This paper discusses theoretical calculations of photonic bandgaps found in the one-stage Sierpinski gasket basis in the hexagonal lattice. Dielectric triangles and cylinders as well as air triangles and cylinders are investigated. All of these structures exhibited complete bandgaps, with the largest complete gap having 6.1% fractional width. The largest TE and TM polarization gaps were 23% and 40% fractional width, respectively. Resonators constructed from these crystals with a Q ten to 2000 times greater than resonators constructed using one cylinder in the hex lattice are demonstrated.
© 2007 Optical Society of America
Original Manuscript: January 26, 2007
Revised Manuscript: May 9, 2007
Manuscript Accepted: May 18, 2007
Published: August 14, 2007
Photonic Metamaterials (2007) JOSA A
D. W. Cooley and David R. Andersen, "Photonic bandgaps and resonators in the one-stage Sierpinski gasket basis," J. Opt. Soc. Am. B 24, A84-A88 (2007)