Abstract

An experimental and theoretical analysis of the angular dependence of the diffracted light beams emerging from three-dimensional colloidal photonic crystals is herein presented. Diffracted beams are identified according to their associated reciprocal-lattice vectors, and their intensities are obtained as a function of the zenithal and azimuthal incidence angles. Significant changes in the beam intensities are observed for large zenithal incidence angles as the azimuthal angle is varied. This phenomenon is related to the excitation of new resonant modes inside the photonic crystal which cannot be observed under normal incidence conditions.

© 2010 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. C. López, “Three-dimensional photonic bandgap materials: semiconductors for light,” J. Opt. A, Pure Appl. Opt. 8, R1–R14 (2006).
    [CrossRef]
  4. G. Lozano, L. A. Dorado, R. A. Depine, and H. Míguez, “Towards a full understanding of the growth dynamics and optical response of self-assembled photonic colloidal crystal films,” J. Mater. Chem. 19, 185–190 (2009).
    [CrossRef]
  5. P. Jiang, J. F. Bertone, K. S. Hwang, and V. L. Colvin, “Single-crystal colloidal multilayers of controlled thickness,” Chem. Mater. 11, 2132–2140 (1999).
    [CrossRef]
  6. S. Wong, V. Kitaev, and G. A. Ozin, “Colloidal crystal films: advances in universality and perfection,” J. Am. Chem. Soc. 125, 15589–15598 (2003).
    [CrossRef] [PubMed]
  7. 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]
  8. G. von Freymann, S. John, S. Wong, V. Kitaev, and G. A. Ozin, “Measurement of group velocity dispersion for finite size three-dimensional photonic crystals in the near-infrared spectral region,” Appl. Phys. Lett. 86, 053108 (2005).
    [CrossRef]
  9. H. Míguez, V. Kitaev, and G. Ozin, “Band spectroscopy of colloidal photonic crystal films,” Appl. Phys. Lett. 84, 1239–1241 (2004).
    [CrossRef]
  10. J. F. Galisteo-López, M. Galli, L. C. Andreani, A. Mihi, R. Pozas, M. Ocaña, and H. Míguez, “Phase delay and group velocity determination at a planar defect state in three dimensional photonic crystals,” Appl. Phys. Lett. 90, 101113 (2007).
    [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, 241101(R) (2007).
    [CrossRef]
  12. J. F. Galisteo-López and C. López, “High-energy optical response of artificial opals,” Phys. Rev. B 70, 035108 (2004).
    [CrossRef]
  13. F. García-Santamaría, J. F. Galisteo-López, P. V. Braun, and C. López, “Optical diffraction and high-energy features in three-dimensional photonic crystals,” Phys. Rev. B 71, 195112 (2005).
    [CrossRef]
  14. 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]
  15. A. Balestreri, L. C. Andreani, and M. Agio, “Optical properties and diffraction effects in opal photonic crystals,” Phys. Rev. E 74, 036603 (2006).
    [CrossRef]
  16. S. Schutzmann, I. Venditti, P. Prosposito, M. Casalboni, and M. V. Russo, “High-energy angle resolved reflection spectroscopy on three-dimensional photonic crystals of self-organized polymeric nanospheres,” Opt. Express 16, 897–907 (2008).
    [CrossRef] [PubMed]
  17. L. A. Dorado, R. A. Depine, and H. Míguez, “Comment on “Observation of higher-order diffraction features in self-assembled photonic crystals”,” Phys. Rev. A 78, 037801 (2008).
    [CrossRef]
  18. R. V. Nair and R. Vijaya, “Reply to “Comment on ‘Observation of higher-order diffraction features in self-assembled photonic crystals’”,” Phys. Rev. A 78, 037802 (2008).
    [CrossRef]
  19. S. G. Romanov, M. Bardosova, I. M. Povey, M. E. Pemble, and C. M. Sotomayor Torres, “Understanding of transmission in the range of high-order photonic bands in thin opal film,” Appl. Phys. Lett. 92, 191106 (2008).
    [CrossRef]
  20. L. A. Dorado, R. A. Depine, D. Schinca, G. Lozano, and H. Míguez, “Experimental and theoretical analysis of the intensity of beams diffracted by three-dimensional photonic crystals,” Phys. Rev. B 78, 075102 (2008).
    [CrossRef]
  21. 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]
  22. T. Inagaki, E. T. Arakawa, R. N. Hamm, and M. W. Williams, “Optical properties of polystyrene from the near-infrared to the x-ray region and convergence of optical sum rules,” Phys. Rev. B 15, 3243–3253 (1977).
    [CrossRef]
  23. N. Stefanou, V. Yannopapas, and A. Modinos, “Heterostructures of photonic crystals: frequency bands and transmission coefficients,” Comput. Phys. Commun. 113, 49–77 (1998).
    [CrossRef]
  24. N. Stefanou, V. Yannopapas, and A. Modinos, “MULTEM 2: a new version of the program for transmission and band-structure calculations of photonic crystals,” Comput. Phys. Commun. 132, 189–196 (2000).
    [CrossRef]
  25. X. Checoury, S. Enoch, C. López, and A. Blanco, “Stacking patterns in self-assembly opal photonic crystals,” Appl. Phys. Lett. 90, 161131 (2007).
    [CrossRef]
  26. The imaginary part of the dielectric constant is not considered as a constant quantity during calculations. We employed a smaller value of the εi parameter in the high-energy spectral range (0.08) which represents the different effects of imperfections have on the different wavelength ranges.
  27. G. Lozano, L. A. Dorado, D. Schinca, R. A. Depine, and H. Míguez, “Optical analysis of the fine crystalline structure of artificial opal films,” Langmuir 25, 12860–12864 (2009).
    [CrossRef] [PubMed]
  28. F. López-Tejeira, T. Ochiai, K. Sakoda, and J. Sánchez-Dehesa, “Symmetry characterization of eigenstates in opal-based photonic crystals,” Phys. Rev. B 65, 195110 (2002).
    [CrossRef]
  29. L. C. Andreani, A. Balestreri, J. F. Galisteo-López, M. Galli, M. Patrini, E. Descrovi, A. Chiodoni, F. Giorgis, L. Pallavidino, and F. Geobaldo, “Optical response with threefold symmetry axis on oriented microdomains of opal photonic crystals,” Phys. Rev. B 78, 205304 (2008).
    [CrossRef]
  30. 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, 17754–17760 (2007).
    [CrossRef] [PubMed]

