Investigation of photonic band gap in a circular photonic crystal

Photonic band gap (PBG) in a circular photonic crystal (CPC) has been theoretically investigated in detail on the basis of transfer matrix method in the cylinder Bragg wave. Analytical results in the PBG have been made based on the reflectance spectrum in a quarter-wavelength stack. It is found that, at azimuthal number m = 0, both wavelength- and frequency-dependent reflection responses for the CPC bear strong resemblances to those of a one-dimensional planar PC (PPC). The reflection spectrum is further shown to be strongly dependent on the azimuthal number. In addition, the PBG is greatly enhanced as the azimuthal number increases. The PBG structure is periodically distributed at odd multiples of design frequency for m = 0, which is consistent with the PPC. This periodic feature, however, is no longer present for a larger m-number.