Abstract
We employ the two stage cut and project scheme to generate a dodecagonal two-dimensional quasiperiodic structure. The finite-differences-time-domain method is applied to simulate the propagation of electromagnetic modes in the system. We compute the transmission coefficients as well as the inverse participation ratio for a quasicrystal consisting of dielectric cylindrical rods. We find that for a small crystal the band gap forms due to destructive interference between extended states. The quasiperiodic geometry exhibits modes with enhanced transmission coefficients. The inverse participation ratio analysis indicates that these modes are localized and that the localization length is estimated to be 0.3207 in the inverse units of a lattice characteristic length scale.
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