2009 (3)

G. Lozano, L. A. Dorado, R. A. Depine, and H. Míguez, “Towards a full understanding of the growth dynamics and optical response of self-assembled photonic colloidal crystal films,” J. Mater. Chem. 19, 185–190 (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]

G. Lozano, L. A. Dorado, D. Schinca, R. A. Depine, and H. Míguez, “Optical analysis of the fine crystalline structure of artificial opal films,” Langmuir 25, 12860–12864 (2009).
[CrossRef] [PubMed]

2008 (6)

L. C. Andreani, A. Balestreri, J. F. Galisteo-López, M. Galli, M. Patrini, E. Descrovi, A. Chiodoni, F. Giorgis, L. Pallavidino, and F. Geobaldo, “Optical response with threefold symmetry axis on oriented microdomains of opal photonic crystals,” Phys. Rev. B 78, 205304 (2008).
[CrossRef]

S. Schutzmann, I. Venditti, P. Prosposito, M. Casalboni, and M. V. Russo, “High-energy angle resolved reflection spectroscopy on three-dimensional photonic crystals of self-organized polymeric nanospheres,” Opt. Express 16, 897–907 (2008).
[CrossRef] [PubMed]

L. A. Dorado, R. A. Depine, and H. Míguez, “Comment on “Observation of higher-order diffraction features in self-assembled photonic crystals”,” Phys. Rev. A 78, 037801 (2008).
[CrossRef]

R. V. Nair and R. Vijaya, “Reply to “Comment on ‘Observation of higher-order diffraction features in self-assembled photonic crystals’”,” Phys. Rev. A 78, 037802 (2008).
[CrossRef]

S. G. Romanov, M. Bardosova, I. M. Povey, M. E. Pemble, and C. M. Sotomayor Torres, “Understanding of transmission in the range of high-order photonic bands in thin opal film,” Appl. Phys. Lett. 92, 191106 (2008).
[CrossRef]

L. A. Dorado, R. A. Depine, D. Schinca, G. Lozano, and H. Míguez, “Experimental and theoretical analysis of the intensity of beams diffracted by three-dimensional photonic crystals,” Phys. Rev. B 78, 075102 (2008).
[CrossRef]

2007 (4)

J. F. Galisteo-López, M. Galli, L. C. Andreani, A. Mihi, R. Pozas, M. Ocaña, and H. Míguez, “Phase delay and group velocity determination at a planar defect state in three dimensional photonic crystals,” Appl. Phys. Lett. 90, 101113 (2007).
[CrossRef]

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, 241101(R) (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, 17754–17760 (2007).
[CrossRef] [PubMed]

X. Checoury, S. Enoch, C. López, and A. Blanco, “Stacking patterns in self-assembly opal photonic crystals,” Appl. Phys. Lett. 90, 161131 (2007).
[CrossRef]

2006 (3)

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]

A. Balestreri, L. C. Andreani, and M. Agio, “Optical properties and diffraction effects in opal photonic crystals,” Phys. Rev. E 74, 036603 (2006).
[CrossRef]

C. López, “Three-dimensional photonic bandgap materials: semiconductors for light,” J. Opt. A, Pure Appl. Opt. 8, R1–R14 (2006).
[CrossRef]

2005 (2)

F. García-Santamaría, J. F. Galisteo-López, P. V. Braun, and C. López, “Optical diffraction and high-energy features in three-dimensional photonic crystals,” Phys. Rev. B 71, 195112 (2005).
[CrossRef]

G. von Freymann, S. John, S. Wong, V. Kitaev, and G. A. Ozin, “Measurement of group velocity dispersion for finite size three-dimensional photonic crystals in the near-infrared spectral region,” Appl. Phys. Lett. 86, 053108 (2005).
[CrossRef]

2004 (2)

H. Míguez, V. Kitaev, and G. Ozin, “Band spectroscopy of colloidal photonic crystal films,” Appl. Phys. Lett. 84, 1239–1241 (2004).
[CrossRef]

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

2003 (1)

S. Wong, V. Kitaev, and G. A. Ozin, “Colloidal crystal films: advances in universality and perfection,” J. Am. Chem. Soc. 125, 15589–15598 (2003).
[CrossRef] [PubMed]

2002 (1)

