Abstract
There are two classes of phononic structures that can support elastic waves with non-conventional topology, namely intrinsic and extrinsic systems. The non-conventional topology of elastic wave results from breaking time reversal symmetry (T-symmetry) of wave propagation. In extrinsic systems, energy is injected into the phononic structure to break T-symmetry. In intrinsic systems symmetry is broken through the medium microstructure that may lead to internal resonances. Mass-spring composite structures are introduced as metaphors for more complex phononic crystals with non-conventional topology. The elastic wave equation of motion of an intrinsic phononic structure composed of two coupled one-dimensional (1D) harmonic chains can be factored into a Dirac-like equation, leading to antisymmetric modes that have spinor character and therefore non-conventional topology in wave number space. The topology of the elastic waves can be further modified by subjecting phononic structures to externally-induced spatio-temporal modulation of their elastic properties. Such modulations can be actuated through photo-elastic effects, magneto-elastic effects, piezo-electric effects or external mechanical effects. We also uncover an analogy between a combined intrinsic-extrinsic systems composed of a simple one-dimensional harmonic chain coupled to a rigid substrate subjected to a spatio-temporal modulation of the side spring stiffness and the Dirac equation in the presence of an electromagnetic field. The modulation is shown to be able to tune the spinor part of the elastic wave function and therefore its topology. This analogy between classical mechanics and quantum phenomena offers new modalities for developing more complex functions of phononic crystals and acoustic metamaterials.
Highlights
A new frontier in wave propagation involves media that have broken time-reversal symmetry associated with non-conventional topology
We revealed the spinorial character of the elastic wave function in the two-chain system and one chain coupled to the ground
We presented phononic structures composed of two coupled one-dimensional harmonic chains and one harmonic chained grounded to a substrate that exhibit intrinsic non-conventional topology
Summary
A new frontier in wave propagation involves media that have broken time-reversal symmetry associated with non-conventional topology. Perturbing the 1D harmonic chain through linear or nonlinear coupling dispersive, but whose amplitude may depend on the frequency and wave vector In this case, the may create resonant phonon modes that are dispersive, but whose amplitude may depend on the interplay between the coupling and dispersion of the system may lead to symmetry breaking frequency and wave vector. The may create resonant phonon modes that are dispersive, but whose amplitude may depend on the interplay between the coupling and dispersion of the system may lead to symmetry breaking frequency and wave vector In this case, the interplay between the coupling and dispersion of the conditions and non-conventional elastic wave topology. There exists two-classes of system may lead to symmetry breaking conditions and non-conventional elastic wave phonon structures possessing non-conventional topology, namely intrinsic and extrinsic systems.
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