Plane Wave Scattering and Absorption Analysis of Periodic Metasurface with Mode Matching Method

Acoustic structures consisting of locally-reacting resonators are widely analyzed both theoretically and numerically. This paper aims to build up a framework to discuss sound properties of scattering involved in a typical locally-reacting structure with a non-uniform distribution of surface impedance. A finite-length structure is not the concern of this paper since many solutions use commercial software to tackle a specific practical problem. A mode-matching method is imposed in a one-dimensional (1-D) infinite structure to show some inspiring phenomena and validated with commercial software simulation. Compared with numerical simulation, the proposed method can reveal information about mode shapes and amplitudes. It allows a clear and detailed understanding of sound fields, rather than just final results, such as pressure or absorption coefficients. One can obtain an analytical expression for the input surface impedance of non-uniform metasurfaces. The 1-D metasurface introduced in this paper is simple while typical. One can replace it equivalently due to its locally-reacting nature with structures composed of a periodic pattern with individual complex geometry, as long as the same distribution of surface impedance is guaranteed.