A study of transmission on cylindrical photonic quasicrystals

Abstract We study the transmittance spectra of light waves propagating on binary quasiperiodic cylindrical stackings. Such structures are called Cylindrical Photonic Quasicrystals (CPQs). In our model, Maxwell's equations are solved, and amplitudes of fields on distinct layers, for each generation of the cylindrical stackings, are linked through appropriate boundary conditions. Then, a transfer-matrix formalism is used to obtain the allowed and forbidden modes. We use both SiO2 and TiO2 as the binary components of the CPQs, and consider four distinct aperiodic stackings: Thue–Morse, Fibonacci, Octonacci, and Double–Period. Our results show that the transmission spectra for TE and TM waves, in all generations of the four sequences, did not present a perfect specular symmetry for both SiO2 and TiO2. Also, we found that the transmission rates of the TE waves are higher than the ones of the TM waves. We also observed for Fibonacci and Octonacci CPQs that, for TM modes only, there exist refraction-index-independent bandgaps.