It is now well established that two-dimensional structures with dielectric variations based on quasicrystalline tilings are able to support photonic band gaps. Here, we have investigated the properties of the localized defect modes with frequencies within the photonic band gap for a certain kind of two-dimensional octagonal photonic quasicrystal with lattice vacancies breaking the quasi-periodic symmetry. The eigenfrequencies of such localized modes are given as a function of filling fractions for four distinct microcavity designs, and the electromagnetic field profiles of the localized modes are explored. The calculations of the eigenfrequencies and electromagnetic field profiles were performed using a supercell approximation in a plane wave method.
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