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Design of two-dimensional photonic crystals using geometry and self-similarity

We show photonic responses of selected two-dimensional photonic crystals that are based on a combination of geometrical design and spatial self-similarity. Structures based on multi-layer circles, squares, and triangles are studied, finding a range of local band gaps that can be varied with the self-similarity of the photonic crystal patterns. Selected photonic modes are shown that couple to different geometrical features of the photonic crystal. The role of boundary sharpness between the two dielectric components is emphasized.