A Fourier-Bessel (FB) basis is used to solve two-dimensional (2D) cylindrical Maxwell's equations for localized states within dielectric structures that possess rotational symmetry. The technique is used to determine the wavelengths and profiles of the stationary states supported by the structure and identify the bandgaps. 12-fold quasi-crystals for the TE and TM polarizations are analyzed. Since the FB approach with 2D photonic crystals in this fashion is new, the accuracy of the results is confirmed using finite-difference time-domain simulations.

Additional Metadata
Persistent URL dx.doi.org/10.1364/JOSAA.29.002344
Journal Journal of the Optical Society of America A: Optics and Image Science, and Vision
Citation
Newman, S.R. (Scott R.), & Gauthier, R. (2012). Fourier-Bessel analysis of localized states and photonic bandgaps in 12-fold photonic quasi-crystals. Journal of the Optical Society of America A: Optics and Image Science, and Vision, 29(11), 2344–2349. doi:10.1364/JOSAA.29.002344