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Journal of the Optical Society of America B

Journal of the Optical Society of America B


  • Vol. 22, Iss. 5 — May. 1, 2005
  • pp: 1075–1084

Optical properties of real photonic crystals: anomalous diffuse transmission

A. Femius Koenderink and Willem L. Vos  »View Author Affiliations

JOSA B, Vol. 22, Issue 5, pp. 1075-1084 (2005)

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Unavoidable structural disorder in photonic crystals causes multiple scattering of light, resulting in extinction of coherent beams and generation of diffuse light. We demonstrate experimentally that the diffusely transmitted intensity is distributed over exit angles in a strikingly non-Lambertian manner, depending strongly on frequency. The angular redistribution of diffuse light reveals both photonic gaps and the diffuse extrapolation length, as confirmed by a quantitative diffusion theory that includes photonic band structures. Total transmission corrected for internal reflection shows that extinction increases slower with frequency than Rayleigh’s law predicts. Hence disorder affects the high-frequency photonic bandgap of fcc crystals less severely than expected previously.

© 2005 Optical Society of America

OCIS Codes
(050.1940) Diffraction and gratings : Diffraction
(160.4670) Materials : Optical materials
(260.1960) Physical optics : Diffraction theory
(260.3160) Physical optics : Interference
(290.1990) Scattering : Diffusion
(290.4210) Scattering : Multiple scattering

A. Femius Koenderink and Willem L. Vos, "Optical properties of real photonic crystals: anomalous diffuse transmission," J. Opt. Soc. Am. B 22, 1075-1084 (2005)

