Controlling sound transmission by space-coiling fractal acoustic metamaterials with broadband on the subwavelength scale

A type of space-coiling acoustic metamaterials (AMs) featuring quasi-fractal geometries is proposed, with filling curves based on the construction for recursive substructures of triangles. The bandgap properties and the acoustic isolation capabilities of the fractal acoustic metamaterials (FAMs) are evaluated by the dispersion relations and the transmission properties on the subwavelength scale. The effective responses for the FAMs with various fractal levels are clarified based on the transfer matrix method and equivalent medium theory. Besides, the behaviors of the zero-phase-difference transmission arising from density-near-zero and the acoustic focusing are also explored in the FAMs applications. The results show that the FAMs exhibit superior broadband properties, with the maximum percentage of complete bandgaps over 33% across the considered spectrum, and the FAMs with higher fractal level possess greater numbers and lower frequency bands. In addition, the FAMs can enable multiple applications including 180 degrees bending transmission, acoustic cloaking, acoustic tunneling, wave front shaping and point source imaging. This design might contribute new insights for controlling low frequency acoustic waves with broadband and developing multifunctional acoustic devices.