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Total reflection or transmission of waves has been explored extensively in different types of zero-index metamaterials (ZIMs). Almost all previous studies have shown that only monopole modes are excited inside the defects if they are cylindrical. However, the underlying physics for excited modes inside defects is wrongly ignored. In this work, we reveal that there is not only a monopole mode but also additional higher modes excited inside cylindrical defects by a system of two-dimensional waveguides. Actually, the total acoustic transmission and additional higher modes can occur simultaneously in a ZIM waveguide embedded with defects. We reveal the physical mechanism of excited higher modes, which will perfect the current perception of the excited modes in the acoustic metamaterials inside defects. Moreover, numerical simulations are carried out to demonstrate our finding concerning the additional modes

Acoustic total transmission and additional modes in the metamaterials embedded with defects