Diffraction grating with varying slit width: Quasi-periodic homogenization and its numerical implementation

We study the diffraction of acoustic waves by thin grating with varying slit width. Using quasi-periodic homogenization, we derive an effective model in which the grating is replaced by effective jump conditions with effective parameters varying along the equivalent interface. The numerical implementations of the actual problem and of its homogenized counterpart are achieved using multimodal methods for a periodic grating with a macro-period containing many slits with varying widths. The ability of the effective grating to reproduce the scattering properties of the actual one is inspected and discussed. (c) 2022 Elsevier Inc. All rights reserved.