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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.M.Soukoulis, ed., Photonic Crystals and Light Localization in the 21st Century (Kluwer Academic, Dordrecht, The Netherlands, 2001). [CrossRef]
  4. O. J. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. O'Brien, P. D. Dapkus, and I. Kim, "Two-dimensional photonic band-gap defect mode laser," Science 284, 1819-1821 (1999). [CrossRef] [PubMed]
  5. S. J. McNab, N. Moll, and Y. A. Vlasov, "Ultra-low loss photonic integrated circuit with membrane-type photonic crystal waveguides," Opt. Express 11, 2927-2939 (2003), http://www.opticsexpress.org. [CrossRef] [PubMed]
  6. H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, "Superprism phenomena in photonic crystals," Phys. Rev. B 58, R10096-R10099 (1998). [CrossRef]
  7. A. F. Koenderink, P. M. Johnson, J. F. Galisteo Lopez, and W. L. Vos, "Three-dimensional photonic crystals as a cage for light," C. R. Phys. 3, 65-77 (2002). [CrossRef]
  8. C. Lopez, "Recent review on fabrication of photonic crystals," Adv. Mater. (Weinheim, Ger.) 15, 1679-1704 (2003).
  9. M. S. Thijssen, R. Sprik, J. E. G. J. Wijnhoven, M. Megens, T. Narayanan, A. Lagendijk, and W. L. Vos, "Inhibited light propagation and broadband reflection in photonic air-sphere crystals," Phys. Rev. Lett. 83, 2730-2733 (1999). [CrossRef]
  10. 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]
  11. Y. A. Vlasov, X. Z. Bo, J. C. Sturm, and D. J. Norris, "On-chip natural assembly of silicon photonic bandgap crystals," Nature (London) 414, 289-293 (2001). [CrossRef]
  12. A. F. Koenderink, L. Bechger, H. P. Schriemer, A. Lagendijk, and W. L. Vos, "Broadband fivefold reduction of vacuum fluctuations probed by dyes in photonic crystals," Phys. Rev. Lett. 88, 143903 (2002). [CrossRef] [PubMed]
  13. P. Lodahl, A. F. van Driel, I. S. Nikolaev, A. Irman, K. Overgaag, D. Vanmaekelbergh, and W. L. Vos, "Controlling the dynamics of spontaneous emission from quantum dots by photonic crystals," Nature (London) 430, 654-657 (2004). [CrossRef]
  14. N. W. Ashcroft and N. D. Mermin, Solid State Physics (Holt, Rinehard & Winston, New York, 1976), pp. 616-620.
  15. J. F. Bertone, P. Jiang, K. S. Hwang, D. M. Mittleman, and V. L. Colvin, "Thickness dependence of the optical properties of ordered silica-air and air-polymer photonic crystals," Phys. Rev. Lett. 83, 300-303 (1999). [CrossRef]
  16. Y. A. Vlasov, V. N. Astratov, A. V. Baryshev, A. A. Kaplyanskii, O. Z. Karimov, and M. F. Limonov, "Manifestation of intrinsic defects in optical properties of self-organized opal photonic crystal," Phys. Rev. E 61, 5784-5793 (2000). [CrossRef]
  17. V. N. Astratov, A. M. Adawi, S. Fricker, M. S. Skolnick, D. M. Whittaker, and P. N. Pusey, "Interplay of order and disorder in the optical properties of opal photonic crystal," Phys. Rev. B 66, 165215 (2002). [CrossRef]
  18. M. Megens, J. E. G. J. Wijnhoven, A. Lagendijk, and W. L. Vos, "Light sources inside photonic crystals," J. Opt. Soc. Am. B 16, 1403-1408 (1999). [CrossRef]
  19. P. A. Lee and T. V. Ramakrishnan, "Disordered electronic systems," Rev. Mod. Phys. 57, 287-337 (1985). [CrossRef]
  20. P. Sheng, Introduction to Wave Scattering, Localization, and Mesoscopic Phenomena (Academic, New York, 1995).
  21. K. Busch and C. M. Soukoulis, "Energy-density CPA: a new effective medium theory for classical waves," Physica B 296, 56-61 (2001). [CrossRef]
  22. Y. A. Vlasov, M. A. Kaliteevski, and V. V. Nikolaev, "Different regimes of light localization in a disordered photonic crystal," Phys. Rev. B 60, 1555-1562 (1999). [CrossRef]
  23. J. Huang, N. Eradat, M. E. Raikh, Z. V. Vardeny, A. A. Zakhidov, and R. H. Baughman, "Anomalous coherent backscattering of light from opal photonic crystals," Phys. Rev. Lett. 86, 4815-4818 (2001). [CrossRef] [PubMed]
  24. A. F. Koenderink, M. Megens, G. van Soest, W. L. Vos, and A. Lagendijk, "Enhanced backscattering from photonic crystals," Phys. Lett. A 268, 104-111 (2000). [CrossRef]
  25. A. F. Koenderink, A. Lagendijk, and W. L. Vos, "Optical loss due to intrinsic structural variations in photonic crystals," preprint, http://arxiv.org/abs/physics/0406052 (2004).
  26. Z. Y. Li and Z. Q. Zhang, "Fragility of photonic band gaps in inverse-opal photonic crystals," Phys. Rev. B 62, 1516-1519 (2000). [CrossRef]
  27. Z. Y. Li, X. D. Zhang, and Z. Q. Zhang, "Disordered photonic crystals understood by a perturbation formalism," Phys. Rev. B 61, 15738-15748 (2000). [CrossRef]
  28. M. M. Sigalas, C. M. Soukoulis, C. T. Chan, R. Biswas, and K. M. Ho, "Effect of disorder on photonic band gaps," Phys. Rev. B 59, 12767-12770 (1999). [CrossRef]
  29. A. F. Koenderink and W. L. Vos, "Light exiting real photonic band gap crystals is diffuse and strongly directional," Phys. Rev. Lett. 91, 213902 (2003). [CrossRef]
  30. L. Bechger, P. Lodahl, and W. L. Vos, "Directional fluorescence spectra of laser dye in opal and inverse opal photonic crystals," J. Phys. Chem. B (to be published).
  31. I. S. Nikolaev, P. Lodahl, and W. L. Vos, "Quantitative analysis of directional spontaneous emission spectra from light sources in photonic crystals," preprint, http://arxiv.org/abs/physics/0410056 (2004).
