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Journal of the Optical Society of America B

Journal of the Optical Society of America B

| OPTICAL PHYSICS

  • Vol. 21, Iss. 10 — Oct. 1, 2004
  • pp: 1866–1875

Statistical theory of multiple scattering of waves applied to three-dimensional layered photonic crystals

Alina Ponyavina, Svetlana Kachan, and Nikolaj Sil'vanovich  »View Author Affiliations


JOSA B, Vol. 21, Issue 10, pp. 1866-1875 (2004)
http://dx.doi.org/10.1364/JOSAB.21.001866


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Abstract

On the basis of the statistical theory of multiple scattering of waves, we offer a numerical approach to calculate coherent transmission and reflection for the three-dimensional (3-D) photonic crystals that consist of partially disordered dielectric spheres. With the proposed scheme, which we call the transfer-matrix (TM) method with quasi-crystalline approximation (QCA), we consider a quasi-regular 3-D assembly of particles as a stack of close-packed monolayers with a short-range ordering. Single-scattering characteristics are determined by Mie theory. Lateral electrodynamic coupling between the particles of a monolayer is treated in the QCA. Multibeam interference between monolayers is described in a manner analogous to the TM technique. We apply the TM-QCA calculation technique to study two revealed effects: (1) short-wavelength attenuation due to particles of finite sizes and (2) nonmonotonic dependence of the pseudogap depth on the particle size, refractive-index contrast, and intermonolayer distances.

© 2004 Optical Society of America

OCIS Codes
(030.1670) Coherence and statistical optics : Coherent optical effects
(160.4760) Materials : Optical properties
(290.4210) Scattering : Multiple scattering
(290.5850) Scattering : Scattering, particles

Citation
Alina Ponyavina, Svetlana Kachan, and Nikolaj Sil'vanovich, "Statistical theory of multiple scattering of waves applied to three-dimensional layered photonic crystals," J. Opt. Soc. Am. B 21, 1866-1875 (2004)
http://www.opticsinfobase.org/josab/abstract.cfm?URI=josab-21-10-1866


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References

  1. C. M. Soukoulis, ed., Photonic Crystals and Light Localization in the 21st Century (Kluwer, Dordrecht, The Netherlands, 2001).
  2. T. Krauss and T. Baba, eds, “Feature section on photonic crystal structures and applications,” IEEE J. Quantum Electron. 38, 724–963 (2002).
  3. E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett. 58, 2059–2062 (1987).
  4. S. John, “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett. 58, 2486–2489 (1987).
  5. K. Ohtaka, “Energy-band of photons and low-energy photon diffraction,” Phys. Rev. B 19, 5057–5067 (1979).
  6. V. G. Vereshchagin and V. V. Morozov, “New type of cutting filters for the long-wave infrared spectrum region,” Zh. Prikl. Spektrosk. 49, 317–320 (1988) (in Russian).
  7. J. Martorell and N. M. Lawandy, “Observation of inhibited spontaneous emission in a periodic dielectric structure,” Phys. Rev. Lett. 65, 1877–1880 (1990).
  8. J. Martorell and N. M. Lawandy, “Distributed feedback oscillation in ordered colloidal suspensions of polystyrene microspheres,” Opt. Commun. 78, 169–173 (1990).
  9. H. S. Sozuer, J. W. Haus, and R. Inguva, “Photonic bands: convergence problems with the plane-wave method,” Phys. Rev. B 45, 13962–13972 (1992).
  10. A. Taflove, “Review of the formulation and applications of the finite-difference time-domain method for numerical modeling of electromagnetic-wave interactions with arbitrary structures,” Wave Motion 10, 547–582 (1988).
  11. P. M. Bell, J. B. Pendry, L. M. Moreno, and A. J. Ward, “A program for calculating photonic band structures and transmission coefficients of complex structures,” Comput. Phys. Commun. 85, 306–322 (1995).
  12. L.-M. Li and Z.-Q. Zhang, “Multiple-scattering approach to finite-sized photonic band-gap materials,” Phys. Rev. B 58, 9587–9590 (1998).
  13. G. Tayeb and D. Mayste, “Rigorous theoretical study of finite-size two-dimensional photonic crystals doped by microcavities,” J. Opt. Soc. Am. A 14, 3323–3332 (1997).
  14. X. D. Wang, X. G. Zhang, Q. L. Yu, and B. N. Harmon, “Multiple-scattering theory for electromagnetic-waves,” Phys. Rev. B 47, 4161–4167 (1993).
  15. N. Stefanou, V. Yannopapas, and A. Modinos, “Heterostructures of photonic crystals: frequency bands and transmis- sion coefficients,” Comput. Phys. Commun. 113, 49–77 (1998).
  16. A. Ishimaru, Wave Propagation and Scattering in Random Media (Academic, New York, 1978).
  17. V. N. Bogomolov, S. V. Gaponenko, I. N. Germanenko, A. M. Kapitonov, E. P. Petrov, N. V. Gaponenko, A. V. Prokofiev, A. N. Ponyavina, N. I. Silvanovich, and S. M. Samoilovich, “Photonic band gap phenomenon and optical properties of artificial opals,” Phys. Rev. E 55, 7619–7625 (1997).
  18. A. N. Ponyavina and N. I. Sil’vanovich, “Interference effects and spectral characteristics of multilayer scattering systems,” Opt. Spectrosc. 76, 581–589 (1994).
  19. M. Lax, “Multiple scattering of waves. 2. The effective field in dense systems,” Phys. Rev. 85, 621–629 (1952).
  20. K. M. Hong, “Multiple scattering of electromagnetic waves by a crowded monolayer of spheres: application to migration imaging films,” J. Opt. Soc. Am. 70, 821–826 (1980).
  21. J. Ziman, Models of Disorder (Cambridge U. Press, Cambridge, UK, 1979).
  22. S. G. Romanov, N. P. Johnson, A. V. Fokin, V. Y. Butko, H. M. Yates, M. E. Pemble, and C. M. S. Torres, “Enhancement of the photonic gap of opal-based three-dimensional gratings,” Appl. Phys. Lett. 70, 2091–2093 (1997).
  23. H. Miguez, C. Lopez, F. Meseguer, A. Blanco, L. Vazquez, R. Mayoral, M. Ocana, V. Fornes, and A. Mifsud, “Photonic crystal properties of packed submicrometric SiO2 spheres,” Appl. Phys. Lett. 71, 1148–1150 (1997).
  24. J. F. Galisteo-Lopez, E. Palacios-Lidon, E. Castillo-Martinez, and C. Lopez, “Optical study of the pseudogap in thickness and orientation controlled artificial opals,” Phys. Rev. B 68, 115109 (2003).
  25. S. G. Romanov, A. V. Fokin, and R. M. De La Rue, “Stop-band structure in complementary three-dimensional opal-based photonic crystals,” J. Phys.: Condens. Matter 11, 3593–3600 (1999).
  26. W. L. Vos, M. Megens, C. M. van Kats, and P. Bosecke, “Transmission and diffraction by photonic colloidal crystals,” J. Phys.: Condens. Matter 8, 9503–9507 (1996).
  27. C. Bohren and D. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).
  28. K. Ohtaka and M. Inoue, “Light-scattering from macroscopic spherical bodies. 2. Reflectivity of light and electromagnetic localized state in a periodic monolayer of dielectric spheres,” Phys. Rev. B 25, 689–695 (1982).
  29. V. P. Dick, V. A. Loiko, and A. P. Ivanov, “Angular structure of radiation scattered by monolayers of particles: experimental study,” Appl. Opt. 36, 4235–4240 (1997).

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