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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.



Also Published In

SIAM Journal on Applied Mathematics

More About This Work

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