Abstract
Complex aperiodic 1D dielectric distributions offer intriguing optical propagation features. For example, Thue–Morse (TM) sequence-based 1D photonic crystals (PCs) exhibit transmission spectra that are characterized by fractal band structure, i.e. they comprise traditional photonic band gaps (TPBGs) and fractal PBGs along with non-intuitive local resonances. These arise out of not-so-apparent positional correlations in the dielectric distribution. We identify inter-cell and intra-cell interaction between hidden dimer-like units in a TM-PC and present a relationship between the topological phase of lowest-order pass bands with reflection phase (φ) in the TPBGs. The analysis reveals that the dielectric filling factor (σ) of a TM-PC could serve as a parameter that determines the topological invariants for the geometry and could be tuned optimally in TM-PC-based heterostructures for exciting optical edge modes, which are disorder resistant (or topologically protected). We also discuss the robustness of optical edge modes.
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