F. López-Tejeira, T. Ochiai, K. Sakoda, and J. Sánchez-Dehesa, “Symmetry characterization of eigenstates in opal-based photonic crystals,” Phys. Rev. B 65, 195110 (2002).
[CrossRef]

2001 (1)

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]

2000 (1)

N. Stefanou, V. Yannopapas, and A. Modinos, “MULTEM 2: a new version of the program for transmission and band-structure calculations of photonic crystals,” Comput. Phys. Commun. 132, 189–196 (2000).
[CrossRef]

1999 (1)

P. Jiang, J. F. Bertone, K. S. Hwang, and V. L. Colvin, “Single-crystal colloidal multilayers of controlled thickness,” Chem. Mater. 11, 2132–2140 (1999).
[CrossRef]

1998 (1)

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

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]

1977 (1)

T. Inagaki, E. T. Arakawa, R. N. Hamm, and M. W. Williams, “Optical properties of polystyrene from the near-infrared to the x-ray region and convergence of optical sum rules,” Phys. Rev. B 15, 3243–3253 (1977).
[CrossRef]

Agio, M.

A. Balestreri, L. C. Andreani, and M. Agio, “Optical properties and diffraction effects in opal photonic crystals,” Phys. Rev. E 74, 036603 (2006).
[CrossRef]

Andreani, L. C.

L. C. Andreani, A. Balestreri, J. F. Galisteo-López, M. Galli, M. Patrini, E. Descrovi, A. Chiodoni, F. Giorgis, L. Pallavidino, and F. Geobaldo, “Optical response with threefold symmetry axis on oriented microdomains of opal photonic crystals,” Phys. Rev. B 78, 205304 (2008).
[CrossRef]

J. F. Galisteo-López, M. Galli, L. C. Andreani, A. Mihi, R. Pozas, M. Ocaña, and H. Míguez, “Phase delay and group velocity determination at a planar defect state in three dimensional photonic crystals,” Appl. Phys. Lett. 90, 101113 (2007).
[CrossRef]

A. Balestreri, L. C. Andreani, and M. Agio, “Optical properties and diffraction effects in opal photonic crystals,” Phys. Rev. E 74, 036603 (2006).
[CrossRef]

Arakawa, E. T.

T. Inagaki, E. T. Arakawa, R. N. Hamm, and M. W. Williams, “Optical properties of polystyrene from the near-infrared to the x-ray region and convergence of optical sum rules,” Phys. Rev. B 15, 3243–3253 (1977).
[CrossRef]

Balestreri, A.

L. C. Andreani, A. Balestreri, J. F. Galisteo-López, M. Galli, M. Patrini, E. Descrovi, A. Chiodoni, F. Giorgis, L. Pallavidino, and F. Geobaldo, “Optical response with threefold symmetry axis on oriented microdomains of opal photonic crystals,” Phys. Rev. B 78, 205304 (2008).
[CrossRef]

A. Balestreri, L. C. Andreani, and M. Agio, “Optical properties and diffraction effects in opal photonic crystals,” Phys. Rev. E 74, 036603 (2006).
[CrossRef]

Bardosova, M.

S. G. Romanov, M. Bardosova, I. M. Povey, M. E. Pemble, and C. M. Sotomayor Torres, “Understanding of transmission in the range of high-order photonic bands in thin opal film,” Appl. Phys. Lett. 92, 191106 (2008).
[CrossRef]

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]

Bertone, J. F.

P. Jiang, J. F. Bertone, K. S. Hwang, and V. L. Colvin, “Single-crystal colloidal multilayers of controlled thickness,” Chem. Mater. 11, 2132–2140 (1999).
[CrossRef]

Blanco, A.

X. Checoury, S. Enoch, C. López, and A. Blanco, “Stacking patterns in self-assembly opal photonic crystals,” Appl. Phys. Lett. 90, 161131 (2007).
[CrossRef]

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. V.

F. García-Santamaría, J. F. Galisteo-López, P. V. Braun, and C. López, “Optical diffraction and high-energy features in three-dimensional photonic crystals,” Phys. Rev. B 71, 195112 (2005).
[CrossRef]

Casalboni, M.

Checoury, X.

X. Checoury, S. Enoch, C. López, and A. Blanco, “Stacking patterns in self-assembly opal photonic crystals,” Appl. Phys. Lett. 90, 161131 (2007).
[CrossRef]

Chiodoni, A.

L. C. Andreani, A. Balestreri, J. F. Galisteo-López, M. Galli, M. Patrini, E. Descrovi, A. Chiodoni, F. Giorgis, L. Pallavidino, and F. Geobaldo, “Optical response with threefold symmetry axis on oriented microdomains of opal photonic crystals,” Phys. Rev. B 78, 205304 (2008).
[CrossRef]

Colvin, V. L.

P. Jiang, J. F. Bertone, K. S. Hwang, and V. L. Colvin, “Single-crystal colloidal multilayers of controlled thickness,” Chem. Mater. 11, 2132–2140 (1999).
[CrossRef]

Depine, R. A.

