Abstract
The layered multiple-scattering method is based on an approximate solution for infinite gratings. In this method, an array of regularly arranged scatterers is viewed as comprising of layers of infinite grating and treated as a multiple transmission-reflection process in a multilayer panel. In this paper, this method is evaluated by comparing with exact solutions obtained by other means. One is a multiple-scattering solution. Another is the exact solution for an infinite grating, which is obtained by combining the T-matrix formulation of the multiple-scattering theory and an alternative representation of the Schlömilch series. The infinity nature enables the waves due to a planar incident wave to be expressed as planar waves and divided into propagating and evanescent modes. The layered multiple-scattering method accounts only for the propagating modes. Details of these modes are analyzed for a single grating, and it is concluded that only the first evanescent modes would have significant presence in a limited frequency range. The layered multiple-scattering method suggests that the only important geometric parameters for wave transmission and reflection are the grating distance and the interlayer distance. Numerical examples indicate that error due to evanescent modes might be significant due to interlayer interactions, such as critical frequencies of a stopband.
Published Version
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