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Diffraction on the Two-Dimensional Square Lattice

Bhat, H. S.; Osting, Braxton

We solve the thin-slit diffraction problem for two-dimensional lattice waves. More precisely, for the discrete Helmholtz equation on the semi-infinite square lattice with data prescribed on the left boundary (the aperture), we use lattice Green's functions and a discrete Sommerfeld outgoing radiation condition to derive the exact solution everywhere in the lattice. The solution is a discrete convolution that can be evaluated in closed form for the wave number $k=2$. For other wave numbers, we give a recursive algorithm for computing the convolution kernel.

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Title
SIAM Journal on Applied Mathematics
DOI
https://doi.org/10.1137/080735345

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Academic Units
Applied Physics and Applied Mathematics
Published Here
June 21, 2011