G. Lozano, L. A. Dorado, R. A. Depine, and H. Míguez, “Towards a full understanding of the growth dynamics and optical response of self-assembled photonic colloidal crystal films,” J. Mater. Chem. 19, 185–190 (2009).
[CrossRef]

G. Lozano, L. A. Dorado, D. Schinca, R. A. Depine, and H. Míguez, “Optical analysis of the fine crystalline structure of artificial opal films,” Langmuir 25, 12860–12864 (2009).
[CrossRef] [PubMed]

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]

L. A. Dorado, R. A. Depine, and H. Míguez, “Comment on “Observation of higher-order diffraction features in self-assembled photonic crystals”,” Phys. Rev. A 78, 037801 (2008).
[CrossRef]

L. A. Dorado, R. A. Depine, D. Schinca, G. Lozano, and H. Míguez, “Experimental and theoretical analysis of the intensity of beams diffracted by three-dimensional photonic crystals,” Phys. Rev. B 78, 075102 (2008).
[CrossRef]

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, 241101(R) (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, 17754–17760 (2007).
[CrossRef] [PubMed]

Descrovi, E.

L. C. Andreani, A. Balestreri, J. F. Galisteo-López, M. Galli, M. Patrini, E. Descrovi, A. Chiodoni, F. Giorgis, L. Pallavidino, and F. Geobaldo, “Optical response with threefold symmetry axis on oriented microdomains of opal photonic crystals,” Phys. Rev. B 78, 205304 (2008).
[CrossRef]

Dorado, L. A.

G. Lozano, L. A. Dorado, D. Schinca, R. A. Depine, and H. Míguez, “Optical analysis of the fine crystalline structure of artificial opal films,” Langmuir 25, 12860–12864 (2009).
[CrossRef] [PubMed]

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]

G. Lozano, L. A. Dorado, R. A. Depine, and H. Míguez, “Towards a full understanding of the growth dynamics and optical response of self-assembled photonic colloidal crystal films,” J. Mater. Chem. 19, 185–190 (2009).
[CrossRef]

L. A. Dorado, R. A. Depine, D. Schinca, G. Lozano, and H. Míguez, “Experimental and theoretical analysis of the intensity of beams diffracted by three-dimensional photonic crystals,” Phys. Rev. B 78, 075102 (2008).
[CrossRef]

L. A. Dorado, R. A. Depine, and H. Míguez, “Comment on “Observation of higher-order diffraction features in self-assembled photonic crystals”,” Phys. Rev. A 78, 037801 (2008).
[CrossRef]

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, 241101(R) (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, 17754–17760 (2007).
[CrossRef] [PubMed]

Enoch, S.

X. Checoury, S. Enoch, C. López, and A. Blanco, “Stacking patterns in self-assembly opal photonic crystals,” Appl. Phys. Lett. 90, 161131 (2007).
[CrossRef]

Galisteo-López, J. F.

L. C. Andreani, A. Balestreri, J. F. Galisteo-López, M. Galli, M. Patrini, E. Descrovi, A. Chiodoni, F. Giorgis, L. Pallavidino, and F. Geobaldo, “Optical response with threefold symmetry axis on oriented microdomains of opal photonic crystals,” Phys. Rev. B 78, 205304 (2008).
[CrossRef]

J. F. Galisteo-López, M. Galli, L. C. Andreani, A. Mihi, R. Pozas, M. Ocaña, and H. Míguez, “Phase delay and group velocity determination at a planar defect state in three dimensional photonic crystals,” Appl. Phys. Lett. 90, 101113 (2007).
[CrossRef]

F. García-Santamaría, J. F. Galisteo-López, P. V. Braun, and C. López, “Optical diffraction and high-energy features in three-dimensional photonic crystals,” Phys. Rev. B 71, 195112 (2005).
[CrossRef]

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

Galli, M.

L. C. Andreani, A. Balestreri, J. F. Galisteo-López, M. Galli, M. Patrini, E. Descrovi, A. Chiodoni, F. Giorgis, L. Pallavidino, and F. Geobaldo, “Optical response with threefold symmetry axis on oriented microdomains of opal photonic crystals,” Phys. Rev. B 78, 205304 (2008).
[CrossRef]

J. F. Galisteo-López, M. Galli, L. C. Andreani, A. Mihi, R. Pozas, M. Ocaña, and H. Míguez, “Phase delay and group velocity determination at a planar defect state in three dimensional photonic crystals,” Appl. Phys. Lett. 90, 101113 (2007).
[CrossRef]

García-Santamaría, F.

F. García-Santamaría, J. F. Galisteo-López, P. V. Braun, and C. López, “Optical diffraction and high-energy features in three-dimensional photonic crystals,” Phys. Rev. B 71, 195112 (2005).
[CrossRef]

Geobaldo, F.

L. C. Andreani, A. Balestreri, J. F. Galisteo-López, M. Galli, M. Patrini, E. Descrovi, A. Chiodoni, F. Giorgis, L. Pallavidino, and F. Geobaldo, “Optical response with threefold symmetry axis on oriented microdomains of opal photonic crystals,” Phys. Rev. B 78, 205304 (2008).
[CrossRef]

Giorgis, F.

L. C. Andreani, A. Balestreri, J. F. Galisteo-López, M. Galli, M. Patrini, E. Descrovi, A. Chiodoni, F. Giorgis, L. Pallavidino, and F. Geobaldo, “Optical response with threefold symmetry axis on oriented microdomains of opal photonic crystals,” Phys. Rev. B 78, 205304 (2008).
[CrossRef]

Hamm, R. N.

