Studying the properties of photonic quasi-crystals by the scaling convergence method

This work introduces the iterative scaling (or inflation) method to systematically approach and analyse the infinite structure of quasi-crystals. The resulting structures preserve local geometric orderings in order to prevent artificial disclination across the boundaries of super-cells, with realistic quasi-crystals coming out under high iteration (infinite super-cell). The method provides an easy way for decorations of quasi-crystalline lattices, and for compact reliefs with a quasi-periodic arrangement to underlying applications. Numerical examples for in-plane and off-plane properties of square-triangle quasi-crystals show fast convergence during iteratively geometric scaling, revealing characteristics that do not appear on regular crystals. (paper)