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We develop a non-overlapping domain decomposition method (DDM) for scalarwave scattering by periodic layered media. Our approach relies on robustboundary-integral equation formulations of Robin-to-Robin (RtR) maps throughoutthe frequency spectrum, including cutoff (or Wood) frequencies. We overcome theobstacle of non-convergent quasi-periodic Green functions at these frequenciesby incorporating newly introduced shifted Green functions. Using the latter inthe definition of quasi-periodic boundary-integral operators leads torigorously stable computations of RtR operators. We develop Nystr\"omdiscretizations of the RtR maps that rely on trigonometric interpolation,singularity resolution, and fast convergent windowed quasi-periodic Greenfunctions. We solve the tridiagonal DDM system via recursive Schur complementsand establish rigorously that this procedure is always completed successfully.We present a variety of numerical results concerning Wood frequencies in twoand three dimensions as well as large numbers of layers.

Domain decomposition for quasi-periodic scattering by layered media via robust boundary-integral equations at all frequencies