Fourier-Bessel analysis of polar space symmetric photonic crystal; resonator modes and heterostructure

A Fourier-Bessel equivalent of the plane wave technique is employed to theoretically analyze a circular photonic crystal structure containing both radial and rotational periodicity. The presence of the 12-fold rotational symmetry in the dielectric profile results in a 12-times reduction in the order of the matrix diagonalized when cast using the Fourier-Bessel basis functions. In addition, the Fourier-Bessel technique is highly suited for extracting the localized modes as it can be tuned to solve for a particular mode order. The possibility of using the circular structure as the defect region of a hexagonal array is also examined by studying the localized states obtained in a heterostructure configuration.