  32. J. F. Galisteo Lòpez and W. L. Vos, "Angle resolved reflectivity of single-domain photonic crystals: effects of disorder," Phys. Rev. E 66, 036616 (2002). [CrossRef]
  33. A. Ishimaru, Wave Propagation and Scattering in Random Media (Academic, New York, 1978).
  34. A. Lagendijk, R. Vreeker, and P. de Vries, "Influence of internal reflection on diffusive transport in strongly scattering media," Phys. Lett. A 136, 81-88 (1989). [CrossRef]
  35. J. X. Zhu, D. J. Pine, and D. A. Weitz, "Internal reflection of diffusive light in random media," Phys. Rev. A 44, 3948-3959 (1991). [CrossRef] [PubMed]
  36. M. U. Vera and D. J. Durian, "Angular distribution of diffusely transmitted light," Phys. Rev. E 53, 3215-3224 (1996). [CrossRef]
  37. D. J. Durian, "Influence of boundary reflection and refraction on diffusive photon transport," Phys. Rev. E 50, 857-866 (1994). [CrossRef]
  38. J. Gómez Rivas, R. Sprik, A. Lagendijk, L. D. Noordam, and C. W. Rella, "Static and dynamic transport of light close to the Anderson localization transition," Phys. Rev. E 63, 046613 (2001). [CrossRef]
  39. F. J. P. Schuurmans, D. Vanmaekelbergh, J. van de Lagemaat, and A. Lagendijk, "Strongly photonic macroporous gallium phosphide networks," Science 284, 141-143 (1999). [CrossRef] [PubMed]
  40. M. Notomi, "Theory of light propagation in strongly modulated photonic crystals: refraction like behavior in the vicinity of the photonic band gap," Phys. Rev. B 62, 10696-10705 (2000). [CrossRef]
  41. H. P. Schriemer, H. M. van Driel, A. F. Koenderink, and W. L. Vos, "Modified spontaneous emission spectra of laser dye in inverse opal photonic crystals," Phys. Rev. A 63, 011801 (2001). [CrossRef]
  42. J. E. G. J. Wijnhoven, L. Bechger, and W. L. Vos, "Fabrication and characterization of large macroporous photonic crystals in titania," Chem. Mater. 13, 4486-4499 (2001). [CrossRef]
  43. M. Megens and W. L. Vos, "Particle excursions in colloidal crystals," Phys. Rev. Lett. 86, 4855-4858 (2001). [CrossRef] [PubMed]
  44. H. M. van Driel and W. L. Vos, "Multiple Bragg wave coupling in photonic band-gap crystals," Phys. Rev. B 62, 9872-9875 (2000). [CrossRef]
  45. S. G. Romanov, T. Maka, C. M. S. Torres, M. Muller, R. Zentel, D. Cassagne, J. Manzanares-Martinez, and C. Jouanin, "Diffraction of light from thin-film polymethylmethacrylate opaline photonic crystals," Phys. Rev. E 63, 056603 (2001). [CrossRef]
  46. T. Yoshiyama and I. Sogami, "Kossel line analysis on colloidal crystals in semidilute aqueous solutions," Phys. Rev. Lett. 53, 2153-2156 (1984). [CrossRef]
  47. T. Yoshiyama and I. Sogami, "Kossel images as direct manifestations of the gap structure of the dispersion surface for colloidal crystals," Phys. Rev. Lett. 56, 1609-1612 (1986). [CrossRef] [PubMed]
  48. Ì. Ì. Tarhan and G. H. Watson, "Photonic band structure of fcc colloidal crystals," Phys. Rev. Lett. 76, 315-319 (1996). [CrossRef] [PubMed]
  49. W. L. Vos and H. M. van Driel, "Higher order Bragg diffraction by strongly photonic fcc crystals: onset of a photonic bandgap," Phys. Lett. A 272, 101-106 (2000). [CrossRef]
  50. W. L. Vos, M. Megens, C. M. van Kats, and P. Bösecke, "Transmission and diffraction by photonic colloidal crystals," J. Phys.: Condens. Matter 8, 9503-9507 (1996).
  51. J. E. G. J. Wijnhoven and W. L. Vos, "Preparation of photonic crystals made of air spheres in titania," Science 281, 802-804 (1998). [CrossRef]
  52. A. Blanco, E. Chomski, S. Grabtchak, M. Ibisate, S. John, S. W. Leonard, C. Lopez, F. Meseguer, 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 micrometers," Nature (London) 405, 437-440 (2000). [CrossRef]
  53. O. D. Velev and E. W. Kaler, "Structured porous materials via colloidal crystal templating: from inorganic oxides to metals," Adv. Mater. (Weinheim, Ger.) 12, 531-534 (2000). [CrossRef]
  54. T. Baba and N. Fukaya, "Light propagation characteristics of defect waveguides in a photonic crystal slab," in Ref. , pp. 105-116 (2000). In pioneering work to quantify propagation losses in state-of-the-art silicon-on-insulator 2D photonic crystals, the authors quote an airhole nonuniformity of <4%.
  55. M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohama, "Extremely large group-velocity dispersion of line defect waveguides in photonic crystal slabs," Phys. Rev. Lett. 87, 253902 (2001). The authors report a resolution of <5% in diameter and <1% in distance between airholes in Si photonic crystal slabs. [CrossRef]
  56. S. Ogawa, K. Tomoda, and S. Noda, "Effects of structural fluctuations on three-dimensional photonic crystals operating at near infrared wavelengths," J. Appl. Phys. 91, 513-515 (2002). The authors report alignment errors less than 7% relative to the wood pile periodicity for optimal strongly photonic GaAs layer-by-layer crystals operating at a 1.2-µm wavelength. [CrossRef]
  57. R. F. Service, "Building better photonic crystals," Science 295, 2399 (2002). [CrossRef] [PubMed]
  58. K. Busch and S. John, "Photonic band gap formation in certain self-organizing systems," Phys. Rev. E 58, 3896-3908 (1998). [CrossRef]

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