T. Inagaki, E. T. Arakawa, R. N. Hamm, and M. W. Williams, “Optical properties of polystyrene from the near-infrared to the x-ray region and convergence of optical sum rules,” Phys. Rev. B 15, 3243–3253 (1977).
[CrossRef]

Hwang, K. S.

P. Jiang, J. F. Bertone, K. S. Hwang, and V. L. Colvin, “Single-crystal colloidal multilayers of controlled thickness,” Chem. Mater. 11, 2132–2140 (1999).
[CrossRef]

Inagaki, T.

T. Inagaki, E. T. Arakawa, R. N. Hamm, and M. W. Williams, “Optical properties of polystyrene from the near-infrared to the x-ray region and convergence of optical sum rules,” Phys. Rev. B 15, 3243–3253 (1977).
[CrossRef]

Jiang, P.

P. Jiang, J. F. Bertone, K. S. Hwang, and V. L. Colvin, “Single-crystal colloidal multilayers of controlled thickness,” Chem. Mater. 11, 2132–2140 (1999).
[CrossRef]

John, S.

G. von Freymann, S. John, S. Wong, V. Kitaev, and G. A. Ozin, “Measurement of group velocity dispersion for finite size three-dimensional photonic crystals in the near-infrared spectral region,” Appl. Phys. Lett. 86, 053108 (2005).
[CrossRef]

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

Kitaev, V.

G. von Freymann, S. John, S. Wong, V. Kitaev, and G. A. Ozin, “Measurement of group velocity dispersion for finite size three-dimensional photonic crystals in the near-infrared spectral region,” Appl. Phys. Lett. 86, 053108 (2005).
[CrossRef]

H. Míguez, V. Kitaev, and G. Ozin, “Band spectroscopy of colloidal photonic crystal films,” Appl. Phys. Lett. 84, 1239–1241 (2004).
[CrossRef]

S. Wong, V. Kitaev, and G. A. Ozin, “Colloidal crystal films: advances in universality and perfection,” J. Am. Chem. Soc. 125, 15589–15598 (2003).
[CrossRef] [PubMed]

Kosobukin, V. A.

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]

Limonov, M. F.

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]

López, C.

X. Checoury, S. Enoch, C. López, and A. Blanco, “Stacking patterns in self-assembly opal photonic crystals,” Appl. Phys. Lett. 90, 161131 (2007).
[CrossRef]

C. López, “Three-dimensional photonic bandgap materials: semiconductors for light,” J. Opt. A, Pure Appl. Opt. 8, R1–R14 (2006).
[CrossRef]

F. García-Santamaría, J. F. Galisteo-López, P. V. Braun, and C. López, “Optical diffraction and high-energy features in three-dimensional photonic crystals,” Phys. Rev. B 71, 195112 (2005).
[CrossRef]

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

López-Tejeira, F.

F. López-Tejeira, T. Ochiai, K. Sakoda, and J. Sánchez-Dehesa, “Symmetry characterization of eigenstates in opal-based photonic crystals,” Phys. Rev. B 65, 195110 (2002).
[CrossRef]

Lozano, G.

G. Lozano, L. A. Dorado, D. Schinca, R. A. Depine, and H. Míguez, “Optical analysis of the fine crystalline structure of artificial opal films,” Langmuir 25, 12860–12864 (2009).
[CrossRef] [PubMed]

G. Lozano, L. A. Dorado, R. A. Depine, and H. Míguez, “Towards a full understanding of the growth dynamics and optical response of self-assembled photonic colloidal crystal films,” J. Mater. Chem. 19, 185–190 (2009).
[CrossRef]

L. A. Dorado, R. A. Depine, D. Schinca, G. Lozano, and H. Míguez, “Experimental and theoretical analysis of the intensity of beams diffracted by three-dimensional photonic crystals,” Phys. Rev. B 78, 075102 (2008).
[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, 17754–17760 (2007).
[CrossRef] [PubMed]

Míguez, H.

G. Lozano, L. A. Dorado, D. Schinca, R. A. Depine, and H. Míguez, “Optical analysis of the fine crystalline structure of artificial opal films,” Langmuir 25, 12860–12864 (2009).
[CrossRef] [PubMed]

G. Lozano, L. A. Dorado, R. A. Depine, and H. Míguez, “Towards a full understanding of the growth dynamics and optical response of self-assembled photonic colloidal crystal films,” J. Mater. Chem. 19, 185–190 (2009).
[CrossRef]

L. A. Dorado, R. A. Depine, and H. Míguez, “Comment on “Observation of higher-order diffraction features in self-assembled photonic crystals”,” Phys. Rev. A 78, 037801 (2008).
[CrossRef]

L. A. Dorado, R. A. Depine, D. Schinca, G. Lozano, and H. Míguez, “Experimental and theoretical analysis of the intensity of beams diffracted by three-dimensional photonic crystals,” Phys. Rev. B 78, 075102 (2008).
[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, 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, 241101(R) (2007).
[CrossRef]

J. F. Galisteo-López, M. Galli, L. C. Andreani, A. Mihi, R. Pozas, M. Ocaña, and H. Míguez, “Phase delay and group velocity determination at a planar defect state in three dimensional photonic crystals,” Appl. Phys. Lett. 90, 101113 (2007).
[CrossRef]

H. Míguez, V. Kitaev, and G. Ozin, “Band spectroscopy of colloidal photonic crystal films,” Appl. Phys. Lett. 84, 1239–1241 (2004).
[CrossRef]

Mihi, A.

