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Diffraction on the Two-Dimensional Square Lattice

H. S. Bhat; Braxton Osting

Title:
Diffraction on the Two-Dimensional Square Lattice
Author(s):
Bhat, H. S.
Osting, Braxton
Date:
Type:
Articles
Department:
Applied Physics and Applied Mathematics
Volume:
70
Permanent URL:
Book/Journal Title:
SIAM Journal on Applied Mathematics
Abstract:
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.
Subject(s):
Applied mathematics
Publisher DOI:
10.1137/080735345
Item views:
445
Metadata:
text | xml

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