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Topological Insulators by Topology Optimization.

Rasmus E Christiansen1, Fengwen Wang1, Ole Sigmund1

  • 1Department of Mechanical Engineering, Solid Mechanics, Technical University of Denmark, Nils Koppels Allé, B. 404, DK-2800 Kgs. Lyngby, Denmark.

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This study demonstrates a novel acoustic topological insulator (TI) designed using topology optimization. The resulting passive TI exhibits high transmission, excellent field confinement, and a wide operational bandwidth, outperforming existing designs.

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Area of Science:

  • Acoustic metamaterials
  • Topological physics
  • Inverse design

Background:

  • Topological insulators (TIs) offer unique wave manipulation properties.
  • Conventional TI design often requires specific topological invariants and explicit band structure engineering.
  • Acoustic TIs are of interest for wave-based applications.

Purpose of the Study:

  • To synthesize an acoustic topological insulator (TI) using topology optimization.
  • To investigate the spontaneous emergence of topological properties without explicit design constraints.
  • To evaluate the performance of the designed TI in terms of transmission, field confinement, and bandwidth.

Main Methods:

  • Topology optimization as a free material inverse design method.
  • Synthesis of a passive acoustic TI using acoustically hard members in an air background.
  • Analysis of field intensity confinement and operational bandwidth.

Main Results:

  • The acoustic TI emerged spontaneously from the optimization process.
  • The TI demonstrated high transmission with an operational bandwidth of approximately 12.5%.
  • Over 99% of the total field intensity was confined within six lattice constants of the TI interface.

Conclusions:

  • Topology optimization can autonomously design acoustic topological insulators.
  • The proposed TI design surpasses previous literature in energy transmission, field confinement, and operational bandwidth.
  • This work offers a new paradigm for designing topological acoustic devices.