J. F. Galisteo-López, M. Galli, L. C. Andreani, A. Mihi, R. Pozas, M. Ocaña, and H. Míguez, “Phase delay and group velocity determination at a planar defect state in three dimensional photonic crystals,” Appl. Phys. Lett. 90, 101113 (2007).
[CrossRef]

Modinos, A.

N. Stefanou, V. Yannopapas, and A. Modinos, “MULTEM 2: a new version of the program for transmission and band-structure calculations of photonic crystals,” Comput. Phys. Commun. 132, 189–196 (2000).
[CrossRef]

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

Nair, R. V.

R. V. Nair and R. Vijaya, “Reply to “Comment on ‘Observation of higher-order diffraction features in self-assembled photonic crystals’”,” Phys. Rev. A 78, 037802 (2008).
[CrossRef]

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]

Ocaña, M.

J. F. Galisteo-López, M. Galli, L. C. Andreani, A. Mihi, R. Pozas, M. Ocaña, and H. Míguez, “Phase delay and group velocity determination at a planar defect state in three dimensional photonic crystals,” Appl. Phys. Lett. 90, 101113 (2007).
[CrossRef]

Ochiai, T.

F. López-Tejeira, T. Ochiai, K. Sakoda, and J. Sánchez-Dehesa, “Symmetry characterization of eigenstates in opal-based photonic crystals,” Phys. Rev. B 65, 195110 (2002).
[CrossRef]

Ozin, G.

H. Míguez, V. Kitaev, and G. Ozin, “Band spectroscopy of colloidal photonic crystal films,” Appl. Phys. Lett. 84, 1239–1241 (2004).
[CrossRef]

Ozin, G. A.

G. von Freymann, S. John, S. Wong, V. Kitaev, and G. A. Ozin, “Measurement of group velocity dispersion for finite size three-dimensional photonic crystals in the near-infrared spectral region,” Appl. Phys. Lett. 86, 053108 (2005).
[CrossRef]

S. Wong, V. Kitaev, and G. A. Ozin, “Colloidal crystal films: advances in universality and perfection,” J. Am. Chem. Soc. 125, 15589–15598 (2003).
[CrossRef] [PubMed]

Pallavidino, L.

L. C. Andreani, A. Balestreri, J. F. Galisteo-López, M. Galli, M. Patrini, E. Descrovi, A. Chiodoni, F. Giorgis, L. Pallavidino, and F. Geobaldo, “Optical response with threefold symmetry axis on oriented microdomains of opal photonic crystals,” Phys. Rev. B 78, 205304 (2008).
[CrossRef]

Patrini, M.

L. C. Andreani, A. Balestreri, J. F. Galisteo-López, M. Galli, M. Patrini, E. Descrovi, A. Chiodoni, F. Giorgis, L. Pallavidino, and F. Geobaldo, “Optical response with threefold symmetry axis on oriented microdomains of opal photonic crystals,” Phys. Rev. B 78, 205304 (2008).
[CrossRef]

Pemble, M. E.

S. G. Romanov, M. Bardosova, I. M. Povey, M. E. Pemble, and C. M. Sotomayor Torres, “Understanding of transmission in the range of high-order photonic bands in thin opal film,” Appl. Phys. Lett. 92, 191106 (2008).
[CrossRef]

Povey, I. M.

S. G. Romanov, M. Bardosova, I. M. Povey, M. E. Pemble, and C. M. Sotomayor Torres, “Understanding of transmission in the range of high-order photonic bands in thin opal film,” Appl. Phys. Lett. 92, 191106 (2008).
[CrossRef]

Pozas, R.

J. F. Galisteo-López, M. Galli, L. C. Andreani, A. Mihi, R. Pozas, M. Ocaña, and H. Míguez, “Phase delay and group velocity determination at a planar defect state in three dimensional photonic crystals,” Appl. Phys. Lett. 90, 101113 (2007).
[CrossRef]

Prosposito, P.

Romanov, S. G.

S. G. Romanov, M. Bardosova, I. M. Povey, M. E. Pemble, and C. M. Sotomayor Torres, “Understanding of transmission in the range of high-order photonic bands in thin opal film,” Appl. Phys. Lett. 92, 191106 (2008).
[CrossRef]

Russo, M. V.

Sakoda, K.

F. López-Tejeira, T. Ochiai, K. Sakoda, and J. Sánchez-Dehesa, “Symmetry characterization of eigenstates in opal-based photonic crystals,” Phys. Rev. B 65, 195110 (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]

Sánchez-Dehesa, J.

F. López-Tejeira, T. Ochiai, K. Sakoda, and J. Sánchez-Dehesa, “Symmetry characterization of eigenstates in opal-based photonic crystals,” Phys. Rev. B 65, 195110 (2002).
[CrossRef]

Schinca, D.

G. Lozano, L. A. Dorado, D. Schinca, R. A. Depine, and H. Míguez, “Optical analysis of the fine crystalline structure of artificial opal films,” Langmuir 25, 12860–12864 (2009).
[CrossRef] [PubMed]

L. A. Dorado, R. A. Depine, D. Schinca, G. Lozano, and H. Míguez, “Experimental and theoretical analysis of the intensity of beams diffracted by three-dimensional photonic crystals,” Phys. Rev. B 78, 075102 (2008).
[CrossRef]

Schutzmann, S.

Sotomayor Torres, C. M.

