The emerging field of topological acoustics provides exciting possibilities for controlling sound propagation with extraordinary robustness. Conventional topological acoustic waveguides built from topological edge states, which arise solely from the nontrivial topology in the momentum space, usually have restricted shapes due to their crystalline structures. Here, we show that, using an acoustic topological system with both nontrivial topologies in the real and momentum spaces, free-form acoustic topological waveguides can be constructed. These topological waveguides support disclination-localized states, caused by the interplay between topological lattice defects and the valley-Hall topology. As demonstrated in our simulations and experiments, such disclination waveguides can take arbitrary shapes and form open arcs within the lattice, which are not possible for previous crystalline acoustic topological waveguides. Furthermore, by increasing the number of topological lattice defects, we can realize more than one topological waveguide in one lattice. They join at the topological lattice defect and form a topological waveguide network, enabling more complicated functionalities such as beam splitting. Our results point to a promising direction for free-form acoustic topological devices with the advantages of embedded forms, easy cascading, and high robustness.

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• Acoustics
• Defects
• Topological phase transition
• Topological phases of matter