Abstract

We construct fourteen complex periodic two-dimensional (2D) photonic structures with different structural symmetries by arranging the small portions of a 12-fold quasicrystal on square or hexagonal lattices. The corresponding reciprocal lattices confirm that all of them demonstrate the 12-fold-like characteristics due to the analogue short-range arrangements. We then investigate their photonic bandgap properties at different dielectric contrast levels (dielectric rods in air background). Our results suggest that all structures possess analogue transverse magnetic (TM) gaps in both Si and glass photonic crystals due to the similarity of their local geometries. However, the arrangements of the basic elements, total symmetries, and the coupling between the local and the lattice symmetries have greater impact on the glass photonic crystals, which show much larger deviation of gap sizes from different structures. Furthermore, we find that the minimal dielectric contrast to achieve the TM gap in the complex lattices (dielectric-in-air) can be as low as ε = 1.44, whereas the inverse structures may open a 2D complete gap in silicon nitride (ε = 4.1).

© 2009 OSA

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History
Original Manuscript: June 15, 2009
Manuscript Accepted: August 31, 2009
Revised Manuscript: August 21, 2009
Published: September 3, 2009

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Author Affiliations

Shih-Chieh Cheng, Xuelian Zhu, Shu Yang

Department of Materials Science & Engineering, University of Pennsylvania, 
3231 Walnut Street, Philadelphia, PA 19104

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