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2011-06-22
Dispersion Relation and Band Gaps of 3D Photonic Crystals Made of Spheres
By
Progress In Electromagnetics Research M, Vol. 19, 1-12, 2011
Abstract
In this paper, we introduce a dispersion equation for 3D photonic crystals made of parallel layers of non-overlapping spheres, valid when both wavelength and separation between layers are much larger than the distance between neighbouring spheres. This equation is based on the Korringa-Kohn-Rostoker (KKR) wave calculation method developed by Stefanou et al.~and can be used to predict the spectral positions of bandgaps in structures made of dispersive spheres. Perfect agreement between the spectral positions of bandgaps predicted with our simplified equation and those obtained with the numerical code MULTEM2 was observed. We find that this simplified relation allows us to identify two types of bandgaps: those related to the constitutive parameters of the spheres and those related to the three dimensional periodicity (distance between layers). Bandgaps of the first type are independent of the frequency and the distance between layers, while those of the second type depend only on these two quantities. We then analyze the influence of the constitutive parameters of the spheres on the spectral position of bandgaps for spheres immersed in dielectric or magnetic homogeneous media. The number and positions of the bandgaps are affected by the permitivity (permeability) of the host medium if the spheres have dispersive permitivity (permeability).
Citation
Francisco Guller Marina E. Inchaussandague Ricardo Depine , "Dispersion Relation and Band Gaps of 3D Photonic Crystals Made of Spheres," Progress In Electromagnetics Research M, Vol. 19, 1-12, 2011.
doi:10.2528/PIERM11051405
http://www.jpier.org/PIERM/pier.php?paper=11051405
References

1. Yablonovitch, E., "Inhibited spontaneous emission in solid-state physics and electronics," Phys. Rev. Lett., Vol. 58, No. 20, 2059-2062, 1987.
doi:10.1103/PhysRevLett.58.2059

2. Sakoda, K., Optical Properties of Photonic Crystals, Springer-Verlag, Berlin, 2001.

3. Joannopoulos, J. R., R. D. Meade, and J. N. Winn, Photonic Crystals, Princeton University Press, Princeton, 1995.

4. Ho, K. M., C. T. Chan, and C. M. Soukoulis, "Existence of a photonic gap in periodic dielectric structures," Phys. Rev. Lett., Vol. 65, No. 25, 3152-3155, 1980.
doi:10.1103/PhysRevLett.65.3152

5. Ohtaka, K., "Scattering theory of low-energy photon diffraction," J. Phys. C, Vol. 13, No. 4, 667, 1980.

6. Modinos, A., "Scattering of electromagnetic waves by a plane of spheres-formalism," Physica A, Vol. 141, No. 2, 575-588, 1987.
doi:10.1016/0378-4371(87)90184-1

7. Stefanou, N., V. Karathanos, and A. Modinos, "Scattering of electromagnetic waves by periodic structures," J. Phys.: Condens. Matter, Vol. 4, No. 36, 7389, 1992.

8. Dorado, L. A., R. A. Depine, and H. Miguez, "Effect of extinction on the high-energy optical response of photonic crystals," Phys. Rev. B, Vol. 75, No. 24, 241101, 2007.

9. Dorado, L. A., R. A. Depine, G. Lozano, and H. Miguez, "Interplay between crystal-size and disorder effects in the high- energy optical response of photonic crystal slabs," Phys. Rev. B, Vol. 76, No. 24, 245103, 2007.

10. Stefanou, N., V. Yannopapas, and A. Modinos, "Heterostructures of photonic crystals: Frequency bands and transmission coeffcients," Comput. Phys. Commun., Vol. 113, No. 1, 49-77, 1998.
doi:10.1016/S0010-4655(98)00060-5

11. Stefanou, N., 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., Vol. 132, No. 1, 189-196, 2000.
doi:10.1016/S0010-4655(00)00131-4

12. Monsoriu, J., R. A. Depine, M. L. Martinez Ricci, and E. Silvestre, "Interaction between non-Bragg band gaps in 1D metamaterial photonic crystals," Opt. Express, Vol. 14, No. 26, 12958, 2006.

13. Li, J., L. Zhou, C. T. Chan, and P. Sheng, "Photonic band gap from a stack of positive and negative index materials," Phys. Rev. Lett., Vol. 90, No. 8, 083901, 2003.

14. Ashcroft, N. W. and Mermin, Solid State Physics, Saunders College Publishing, Philadelphia, 1976.

15. Kapitza, P. L. and A. M. Dirac, "The reflection of electrons from standing light waves," Mathematical Proceedings of the Cambridge Philosophical Society, Vol. 29, No. 2, 297-300, 1933.
doi:10.1017/S0305004100011105

16. Zachariasen, W. H., Theory of X-ray Diffraction in Crystals, Courier Dover Publications, New York, 2004.