Edge Modes of Scattering Chains with Aperiodic Order

Abstract

We study the scattering resonances of one-dimensional deterministic aperiodic chains of electric dipoles using the vectorial Green's matrix method, which accounts for both short- and long-range electromagnetic interactions in open scattering systems. We discover the existence of edge-localized scattering states within fractal energy gaps with characteristic topological band structures. Notably, we report and characterize edge-localized modes in the classical wave analogues of the Su-Schrieffer-Heeger (SHH) dimer model, quasiperiodic Harper and Fibonacci crystals, as well as in more complex Thue-Morse aperiodic systems. Our study demonstrates that topological edge-modes with characteristic power-law envelope appear in open aperiodic systems and coexist with traditional exponentially localized ones. Our results extend the concept of topological states to the scattering resonances of complex open systems with aperiodic order, thus providing an important step towards the predictive design of topological optical metamaterials and devices beyond tightbinding models.

4 pages, 4 figures

References in corpus (5)

• Experimental observation of optical Weyl points
• Topological Pumping over a Photonic Fibonacci Quasicrystal
• Measuring topological invariants from generalized edge states in polaritonic quasicrystals
• Photonic Chern insulator through homogenization of an array of particles
• Topological Boundary States in 1D: An Effective Fabry-Perot Model

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• Phononic Topological States in 1D Quasicrystals
• Wideband tunable infrared topological plasmon polaritons in dimerized chains of doped-silicon nanoparticles
• Terahertz topological plasmon polaritons for robust temperature sensing
• Topological quantum optical states in quasiperiodic cold atomic chains
• Topological phonon polariton enhanced radiative heat transfer in bichromatic nanoparticle arrays mimicking Aubry-André-Harper model