaka, K.

K. Ohtaka, “Scattering theory of low-energy photon diffraction,” J. Phys. C: Solid State 13(4), 667–680 (1980).
[CrossRef]

Ozin, G. A.

H. Míguez, V. Kitaev, and G. A. Ozin, “Band spectroscopy of colloidal photonic crystal films,” Appl. Phys. Lett. 84(8), 1239 (2004).
[CrossRef]

Patrini, M.

Salib, M.

Scharrer, M.

H. Noh, M. Scharrer, M. A. Anderson, R. P. H. Chang, and H. Cao, “Photoluminescence modification by a high-order photonic band with abnormal dispersion in ZnO inverse opal,” Phys. Rev. B 77(11), 115136 (2008).
[CrossRef]

M. Scharrer, A. Yamilov, X. Wu, H. Cao, and R. P. H. Chang, “Ultraviolet lasing in high-order bands of three-dimensional ZnO photonic crystals,” Appl. Phys. Lett. 88(20), 201103 (2006).
[CrossRef]

Settle, M. D.

Stefanou, N.

N. Stefanou, V. Yannopapas, and A. Modinos, “Heterostructures of photonic crystals: Frequency bands and transmission coefficients,” Comput. Phys. Commun. 113(1), 49–77 (1998).
[CrossRef]

N. Stefanou, V. Karathanos, and A. Modinos, “Scattering of electromagnetic waves by periodic structures,” J. Phys. Condens. Matter 4(36), 7389–7400 (1992).
[CrossRef]

Trull, J.

Velasco, D.

A. Molinos-Gómez, M. Maymó, X. Vidal, D. Velasco, J. Martorell, and F. López-Calahorra, “Synthesis of Colloidal Photonic Crystals with High Nonlinear Optical Performance: Towards Efficient Second-Harmonic Generation with Centrosymmetric Structures,” Adv. Mater. 19(22), 3814–3818 (2007).
[CrossRef]

Vidal, X.

A. Molinos-Gómez, M. Maymó, X. Vidal, D. Velasco, J. Martorell, and F. López-Calahorra, “Synthesis of Colloidal Photonic Crystals with High Nonlinear Optical Performance: Towards Efficient Second-Harmonic Generation with Centrosymmetric Structures,” Adv. Mater. 19(22), 3814–3818 (2007).
[CrossRef]

Vilaseca, R.

M. Botey, J. Martorell, J. Trull, and R. Vilaseca, “Suppression of radiation in a momentum-nonconserving nonlinear interaction,” Opt. Lett. 25(16), 1177–1179 (2000).
[CrossRef]

J. Martorell, R. Vilaseca, and R. Corbalán, “Second-harmonic generation in a photonic crystal,” Appl. Phys. Lett. 70(6), 702–704 (1997).
[CrossRef]

Vlasov, Y. A.

Y. A. Vlasov, M. O’Boyle, H. F. Hamann, and S. J. McNab, “Active control of slow light on a chip with photonic crystal waveguides,” Nature 438(7064), 65–69 (2005).
[CrossRef] [PubMed]

Wu, X.

M. Scharrer, A. Yamilov, X. Wu, H. Cao, and R. P. H. Chang, “Ultraviolet lasing in high-order bands of three-dimensional ZnO photonic crystals,” Appl. Phys. Lett. 88(20), 201103 (2006).
[CrossRef]

Yamilov, A.

M. Scharrer, A. Yamilov, X. Wu, H. Cao, and R. P. H. Chang, “Ultraviolet lasing in high-order bands of three-dimensional ZnO photonic crystals,” Appl. Phys. Lett. 88(20), 201103 (2006).
[CrossRef]

Yannopapas, V.

N. Stefanou, V. Yannopapas, and A. Modinos, “Heterostructures of photonic crystals: Frequency bands and transmission coefficients,” Comput. Phys. Commun. 113(1), 49–77 (1998).
[CrossRef]

Adv. Mater. (3)

A. Mihi, M. Ocaña, and H. Míguez, “Oriented Colloidal-Crystal Thin Films by Spin-Coating Microspheres Dispersed in Volatile Media,” Adv. Mater. 18(17), 2244–2249 (2006).
[CrossRef]

B. H. Juárez, P. D. García, D. Golmayo, A. Blanco, and C. López, “ZnO Inverse Opals by Chemical Vapor Dposition,” Adv. Mater. 17(22), 2761–2765 (2005).
[CrossRef]

A. Molinos-Gómez, M. Maymó, X. Vidal, D. Velasco, J. Martorell, and F. López-Calahorra, “Synthesis of Colloidal Photonic Crystals with High Nonlinear Optical Performance: Towards Efficient Second-Harmonic Generation with Centrosymmetric Structures,” Adv. Mater. 19(22), 3814–3818 (2007).
[CrossRef]

Appl. Phys. Lett. (4)

M. Scharrer, A. Yamilov, X. Wu, H. Cao, and R. P. H. Chang, “Ultraviolet lasing in high-order bands of three-dimensional ZnO photonic crystals,” Appl. Phys. Lett. 88(20), 201103 (2006).
[CrossRef]

H. Míguez, V. Kitaev, and G. A. Ozin, “Band spectroscopy of colloidal photonic crystal films,” Appl. Phys. Lett. 84(8), 1239 (2004).
[CrossRef]

J. Martorell, R. Vilaseca, and R. Corbalán, “Second-harmonic generation in a photonic crystal,” Appl. Phys. Lett. 70(6), 702–704 (1997).
[CrossRef]

A. A. Fedyanin, O. Aktsipetrov, D. A. Kurdyukov, V. G. Golubev, and M. Inoue, “Nonlinear diffraction and second-harmonic generation enhancement in silicon-opal photonic crystals,” Appl. Phys. Lett. 87(15), 151111 (2005).
[CrossRef]

Comput. Phys. Commun. (1)

N. Stefanou, V. Yannopapas, and A. Modinos, “Heterostructures of photonic crystals: Frequency bands and transmission coefficients,” Comput. Phys. Commun. 113(1), 49–77 (1998).
[CrossRef]

J. Phys. C: Solid State (1)

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In preparation.

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Figures (3)

Fig. 1
Fig. 1

Experimental spectral reflectance (black solid curve), calculated specularly reflected intensity (grey dotted curve), experimental transmittance (green solid curve), and calculated transmitted intensity (green dotted curve) as a function of wavelength, λ, in vacuum. As the structure is slightly distorted we have used a smaller lattice parameter at the lower energy spectral range.

Fig. 2
Fig. 2

Spectral reflectance as a function of wavelength (black solid curve) and SHG intensity as a function of the generated SH wavelength, (violet solid dots). The dotted line is only a guide for the eye. The inset: Schematic drawing of the opal sample used in the experiments.

Fig. 3
Fig. 3

Reflected wave group velocity (black solid curve), transmitted wave group velocity (green dotted curve) and measured SHG intensity (violet dotted points) for a 10 [111] planes opal made of polystyrene spheres in air on a semi-infinite glass substrate. All plotted as a function of frequency in reduced a/λ units where a is the lattice parameter. The dashed line in violet is only a guide for the eye. The red horizontal line corresponds to a constant average group velocity for the fcc close-packed structure: vg=(0.74*2.5+0.26)1 . Group velocities are expressed in c units, where c is the speed of light in vacuum.

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