Manipulation of acoustic transmission by zero-index metamaterial with rectangular defect

Acoustic zero-index metamaterials (ZIMs) with extremely large phase velocity can be used to manipulate the acoustic transmission by introducing various kinds of defects. However, previous works are based on ideal effective zero-index materials and are restricted to cylindrical defects to predigest the model complexity, which may hamper the practical applications. Here, we theoretically and numerically investigate the acoustic transmission through a ZIM waveguide structure embedded with a rectangular defect. The consistent results demonstrate that the total reflection, total transmission, and cloaking effect can be achieved by introducing suitable rectangular defect into the ideal ZIM. Moreover, the labyrinthine metamaterial, whose effective mass density and reciprocal modulus are simultaneously near zero in a certain frequency region, is further employed to implement a practical ZIM. Numerical simulations show that the transmission amplitude of the labyrinthine ZIM waveguide can cover an entire range of [0, 1] by tailoring the acoustic parameters of the rectangular defect, resulting in the similar intriguing transmission properties obtained with the ideal ZIM. This work provides a systematical study in manipulating acoustic wave propagation through labyrinthine ZIM with rectangular defect in addition to the widely studied cylindrical defects.