Designing topological acoustic lattices via electroacoustic analogies

Topological acoustics has recently witnessed a spurt in research activity, owing to their unprecedented properties transcending typical wave phenomena. In recent years, the use of coupled arrays of acoustic chambers has gained popularity in designing topological acoustic systems. In their common form, an array of acoustic chambers with relatively large volume is coupled via narrow channels. Such configuration is generally modeled as a full three-dimensional system, requiring extended computational time for simulating its harmonic response. To this end, this paper establishes a comprehensive mathematical treatment of the use of electroacoustic analogies for designing topological acoustic lattices. The potential of such analytical approach is demonstrated via two types of topological systems: (1) edge states with quantized winding numbers in an acoustic diatomic lattice and (2) valley Hall transition in an acoustic honeycomb lattice that leads to robust waveguiding. In both cases, the established analytical approach exhibits an excellent agreement with the full three-dimensional model, whether in dispersion analyses or the response of an acoustic system with a finite number of cells. The established analytical framework is invaluable for designing a variety of acoustic topological insulators with minimal computational cost.