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Applied Optics

Applied Optics


  • Editor: Joseph N. Mait
  • Vol. 50, Iss. 24 — Aug. 20, 2011
  • pp: 4868–4872

Photonic bandgaps of different unit cells in the basic structural unit of germanium-based two-dimensional decagonal photonic quasi-crystals

Jianjun Liu, Zhigang Fan, Haosu Xiao, Wang Zhang, Chunying Guan, and Libo Yuan  »View Author Affiliations

Applied Optics, Vol. 50, Issue 24, pp. 4868-4872 (2011)

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Based on the infrared optical material germanium, in the basic structural unit of a two-dimensional decagonal photonic quasi-crystal, photonic bandgaps of four square unit cells with a scattering radius in the range of [ 0 , 0.3 a ] have been calculated within two cases of construction (i.e., air cylinders arranged in germanium and germanium cylinders arranged in air) by using the plane wave expansion method. In considering the Bragg-like scattering effect in two-dimensional photonic quasi-crystals as the elastic collision in physics, we put forward the photonic bandgap impact function F = q 1 q 2 q 3 ε π r 2 for the first time, to the best of our knowledge. A certain unit cell structure shares some similar photonic bandgap properties with a periodic structure. For a certain structure of the unit cell, the center frequency change trends of the photonic bandgap and the type of photonic bandgap generated are not related with the period of the photonic crystal, but with the relative dielectric constant and the construction, respectively. Different unit cell structures own different photonic bandgap structures. This occurs because the high degree of rotational symmetry of the quasi-periodic structure and weak long-range order of the basic structural unit lead to different Bragg-like scattering effects within the unit cell structures.

© 2011 Optical Society of America

OCIS Codes
(160.5293) Materials : Photonic bandgap materials
(160.5298) Materials : Photonic crystals

ToC Category:

Original Manuscript: April 4, 2011
Manuscript Accepted: July 12, 2011
Published: August 19, 2011

Jianjun Liu, Zhigang Fan, Haosu Xiao, Wang Zhang, Chunying Guan, and Libo Yuan, "Photonic bandgaps of different unit cells in the basic structural unit of germanium-based two-dimensional decagonal photonic quasi-crystals," Appl. Opt. 50, 4868-4872 (2011)

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