Geometrically navigating topological platonic modes around gentle and sharp bends

Abstract

Predictive theory to geometrically engineer devices and materials in continuum systems to have desired topological-like effects is developed here by bridging the gap between quantum and continuum mechanical descriptions. A platonic crystal, a bosonic-like system in the language of quantum mechanics, is shown to exhibit topological valley modes despite the system having no direct physical connection to quantum effects. We emphasise a predictive, first-principle, approach, the strength of which is demonstrated by the ability to design well-defined broadband edge states, resistant to backscatter, using geometric differences; the mechanism underlying energy transfer around gentle and sharp corners is described. Using perturbation methods and group theory, several distinct cases of symmetry-induced Dirac cones which when gapped yield non-trivial band-gaps are identified and classified. The propagative behavior of the edge states around gentle or sharp bends depends strongly upon the symmetry class of the bulk media and we illustrate this via numerical simulations.

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• Abnormal topological refraction into free medium at sub-wavelength scale in valley phononic crystal plates
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• Observation of topological gravity-capillary waves in a water wave crystal
• Observations of symmetry induced topological mode steering in a reconfigurable elastic plate
• Experimental observations of topologically guided water waves within non-hexagonal structures
• Tailored Topological Edge Waves via Chiral Hierarchical Metamaterials
• Tunable three-way valley Hall energy-splitter: venturing beyond graphene-like structures
• Near- and Far-Field Excitation of Topological Plasmonic Metasurfaces
• Flat Lensing by Graded Line Meta-arrays
• Valley and Valley-like Split-ring Topological Photonic Crystal
• Tutorial: Topology, waves, and the refractive index
• Rayleigh-Bloch, topological edge and interface waves for structured elastic plates
• Acoustic topological circuitry in square and rectangular phononic crystals