S. G. Romanov, M. Bardosova, I. M. Povey, M. E. Pemble, and C. M. Sotomayor Torres, “Understanding of transmission in the range of high-order photonic bands in thin opal film,” Appl. Phys. Lett. 92, 191106 (2008).
[CrossRef]

Stefanou, N.

N. Stefanou, V. Yannopapas, and A. Modinos, “MULTEM 2: a new version of the program for transmission and band-structure calculations of photonic crystals,” Comput. Phys. Commun. 132, 189–196 (2000).
[CrossRef]

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

Usvyat, D. E.

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]

Venditti, I.

Vijaya, R.

R. V. Nair and R. Vijaya, “Reply to “Comment on ‘Observation of higher-order diffraction features in self-assembled photonic crystals’”,” Phys. Rev. A 78, 037802 (2008).
[CrossRef]

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]

von Freymann, G.

G. von Freymann, S. John, S. Wong, V. Kitaev, and G. A. Ozin, “Measurement of group velocity dispersion for finite size three-dimensional photonic crystals in the near-infrared spectral region,” Appl. Phys. Lett. 86, 053108 (2005).
[CrossRef]

Williams, M. W.

T. Inagaki, E. T. Arakawa, R. N. Hamm, and M. W. Williams, “Optical properties of polystyrene from the near-infrared to the x-ray region and convergence of optical sum rules,” Phys. Rev. B 15, 3243–3253 (1977).
[CrossRef]

Wong, S.

G. von Freymann, S. John, S. Wong, V. Kitaev, and G. A. Ozin, “Measurement of group velocity dispersion for finite size three-dimensional photonic crystals in the near-infrared spectral region,” Appl. Phys. Lett. 86, 053108 (2005).
[CrossRef]

S. Wong, V. Kitaev, and G. A. Ozin, “Colloidal crystal films: advances in universality and perfection,” J. Am. Chem. Soc. 125, 15589–15598 (2003).
[CrossRef] [PubMed]

Yablonovitch, E.

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

Yannopapas, V.

N. Stefanou, V. Yannopapas, and A. Modinos, “MULTEM 2: a new version of the program for transmission and band-structure calculations of photonic crystals,” Comput. Phys. Commun. 132, 189–196 (2000).
[CrossRef]

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

Appl. Phys. Lett. (5)

G. von Freymann, S. John, S. Wong, V. Kitaev, and G. A. Ozin, “Measurement of group velocity dispersion for finite size three-dimensional photonic crystals in the near-infrared spectral region,” Appl. Phys. Lett. 86, 053108 (2005).
[CrossRef]

H. Míguez, V. Kitaev, and G. Ozin, “Band spectroscopy of colloidal photonic crystal films,” Appl. Phys. Lett. 84, 1239–1241 (2004).
[CrossRef]

J. F. Galisteo-López, M. Galli, L. C. Andreani, A. Mihi, R. Pozas, M. Ocaña, and H. Míguez, “Phase delay and group velocity determination at a planar defect state in three dimensional photonic crystals,” Appl. Phys. Lett. 90, 101113 (2007).
[CrossRef]

S. G. Romanov, M. Bardosova, I. M. Povey, M. E. Pemble, and C. M. Sotomayor Torres, “Understanding of transmission in the range of high-order photonic bands in thin opal film,” Appl. Phys. Lett. 92, 191106 (2008).
[CrossRef]

X. Checoury, S. Enoch, C. López, and A. Blanco, “Stacking patterns in self-assembly opal photonic crystals,” Appl. Phys. Lett. 90, 161131 (2007).
[CrossRef]

Chem. Mater. (1)

P. Jiang, J. F. Bertone, K. S. Hwang, and V. L. Colvin, “Single-crystal colloidal multilayers of controlled thickness,” Chem. Mater. 11, 2132–2140 (1999).
[CrossRef]

Comput. Phys. Commun. (2)

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

N. Stefanou, V. Yannopapas, and A. Modinos, “MULTEM 2: a new version of the program for transmission and band-structure calculations of photonic crystals,” Comput. Phys. Commun. 132, 189–196 (2000).
[CrossRef]

J. Am. Chem. Soc. (1)

S. Wong, V. Kitaev, and G. A. Ozin, “Colloidal crystal films: advances in universality and perfection,” J. Am. Chem. Soc. 125, 15589–15598 (2003).
[CrossRef] [PubMed]

J. Mater. Chem. (1)

G. Lozano, L. A. Dorado, R. A. Depine, and H. Míguez, “Towards a full understanding of the growth dynamics and optical response of self-assembled photonic colloidal crystal films,” J. Mater. Chem. 19, 185–190 (2009).
[CrossRef]

J. Opt. A, Pure Appl. Opt. (1)

C. López, “Three-dimensional photonic bandgap materials: semiconductors for light,” J. Opt. A, Pure Appl. Opt. 8, R1–R14 (2006).
[CrossRef]

Langmuir (1)

G. Lozano, L. A. Dorado, D. Schinca, R. A. Depine, and H. Míguez, “Optical analysis of the fine crystalline structure of artificial opal films,” Langmuir 25, 12860–12864 (2009).
[CrossRef] [PubMed]

Nature (1)

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 (2)

Phys. Rev. A (2)

L. A. Dorado, R. A. Depine, and H. Míguez, “Comment on “Observation of higher-order diffraction features in self-assembled photonic crystals”,” Phys. Rev. A 78, 037801 (2008).
[CrossRef]

