Generalized acoustic impedance metasurface

Impedance theory has become a favorite method for metasurface design as it allows perfect control of wave properties. However, its functionality is strongly limited by the condition of strict continuity of normal power flow. In this paper, it is shown that acoustic impedance theory can be generalized under the integral equivalence principle without imposing the continuity of power flow. Equivalent non-local power flow transmission is instead realized through local design of metasurface unit cells that are characterized by a passive, asymmetric impedance matrix. Based on this strategy, a beam splitter loosely respecting local power flow is designed and demonstrated experimentally. It is concluded that arbitrary wave fields can be connected through arbitrarily shaped boundaries, i.e. transformed into one another. Generalized impedance metasurface theory is expected to extend the possible design of metasurfaces and the manipulation of acoustic waves.