Fourier modal method with enhanced transmittance matrix for diffraction analysis of multilayer two-dimensional acoustic metamaterial gratings

This paper adapts a well-established optical Fourier modal method to acoustics and proposes a Fourier modal method with an enhanced transmittance matrix for investigating the diffraction characteristics of multilayer two-dimensional acoustic metamaterial gratings. This method analytically solves the acoustics equation in the Fourier domain and matches the analytical solutions at boundaries to obtain the overall diffraction information. Numerical results demonstrate that this method yields results consistent with those of the finite-element method for both oblique and normal incidence, while offering significant computational advantages compared with full-wave spatial discretization for relatively simple periodic unit-cell geometries. The primary practical value of the framework lies in the rapid prediction of the overall reflection and transmission of multilayer periodic acoustic gratings, which is particularly attractive for parameter sweeps and design optimization. When higher-order propagating channels are open, this method also provides direct access to the contributions of individual diffraction orders. The proposed framework therefore provides a fast and accurate tool for the analysis and design of multilayer acoustic-metamaterial gratings.