R. V. Nair and R. Vijaya, “Reply to “Comment on ‘Observation of higher-order diffraction features in self-assembled photonic crystals’”,” Phys. Rev. A 78, 037802 (2008).
[CrossRef]

Phys. Rev. B (9)

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, 241101(R) (2007).
[CrossRef]

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

F. García-Santamaría, J. F. Galisteo-López, P. V. Braun, and C. López, “Optical diffraction and high-energy features in three-dimensional photonic crystals,” Phys. Rev. B 71, 195112 (2005).
[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]

F. López-Tejeira, T. Ochiai, K. Sakoda, and J. Sánchez-Dehesa, “Symmetry characterization of eigenstates in opal-based photonic crystals,” Phys. Rev. B 65, 195110 (2002).
[CrossRef]

L. C. Andreani, A. Balestreri, J. F. Galisteo-López, M. Galli, M. Patrini, E. Descrovi, A. Chiodoni, F. Giorgis, L. Pallavidino, and F. Geobaldo, “Optical response with threefold symmetry axis on oriented microdomains of opal photonic crystals,” Phys. Rev. B 78, 205304 (2008).
[CrossRef]

L. A. Dorado, R. A. Depine, D. Schinca, G. Lozano, and H. Míguez, “Experimental and theoretical analysis of the intensity of beams diffracted by three-dimensional photonic crystals,” Phys. Rev. B 78, 075102 (2008).
[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]

T. Inagaki, E. T. Arakawa, R. N. Hamm, and M. W. Williams, “Optical properties of polystyrene from the near-infrared to the x-ray region and convergence of optical sum rules,” Phys. Rev. B 15, 3243–3253 (1977).
[CrossRef]

Phys. Rev. E (1)

A. Balestreri, L. C. Andreani, and M. Agio, “Optical properties and diffraction effects in opal photonic crystals,” Phys. Rev. E 74, 036603 (2006).
[CrossRef]

Phys. Rev. Lett. (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]

Other (1)

The imaginary part of the dielectric constant is not considered as a constant quantity during calculations. We employed a smaller value of the εi parameter in the high-energy spectral range (0.08) which represents the different effects of imperfections have on the different wavelength ranges.

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Figures (6)

Fig. 1
Fig. 1

(a) Sketch of the experimental setup. (b) Scheme of the diffracted beams emerging from the colloidal crystal. Diagrams showing the two primitive vectors used to describe the (c) real and (d) reciprocal lattices.

Fig. 2
Fig. 2

(a) Calculated total reflectance spectrum. (b) Measured (red thick line) and calculated (gray thin line) specular reflectance spectra. Vertical dashed line indicates the onset of diffraction for reflected modes.

Fig. 3
Fig. 3

(a) Diffraction patterns of reflected beams projected on a screen parallel to the x y plane, when light illuminates the slab at (a) θ i = 0 ° and (b) θ i = 5 ° . Photographs 1–4 correspond to the azimuthal angles ϕ i = 0 ° , 15°, 30°, and 60°, respectively. Each spot is labeled according to its associated reciprocal-lattice vector. In all cases the arrow points at the (1,0) mode. The wavelength of the blue laser is 473 nm.

Fig. 4
Fig. 4

(a) Measured (blue squares) and calculated (gray line) reflection efficiencies of the diffracted channel (0,0) when the photonic crystal is illuminated at θ i = 10 ° and the azimuthal angle ( ϕ i ) is varied. (b) Diffraction patterns of reflected beams. Photographs 1–4 correspond to the azimuthal angles ϕ i = 0 ° , 15°, 30°, and 60°, respectively. Each spot is labeled according to its associated reciprocal-lattice vector. The arrow is always pointing at the (1,0) mode. The wavelength of the blue laser is 473 nm. Dashed vertical lines in (a) indicate the azimuthal angles at which the photographs in (b) were taken. The connecting solid blue line in (a) is only a guide for the eye.

Fig. 5
Fig. 5

(a) Measured intensity (blue squares) and calculated reflection efficiency (gray line) of the diffracted channel (1,−1) when the photonic crystal is illuminated at θ i = 30 ° and the azimuthal angle ( ϕ i ) is varied. (b) Images of the emerged diffracted beams at ϕ i = 17 ° (1), 8° (2), and 78° (3); the (1,−1) mode is artificially colored to highlight its intensity. All the spots are labeled according to their associated reciprocal-lattice vectors. Intensity color scale is also indicated. Dashed vertical lines in (a) indicate the azimuthal angles at which the images in (b) were obtained. The connecting solid blue line in (a) is only a guide for the eye.

Fig. 6
Fig. 6

(a) Measured intensity (blue squares) and calculated reflection efficiency (gray line) of the diffracted channel (1,−1) when the photonic crystal is illuminated at θ i = 50 ° and the azimuthal angle ( ϕ i ) is varied. (b) Images of the emerged diffracted beams at ϕ i = 32 ° (1), 33° (2), and 93° (3); the (1,−1) mode is artificially colored to highlight its intensity. All the spots are labeled according to their associated reciprocal-lattice vectors. Intensity color scale is also indicated. Dashed vertical lines in (a) indicate the azimuthal angles at which the images in (b) were obtained. The connecting solid blue line in (a) is only a guide for the eye.

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