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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 18, Iss. 15 — Jul. 19, 2010
  • pp: 15682–15690

Anomalous group velocity at the high energy range of a 3D photonic nanostructure

Muriel Botey, Jordi Martorell, Luis A. Dorado, Ricardo A. Depine, Gabriel Lozano, and Hernán Míguez  »View Author Affiliations

Optics Express, Vol. 18, Issue 15, pp. 15682-15690 (2010)

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We report on a study of electromagnetic waves propagation in thin periodically ordered photonic nanostructures in the spectral range where the light wavelength is on the order of the lattice parameter. The vector KKR method we use allows us to determine the group index from finite photonic structures including extinction providing confirmation of recently emerged results. We show that for certain frequencies the group velocity of opal slabs can either be superluminal or approach zero depending on the crystal thickness and the unavoidable presence of losses. In some cases, group velocity can be negative. Such behavior can be clearly attributed to the finite character of the three-dimensional structure and reproduces previously reported experimental observations. Calculations show that contrary to the predictions of extraordinary group velocity reductions for infinite periodic structures, the group velocity of real opals may exhibit strong fluctuations at the high energy range. Hence, a direct identification between the calculated anomalous group velocities, for an actual opal film, and the predicted propagating low dispersion modes for an ideal infinite ordered structure seems difficult to establish.

© 2010 OSA

OCIS Codes
(160.4236) Materials : Nanomaterials
(160.5293) Materials : Photonic bandgap materials
(050.5298) Diffraction and gratings : Photonic crystals

ToC Category:
Photonic Crystals

Original Manuscript: February 19, 2010
Revised Manuscript: April 5, 2010
Manuscript Accepted: April 6, 2010
Published: July 9, 2010

Muriel Botey, Jordi Martorell, Luis A. Dorado, Ricardo A. Depine, Gabriel Lozano, and Hernán Míguez, "Anomalous group velocity at the high energy range of a 3D photonic nanostructure," Opt. Express 18, 15682-15690 (2010)

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  1. K. Sakoda, “Optical properties of photonic crystals,” Springer-Verlag, Berlin (2005).
  2. 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]
  3. 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]
  4. 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]
  5. M. Botey, M. Maymó, A. Molinos-Gómez, L. A. Dorado, R. A. Depine, G. Lozano, A. Mihi, H. Míguez, and J. Martorell, “Second Harmonic Generation at the High Energy Range in a Nonlinear Opal Film,” Opt. Express 17, 12210 (2009), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-15-12210 . [CrossRef] [PubMed]
  6. J. F. Galisteo-López, M. Galli, A. Balestreri, L. C. Andreani, and C. López, “Optical response of artificial opals oriented along the ΓX direction,” Appl. Phys. Lett. 90(23), 231112 (2007). [CrossRef]
  7. 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), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-15-23-15342 . [CrossRef] [PubMed]
  8. L. A. Dorado, R. A. Depine, G. Lozano, and H. Míguez, “Interplay between crystal-size and disorder in the high-energy optical response of photonic crystals slabs,” Phys. Rev. B 76(24), 245103 (2007). [CrossRef]
  9. R. J. P. Engelen, D. Mori, T. Baba, and L. Kuipers, “Two regimes of slow-light losses revealed by adiabatic reduction of group velocity,” Phys. Rev. Lett. 101(10), 103901 (2008). [CrossRef] [PubMed]
  10. M. Botey, L. A. Dorado, R. A. Depine, G. Lozano, H. Miguez, and J. Martorell, “Anomalous group velocity in a 3D photonic nanostructure,” in Conference on Lasers and Electro-Optics Europe/European Quantum Electronics Conference, Technical Digest (CD), (Optical Society of America, 2009), paper CK3.2Tue.
  11. J. G. Pedersen, S. Xiao, and N. A. Mortensen, “Limits of slow light in photonic crystals,” Phys. Rev. B 78(15), 153101 (2008). [CrossRef]
  12. N. Stefanou, V. Karathanos, and A. Modinos, “Scattering of electromagnetic waves by periodic structures,” J. Phys. Condens. Matter 4(36), 7389–7400 (1992). [CrossRef]
  13. 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]
  14. K. Ohtaka, “Scattering theory of low-energy photon diffraction,” J. Phys. C: Solid State 13(4), 667–680 (1980). [CrossRef]
  15. A. Modinos, “Scattering of electromagnetic waves by a plane of spheres-formalism,” Physica A 141(2-3), 575–588 (1987). [CrossRef]
  16. 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), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-15-26-17754 . [CrossRef] [PubMed]
  17. F. García-Santamaría and P. V. Braun, “Are artificial opals non-close-packed fcc structures?” Appl. Phys. Lett. 90(24), 241905 (2007). [CrossRef]
  18. 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(7), 075102 (2008). [CrossRef]
  19. G. S. 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(2), 185–190 (2008). [CrossRef]
  20. M. Botey, M. Maymó, and J. Martorell, “Band-structure determination for finite 3-D photonic crystals,” Appl. Phys. B 81(2-3), 277–281 (2005). [CrossRef]
  21. X. Ma, J. Q. Lu, R. S. Brock, K. M. Jacobs, P. Yang, and X.-H. Hu, “Determination of complex refractive index of polystyrene microspheres from 370 to 1610 nm,” Phys. Med. Biol. 48(24), 4165–4172 (2003). [CrossRef]
  22. 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(22), 12860–12864 (2009). [CrossRef] [PubMed]
  23. L. A. Dorado and R. A. Depine, “Modeling of disorder effects and optical extinction in three-dimensional photonic crystals,” Phys. Rev. B 79(4), 045124 (2009). [CrossRef]

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