Diffraction on the TwoDimensional Square Lattice

Title:

Diffraction on the TwoDimensional Square Lattice

Author(s):

Bhat, H. S.
Osting, Braxton

Date:

2009

Type:

Articles

Department:

Applied Physics and Applied Mathematics

Volume:

70

Permanent URL:

http://hdl.handle.net/10022/AC:P:10563

Book/Journal Title:

SIAM Journal on Applied Mathematics

Abstract:

We solve the thinslit diffraction problem for twodimensional lattice waves. More precisely, for the discrete Helmholtz equation on the semiinfinite 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:

545
 Metadata:

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 Suggested Citation:

H. S. Bhat, Braxton Osting,
2009,
Diffraction on the TwoDimensional Square Lattice, Columbia University Academic Commons,
http://hdl.handle.net/10022/AC:P:10563.