Abstract
The modification of the bandgap structure of optical Fibonacci lattices that arises from an increase in the system size is analyzed. It is found that there is a minimum critical size of the Fibonacci lattice necessary to form a photonic bandgap. The analysis of localized photonic modes of Fibonacci lattices shows that the removal of two layers of a lattice makes the lattice mirror-symmetric. The “method of oblique bands” is developed to analyze the bandgap structure of quasi-crystals. This method can also be applied to study two-and three-dimensional photonic and atomic quasi-crystals.
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