Fourier–Bessel analysis of localized states and photonic bandgaps in 12-fold photonic quasi-crystals

Abstract

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.

Reconfigurable 3D photonic crystal structures

“…The P 3 QC is formed by perforating a pattern of "square" holes in the dielectric such that 8 radial units are present with a 12-fold rotational symmetry 9 . These structures are known to support a number of different mode types and may be calculated using a Fourier-Bessel equivalent of the plane wave analysis for the Gamma point of a traditional band diagram 10 . The radius of the structures is set at 2.5 µm and the normalized frequencies versus solution order (n) are obtained for the monopoles only.…”

Fourier-Bessel Analysis of Polar Space Symmetric Photonic Crystal; Resonator Modes and Heterostructure

“…The super cell required is large enough to ensure negligible fields at the cell boundary for the localized states. It has recently been shown that for circularly symmetric photonic crystals, a Fourier-Bessel (FB) equivalent of the plane-wave expansion method will directly provide the defect state information in the structure and does not require the periodic repetition of the unit super cell [22]. In addition the FB technique can be tuned to search for a specific mode type (monopole, dipole, quadrupole, …) making this technique ideally suited for the modal analysis of the structures displayed in Fig.…”

“…These two properties play a key role in simplifying the FB analysis technique as the next step is to make use of the orthogonality of the basis functions and recast equation 5into the eigenvalue expression, (6). The orthogonality integration is performed over a disc of radius " and the eigenvalues, the normalized frequencies 28 [3 , for the steady states are obtained [22]:…”

Theoretical Analysis of the Micro-optic Bottle Resonator and its Applications

“…The computational technique utilized in this thesis is known as the Fourier-Fourier-Bessel (FFB) mode solver. It closely resembles PWEM's formulation approach on a cylindrical coordinate system [79].…”