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.
© 2012 Optical Society of America
Original Manuscript: May 29, 2012
Revised Manuscript: September 13, 2012
Manuscript Accepted: September 25, 2012
Published: October 18, 2012
Scott R. Newman and Robert C. Gauthier, "Fourier–Bessel analysis of localized states and photonic bandgaps in 12-fold photonic quasi-crystals," J. Opt. Soc. Am. A 29, 2344-2349 (2012)